This document discusses supersymmetry and the Higgs boson. It introduces supersymmetry as a way to solve issues with the Higgs boson mass and cancel divergences. Supersymmetry predicts partner particles to every standard model particle. The document also discusses implications for cosmology, such as gravitinos as a dark matter candidate. It outlines the minimal supersymmetric standard model which extends the standard model to include two Higgs doublets.
Geometry of Noninertial Bases in Relativistic Mechanics of Continua and Bell'...ijrap
From obtained equations of structure (integrability conditions of continuum equations) the elemental noninertial reference frames (NRF) are investigated: relativistic global uniformly accelerated Born’s hard NRF, relativistic Born’s rigid uniformly rotating RF free of horizon, rigid vortex-free spherically symmetrical NRF. All these systems are not described in Minkowski space. Riemann space-time of these RF does not directly connect with general theory of relativity (GR). However the exact equations of structure restrict the possibilities of application of the Einstein's equations.
Evaluation of post-Einsteinian gravitational theories through parameterized p...Nicolae Sfetcu
Right after the elaboration and success of general relativity (GR), alternative theories for gravity began to appear. In order to verify and classify all these theories, specific tests have been developed, based on self-consistency and on completeness. In the field of experimental gravity, one of the important applications is formalism. For the evaluation of gravity models, several sets of tests have been proposed. Parameterized post-Newtonian formalism considers approximations of Einstein's gravity equations by the lowest order deviations from Newton's law for weak fields.
DOI: 10.13140/RG.2.2.25994.82881
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
DOI: 10.13140/RG.2.2.22006.45124/1
Geometry of Noninertial Bases in Relativistic Mechanics of Continua and Bell'...ijrap
From obtained equations of structure (integrability conditions of continuum equations) the elemental noninertial reference frames (NRF) are investigated: relativistic global uniformly accelerated Born’s hard NRF, relativistic Born’s rigid uniformly rotating RF free of horizon, rigid vortex-free spherically symmetrical NRF. All these systems are not described in Minkowski space. Riemann space-time of these RF does not directly connect with general theory of relativity (GR). However the exact equations of structure restrict the possibilities of application of the Einstein's equations.
Evaluation of post-Einsteinian gravitational theories through parameterized p...Nicolae Sfetcu
Right after the elaboration and success of general relativity (GR), alternative theories for gravity began to appear. In order to verify and classify all these theories, specific tests have been developed, based on self-consistency and on completeness. In the field of experimental gravity, one of the important applications is formalism. For the evaluation of gravity models, several sets of tests have been proposed. Parameterized post-Newtonian formalism considers approximations of Einstein's gravity equations by the lowest order deviations from Newton's law for weak fields.
DOI: 10.13140/RG.2.2.25994.82881
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
DOI: 10.13140/RG.2.2.22006.45124/1
Formal Unification of Gravity and Particle Physics in Lagrangian Euclidean Sp...Hontas Farmer
Formal Unification of Gravity and Particle Physics in Lagrangian Euclidean Space with Experimental Predictions - http://meetings.aps.org/Meeting/APR19/Session/Z13.5
The objective of this paper is to propose an approach to the unification of physics by attempting
to construct a physical worldview which can be used as the context for a unified physical theory.
The underlying principle is that we have to construct a clear description of the physical world
before we can build a unified physical theory.
The present state of physics is such that there are many theories which all differ in the descriptive
context in which they operate. The theories of general relativity, quantum theory, quantum
electrodynamics, string theory and the standard model of particle physics are based on differing
concepts of the nature of the physical world.
Einstein's General Theory of Relativity interpreted in terms of a polarizable quantum vacuum. Electromagnetic wavelength increase corresponds to apparent time dilation while a frequency increase corresponds to an apparent space contraction as a result of a spectral energy density gradient.
Lorentz Length Contraction (More Discussion)Gerges francis
The Special Theory of Relativity tells us that
The matter is created of electromagnetic wave or at least depend on it
i.e.
The Universe Matter Is Related To Electromagnetic Waves
Talk given in London, 3 January 2017. The talk has three aims:
(i) To clarify the use of these concepts (‘emergence’ and ‘reduction’) in science, especially in physics.
(ii) Specifically: to argue that the contrast ‘emergence vs. reduction’ poses a false dichotomy, since these two concepts are independent.
(iii) To point out that the independence of the two concepts may open interesting avenues for the philosophy of mind. But I will not work this out in a theory of the mind.
A unification of gravity with electromagnetism and quantumJeffrey Huang
It is known that there is an incompatibility issue between general relativity and quantum mechanics. This paper shows that it is possible to resolve the conflict by deriving gravitational acceleration using a generalized fundamental equation in quantum mechanics that governs the motion of all particles (bosons and fermions). The new theory of gravity makes predictions at the cosmic scale which can be easily verified using existing astrophysics data where general relativity failed to do. It can restore Newtonian gravity as a low speed, quasi-static limit and Einstein’s general relativity as the classical limit at the macroscopic scale. The later includes restoring general relativity’s key concept, the metric tensor and its key equation, the geodesic equation. Curved spacetime is just the manifestation of the quantum motion equation, rather than being the cause of gravity. The new theory makes almost the same predictions as Einstein’s general relativity on gravitational time dilation, gravitational light bending, the extra precession of the perihelion of Mercury, and gravitational waves where the small differences between the two theories are beyond the power of any existing apparatus to detect.
Talk given at Oxford Philosophy of Physics, LSE's Sigma Club, the Munich Center for Mathematical Philosophy, Carlo Rovelli's 60th birthday conference.
I construe dualities in physics as particular cases of theoretical equivalence. The question then naturally arises whether duality is compatible with emergence. For the the focus of emergence is on novelty rather than on equivalence.
