1. 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)

3. Standard Model in Particle Physics

5. 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

11. 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

13. 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

14. Singles equation (T 1 ) Doubles equation (T 2 ) non linear diagrams

15. 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)

16. Singles and doubles S diagrams Using T2 and S2, we get approximate triples..

17. Ba + ion E1PNC evaluation using sum over states approach Expt – Fortson et al (PRL,7383,1993) Mixed parity approach

19. Basis set

20. IP and EE calculations (energy check)

21. Check on Dipole and EE

22. 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

23. 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

24. ∆ 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