Highly improved staggered quarks on the lattice with applications to charm physics

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 75, Issue 5, 2007, Pages

  Follana, E ^a   Mason, Q ^b   Davies, C ^a   Hornbostel, K ^c   Lepage, G P ^d   Shigemitsu, J ^e   Trottier, H ^f   Wong, K ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c SOUTHERN METHODIST UNIVERSITY   (United States)

^d Newman Laboratory for Elementary Particle Physics   (United States)

^e OHIO STATE UNIVERSITY   (United States)

^f SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947191931     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.75.054502     Document Type: Article

References (52)

1. C.T.H. Davies (HPQCD Collaboration, Fermilab Collaboration, MILC Collaboration, and UKQCD Collaboration), Phys. Rev. Lett. 92, 022001 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.022001
2. C. Aubin (MILC Collaboration), Phys. Rev. D 70, 114501 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.70.114501
3. Q. Mason (HPQCD Collaboration), Phys. Rev. Lett. 95, 052002 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.052002
4. C. Aubin, Phys. Rev. Lett. 95, 122002 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.122002
5. Q. Mason, H.D. Trottier, R. Horgan, C.T.H. Davies, and G.P. Lepage (HPQCD Collaboration), Phys. Rev. D 73, 114501 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.114501
6. S. Naik, Nucl. Phys. NUPBBO 0550-3213 B316, 238 (1989). 10.1016/0550-3213(89)90394-5
7. D. Toussaint and K. Orginos (MILC Collaboration), Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 73, 909 (1999); 10.1016/S0920-5632(99)85241-4
8. D. Toussaint K. Orginos MILC Collaboration Phys. Rev. D 59, 014501 (1998). PRVDAQ 0556-2821 10.1103/PhysRevD.59.014501
9. G.P. Lepage, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 60, 267 (1998). 10.1016/S0920-5632(97)00489-1
10. J.F. Lagae and D.K. Sinclair, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 63, 892 (1998); 10.1016/S0920-5632(97)00932-8
11. J.F. Lagae D.K. Sinclair Phys. Rev. D 59, 014511 (1998). PRVDAQ 0556-2821 10.1103/PhysRevD.59.014511
12. G.P. Lepage, Phys. Rev. D 59, 074502 (1999). PRVDAQ 0556-2821 10.1103/PhysRevD.59.074502
13. A. Hasenfratz and F. Knechtli, Phys. Rev. D 64, 034504 (2001). PRVDAQ 0556-2821 10.1103/PhysRevD.64.034504
14. See, for example, A. Gray, I. Allison, C.T.H. Davies, E. Gulez, G.P. Lepage, J. Shigemitsu, and M. Wingate (HPQCD Collaboration and UKQCD Collaboration), Phys. Rev. D 72, 094507 (2005). PRVDAQ 0556-2821 10.1103/PhysRevD.72.094507
15. See, for example: C. Bernard, M. Golterman, and Y. Shamir, hep-lat/0610003;
16. M. Creutz, hep-lat/0608020;
17. Y. Shamir, hep-lat/0607007;
18. C. Bernard, M. Golterman, Y. Shamir, and S.R. Sharpe, hep-lat/0603027;
19. M. Creutz, hep-lat/0603020.
20. S. Sharpe, Proc. Sci. LAT2006 (2006) 022 [hep-lat/0610094].
21. C.R. Allton (UKQCD Collaboration), Phys. Rev. D 65, 054502 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.65.054502
22. See, for example, C. Aubin, Phys. Rev. D 70, 094505 (2004); PRVDAQ 0556-2821 10.1103/PhysRevD.70.094505
23. C. Aubin (MILC Collaboration), Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 129, 227 (2004). 10.1016/S0920-5632(03)02538-6
24. The requirement m>0 is necessary so that |det(D)|=det(D(U))>0. The naive-quark theory does not give correct results when m<0 since then det(D•γ+m) can be negative (if instantons are present). Fortunately the masses of real quarks are not negative. Creutz has suggested that the exact m→-m symmetry of this theory might lead to problems for small positive quark masses as well, but the issue he raises is resolved by Bernard et al. and does not lead to problems for any m>0 provided the continuum limit is taken before the chiral limit.
25. C. Aubin and C. Bernard, Phys. Rev. D 73, 014515 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.014515
26. E. Follana, A. Hart, C.T.H. Davies, and Q. Mason (HPQCD Collaboration), Phys. Rev. D 72, 054501 (2005); PRVDAQ 0556-2821 10.1103/PhysRevD.72.054501
27. E. Follana, A. Hart, and C.T.H. Davies (HPQCD Collaboration), Phys. Rev. Lett. 93, 241601 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.241601