In the first part of the talk, I review recent work dealing with this question. I exhibit two ways in which duality and equivalence can be made compatible, and I give an example of emergence in gauge/gravity dualities: dualities between a theory of gravity in (d+1) dimensions and a quantum field theory (QFT) in d dimensions.
In the second part of the talk, I present new results on the question whether diffeomorphisms in gravity theories emerge from QFTs. I critically assess the following idea, taken from the physics literature: given that (a) the QFT is not a diffeomorphism invariant theory, and that (b) there is a duality between the QFT and the gravity theory, are we entitled to (c) conclude that the diffeomorphisms of the gravity theory emerge from the QFT?
I argue that one must distinguish different kinds of diffeomorphisms: some diffeomorphisms are ‘invisible’ to the QFT: all of the QFT’s quantities are invariant under them, therefore the QFT does not ‘see’ them. But other diffeomorphisms are ‘visible’ to the QFT. The invisible diffeomorphisms prompt a ‘Bulk Argument’, in analogy with the Hole Argument. The analysis of emergence is different for these different kinds of diffeomorphisms, and I discuss the way in which we can speak of emergence of diffeomorphisms in gauge/gravity dualities.
Energy in form of space may solve the dark energy problemPremier Publishers
A review of recent observations suggests a universe that is light weight (matter density is 1/3rd of the critical value), accelerating and flat. This implies the existence of a cosmic Dark Energy that overcomes the gravitational self-attraction force of matter and causes the accelerating expansion. Finding out the cause of expansion and acceleration of the universe is a challenging job in present day cosmology. Cosmological models with different types of dark energy are becoming viable standard models to analyze and simulate experimental data from a number of high red shift supernovae. In this article, physical significance and analytical expression for dark energy related to total energy (or energy density) and matter (or matter density) in the universe is presented. It is assumed that 'space' or 'vacuum' is another form of energy (other form is mass which is related as E = mc2). With this assumption new cosmological equation of state is constructed which is in very good agreement with present observations. Thus energy evolves from matter to radiation to space. It is also predicted that the existence of a fundamental particle with mass less than the mass of a quark is possible.
Analogous to Maxwell stress tensor in electric and magnetic fields, a stress tensor is defined in a vorticity field. Thus by treating vortices as physical structures, it is possible to study the forces on a surface element in it. Based on this the force between vortex lines, the pressure and the shearing stress that deform the volume element can also be defined.
Reality in a few thermodynamic reference frames: Statistical thermodynamics ...Vasil Penchev
The thesis is: The starting point of initial reality is changed as follows:
0. (Carnot) Classical thermodynamics describes laws in terms of quantities of that reality, which is as
macroscopic as empirically and experimentally observable.
1. (Boltzmann) The mechanical motions of the huge number of microscopic elements of a statistical
ensemble result into the thermodynamic quantities of any macroscopic physical object averagely. The
empirically and experimentally observable quantities are deduced as derivative from a hidden
theoretical reality of microscopic elements such as atoms and molecules.
2. (Gibbs) The mechanical motions of the huge number of microscopic elements are substituted by
different possible states of a macroscopic physical object equivalently and mathematically. The
empirically and experimentally observable thermodynamic quantities are deduced as derivative from a
hidden theoretical reality of different possible macroscopic states of the physical object as a whole.
3. (Einstein) The mechanically and experimentally observable thermodynamic quantities are some
function of the Gibbs ensemble of all possible states (and thus some relation to it). They can be
furthermore also referred to the Boltzmann ensemble of microscopic elements. Reality includes both the
observable object and the hidden theoretical model as whether a Gibbs or a Boltzmann ensemble as well
as the function or relation between the object and that model.
Conclusion: Reality in those reference frames can be identified in the following oppositions: macroscopic
– microscopic; elements – states; relational – non-relational; observable – theoretical:
0. (Carnot): Macroscopic, both observable and theoretical.
1. (Boltzmann): Microscopic, elements, non-relational, theoretical.
2. (Gibbs): Macroscopic, states, non-relational, theoretical.
3. (Einstein): Both macroscopic and microscopic, both elements and states, relational, both observable
and theoretical.
One can admit that still one synthesis has happen later to that reality, which can be utilized in a
statistical and thermodynamic theory: both relational and non-relational. All other syntheses, which are
implicit in the development of the concept of statistic and thermodynamic reality before it, are already
completed in the Einstein theory.
One hypothesis might be that quantum statistical thermodynamics is what accomplished that last
synthesis along that it involves still one dimension of another opposition as to reality: continuous
(smooth) – discrete (quantum). All four theories mentioned above mean the thermodynamic and
mechanical quantities implicitly only as continuous (smooth) though some of them introduce discrete
elements.
Summarizing: The examples of a few statistical thermodynamic theories demonstrate that the concept of
“reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another.
The change can be described as the
Formal Unification of Gravity and Particle Physics in Lagrangian Euclidean Sp...Hontas Farmer
Formal Unification of Gravity and Particle Physics in Lagrangian Euclidean Space with Experimental Predictions - http://meetings.aps.org/Meeting/APR19/Session/Z13.5
The objective of this paper is to propose an approach to the unification of physics by attempting
to construct a physical worldview which can be used as the context for a unified physical theory.
The underlying principle is that we have to construct a clear description of the physical world
before we can build a unified physical theory.
The present state of physics is such that there are many theories which all differ in the descriptive
context in which they operate. The theories of general relativity, quantum theory, quantum
electrodynamics, string theory and the standard model of particle physics are based on differing
concepts of the nature of the physical world.
Einstein's General Theory of Relativity interpreted in terms of a polarizable quantum vacuum. Electromagnetic wavelength increase corresponds to apparent time dilation while a frequency increase corresponds to an apparent space contraction as a result of a spectral energy density gradient.
