Isospin Symmetry Breaking Effects in Hadron Masses Taku Izubuchi for Riken-BNL-Columbia/UKQCD collaboration RIKEN BNL Reserch Center Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 1
RBC and UKQCD Collaboration C. Allton, D.J. Antonio, Y. Aoki, T. Blum, P.A. Boyle, N.H. Christ, S.D. Cohen, M.A. Clark, C. Dawson, M.A. Donnellan, J.M. Flynn, A. Hart, T. Ishikawa, T. Izubuchi, A. Jüttner, C. Jung, A.D. Kennedy, R.D. Kenway, M. Li, S. Li, M.F. Lin, R.D. Mawhinney, C.M. Maynard, S. Ohta, B.J. Pendleton, C.T. Sachrajda, S. Sasaki, E.E. Scholz, A. Soni, R.J. Tweedie, R. Van de Water, O. Witzel, J. Wennekers, T. Yamazaki, J.M. Zanotti • [C.Allton et al.] Pys.Rev.D76:014504[arXiv:0804.0473] “Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory” • [D. J. Antonio et al.] Phys. Rev. Lett. 100 (2008) 032001 [arXiv:hep-ph/0702042] “Neutral kaon mixing from 2+1 flavor domain wall QCD” , • [T. Blum, T. Doi, M. Hayakawa, TI, N. Yamada] , Phys. Rev.D76 (2007) 114508, “Determination of light quark masses from the electromagnetic splitting of psedoscalar meson masses computed with two flavors of domain wall fermions” • [R.Zhou, T.Blum, T.Doi, M.Hayakawa, TI, and N.Yamada] , PoS(LATTICE 2008) 131. “Isospin symmetry breaking effects in the pion and nucleon masses” Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 2
Full QCD (including dynamical quarks) • unquenched lattice QCD simulations Prob [ U µ ] ∝ det � De − Sg , • Quenched simulations quench: det � D → 1 ignores quark loops (sea quark loop) in QCD vacuum, and only using the external quarks (valence quarks) representing hadrons. • This approximation causes the quenched pathologies. • Lack of Unitarity. • quenched chiral divergences ( η ′ loops): M 2 π = 2 B 0 m q [1 − 2 δ ln( m f )] δ ∝ m f in Full QCD. • can’t decays. e.g. ρ → ππ : • quark mass with less than ∼ Λ QCD should play a significant role : N F = 2 + 1 . Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 3
Unitarity violation in Non-singlet scalar meson ( a 0 ) • Point to point propagator of non-singlet scalar meson, C a 0 ( t ) , was found to be negative in quenched QCD, which is a clear signal of the unitarity violation in quenched QCD. • In the language of mesons (ChPT), a 0 → η ′ + π → a 0 η ′ has double pole in (partially) quenched QCD. This contribution was argued to give a negative contribution (also finite size effect), and predicted using Quenched ChPT in finite volume. [Bardeen, Duncan, Eichten, Isgur, Thacker, PRD65 (02) 014509] ´ 0 a 0 a 0 Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 4
[ S. Prelovsek, C. Dawson, T.I. K. Orginos, A. Soni, PRD70 (04) 094503] • By fixing m sea and changing m val we confirmed D E a † C a 0 ( t ) = 0 ( t ) a 0 (0) < 0 ( m v < m s ) C a 0 ( t ) > 0 ( m v ≥ m s ) • This behaviour could be understood by NLO Partially Quenched ChPT also. ! C a 0 ( t ) → B 2 e − 2 Mvst 2 − e − 2 Mvvt M 2 vv + M 2 , R = M 2 ss − M 2 N F 1 0 ss vv + RM vv t 2 L 3 M 2 M 2 M 2 N F N F vv vv vv point−point correlator (set pp 1 in Table 1) 0.002 ´ 0 data, m val =0.01 data, m val =0.02 scalar correlator, m sea =0.02 data, m val =0.03 PQChPT, m val =0.01 0.001 a 0 a 0 0 Φ a o p+k qq qq qq qq −0.001 o f ao k 128 µ 128 µ f ao − − µ 2 µ 2 o o o Φ ’ −0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (a) (b) t Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 5
