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Meson correlators of two-flavor QCD in the epsilon -regime

Meson correlators of two-flavor QCD in the epsilon -regime. Hidenori Fukaya (RIKEN) with S.Aoki, S.Hashimoto, T.Kaneko, H.Matsufuru, J.Noaki, K.Ogawa, T.Onogi and N.Yamada [JLQCD collaboration]. 1. Introduction. The chiral limit is difficult. The standard way requires before .

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Meson correlators of two-flavor QCD in the epsilon -regime

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  1. Meson correlators of two-flavor QCD in the epsilon-regime Hidenori Fukaya (RIKEN) with S.Aoki, S.Hashimoto, T.Kaneko, H.Matsufuru, J.Noaki, K.Ogawa, T.Onogi and N.Yamada [JLQCD collaboration]

  2. 1. Introduction • The chiral limit is difficult. • The standard way requires before . • Lattice QCD in ( ) [Necco (plenary), Akemann, DeGrand, Shindler (poster) , Cecile, Hierl (chiral), Hernandez (weak)…] • Finite effects can be estimated within ChPT ( ). • is not very expensive. • ->the chiral symmetry is essential. ->the dynamical overlap fermions.

  3. 1. Introduction • JLQCD collaboration • achieved 2-flavor QCD simulations with the dynamical overlap quarks on a 16332(~1.7-2fm) lattice with a~0.11-0.13fm at Q=0 sector. • the quark mass down to ~3MeV ! (enough to reach the epsilon-regime.) • The Dirac spectrum[JLQCD, Phys.Rev.Lett.98,172001(2007)] • shows a good agreement with Banks-Casher relation. • with finite V correction via Random Matrix Theory (RMT), we obtained the chiral condensate, systematic statistical

  4. 1. Introduction • ChPT in the epsilon-regime [Gasser & Leutwyler, 1987] • RMT does not know . • Direct comparison with ChPT at -> more accurate (condensate). ->pion decay constant • Meson correlators in the epsilon-regime [Hansen, 1990, 1991, Damgaard et al, 2002] • are quadratic function of t; where A and B are expressed by the “finite volume” condensate, which is sensitive to m and topological charge Q.

  5. 1. Introduction • Partially quenched ChPT in the epsilon-regime [P.H.Damgaard & HF, arXiv:0707.3740, Bernardoni & Hernandez, arXiv:0707.3887] • The previous known results are limited to degenerate cases. • We extend ChPT to the partially quenched theory. • Pseudoscalar and scalar channels are done; the correlators are expressed by of the “partially quenched finite volume” condensate, with which we can use the different valence quark masses to extract and . • Axial vector and vector channels are in preparation. • A0+V0 calculated by the latter authors.

  6. 1. Introduction • The goal of this work • On a (1.8fm)4 lattice with a~0.11fm, 2-flavor QCD simulation with m~3MeV is achieved. • The Dirac spectrum shows a qualitative agreementwith RMT prediction, however, has ~10% error of effects. • Therefore, our goal is to determine to by comparing meson correlators with (partially quenched) ChPT.

  7. Contents • Introduction • Lattice simulations • Results • Conclusion Related talks and posters • Plenary talk by H.Matsufuru, • “meson spectrum” by J.Noaki (chiral), • “2+1 flavor simulations” by S.Hashimoto (hadron spectroscopy), • “topology” by T.W.Chiu and T.Onogi (chiral), • “pion form factor” by T.Kaneko (hadron structure), • “pi±pi0 difference” by E.Shintani (hadron spectroscopy), • “BK” by N.Yamada (weak).

  8. 2. Lattice simulations • Lattice size = 16332 (L~1.8fm.). • a~0.11 fm. (determined by Sommer scale r0=0.49fm.) • Iwasaki gauge action with . • Extra topology fixing determinant. • 2-flavor dynamical overlap quarks. • ma = 0.002 (~3MeV). • mv a=0.0005, 0.001,0.002, 0.003 [1-4MeV]. • topological sector is limited to Q=0. • 460 confs from 5000 trj. • Details -> Matsufuru’s plenary talk.