Lorentz Length Contraction (More Discussion)Gerges francis
The Special Theory of Relativity tells us that
The matter is created of electromagnetic wave or at least depend on it
i.e.
The Universe Matter Is Related To Electromagnetic Waves
Talk given in London, 3 January 2017. The talk has three aims:
(i) To clarify the use of these concepts (‘emergence’ and ‘reduction’) in science, especially in physics.
(ii) Specifically: to argue that the contrast ‘emergence vs. reduction’ poses a false dichotomy, since these two concepts are independent.
(iii) To point out that the independence of the two concepts may open interesting avenues for the philosophy of mind. But I will not work this out in a theory of the mind.
A unification of gravity with electromagnetism and quantumJeffrey Huang
It is known that there is an incompatibility issue between general relativity and quantum mechanics. This paper shows that it is possible to resolve the conflict by deriving gravitational acceleration using a generalized fundamental equation in quantum mechanics that governs the motion of all particles (bosons and fermions). The new theory of gravity makes predictions at the cosmic scale which can be easily verified using existing astrophysics data where general relativity failed to do. It can restore Newtonian gravity as a low speed, quasi-static limit and Einstein’s general relativity as the classical limit at the macroscopic scale. The later includes restoring general relativity’s key concept, the metric tensor and its key equation, the geodesic equation. Curved spacetime is just the manifestation of the quantum motion equation, rather than being the cause of gravity. The new theory makes almost the same predictions as Einstein’s general relativity on gravitational time dilation, gravitational light bending, the extra precession of the perihelion of Mercury, and gravitational waves where the small differences between the two theories are beyond the power of any existing apparatus to detect.
Talk given at Oxford Philosophy of Physics, LSE's Sigma Club, the Munich Center for Mathematical Philosophy, Carlo Rovelli's 60th birthday conference.
I construe dualities in physics as particular cases of theoretical equivalence. The question then naturally arises whether duality is compatible with emergence. For the the focus of emergence is on novelty rather than on equivalence.
In the first part of the talk, I review recent work dealing with this question. I exhibit two ways in which duality and equivalence can be made compatible, and I give an example of emergence in gauge/gravity dualities: dualities between a theory of gravity in (d+1) dimensions and a quantum field theory (QFT) in d dimensions.
In the second part of the talk, I present new results on the question whether diffeomorphisms in gravity theories emerge from QFTs. I critically assess the following idea, taken from the physics literature: given that (a) the QFT is not a diffeomorphism invariant theory, and that (b) there is a duality between the QFT and the gravity theory, are we entitled to (c) conclude that the diffeomorphisms of the gravity theory emerge from the QFT?
I argue that one must distinguish different kinds of diffeomorphisms: some diffeomorphisms are ‘invisible’ to the QFT: all of the QFT’s quantities are invariant under them, therefore the QFT does not ‘see’ them. But other diffeomorphisms are ‘visible’ to the QFT. The invisible diffeomorphisms prompt a ‘Bulk Argument’, in analogy with the Hole Argument. The analysis of emergence is different for these different kinds of diffeomorphisms, and I discuss the way in which we can speak of emergence of diffeomorphisms in gauge/gravity dualities.
Energy in form of space may solve the dark energy problemPremier Publishers
A review of recent observations suggests a universe that is light weight (matter density is 1/3rd of the critical value), accelerating and flat. This implies the existence of a cosmic Dark Energy that overcomes the gravitational self-attraction force of matter and causes the accelerating expansion. Finding out the cause of expansion and acceleration of the universe is a challenging job in present day cosmology. Cosmological models with different types of dark energy are becoming viable standard models to analyze and simulate experimental data from a number of high red shift supernovae. In this article, physical significance and analytical expression for dark energy related to total energy (or energy density) and matter (or matter density) in the universe is presented. It is assumed that 'space' or 'vacuum' is another form of energy (other form is mass which is related as E = mc2). With this assumption new cosmological equation of state is constructed which is in very good agreement with present observations. Thus energy evolves from matter to radiation to space. It is also predicted that the existence of a fundamental particle with mass less than the mass of a quark is possible.
Analogous to Maxwell stress tensor in electric and magnetic fields, a stress tensor is defined in a vorticity field. Thus by treating vortices as physical structures, it is possible to study the forces on a surface element in it. Based on this the force between vortex lines, the pressure and the shearing stress that deform the volume element can also be defined.
Reality in a few thermodynamic reference frames: Statistical thermodynamics ...Vasil Penchev
The thesis is: The starting point of initial reality is changed as follows:
0. (Carnot) Classical thermodynamics describes laws in terms of quantities of that reality, which is as
macroscopic as empirically and experimentally observable.
1. (Boltzmann) The mechanical motions of the huge number of microscopic elements of a statistical
ensemble result into the thermodynamic quantities of any macroscopic physical object averagely. The
empirically and experimentally observable quantities are deduced as derivative from a hidden
theoretical reality of microscopic elements such as atoms and molecules.
2. (Gibbs) The mechanical motions of the huge number of microscopic elements are substituted by
different possible states of a macroscopic physical object equivalently and mathematically. The
empirically and experimentally observable thermodynamic quantities are deduced as derivative from a
hidden theoretical reality of different possible macroscopic states of the physical object as a whole.
3. (Einstein) The mechanically and experimentally observable thermodynamic quantities are some
function of the Gibbs ensemble of all possible states (and thus some relation to it). They can be
furthermore also referred to the Boltzmann ensemble of microscopic elements. Reality includes both the
observable object and the hidden theoretical model as whether a Gibbs or a Boltzmann ensemble as well
as the function or relation between the object and that model.
Conclusion: Reality in those reference frames can be identified in the following oppositions: macroscopic
– microscopic; elements – states; relational – non-relational; observable – theoretical:
0. (Carnot): Macroscopic, both observable and theoretical.
