Good morning everybody… I hope you all had a great evening yesterday.. I missed the party…I am sure prof. Saue along with others must have enjoyed the Japanese dinner very much.. Ok let me come to the discussion…. Today I will be talking about Many body studies of PNC/EDM as probes of physics beyond the Standard model.. I choose this subject as our guest prof. Saue has worked on EDM in molecules. I will be talking more in detail about the relativistic many body studies which we used rather than the particle physics aspects… This is a work which I did for my research under the guidance of Prof. Bhanu Pratap Das from 1996 to 2001. Apart from many body perturbation methods we used mainly coupled cluster methods and for this part we have a long time colloboration with prof. Mukherjee of Indian Association of Cultivation of Science, Culcutta. For my post doctoral position I did work at university of tokyo under Prof. Hirao with whom I completed some of my work on pnc and then started working on EDM in molecules. Now I am at Prof. Hada’s lab and I continue to get my exposure in molecules and at present we are working on photoassociation spectroscopy on cold molecules .. For this we work on YbLi molecule along with Abe san who has always been with me teaching me the fundamentals of molecular chemistry..
This is the outline of my talk… First I will give a brief overview of kind of transformations which we are talking about Followed by the observables which we compute.. In brief I will mention the source of PNC and EDM in atoms… The major part of the talk will be devoted to the atomic many body theory aspects where I will talk in detail about 4 component relativistic coupled cluster method.. In order to check the accuracy of the PNC and EDM observables, we also did compute various experimentally available quantities closely related to these quantities…I have them listed here…like Ionisation potential, excitation energy, lifetime, hyperfine constant and so on.. At the end I will discuss about the implications of this study and the limits which this study can put to Standard model of particle physics…
Edm Pnc Standard ModelPresentation Transcript
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Many Body Studies of PNC/EDM as probes of physics beyond the Standard Model Geetha Gopakumar (TMU, Japan) Prof. Bhanu Pratap Das (IIA, India) Prof. D. Mukherjee (IACS, India) Prof. Kimihiko Hirao (RIKEN, Japan) Prof. Hada (TMU, Japan) Minori Abe (TMU, Japan)
The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2008 with one half to
Yoichiro Nambu , Enrico Fermi Institute, University of Chicago, IL, USA
"for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"
and the other half jointly to
Makoto Kobayashi , High Energy Accelerator Research Organization (KEK), Tsukuba, Japan and Toshihide Maskawa , Yukawa Institute for Theoretical Physics (YITP), Kyoto University, and Kyoto Sangyo University, Japan
"for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature"
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Fundamental transformation leading to symmetries C Particle ---------------- antiparticle (Q > -Q) Position --------------- inverted (r > -r) T Time ----------------- reversed (t > -t ) Charge-Parity-Time Reversal – CPT theorem This means that if any particle is replaced with its corresponding antiparticle, and the space coordinate and time are reversed, the physical laws are unchanged. A Physical system/process can violate each of these symmetries individually as long as the combined CPT is conserved A symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is "preserved" under some change
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P Violation – E1PNC
State vector under parity transformation
Hamiltonian under parity transformation
ie.