28. See also, K.Y. Wong and R.M. Woloshyn, Phys. Rev. D 71, 094508 (2005); PRVDAQ 0556-2821 10.1103/PhysRevD.71.094508
29. S. Durr and C. Hoelbling, Phys. Rev. D 71, 054501 (2005); PRVDAQ 0556-2821 10.1103/PhysRevD.71.054501
30. S. Durr, C. Hoelbling, and U. Wenger, Phys. Rev. D 70, 094502 (2004); PRVDAQ 0556-2821 10.1103/PhysRevD.70.094502
31. S. Durr and C. Hoelbling, Phys. Rev. D 69, 034503 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.69.034503
32. Specifically, the minimum mass is related to the eigenvalues which correspond in the continuum to zero modes caused by instantons. In our lattice formalisms these eigenvalues are O(a2), and so are small rather than zero. It is important that quark masses be kept significantly larger than these eigenvalues in order to capture instanton effects accurately; for a detailed discussion see and references therein.
33. Tadpole improvement requires dividing every Uμ in the final action by a mean link factor u0 (after expanding products of operators so as to remove factors of Uν(x)†Uν(x)=1);
34. see G.P. Lepage and P.B. Mackenzie, Phys. Rev. D 48, 2250 (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.48.2250
35. G.P. Lepage, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 26, 45 (1992). 10.1016/0920-5632(92)90228-K
36. G.P. Lepage, " Redesigning Lattice QCD, " in Proceedings of the 35th International School on Nuclear and Particle Physics, Schladming, Austria, 1996 (to be published), hep-lat/9607076.
37. Q.J. Mason, Ph.D. Thesis, Cornell University [Institution Report No. UMI-31-14569, 2004 (unpublished)].
38. See, for example, Fig. 2 in where the upper line in each pair of closely spaced lines comes from a simulation with twice the u/d sea-quark mass.
39. S. Aoki, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 42, 303 (1995). 10.1016/0920-5632(95)00233-Y
40. W.-M. Yao (Particle Data Group), J. Phys. G JPGPED 0954-3899 33, 1 (2006). 10.1088/0954-3899/33/1/001
41. G.T. Bodwin, E. Braaten, and G.P. Lepage, Phys. Rev. D 51, 1125 (1995); PRVDAQ 0556-2821 10.1103/PhysRevD.51.1125
42. G.T. Bodwin E. Braaten G.P. Lepage Phys. Rev. D 55, 5853 (1997). PRVDAQ 0556-2821 10.1103/PhysRevD.55.5853
43. The perturbative result for a ηc is the same, up to an overall factor, as for parapositronium. See, for example, G. Adkins in Relativistic, Quantum Electrodynamic and Weak Interaction Effects in Atoms, edited by, W. Johnson,,, AIP Conf. Proc. No. 189 (AIP, New York, 1989).
44. E. Follana, Q. Mason, C. Davies, K. Hornbostel, P. Lepage, and H. Trottier (HPQCD Collaboration), Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 129, 447 (2004). 10.1016/S0920-5632(03)02610-0
45. W. Kamleh, D.B. Leinweber, and A.G. Williams, Phys. Rev. D 70, 014502 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.70.014502
46. C. Morningstar and M.J. Peardon, Phys. Rev. D 69, 054501 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.69.054501
47. See, for example, Section 4.3 in I. Montvay and G. Munster, Quantum Fields on a Lattice (Cambridge University Press, Cambridge, England, 1994);
48. also Section 4.5 in H.J. Rothe, World Sci. Lect. Notes Phys. 59, 1 (1997).
49. For a similar argument, applied to staggered quarks directly, see S.R. Sharpe, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 34, 403 (1994); 10.1016/0920-5632(94)90403-0
50. S.R. Sharpe, hep-ph/9412243. One could easily design a different blocking scheme that suppressed other tastes up to order a2 or a3 corrections by averaging appropriately over larger lattice volumes than 24 hypercubes. The actions for these new blocked fields would then have a2 or a3 taste violations, respectively. Obviously such errors cannot be fundamental since the underlying equations are the same in each case. Indeed by smearing appropriately over the entire lattice volume, all an errors of this sort can be removed:, for example, we can do this by using Fourier transforms to isolate different corners of the Brillouin zone exactly rather than approximately.
51. W. Lee and S.R. Sharpe, Phys. Rev. D 66, 114501 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.66.114501
52. M. Wingate, J. Shigemitsu, C.T.H. Davies, G.P. Lepage, and H. Trottier, Phys. Rev. D 67, 054505 (2003). PRVDAQ 0556-2821 10.1103/PhysRevD.67.054505