1. (Boltzmann): Microscopic, elements, non-relational, theoretical.
2. (Gibbs): Macroscopic, states, non-relational, theoretical.
3. (Einstein): Both macroscopic and microscopic, both elements and states, relational, both observable
and theoretical.
One can admit that still one synthesis has happen later to that reality, which can be utilized in a
statistical and thermodynamic theory: both relational and non-relational. All other syntheses, which are
implicit in the development of the concept of statistic and thermodynamic reality before it, are already
completed in the Einstein theory.
One hypothesis might be that quantum statistical thermodynamics is what accomplished that last
synthesis along that it involves still one dimension of another opposition as to reality: continuous
(smooth) – discrete (quantum). All four theories mentioned above mean the thermodynamic and
mechanical quantities implicitly only as continuous (smooth) though some of them introduce discrete
elements.
Summarizing: The examples of a few statistical thermodynamic theories demonstrate that the concept of
“reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another.
The change can be described as the
On Rational Physics: a Basic Formalism for Relativistic Physics and "A Unique...Ramin (A.) Zahedi
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International.
License URL: https://creativecommons.org/licenses/by-nc-nd/ .
Comments: 99 Pages. A summary of a submitted and accepted research project, Ramin Zahedi, (On "Foundations of Physics"), Japan, 2012 - 2015; (Expanded version).
KeyWords: "A Unique Mathematical (Axiomatic) Prediction of Eight New Elementary Particles, Including: 'Four Charge-less Raight-Handed Spin-1/2 Fermions (Two Leptons and Two Quarks)', 'One Spin-3/2 Fermion', and 'Three Spin-1 (massive) Gauge Bosons';" CPT Symmetry as the Only Combunation of C, P, and T Symmetries Definable for Interacting Fields"; Time-Reversal Symmetry and the Numebr of Space-Time Dimensions; Monopoles and the Issue of their Existence in Nature.
This article has been invited and presented at the following international conferences:
- The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16)
- The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb)
-The 4th International Conference on New Frontiers in Physics, CERN Organized Conference (Europe). (https://indico.cern.ch/e/icnfp2015)
- The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/)
- The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37)
- The GRavitational-wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by European Union's 7th Framework Prog.: FP7/PEOPLE-2011-CIG,‘ 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx)
- The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Australia, 2016. (http://appc-aip2016.org.au)
- The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org).
External URLs: https://Cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, http://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/, https://www.OpenAire.EU/search/publication?articleId=dedup_wf_001::422af8dcdfbae42429965b16b61f0e94, https://Hal-UNIV-PARIS3.archives-ouvertes.fr/USPC/hal-01547739 , http://mts-srep.NATURE.com/srep_files/2017/07/20/00174434/00/174434_0_related_ms_4909193_pttcpw.pdf , https://hal-PARIS1.archives-ouvertes.fr/hal-01547739 , https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf.
The electromagnetism and gravity are unified where, while the first originates from the electric charges in a
linear exposition, the second emerges in a quadratic manifestation of it, making the gravity always
attractive. This helps identify the inner structures of all the primary particles—quarks, leptons, and the
{Z,W} bosons as well as the 125 GeV state without the Higgs mechanism—to predict their masses by one
integer parameter formulas in close agreement with the observed values. This in turn enables
determination of the mechanism for building their ground and excited compound states. The consequences
are far-reaching and embracing, for examples, from identifying dark matter and energy that makes the
explanation of masses in the Universe 100 % inclusive, to solving the hackneyed yet equally elusive puzzle
of why the inertial mass is equal to the gravitational mass.
The electromagnetism and gravity are unified where, while the first originates from the electric charges in a
linear exposition, the second emerges in a quadratic manifestation of it, making the gravity always
attractive. This helps identify the inner structures of all the primary particles—quarks, leptons, and the
{Z,W} bosons as well as the 125 GeV state without the Higgs mechanism—to predict their masses by one
integer parameter formulas in close agreement with the observed values. This in turn enables
determination of the mechanism for building their ground and excited compound states. The consequences
are far-reaching and embracing, for examples, from identifying dark matter and energy that makes the
explanation of masses in the Universe 100 % inclusive, to solving the hackneyed yet equally elusive puzzle
of why the inertial mass is equal to the gravitational mass.
The electromagnetism and gravity are unified where, while the first originates from the electric charges in a
linear exposition, the second emerges in a quadratic manifestation of it, making the gravity always
attractive. This helps identify the inner structures of all the primary particles—quarks, leptons, and the
{Z,W} bosons as well as the 125 GeV state without the Higgs mechanism—to predict their masses by one
integer parameter formulas in close agreement with the observed values. This in turn enables
determination of the mechanism for building their ground and excited compound states. The consequences
are far-reaching and embracing, for examples, from identifying dark matter and energy that makes the
explanation of masses in the Universe 100 % inclusive, to solving the hackneyed yet equally elusive puzzle
of why the inertial mass is equal to the gravitational mass.
General Relativity and gravitational waves: a primerJoseph Fernandez
A short introduction to the one of the nicest bits of physical reasoning ever, which led to Albert Einstein's General Relativity, gravitational waves and our research on gravitational wave sources.
Designed by Joseph John Fernandez for LJMU FET Research Week.
Gravity and the cosmic microwave background radiation (cmbr)Eran Sinbar
Based on Einstein’s field equations, mass curves space time and curvature of space-time dictates the gravitational field around the mass. In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the force experienced by an observer in an accelerated frame of reference. Since acceleration consume energy, it’s a worthy question to ask how curvature of space time can supply this equivalent required energy for acceleration.