Dynamical quark effects Quenching error (dynamical quark effect) is not a minor issue. Other quantities very sensitive to dynamical quarks [M. Golterman, TI, Y. Shamir, PRD74 (05) 114508] • I = 0 ππ scattering length (Nucleon-Nucleon potential ?) ∆ E I =0 8 f 2 ML 3 + 1 7 π 1 ( M 2 ss − M 2 = − 2 B 0 ( ML ) R, R = vv ) + · · · 2 M N F • Static quark potential V QQ ( r ) [K. Hashimoto, RBC (04) RBC-UKQCD(07) thesis (08)] In shorter distance, r Λ QCD ≪ 1 , coupling is stronger for N F = 2 : α S ( r ; N F = 0) < α S ( r ; N F = 2) . asymptotic freedom b 0 = (33 − 2 N F ) / 2 t=4,5, R=1.2-7.5 0 t=4 t=6 -1 1.5 t=5 fit curve potential 1 -2 dynamical mf=0.02 quenched DBW2 beta=1.04 0.5 -3 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 r Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 6
Various Lattice actions • Improvements in algorithms & faster machine. • Vacuum polarization effects from the sea up, down, strange quarks, whose masses are lighter than Hadronic scale, m i < Λ QCD , are turned on. • Have entered Era of Dynamical quark simulations. Truly the first principle calculation various Lattice quarks • staggered [MILC, LHPC, J-Lab, FNAL...] 0.15 ETMC N f = 2 a [fm] QCDSF N f = 2 CERN-ToV N f = 2 CLS N f = 2 • 4D Wilson-types JLQCD N f = 2 0.10 JLQCD N f = 2 + 1 [CP-PACS, PACS-CS, BMW, ETM,...] PACS-CS N f = 2 + 1 RBC-UKQCD N f = 2 + 1 MILC N f = 2 + 1 JLQCD (2001) N f = 2 0.05 experiment • DWF [RBC/UKQCD] [this talk] 0.00 100 200 300 400 500 600 m PS [MeV] • overlap [JLQCD] [K.Jansen] Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 7
Dynamical Domain Wall Fermions (DWF) U(L) U(R) Ω • [ Furman & Shamir NPB439 (95) 54] q(L) q(R) • [ Blum & Soni PRL79 (97) 3595] • RBC (98-) CP-PACS (99-) quenched DWF spectrum, decay constant, B K , ǫ ′ /ǫ Ls-1 0 2 ... ... Ls/2-1 mf • DWF has exact flavor symmetry and a good chiral symmetry on a > 0 . chiral symmetry: q L → e iθL q L , q R → e iθR q R S f = ¯ q � Dq = ¯ q L � Dq L + ¯ q R � Dq R • discretization error is small.( lattice spacing, a > 0 ) No local operator with dimension five preserving chiral symmetry. qD 2 q L lat = Z L cont. + ( a Λ QCD ) 2 O 6 + · · · O 5 = F µν ¯ qσ µν q, ¯ O(a) error is suppressed. Results on relatively coarse lattice (large a ,smaller compu- tational cost) is much closer to the continuum limit: ( a Λ QCD ) 2 ∼ 1% • unphysical operator mixing is prohibited by χ -sym. • Continuum-like ChPT and renormalization = ⇒ Optimal for Hadron matrix elements comp. Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 8
