03/15/2007 Talk @ DWF 10yrs 1 Isospin breaking Study wit Isospin breaking Study wit h Nf=2 domain-wall QCD + h Nf=2 domain-wall QCD + Quenched QED Simulation Quenched QED Simulation Takumi Doi (Univ. of Kentucky / RBRC) In collaboration with T.Blum (Univ. of Connecticut, RBRC) M.Hayakawa (Nagoya Univ.) T.Izubuchi (Kanazawa Univ., RB RC) N.Yamada (KEK) for RBC Collaboration
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Isospin breaking Study with Nf=2 domain-wall QCD + Quenched QED Simulation
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03/15/2007 Talk @ DWF 10yrs 1
Isospin breaking Study with Nf=Isospin breaking Study with Nf=2 domain-wall QCD + Quenched 2 domain-wall QCD + Quenched
QED SimulationQED Simulation
Takumi Doi(Univ. of Kentucky / RBRC)
In collaboration withT.Blum (Univ. of Connecticut, RBRC) M.Hayakawa (Nagoya Univ.)T.Izubuchi (Kanazawa Univ., RBRC)N.Yamada (KEK)
for RBC Collaboration
03/15/2007 Talk @ DWF 10yrs 2
Isospin breaking important physics in QCD/QED. Mass splitting:
Light quark mass can be determined by introducing QED Most fundamental parameters in the standard model Precise check for the “massless” scenario for strong CP problem
(p-n) : fundamental parameter in nuclear physics Controls the lifetime of neutron (through the phase space) Charge symmetry breaking in the N-N interaction
Introduction
dominated by QED QED +QCD
(mu-md)
03/15/2007 Talk @ DWF 10yrs 3
Introduction Precise theoretical calculation of muon g-2
Muon is expected to be sensitive to short-range New Physics ?
Large uncertainty from hadronic contribution
Bs
QCD+QED simulation !
03/15/2007 Talk @ DWF 10yrs 4
QED configurations Quenched non-compact QED
No photon self-coupling free theory, coupling does not run
Generating QED configs: Generate A(em) in momentum-space
We must fix the gauge redundancy Coulomb gauge + additional gauge fixing for A0
Gauge fixing condition can be solved analytically and the action becomes gaussian simple gaussian random number generation
No autocorrelation (int=0) even for arbitrary small coupling Fourier inversion to x-space Wilson line U(em)=exp[iA(em))] to c
onnect next-neighbor-site
A.Duncan, E.Eichten, H.Thacker, PRL76(1996)3894
Qu=+2/3e, Qd=-1/3e
03/15/2007 Talk @ DWF 10yrs 5
QCD configurations Light quark sector chiral symmetry is essential !
The most fundamental LEC with QED on For Iz=0, S=0 channel, we
ignore the disconnected diagram, we ignore the mixing of - , –’ (expected to be higher order)
03/15/2007 Talk @ DWF 10yrs 8
Extract the mass difference
We focus on the mass difference directly. (e=0) = A(e=0) exp(-m(e=0) t) (e) = A(e) exp(-m(e) t)
[For visibility] R= (e)/(e=0)
R (1+ A) – [ m(e)-m(e=0) ] t , (A=(A(e)-A(e=0))/A(e=0)) The slope of t is directly related to the mass difference Statistical fluctuation is expected to be canceled in the ratio,
which improves S/N In the final analysis, we take exp-fit to assure the ground state
dominance
03/15/2007 Talk @ DWF 10yrs 9
The QED effect on PS-meson
(msea=0.04) (msea=0.03)
03/15/2007 Talk @ DWF 10yrs 10
Quark mass determination Offset of quark mass in DWF
Residual quark mass with QED on determined by PCAC Fit to the quark mass dependence of neutron mesons
and pion mass splittings LECs are determined
LECs obtained + experimental inputs M(0)2 sensitive to (mu+md), insensitive to (mu-md)
determine (mu+md) M(K+)2+M(K0)2 sensitive to ms, (mu+md), insensitive to (mu-md)
determine ms [M(K0)2-M(K+)2] - [M(0)2-M(+)2] sensitive to (mu-md), ms, ins
ensitive to (mu+md) determine (mu-md)
03/15/2007 Talk @ DWF 10yrs 11
Quark masses and splittings Masses
By employing RBC nonperturbative 1/Zm=0.62
Systematic error neglection of nondegenate mass effect finite V: estimation by Cottingham formula
+ vector saturation model would be negligible Splittings
MILC w/o QED
Kaon suffer from large systematic error
03/15/2007 Talk @ DWF 10yrs 12
Isospin breaking in baryons Mass splitting between octets