Let’s imagine that two similar small objects (e.g. mass A and mass B) are standing still in space-time relative to each other in their frame of reference. Now imagine that mass A absorbs an energetic pulse of gamma ray burst and starts to increase its mass (for example by absorbing radiation and increasing its thermal energy) .Its new effective mass will be signed as A’ where A’>>A.
Based on the interpretation today of the Einstein’s field equations the curvature of space time causes mass B to move towards mass A’ since it is the shortest geodesic path in the curved space-time. The curvature of space time is practically the potential energy.
But from mass B point of view (in its frame of reference where both mass A and B were standing still before the increase of mass A), it feels suddenly a force towards mass A’ and an increase in its kinetic energy and it is a worthy question to ask where does this extra kinetic energy come from? How can curvature in space-time explain this extra kinetic energy of mass B?
This article tries to analyze the Einstein field equations in a new heuristic approach and to explain the cause for the movement of mass B towards the increasing mass A’ due to what is related as gravitational force. The article also suggests that the source of the extra kinetic energy given to mass B comes from the CMBR (Cosmic Micro wave Background Radiation).
I forgot... for a moment. He's in our lab in Sinaloa, too, and they brought his stuff.
Not only do we have the only real neuroscientists there, but also a gifted brain surgeon with a ton of info from a slightly different angle.
Limit radius in a binary system: Cosmological and Post-Newtonian effectsPremier Publishers
Frequently, in dynamical astronomy, the quantitative effect of the large-scale cosmological expansion on local systems is studied in the light of Newtonian approach. We, however, analyze the influence of cosmological expansion on binary systems (galaxies or black holes) in the light of Post-Newtonian approximation. Furthermore, we obtain the new radius at which the acceleration due to the cosmological expansion has the same magnitude as the two-body attraction, and the classical limit radius is obtained when the Schwarzschild radius approaches zero (for example, the Solar System).
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Outline I
1 Introduction
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
2 Cosmology/Astrophysics Implications
Unstable Gravitinos as DM
Extra Dimensional Theories
3 MSSM
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
2 / 44
3. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Outline II
4 The Higgs Mass - Evidence for Physics beyond SM
5 Summarising MSSM Higgs Results
6 References
3 / 44
4. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Introduction I
If one looks at the Higgs boson H, its mass cannot be understood.
Quantum oscillations give rise to self mass of the scalar particle
which quadratically diverges. The divergent graph arises due to the
self coupling of the scalar field as shown in Figure 1.
S
H H H H
F
F
Figure 1 : Loop diagrams
4 / 44
5. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Introduction II
∆(mH)2
S =
λs
16π2
Λ2
− m2
s ln
Λ2
m2
s
+ . . . (1)
∆(mH)2
F =
λf i2
8π2
−Λ2
− 3m2
F ln
Λ2
m2
f
(2)
This divergence is cancelled if one has a corresponding partner
coupled with comparable strength to the scalar Higgs but opposite
in sign as in (2), i.e., if λs = 2|λf |2.
This is fine tuning of coupling and the ultraviolet divergence
(quadrative in mass) essentially defines a cut-off mass squared,
that fixes the limit to the Standard Model (SM) beyond which the
new physics starts – the hierarchy problem.
5 / 44
6. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Introduction III
The existence of the matching fermion (spin 1
2) to the scalar Higgs
boson is a requirement of supersymmetry (SUSY) which gives rise
to a fermion to every boson and vice versa carrying equal mass in
the exact symmetry limit in order for the cancellation of the
divergence. This is ’naturalness problem’. In other words, in order
to have a ’natural Higgs mass’ SUSY sets an important choice on
New Physics (NP) or physics beyond SM. Further, the Higgs boson
receives quantum (or loop order) corrections that are limited by
the extent of SUSY breaking (in masses and couplings). A new
scale then appears in mass, that is a O(TeV).
At this point a need for SUSY (a theory not a female!) arises.
6 / 44
7. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Fundamental Constituents I
Phenomenologically, there are other indicators of SUSY, they are:
The fact that in the SM the constituents of matter like quarks and
leptons are fermions (spin 1
2) [obeying Fermi-Dirac statistics
leading to Pauli Exclusion Principle, i.e., no two identical fermions
can occupy the same state] and bosons carrying force field (spin 1,
vector) [obeying Bose statistics, i.e., more than one particles
occupying the same state] – why this asymmetry?
Does nature choose this or is there some underlying subtle
symmetry broken at ordinary energies but may be seen at higher
energies.
SUSY affords such symmetrisation between bosons and fermions.
In the exact form (unbroken) which is not seen at ordinary energies
7 / 44
8. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Fundamental Constituents II
(everyday it has the same masses and couplings for both fermions
and bosons).
8 / 44
9. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
The Couplings Unification I
It is found that extrapolation of electromagnetic, weak, and strong
couplings with energy do not meet at a point as shown in Figure 2
(i.e., they do not unite or corresponding forces cannot be unified):
9 / 44
10. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
The Couplings Unification II
Figure 2 : Coupling Unification
10 / 44
11. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
The Couplings Unification III
Gauge coupling constants αi = g2
i /4π , using Renormalisation
Group (RG) equations, start varying with energy in such a way
that they unify using SUSY at energies of the order of ∼ 1016GeV.
In this evolution of various interaction couplings or their inverse to
be precise (in the RG equation), one uses SUSY particles in the
1-loop quantum corrections where the coefficients bi of the
Renormalisation Group Equation (RGE) assume larger values than
their SM corresponding coeffiecients. Here bi is defined as
bi = −2π
d
dt
(α−1
i ), (3)
11 / 44
12. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
The Couplings Unification IV
where t = ln q
q0
, with q the RGE scale and q0 the SM scale.
Further one uses SU(5) or SO(10) as a grand unified gauge group
and RGE for extrapolation.