[Parity Conservation ]
Systems of Interest > Atom where chiral property arises from the interactions between the constituents which favours one orientation with respect to other
Weak Interactions > Nucleons and Electrons (Parity non conserving)
(Interaction being weak considered perturbatively)
E1PNC = <ψ α |D|ψ β > ≠ 0 α and β are of same parity
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P & T violation EDM
Molecules of ammonia, water permanent EDMs due to degeneracy of states
EDMs of interest > P and T violations in non-degenerate systems
Any vector is aligned either parallel or anti-parallel to J (Projection Theorem ) Quantity P T D - D + D J J - J D = αJ D = -αJ D = -αJ α = 0 ; implies P and T are not violated α ≠ 0 ; implies P and T are violated edm P T J J J J |ψ> = |ψ (0) > + ʎ |ψ （１） > （ even/odd) (odd/even) EDM = < ψ α |D|ψ α > ≠ 0
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Sources of PNC in atoms
Nuclear Weak Current Interaction between nucleus and the electrons (mediated by Z 0 bosons
EM interaction between nuclear anapole moment and the electrons
G F = Fermi Coupling constant ~ 2.2 X 10-11 au (measure of weakness of the interaction) ρN （ｒ） ---- H PNC ≠ 0 only for electron wavefunctions with finite value at the nucleus hence connects only s(1/2) and p(1/2) orbital n p e C 1n C 1p H NSI PNC = G F /2 √ 2 Q w γ 5 ρ N （ｒ） Qw = 2(C1p Z + C1n N) ∞ Z ρN （ｒ） = nucleon number density ∞ Z γ 5 = Dirac matrix >> σ.p ∞ velocity ∞ Z E1PNC ∞ Z 3 >>> HEAVY ATOMS
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Electron EDM
Nuclear EDM
P and T violating interactions between electrons and nucleons
H e-N = Σ N G F 2√2 C T βα.I ρ N (r) Sources of EDMs in atoms Closed shell atoms: Nuclear EDM and electron-nucleon tensor pseudo tensor interaction and Schiff moment Eg. Yb, Hg (J ≠0) Open Shell Atoms : Electron EDM and electron-nucleon scalar-pseudo scalar interaction Eg. Cs, Fr with single free electron outside the core C T = (Z C T,p + N C T,n ) ∞ Z β, α = Dirac Matrix ∞ Z ; I – Spin ρ N(r) =nucleon number density ∞ Z EDM ∞ Z 3 >>> HEAVY ATOMS
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= unperturbed Hamiltonian Atomic Many Body Thoery to compute E1PNC/EDM
We need to know
Hamiltonian of the system
Accurate relativistic electron wave functions
H= Dirac Hamiltonian for a many-electron atom In the presence of a (P, PT) violating interactions, H t = H + λ H PNC (Parity Non Conserving interaction) H t = H + λ H PTV (Parity and Time Violating interaction)
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The Schrödinger equation for an exact atomic state is H t | where | (0) λ (1) Unperturbed wave function First-order perturbed wave function (0) 's are obtained by solving the unperturbed Schrödinger equation, (0) (0) (0) The perturbed Schrödinger equation hence becomes (H - E (1) PNC EDM (1) The E1PNC / EDM is given by
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Coupled Cluster Method (CCM) Many-electron wf in closed-shell CC is given by e T | Φ 0 > T is the cluster operators which considers excitations from core to virtuals |Φ 0 > N-1 electron closed shell DF reference state H a | Subtracting <Φ 0 |H a |Φ 0 > from both sides we get H N | is correlation energy Using the exponential form of and pre multiplying by e- T , we get H - N |Φ 0 > = |Φ 0 > <Φ 0 gives < Φ 0 H - N |Φ 0 Φ 0 * gives <Φ 0 H - N |Φ 0 H - N = e -T H N e T = (H N e T ) C linear : H N + (H N T) C non linear : H N + (H N T) C + (H N TT) C + (H N TTT) C + (H N TTTT) C T 1 T 1 , T 1 T 2 , T 2 T 2 , T 1 T 1 T 2 , T 1 T 1 T 1 T 1 - negligible
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Singles equation (T 1 ) Doubles equation (T 2 ) non linear diagrams
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Coupled Cluster method for open shell systems Single valence case S considers excitations from valence to virtual One electron is added to the k th virtual orbital Using the similar techniques used in the closed shell case ( IP equ.) The above equation is non-linear as IP itself depends on S Excitation energy (EE) = IP (valence) – IP (appropriate orbital)
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Singles and doubles S diagrams Using T2 and S2, we get approximate triples..
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Ba + ion E1PNC evaluation using sum over states approach Expt – Fortson et al (PRL,7383,1993) Mixed parity approach
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Basis set
Part numerical + part analytical
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Basis set
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IP and EE calculations (energy check)
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Check on Dipole and EE
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Check on Dipole and H PNC matrix elements PNC and hyperfine matrix elements depends on the overlap of the orbital wave function with the nuclear region
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Probing physics beyond the SM Q W = E1 PNC (expt)/ X (theory) ; E1PNC (expt) ~ Φ (M1/E2) Theory and Experiment should have to be found accurately in order to test SM
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∆ Q W = Q W – Q W SM if ∆ Q W ≠ 0 , Physics beyond the Standard Model Caesium (55) Q W = -72.57 ± (0.29) expt ±(0.36) theo SM Q w = -73.09(0.3) Present Limits
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Implications to particle physics Work being pursued ..
EDM in YbF /YbLi molecule
2. PNC in Ra+ ion
Photo association spectroscopy calculations in YbLi molecule
Atom smasher sets record energy levels : CERN http://uk.news.yahoo.com/