Lattice approaches to the neutron electric dipole moment with dynamical clover fermions

1
Lattice approaches to the neutron electric dipole
moment with dynamical clover fermions

• Eigo Shintani (Univ. of Tsukuba)
• In collaboration with
• Sinya Aoki (Univ. of Tsukuba)
• Yoshinobu Kuramashi (Univ. of Tsukuba)
• ???????2007?????, 2007/3/28

2
Introduction

• P, T violation
• Ratio of direct and indirect CP violation in K0
  (e/e)
• Kobayashi-Masukawa mechanism
• ? term, strong CP problem (NEDM, axion model)
• Baryon number asymmetry,
• Neutron electric dipole moment (NEDM)
• Its sensitive object to T violation in
  strong interaction, and if ? term is present, it
  has a finite value in proportional to ?.
• Now its value is known as much small order
  by experiment
• dN lt 6.310-13 efm
• ? is estimated to be O(10-10) by effective
  models.

Harris, et al. (1999)
3
Lattice works

• Lattice QCD
• first principle calculation, model independent
• rigorous evaluation of dN
• ? theoretical range of ? with precise
  experiment in future
• Recent lattice works
• Quench approximation (focus on methodology)
• NEDM form factor with domain-wall (DW) fermion
  ES (2005)
• External electric field method with clover and DW
  ES (2006)
• Full QCD simulation
• RBC groupNEDM form factor, Nf2 dynamical DW
  T.Blum (2006)
• External electric field (direct method) with Nf2
  dynamical clover
• 
  ES
  (2006)

4
Contents

• Introduction
• Recent results with external electric field
• New challenge NEDM form factor with clover
  fermion
• Formulation
• Results in Quench QCD
• Momentum extrapolation ? NEDM
• Disconnected diagram
• Summary

5
External electric field method

• Spin dependent energy difference
• In presence of static and uniform electric field
  and ? term,
• ms(E) -m-s(E) dN (sE)? O(?2)
• ms spin dependent nucleon energy, s nucleon
  spin
• Ratio of different spinor components with E,?
• Sensitive to the discontinuity of Minkovski E
  field ES (2006)
• Chirality of lattice fermion is not so important.
• ? possibility in clover fermion action

6
Full QCD results (1)

• Nf 2 dynamical clover fermion
• 24348, a0.1 fm (CP-PACS), best configs. for
  topology
• Huge statistics O(104)

mp760 MeV
mp760 MeV
7
Full QCD results (2)

• Nf 2 dynamical clover fermion
• mp5001100 MeV
• topological susceptibility ?t17042204 MeV4
• finite value of NEDM in full QCD at heavier quark
  mass

8
NEDM form factor with clover fermion

• Challenging task
• Chiral extrapolation, lighter quark mass
• Nf3 dynamical simulation, continuum limit,
• but, it seems to be difficult to do these
  tasks in external electric field method due to
  large statistical error.
• Another possibility
• NEDM form factor using clover fermion action
• ? reduce the computational cost in comparison
  with DW
• ? reduce the lattice momentum (p2p/L)
• violation of chiral symmetry will not become
  large effect (that is prediction in the previous
  works)

9
Results in quench QCD (1)

• Formulation ES (2005)
• Extraction from next leading 3-pt function
• After calculation of F1,2 and fN we can obtain
  F3.
• Connected diagram

• 24332 lattice
• 1/a1.8 GeV
• Same configs. in
• E field method.
• lightest quark mass

p1
tEM6
source
sink
10
Results in quench QCD (2)

• Momentum extrapolation
• Linear fit
• cf. E field method
• -0.0391(125) efm
• Consistent with a result
• in E field method
• Error 60 reduction !
• Applicable to full QCD

11
Results in quench QCD (3)

• Disconnected diagram

tEM6

• flavor SU(3) limit (mu,dms)
• eu ed es0 ? ignore the disc. part
• In fact, mu,d/ms 1/30 then that is not
• good approximation.
• computation of disc. part using
• U(1) noise method

u,d,s

• noise60
• mu,d/ms1/3
• its contribution will
• be small.
• fit -0.0230(69) efm
• (con. -0.0239(30) efm)

12
Summary

• Full QCD calculation in E field method
• Dynamical clover fermion (Nf2)
• obtain the finite value (inconsistent with zero)
  at mp5001100 MeV
• Its hard to do the chiral extrapolation due to
  large error.
• ? heavy sea-quark mass range (topological
  susceptibility is also large)
• Form factor approach in clover fermion action
• Computational cost is much smaller than DW.
• Large size, then small momentum ? zero momentum
  extrapolation
• In quenched study, we can obtain consistent
  results in E field method.
• Moreover error is reduced by 60 .
• Disconnected part is small, it means that
  connected part is dominant.
• Applicable to full QCD ? possibility of obtaining
  the physical NEDM.