12 / 44
13. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Gravity Force and Quantum description I
Another important requirement for unification theories is the force
of gravity. Theoretically, it is very difficult to develop a quantum
theory of gravity because of divergence problem associated with
Feynman diagrams involving interaction with gravity through
gravitons.
Superstrings afford a possibility to offset the difficulties of
renormalisation associated with gravitational field. Supersymmetric
gravity theories have been formulated to incorporate grand
unification of forces including gravity as SUSY GUTS.
Supersymmetry is used as a precursor in most of these theories.
However, there is no experimental evidence of SUSY particles even
in the lightest mass scale, so far. As usual, for NP, physicists wait
for upgradation of accelerator energies.
13 / 44
14. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Salam’s contribution I
Abdus Salam’s contribution to Supersymmetry was seminal. He
alongwith John Strathdee published an important paper on
Supergauge transformations (Nucl. Phys B 76, p.477 (1974)) and
later the concept of Superfields which puts bosons and fermions
together in the form of Supersymmetric multiplets as Superfields.
These superfields are, however defined over extended coordinate
containing self-commuting (ordinary) space-time coordinate xµ as
well as four non-commuting fermionic Grassmnian variables θµ.
Steven Weinberg in his book titled ”The Quantum Theory of
Fields, Vol III: Supersymmetry” refers to Salam’s (and Strathdee’s)
fundamental contribution to Supersymmetry and underlying
framework of Super Algebra.
14 / 44
15. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Fundamental Constituents
The Couplings Unification
Gravity Force and Quantum description
Salam’s contribution
Salam’s contribution II
In the words of Weinberg: ”a great deal of work can be saved by
using a formalism invented by Salam and Strathdee in which the
fields in any supermultiplet are assembled into a simple superfield.”
(A. Salam & J. Strathdee, Nucl. Phys. B 76, p. 477 (1974))
15 / 44
16. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Unstable Gravitinos as DM
Extra Dimensional Theories
Cosmology/Astrophysics Implications I
SUSY postulates the Lightest Sypersymmetric Particle (LSP)
called Neutralino ( ˜X) which is thought to be a neutral particle
existing as a supersposition state of Higgsino (supersymmetric
Higgs bosons, ˜h0
1, ˜h0
2), Zino (supersymmetric Z0 boson) and
photino (˜γ, supersymmetric partner of the photon γ). This particle
is believed to be comprising over 20% of matter/energy density
compared to the corresponding critical energy density required to
close the Universe since the Big Bang. Such an invisible particle of
matter is called Dark Matter (DM). The mass limit for such a DM
candidate is of the order of hundreds of Giga electron volts. There
are other DM candidates such as axion, CP (strong) violating
particle. Such particles energies may be accessible to neutrino
telescopes which are designed to detect 100’s of GeV particles.
16 / 44
17. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Unstable Gravitinos as DM
Extra Dimensional Theories
Cosmology/Astrophysics Implications II
However, the annihilation rates of neutralinos predicted from
Minimal Supersymmetric SM (MSSM) variants in celestial bodies
are low if contraints from (Wilkinson Microwave Anisotropy Probe)
WMAP and (Large Hadron Collider) LHC are taken into account.
17 / 44
18. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Unstable Gravitinos as DM
Extra Dimensional Theories
SUSY also predicts through its R-parity violating model a long
lived but unstable viable candidate of DM called ’gravitino’. This
is estimated at a mass of few to a few hundred GeV and may be
present in the halos of galaxies as a component of DM.
Gravitinos decay could be seen in neutrino telescopes. However,
gravitino DM cannot be detected directly in normal detectors
because its interaction with normal matter falls inversely with
fourth power of the Planck constant G−4
planck.
18 / 44
19. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Unstable Gravitinos as DM
Extra Dimensional Theories
Involving extra dimension range of the order of 10−3 − 10−15
meters can also provide DM candidates. Extra dimensions can also
be accomodated or required by Supersymmetry, string theory or
M-theory, where they give rise to ’branons’, weakly interacting and
massive fluctuations of the field that represent the 3-D brane on
which the Standard world lives. A stable and weakly interacting
object, branon makes a good candidate for DM as a usual ’relic
branon’ left over after a freeze out period during the evolution of
the Universe accumulating gravitationally in the halos of galaxies
where due to their high energies they annihilate into SM particles.
Such particles as products fo annihilation can then be detected by
gamma-ray telescopes, surface arrays or neutrino telescopes.
19 / 44
20. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
MSSM I
In order to look for physics beyon SM, higher energy data and more
lumminosity collisions are awaited from the LHC. One should then
expect to study Higgs couplings more accurately. One also looks
for higher energy accelerators like ILC, Higgs e+e− factories, etc.
The objectives are to look for (additional) CP-even states predicted
by MSSM or NMSSM (one having an additional doublet and one
complex singlet to the normal Higgs doublet invariant under
SU(2) U(1) gauge group).
20 / 44
21. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
MSSM II
In the MSSM one has two Higgs doublets,
H1 =
H1
1
H2
1
=
(φ0
1)∗
−φ−
1
(4)
H2 =
H1
2
H2
2
=
φ+
2
φ0
2
. (5)
Symmetry is broken through vacuum expectation values of the
Higgs doublets as,
< H1 >=
v1
0
< H2 >=
0
v2
. (6)
21 / 44
22. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
MSSM III
Mixing of Higgs states is introduced through the mixing angles α
and β,
tan β =
v2
v1
, (7)
where v1, v2 > 0 and 0 ≤ β ≤ π
2 .
