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Talk by Prof. Kamaludin Ahmed, NCP, Islamabad Pakistan. Prepared by Imran.

Talk by Prof. Kamaludin Ahmed, NCP, Islamabad Pakistan. Prepared by Imran.

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- 1. Introduction Cosmology/Astrophysics Implications MSSM The Higgs Mass - Evidence for Physics beyond SM Summarising MSSM Higgs Results References Minimal Supersymmetry and Higgs Boson(s) K. Ahmed 1 / 44
- 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) 34 / 44
- 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. 35 / 44
- 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) 36 / 44
- 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: 37 / 44
- 38. Introduction Cosmology/Astrophysics Implications MSSM The Higgs Mass - Evidence for Physics beyond SM Summarising MSSM Higgs Results References Figure 3 : Higgs mass Mh in GeV 38 / 44
- 39. Introduction Cosmology/Astrophysics Implications MSSM The Higgs Mass - Evidence for Physics beyond SM Summarising MSSM Higgs Results References Figure 4 : Higgs pole mass Mh in GeV 39 / 44
- 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. 41 / 44
- 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) 42 / 44
- 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) 44 / 44

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