Neutron Electric Dipole Moment from Lattice QCD

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1 Neutron Electric Dipole Moment from Lattice QCD Sinya Aoki (University of Tsukuba) in collaboration with N. Ishizuka,Y. Kikukawa, Y. Kuramashi, E. Shintani for CP-PACS collaboration Exploration of Hadron Structure and Spectroscopy using Lattice QCD INT, University of Washington, March 6 - May 26, 2006

2 term in QCD Introduction CP odd Neutron Electric Dipole Moment(NEDM) Experimental bound Model estimate Strong CP problem! PQ symmetry, Axion...

3 rude model estimates are enough for the upper bound on If non-zero is observed in the future, however, a reliable theoretical calculation of will be required to determine non-zero value of The first principle calculation of NEDM is desired. This Talk: Feasibility study for lattice QCD Calculations of NEDM by two different methods E. Shintani, S. Aoki, N. Ishizuka, K. Kanaya, Y. Kikukawa, Y. Kuramashi, M. Okawa, Y. Taniguchi, A. Ukawa and T. Yoshie, PRD72, (2005)

4 Previous (Lattice) Studies 989: Aoki-Gocksch quenched QCD with Wilson fermion term in quark mass External Electric Field mass difference between spin up and down Seiler-Stamatescu obtain non-zero lattice artifact! twisted mass QCD some of model estimates also contain artifacts New estimate by ChPT 1990: Aoki-Gocksch-Manohar-Sharpe Baluni, Cea-Nardulli, Morgan-Miller 1992: Aoki-Hatsuda (tree) (1-loop) 1979: Crewther-DiVecchia-Veneziano-Witten

5 Importance of chiral symmetry Anomalous flavor-singlet chiral WT identities term complex mass term Good chiral behaviour on the lattice is crucial! The 1st method Domain-wall quark (good chiral symmetry) quenched QCD Form factor NEDM Lattice calculation Form factor (This is non-trivial) hep-lat/ : Berruto-Blum-Originos-Soni (quenched/full)dwqcd, form factor signal but within errors?!

6 From form factor to NEDM Form Factor CP-odd part Effective interaction NEDM

7 QCD with -vacuum 3-pt function From lattice data to form factor reduction formula

8 where ince CP is broken, on-shell spinors satisfy Form factor

9 Combining all Path integral expression

10 small expansion operator side path-integral side

11 Mixing contributions parity-odd form factors

12 Structure of form factor P even P odd

13 2-pt function Extraction of operator side path-integral side Combining 2- and 3- pt functions, we can extract all form factors.

14 Numerical simulations of lattice QCD quenched QCD RG improved (Iwasaki) gauge action domain-wall quarks(good chiral behaviour) 716 conf.

15 Topological charge (improved) bosonic definition + cooling

16 History and distribution of topological charge Enough sampling!

17 Nucleon propagator with smeared source

18 Nucleon propagator with Q from Consistent!

19 cf. Parity odd part without Q

20 Correlation between Q and quark is very important to get signals Same use of domain-wall quarks enough sampling of Q Success for extracting

21 Form factors from 3-pt functions conserved EM current is inserted in a quark line of nucleon propagator at (source method), t of nucleon sink is varied disconnected contribution is neglected u d d u,d,s

22 Parity-even form factors Neutron Proton source current current source

23 Neutron Proton

24 electric form factor magnetic form factor Proton ours 0.502(33) (60) 0.58 exp (8) (11) 0.58 Neutron ours (37) 0.58 exp (62)(34 ) (7)(15) 0.6

25 Parity-odd form factors Two different projections Projection A 3-pt function subtraction Projection B 3-pt function subtraction

26 Neutron Proton subtraction Projection A 3-pt function 3-pt function subtraction subtraction 3-pt function Projection B 3-pt function subtraction

27 Neutron Proton B B A A cf. Crewther-DiVicchia-Veneziano-Witten:

28 Conclusions on the 1st method formula to extract CP odd form factors from correlation functions possible to calculate a CP odd form factor in quenched lattice QCD domain-wall quark (good chiral behaviour) enough sampling of Q need several extrapolations is difficult --> try another method

29 NEDM from Energy Shift spin-dependent energy shift in the presence of the constant electric fields 1989: Aoki-Gocksch real electric field in link variables Periodicity in time is broken no extrapolation

30 Extraction of NEDM where reweighting in Q sampling of Q is important. small helps.

31 Lattice parameters quenched QCD RG improved (Iwasaki) gauge action: Lattice size: # of configurations = 1000 Domain-wall quarks: Nucleon mass: Electric field:

32 Expected behaviour

33 Effective mass plot Neutron

34 cf. Crewther-DiVicchia-Veneziano-Witten:

35 Clover vs. DWF Our full QCD configurations are generated by Clover quarks. Does this method work for Clover quarks? Clover DWF The method works also for Clover fermions Good sampling of Q seems more important.

36 Volume dependence Since simulations with Clover quarks are easier, a larger volume are possible conf conf. Smaller errors. Consistent within large errors.

37 Boundary Effect Periodicity is broken by the electric field Large Gap t=1 source t=8 new source t=16 t=32 t=17 Large gap exists between t=1 and 32 boundary effect To investigate how large this boundary effect is we put source at t=8.

38 source at t=1 source at t=8 difference is observed boundary effect!

39 Effective mass plot source at t=1 source at t=8 Fake? Larger Combined t is required fit givesfor t=1 source.

40 Mass dependence

41

42 Quark mass dependence Preliminary! Neutron Proton It is unlikely that EDM vanishes in the chiral limit. (Quenched artifact)

43 Conclusions The 1st method(edm form factor) works with quenched DWF. The 2nd method(energy shift) also seems to work. quenched DWF quenched Clover fermions source away from boundary is better Future works with Clover fermions try the 1st method with quenched Clover fermions NEDM with Clover fermion on 2 and 2+1 flavor dynamical configurations of CP-PACS/JLQCD (Wilson)ChPT formula for EDM in full QCD