22 / 44
23. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
At the LHC, the SM Higgs boson is produced through four
different channels:
Gluon gluon fusion channel: gg → hX
Vector Boson Fusion (VBF) channel: qq → hjjX
Higgs boson strahlung channel: q¯q → hVX
Higgs boson and top quark pair
associated production channel: ¯q(gg) → ht¯tX
23 / 44
24. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
Higgs Decays I
(S. Heinemeyer et al. LHC Higgs Section Working Group
Collaboration); arXiv:1307.1347 [hep-ph]
The Higgs decay rate into a pair of fermion is given at tree level by
Γ(H → ¯f f ) = Ne
GF mH
4π
√
2
m2
f , (8)
where Ne = 3(1) for decays into quaks (leptons). Since the tree
level couplings to other particles are propotional to their masses
(squared in the cases of massive vector bosons), the dominant
Higgs decays are into the heaviest particles that are kinematically
accessible, such as, ¯bb, ¯c¯c and τ+τ−. However, only τ+τ− decay
mode, i.e., H →τ+τ− has recently been observed unambiguously
24 / 44
25. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
Higgs Decays II
(ATLAS and CMS collaborations files).
Further
Γ(H → WW ∗
) =
GF m3
H
8π
√
2
F(r), (9)
where F(r ≡ mW /mH is a kinematic factor) has been observed.
25 / 44
26. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
Two Higgs Doublet Model (2HDM) Analysis I
Now that Higgs Boson has been discovered, a question arises
whether it is the Higgs Boson of the SM, or whether there are
more?
Two Higgs Doublet model and Supersymmetry offer a possibility of
more Higgs bosons. We now turn our attention to this possibility.
Let φ1 and φ2 be two doublet complex scalar fields with weak
hypercharge Y = 1, and belonging to symmetry group SU(2)L.
26 / 44
27. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
Two Higgs Doublet Model (2HDM) Analysis II
The Higgs potential which breaks (spontaneously)
SU(2)L U(1)Y down to U(1)EM is,
V (φ1, φ2) = λ1(φ†
1φ1 − v2
1 )2
+ λ2(φ†
2φ2 − v2
2 )2
+ λ3 (φ†
1φ1 − v2
1 ) + (φ†
2φ2 − v2
2 )
2
+ λ4[(φ†
1φ1)(φ†
2φ2) − (φ†
1φ2)(φ†
2φ1)]
+ λ5[Re(φ†
1φ2) − v1v2 cos ξ]2
+ λ6[Im(φ†
1φ2) − v1v2 sin ξ]2
(10)
where the λi are real parameters (Hermiticity requirement). Above
equation gives the most general scalar doublet potential subject to
discrete symmetry φ1 → −φ1 which is only softly violated
27 / 44
28. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
Two Higgs Doublet Model (2HDM) Analysis III
(by dim. 2 terms, viz: whose coefficient is λ4).
Assuming that all λi are non-negative, then the minimum of the
potential is manifestly,
< φ1 >=
0
v1
< φ2 >=
0
v2eiξ , (11)
which breaks SU(2)L U(1)Y down to U(1)EM, as desired.
Now taking CP-conserving state which requires the phase ξ to
vanish and λ5 = λ6, then the last two terms can be combined as,
|φ1†φ2 − v1v2eiξ
|2
→ |φ1†φ2 − v1v2|2
(ξ → 0) (12)
28 / 44
29. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
Two Higgs Doublet Model (2HDM) Analysis IV
Next let tan β = v2/v1 (Ratio of expectation values of φ2 to that
of φ1) be an important parameter associated with the 2HDM.
Next one removes the Goldstone Boson and determines the Higgs
states by rotating:
G±
= φ±
1 cos β + φ±
2 sin β, (13)
and Higgs states taken as orthogonal to Goldstone Bosons,
H±
= −φ±
1 sin β + φ±
2 cos β (14)
with mass m2
H± = λ4(v2
1 + v2
2 ). Due to CP invariance assumed
before, the imaginary parts and the real parts of the neutral scalar
29 / 44
30. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
Two Higgs Doublet Model (2HDM) Analysis V
fields decouple. In the imaginary (CP-odd) sector, the neutral
Goldstone boson is,
G0
=
√
2(Im φ0
1 cos β + Im φ0
2 sin β) (15)
and the orthogonal neutral physical state is,
A0
=
√
2(−Im φ0
1 sin β + Im φ0
2 cos β) (16)
with mass m2
A0 = λ6(v2
1 + v2
2 ).
30 / 44
31. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
MSSM extension to two Higgs doublets I
Supersymmetry requires (for minimal case) 2 Higgs doublets; one
to give masses to charge +2
3 quarks, Hu and the other to charge
−1
3 quarks and charged leptons, Hd . The ratio of their vacuum
expectation values are denoted as β = v2
v1
. Simulations have
been done to see that the renormalisation by the top quark
coupling is important for one of the Higgs multiplet, and may drive
m2
Hu
negative at the electroweak scale resulting in the electroweak
symmetry breaking and thus may explain negative sign in the
quartic term in the effective SM potential. For a heavy top quark
mass, it is then possible for the electroweak scale to be generated
around 100 GeV if mt ∼ 100 GeV. For this reason SUSY theorists
actually suggested heavy momentum for the top quark, before its
31 / 44
32. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
MSSM extension to two Higgs doublets II
discovery!
Now 2 complex Higgs complex Higgs doublets of the MSSM have
eight degrees of freedom, of which 3 are used by the Higgs
Mechanism for electroweak symmetry breaking to give mass to the
W ± boson and Z0, leaving 5 physical Higgs bosons states of these
2 (h, H) are neutral Higgs that are CP-even (scalar), one A is
neutral CP-odd (pseudoscalar) and 2 are charged, the H±. At tree
level the masses of the scalar Higgs(es) are:
m2
h,H =
1
2
(m2
A + m2
Z ((m2
A + m2
Z )2
− 4m2
Am2
Z cos2
β)) (17)
32 / 44
33. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
Higgs Production at the LHC
Higgs Decays
Two Higgs Doublet Model (2HDM) Analysis
MSSM extension to two Higgs doublets
MSSM extension to two Higgs doublets III
In general their coupling compared to SM couplings are:
ghVV = sin(β − α)gSM
HVV , gHVV = cos(β − α)gSM
HVV (18)
ghAZ = cos(β − α)(
g
) , gh¯bb+
, ghτ+τ− = −
sin α
cos β
gSM
h¯bb
, gSM
hτ+τ− .
