Isospin and Electromagnetism

Transcription

1 Extreme Scale Computing Workshop, December 9 11, 2008 p. 1/11 Isospin and Electromagnetism Steven Gottlieb

2 Extreme Scale Computing Workshop, December 9 11, 2008 p. 2/11 Questions In the exascale era, for what quantities will the precision have reached the point that EM and isospin breaking effects need to be included? How are such effects best included in practice? Should one do simulations with u and d quarks non-degenerate (at what cost?), or partial quenching?

3 Extreme Scale Computing Workshop, December 9 11, 2008 p. 3/11 Where are EM and isospin breaking needed? Hadron Spectrum Quark Masses Decay properties of light hadrons, e.g., f π and f K Potential concern for any quantities with 1% precision

4 There have already been some attempts to calculate either isospin or electromagnetic contributions to these differences. Extreme Scale Computing Workshop, December 9 11, 2008 p. 4/11 Hadron Spectrum There are a number of precisely known electromagnetic mass splittings m π ± m π 0 = 4.6MeV m K 0 m K ± = 4.0MeV m D ± m D 0 = 4.7MeV m n m p = 1.3MeV m 0 m + = 2.7MeV m 0 m + = 2.7MeV m Σ m Σ + = 8.1MeV m Ξ m Ξ 0 = 6.4MeV

5 Extreme Scale Computing Workshop, December 9 11, 2008 p. 5/11 Quark Masses N f = Asqtad quarks without QED: C. Aubin et al., PR D70, (2004), Q. Meson et al., PR D73, (2005). m s = 88(0)(3)(4)(0) MeV m u = 1.9(0)(1)(1)(1) MeV ˆm = 3.2(0)(1)(2)(0) MeV m d = 4.6(0)(2)(2)(1) MeV m s / ˆm = 27.2(1)(3)(0)(0) m u /m d = 0.42(0)(1)(0)(4). Errors are statistical, lattice-systematic, perturbative (two-loop PT) and electromagnetic. N f = 2 Domain Wall calculation include quenched QED: T. Blum, T. Doi, M. Hayakawa, T. Isubuchi, N. Yamada, PR D76, (2007). m s = 119.5(56)(74) MeV m u = 3.02(27)(19) MeV m d = 5.49(20)(34) MeV Errors are statistical and from non-perturbative renormalization. Only one lattice spacing was used here.

6 Extreme Scale Computing Workshop, December 9 11, 2008 p. 6/11 Neutron Proton Mass Difference Quenched Domain Wall valence quarks with N f = Asqtad sea quarks: S. R. Beane, K. Orginos and M. J. Savage, Nucl. Phys. B 768, 38 (2007) [arxiv:hep-lat/ ]. M n M p (d u) = 2.26 ± 0.57 ± 0.42 ± 0.10MeV where the first error is statistical, the second error is due to the uncertainty in the ratio of light-quark masses m u /m d determined by MILC, and the third error due to chiral extrapolation. Done on MILC coarse (a 0.12 fm) ensembles. Baryons were also considered by Doi et al, PoS(LAT2006) 174; arxiv:

7 Extreme Scale Computing Workshop, December 9 11, 2008 p. 7/11 How to Include These Effects Last few years have seen increased attention in both computing and theory (χpt). Pioneering work by Duncan, Eichten and Thacker in 1996 used Wilson quarks on quenched QCD, QED configs., Phys. Rev. Lett. 76, 3894 (1996) [arxiv:hep-lat/ ] First work with dynamical sea quarks using N f = 2 domain wall configurations from RBC collaboration by N. Yamada, T. Blum, M. Hayakawa and T. Izubuchi [RBC Collaboration], PoS LAT2005, 092 (2006) [arxiv:hep-lat/ ]. Isospin breaking for nucleon (discussed on previous slide), S. R. Beane, K. Orginos and M. J. Savage, Nucl. Phys. B 768, 38 (2007) [arxiv:hep-lat/ ] N f = Asqtad quarks from MILC collaboration S. Basak et al., PoS (LATTICE 2008) 127.

8 χ Perturbation Theory R. Urech, Virtual photons in chiral perturbation theory, Nucl. Phys. B 433, 234 (1995) [arxiv:hep-ph/ ]. J. Bijnens and J. Prades, Electromagnetic corrections for pions and kaons: Masses and polarizabilities, Nucl. Phys. B 490, 239 (1997) [arxiv:hep-ph/ ]. J. Bijnens and N. Danielsson, Electromagnetic Corrections in Partially Quenched Chiral Perturbation Theory, Phys. Rev. D 75, (2007) [arxiv:hep-lat/ ]. C. Haefeli, M. A. Ivanov and M. Schmid, Electromagnetic low-energy constants in ChPT, Eur. Phys. J. C 53, 549 (2008) [arxiv: [hep-ph]]. M. Hayakawa and S. Uno, QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons, Prog. Theor. Phys. 120, 413 (2008) [arxiv: [hep-ph]]. Extreme Scale Computing Workshop, December 9 11, 2008 p. 8/11

9 Another Approach Extreme Scale Computing Workshop, December 9 11, 2008 p. 9/11 A. Duncan, E. Eichten and R. Sedgewick, Phys. Rev. D 71, (2005) [arxiv:hep-lat/ ].

10 Extreme Scale Computing Workshop, December 9 11, 2008 p. 10/11 What Should We Do? There is plenty of time to get experience here before the Exascale Era. Much can be done with quenched QED on current configurations. Simulations with u and d quarks non-degenerate With RHMC this should be very low cost if QED is quenched Dynamical QED may only cost about a factor of two as charged 2/3 and -1/3 quarks will be treated separately. If U(1) can be added after inversion considering SU(3) gauge fields, it may be even cheaper.

11 Extreme Scale Computing Workshop, December 9 11, 2008 p. 11/11 What Should We Do? II Partial quenching This is likely to continue as it is so useful for the valence sector. Cost is not that high with multimass inverters. Benefit from increase in data to fit is huge. Now is the time to begin fully dynamical QCD + QED calculations.