  9. 2. Lattice simulations • Numerical cost • Finite volume helps us to simulate very light quarks since the lowest eigenvalue of the Dirac operator are uplifted by an amount of 1/V. • m~3MeV is possible with L~1.8fm !

  10. PS-PS A0-A0 2. Lattice simulations • Low-mode averaging [DeGrand & Schaefer, 2004,, Giusti,Hernandez,Laine,Weisz & Wittig,2004.] • We calculate PS, S, V0, A0 correlation functions with a technique called low-mode averaging (LMA) with the lowest 100 Dirac-eigenmodes. PS, S ->the fluctuation is drastically suppressed. V0, A0 -> the improvement is marginal.

  11. 3. Results • Axial vector correlator (mv=msea=3MeV) • We use the ultra local definition of A0 which is not a conserved current ->need renormalization. • We calculate • From 2-parameter fit with ChPT, • chiral condensate , • pion decay const , 　　（Fit range : t=12-20, chi2/d.o.f. ~ 0.01) are obtained. Note: A0A0 is not very sensitive to .

  12. 3. Results • Pseudoscalar correlators (mv=msea=3MeV) • With as an input, 1-parameter fit of PP correlator works well and • condensate is obtained. (fit range: t=12-20, chi2/d.o.f.=0.07.) • PP correlator is sensitive to . • A0A0 is sensitive to . ->With the simultaneous 2-parameter fit with PP and A0A0 correlator, we obtain to in lattice unit. (fit range : t=12-20, chi2/d.o.f.=0.02.)

  13. SS V0V0 3. Results • Consistency with SS and V0V0 (mv=msea=3MeV) • are consistent with SS and V0V0 channels ! (No free parameter left. )

  14. 3. Results • Consistency with Partially quenched ChPT • are also consistent with partially quenched ChPT but the valence quark mass dependence is weak. (No free parameter left)

  15. 3. Results • Consistency with Dirac spectrum • If non-zero modes of ChPT are integrated out, there remains the zero-mode integral with “effective” chiral condensate, • In fact, this value agree well with the value via Dirac spectrum compared with RMT, ->support our estimate of correction.

  16. (non-perturbative) (tree) 3. Results • Non-perturbative renormalization Since is the lattice bare value, it should be renormalized. We calculated • the renormalization factor in a non-perturbative RI/MOM scheme on the lattice, • match with MS bar scheme, with the perturbation theory, • and obtained

  17. 3. Results • Systematic errors • Different channels, PP, A0A0, SS, V0V0, their partially quenched correlators, and the Dirac spectrum are all consistent. • Fit range : from tmin~10(1.1fm) to 15 (1.7fm), both are stable (within 1%) with similar error-bars. • Finite V :taken into account in the analysis. • Finite a : overlap fermion is automatically free from O(a). • Finite m : m~3MeV is already very close to the chiral limit. But =87.3(5.5)MeV slightly different from the value [~78(3)(1)MeV] (Noaki’s talk) in the p-regime.

  18. 4. Conclusion • On a (1.8fm)4 lattice with a~0.11fm, 2-flavor QCD simulation with m~3MeV is achieved, which is in the epsilon-regime. • We calculate the various meson correlators with low-mode averaging (LMA). • From PP (sensitive to ) and A0A0 (sensitive to ) channels, compared with ChPT, to accuracy, are obtained (preliminary). • They are consistent with SS and V0V0 channels. • Also consistent with partially quenched ChPT. • Also consistent with result from Dirac spectrum. • But slightly deviate from p-regime results.

  19. 4. Conclusion • Future works • Larger volumes • Smaller lattice spacings • Partially quenched analysis for A0A0 and V0V0 channels. • 2+1 flavors…

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