(19)
If mA >> mW , then from (17) ma ∼ mH ∼ mH± . However if mA
is small and mH ∼ 125 GeV, then mA is smal then mH is 2nd
lightest discovered.
33 / 44
34. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
The Higgs Mass - Evidence for Physics beyond SM? I
(J. Ellis, arXiv:1312.5672 [hep-ph]) CMS and ATLAS results of
Higgs mass are quite consistent and a naive global average (for the
Higgs mass) is
mH = (125.6 ± 0.4)GeV (20)
And this average is quite consistent with the electroweak data
based on one-loop level SM collaboration to ∆X2 ∼ 1.5 level.
However, when effective Higgs potential is considered then there
are problems. When self renormalisation effects are taken into
account for the Higgs field coming from Higgs self-coupling and
Ht¯t coupling, one can write the Higgs self-coupling as:
λQ =
λ(v)
1 − 3
4π2 λ(v) ln Q2
v2
+ . . . , (21)
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35. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
The Higgs Mass - Evidence for Physics beyond SM? II
where Q is some renormalisation scale above the electroweak scale
v. And due to Ht¯t coupling; i.e., when
λ(Q) = λ(v) 1 −
3
4π2
λ(v) ln
Q2
v2
−1
= λ(v) −
3m4
t
4π2v4
ln
Q2
v2
+ . . . , (22)
Where in the above equation, non-leading terms with RGE solution
have been ignored.
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36. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
One notes that renormalisation of the Higgs self coupling in the
RGE solution for large Q values tends to
increase λ(Q) in (18) leading to a landau singullarity (Landau Pole
arises for large
Q2 values relative to v2 as: Q2 = v2 exp(4π2/3λ(v)) ). While in
(19) it decreases the Higgs self coupling λ(Q) with increasing
Q-values. At some point when Q is sufficiently large relative to v
(electroweak scale), λ(Q) is driven to negative values. This would
set instability in the electroweak vacuum if,
mH < 129.4 + 1.4
mt − 173.1GeV
0.7
− 0.5
αS (mZ ) − 0.1184
0.0007
± 1.0TH ]GeV (23)
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37. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
[G. Degrassi, et al. JHEP 1208, (2012) 098]
The measured value of mH plus mt 173 GeV would drive the
quartic self-coupling λ to negative values for some energy scale
∼ 1010 to 1014 GeV, if no physics beyond SM intervenes at lower
energy scale as shown:
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40. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
The instability of the vacuum having large negative value for large
Q−value of the order of 1010 to 1014 GeV (approaching Planck
scale/Planckian era) is hard to reconcile with the present value of
cosmological constant related to vacuum energy is nearly zero.
Within SM such a low mass (23) is hard to realise with SUSY.
Once this is done at the one-loop level, then it is shown that the
mass of the Higgs boson can be extended and defined to higher
loops graphs also, in the same self-consistent way. Also as we saw
that existence of the Higgs mass as found alongwith top quark
mass found also empirically provides through electroweak vacuum
stability the requirement that Higgs mass satisfying:
mH < 129.4 + 1.4
mt − 173.1GeV
0.7
− 0.5
αS (mZ ) − 0.1184
0.0007
± 1.0TH ]GeV
40 / 44
41. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
The implications of the mass requirement of mH and mt are
plotted in Figures 3 and 4. The result in (23) is based on
NNLO-SM calculation by Giuseppe Degrassi et al,
(CERN-PH-TH/2012 134 RM3-TH/12-9) and says that for
vacuum stability for Q values from 1013 − 1014 GeV, the mass of
MH > (129.4 ± 1.8) GeV.
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42. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
It predicts, Higgs mass
m2
h,H =
1
2
(m2
A + m2
Z (m2
A + m2
Z )2 − 4m2
Am2
Z cos2 2β) (24)
β = tan− 1 v2
v1
Couplings,
ghVV = sin(β − α)gSM
HVV
gHVV = cos(β − α)gS
MHVV
ghAZ = cos(β − α)
g
2 cos θW
gh¯bb, ghτ+.τ− = −
sin α
cos β
gSM
h¯bb
, gSM
hτ+.τ− , (25)
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43. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
where α, β are two mixing angles for the 2 complex doublet as in
2HDM.
For mA >> mW , as seen mH ∼ mA ∼ m±
H are very similar. But
formA small compared to mZ such that
m2
A
m2
Z
0, then mA may be a
Higgs lighter than the one discovered at mh 125GeV.
43 / 44
44. Introduction
Cosmology/Astrophysics Implications
MSSM
The Higgs Mass - Evidence for Physics beyond SM
Summarising MSSM Higgs Results
References
References
A. Salam & J. Strathdee, Nucl. Phys. B 76, p. 477 (1974)
S. Weinberg, The Quantum Theory of Fields, Vol III:
Supersymmetry, Cambridge University Press (2000)
S. Heinemeyer et al., LHC Higgs Section Working Group
Collaboration (arXiv:1307.1347 [hep-ph])
J. Ellis, Higgs Physics (arXiv:1312.5672 [hep-ph])
G. Degrassi, et al., Higgs mass and vacuum stability in the
Standard Model at NNLO, JHEP 1208, (2012) 098
(arXiv:1205.6497 [hep-ph])
P. Bin´etruy, Supersymmetry: Theory, Experiment and
Cosmology, Oxford University Press (2006)
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