m res • A measure of χ -sym breaking using PS density made of the mid-point quarks. m l = 0.005 0.0036 m l = 0.01 � P x J a x, t ) P a ( � m l = 0.02 5 q ( � 0 , 0) � � m l = 0.03 R ( t ) = , � P x, t ) P a ( � 0.0034 x P a ( � 0 , 0) � � m res 0.0032 • Roughly two times physical u,d quark mass, ∼ 9 MeV. 0.003 m res = 0 . 00315(2) . 0.0028 • Universally correct shift of quark 0 0.01 0.02 0.03 0.04 mass at NLO ChPT: m x ( = m y ) m = m + m res ˜ Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 9
Lattice spacing a from Ω mass • Ω − mass, 1672 MeV, is used to set the scale rather than m ρ or r 0 . • At NLO ChPT, there is no log: m Ω = m 0 Ω + cm l + · · · 1.12 1.08 • The single value of sea strange mass in our simulation, m h = baryon mass 1.04 0 . 04 , turns out to be ∼ 15 % heav- ier than the experimental. 1 • This systematic error is estimated by half of m l dependence, which is 0.96 ∼ - 1 % smaller than stat. error. 0.92 • We could measure the bounds from -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 m l the reweighting method. • After solving the coupled equations for Ω , π, K masses, a − 1 = 1 . 749(14) GeV Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 10
Pion sector • f PS is calculated from � A µ J 5 � using wall source. SU(2) PQChPT fit with cut ( m x + m y ) / 2 ≤ 0 . 01 for m l = 0 . 005 , 0 . 01 . χ 2 is degraded for larger cut. m s dependence is estimated from conv’ed SU (3) ChPT. • PQChPT Low Energy Constants, L (2) and ChPT LEC l r i 3 , 4 ¯ ¯ B f l 3 l 4 2.414(61) 0.0665(21) 3.13(.33) 4.43(.14) L (2) L (2) (2 L (2) − L (2) (2 L (2) − L (2) Λ χ 4 ) 5 ) 4 5 6 8 770 MeV 3.3(1.3) 9.30(.73) 0.32(.62) 0.50(.43) 1 GeV 1.3(1.3) 5.16(.73) -0.71(.62) 4.64(.43) ¯ ¯ N f l 3 l 4 type this work, direct SU(2) fit 2+1 DWF 3.13(.33)(.24) 4.43(.14)(.77) this work, conv. from SU(3) 2+1 DWF 2.87(.28)(--) 4.10(.05)(--) MILC, direct SU(2) fit 2+1 stagg 2.85(.07)(--) -- MILC, conv. from SU(3) 2+1 stagg 0.6(1.2) 3.9(0.5) ETMC 2 TM-Wilson 3.44(.08)(.35) 4.61(.04)(.11) CERN 2 impr. Wilson 3.0(0.5)(0.1) 4.1(0.1)(--) CERN NNLO 3.3(0.8)(--) phenom. 2.9(2.4) 4.4(0.2) Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 11
Pion sector results • The physical averaged u, d quark masses m ud = ( m u + m d ) / 2 is obtained by requiring extrapolated m PS = 135 . 0 MeV, corresponding to the neutral pion π 0 to avoid the leading QED effect. f xy 0.11 2 / (m avg +m res ) m xy m l = 0.005, m s = 0.04 5 fit: m avg ≤ 0.01 m x =0.001 0.1 4.8 m x =0.005 m x =0.01 m x =0.02 4.6 m x =0.03 0.09 m x =0.04 m x =0.001 m x =0.005 4.4 m x =0.01 m x =0.02 0.08 m x =0.03 m l = 0.005, m s = 0.04 4.2 m x =0.04 fit: m avg ≤ 0.01 0 0.01 0.02 0.03 0.04 0 0.01 0.02 0.03 0.04 m y m y 2 / (m avg +m res ) f xy m xy 0.11 5 m l = 0.01, m s = 0.04 fit: m avg ≤ 0.01 m x =0.001 4.8 0.1 m x =0.005 m x =0.01 m x =0.02 4.6 m x =0.03 m x =0.04 0.09 m x =0.001 4.4 m x =0.005 m x =0.01 m x =0.02 m l = 0.01, m s = 0.04 0.08 4.2 m x =0.03 fit: m avg ≤ 0.01 m x =0.04 0 0.01 0.02 0.03 0.04 0 0.01 0.02 0.03 0.04 m y m y Taku Izubuchi, Fermilab Theory Seminar, May 19, 2009 12
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