The pion vector form factor from lattice QCD and NNLO chiral perturbation theory

Journal of High Energy Physics

Volumn 2013, Issue 11, 2013, Pages

  Brandt, Bastian B ^a   Jüttner, Andreas ^b   Wittig, Hartmut ^c  

^a UNIVERSITY OF REGENSBURG   (Germany)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^c JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Chiral Lagrangians; Lattice QCD; Nonperturbative effects

Indexed keywords

EID: 84896289282     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP11(2013)034     Document Type: Article

References (70)

1. M. Hasenbusch, Speeding up the hybrid Monte Carlo algorithm for dynamical fermions, Phys. Lett. B 519 (2001) 177 [hep-lat/0107019] [INSPIRE].
2. M. Lüscher, Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD, Comput. Phys. Commun. 165 (2005) 199 [hep-lat/0409106] [INSPIRE].
3. C. Urbach, K. Jansen, A. Shindler and U. Wenger, HMC algorithm with multiple time scale integration and mass preconditioning, Comput. Phys. Commun. 174 (2006) 87 [hep-lat/0506011] [INSPIRE].
4. M. Clark and A. Kennedy, Accelerating dynamical fermion computations using the rational hybrid Monte Carlo (RHMC) algorithm with multiple pseudofermion fields, Phys. Rev. Lett. 98 (2007) 051601 [hep-lat/0608015] [INSPIRE].
5. M. Lüscher, Local coherence and deflation of the low quark modes in lattice QCD, JHEP 07 (2007) 081 [arXiv:0706.2298] [INSPIRE].
6. M. Lüscher, Deflation acceleration of lattice QCD simulations, JHEP 12 (2007) 011 [arXiv:0710.5417] [INSPIRE].
7. M. Lüscher and F. Palombi, Fluctuations and reweighting of the quark determinant on large lattices, PoS(LATTICE 2008)049 [arXiv:0810.0946] [INSPIRE].
8. M. Marinkovic and S. Schaefer, Comparison of the mass preconditioned HMC and the DD-HMC algorithm for two-flavour QCD, PoS(LATTICE 2010)031 [arXiv:1011.0911] [INSPIRE].
9. G. Colangelo et al., Review of lattice results concerning low energy particle physics, Eur. Phys. J. C 71 (2011) 1695 [arXiv:1011.4408] [INSPIRE].
10. QCDSF/UKQCD collaboration, D. Brömmel et al., The Pion form-factor from lattice QCD with two dynamical flavours, Eur. Phys. J. C 51 (2007) 335 [hep-lat/0608021] [INSPIRE].
11. ETM collaboration, R. Frezzotti, V. Lubicz and S. Simula, Electromagnetic form factor of the pion from twisted-mass lattice QCD at N(f) = 2, Phys. Rev. D 79 (2009) 074506 [arXiv:0812.4042] [INSPIRE].
12. P. Boyle et al., The Pion's electromagnetic form-factor at small momentum transfer in full lattice QCD, JHEP 07 (2008) 112 [arXiv:0804.3971] [INSPIRE].
13. JLQCD Collaboration, TWQCD collaboration, S. Aoki et al., Pion form factors from two-flavor lattice QCD with exact chiral symmetry, Phys. Rev. D 80 (2009) 034508 [arXiv:0905.2465] [INSPIRE].
14. f = 2 + 1 dynamical flavor QCD, JHEP 04 (2011) 122 [arXiv:1102.3652] [INSPIRE].
15. B.B. Brandt, A. Juttner and H. Wittig, Calculation of the pion electromagnetic form factor from lattice QCD, arXiv:1109.0196 [INSPIRE].
16. J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].
17. J. Gasser and H. Leutwyler, Low-Energy Expansion of Meson Form-Factors, Nucl. Phys. B 250 (1985) 517 [INSPIRE].
18. J. Bijnens, G. Colangelo and P. Talavera, The vector and scalar form-factors of the pion to two loops, JHEP 05 (1998) 014 [hep-ph/9805389] [INSPIRE].
19. J. Bijnens and P. Talavera, Pion and kaon electromagnetic form-factors, JHEP 03 (2002) 046 [hep-ph/0203049] [INSPIRE].
20. C. Aubin and T. Blum, Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks, Phys. Rev. D 75 (2007) 114502 [hep-lat/0608011] [INSPIRE].
21. X. Feng, K. Jansen, M. Petschlies and D.B. Renner, Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling, Phys. Rev. Lett. 107 (2011) 081802 [arXiv:1103.4818] [INSPIRE].
22. P. Boyle, L. Del Debbio, E. Kerrane and J. Zanotti, Lattice Determination of the Hadronic Contribution to the Muon g - 2 using Dynamical Domain Wall Fermions, Phys. Rev. D 85 (2012) 074504 [arXiv:1107.1497] [INSPIRE].
23. M. Della Morte and A. Jüttner, Quark disconnected diagrams in chiral perturbation theory, JHEP 11 (2010) 154 [arXiv:1009.3783] [INSPIRE].
24. μ, JHEP 03 (2012) 055 [arXiv:1112.2894] [INSPIRE].
25. P.F. Bedaque, Aharonov-Bohm effect and nucleon nucleon phase shifts on the lattice, Phys. Lett. B 593 (2004) 82 [nucl-th/0402051] [INSPIRE].
26. G. de Divitiis, R. Petronzio and N. Tantalo, On the discretization of physical momenta in lattice QCD, Phys. Lett. B 595 (2004) 408 [hep-lat/0405002] [INSPIRE].
27. C. Sachrajda and G. Villadoro, Twisted boundary conditions in lattice simulations, Phys. Lett. B 609 (2005) 73 [hep-lat/0411033] [INSPIRE].
28. P. Boyle, J. Flynn, A. Juttner, C. Sachrajda and J. Zanotti, Hadronic form factors in Lattice QCD at small and vanishing momentum transfer, JHEP 05 (2007) 016 [hep-lat/0703005] [INSPIRE].
29. B.B. Brandt et al., Wilson fermions at fine lattice spacings: scale setting, pion form factors and (g-2)μ, PoS(LATTICE 2010)164 [arXiv:1010.2390] [INSPIRE].
30. B. Brandt et al., Form factors in lattice QCD, Eur. Phys. J. ST 198 (2011) 79 [arXiv:1106.1554] [INSPIRE].
31. B.B. Brandt, A. Jüttner and H. Wittig, The electromagnetic form factor of the pion in two-flavour lattice QCD, PoS(Confinement X)112 [arXiv:1301.3513] [INSPIRE].
32. UKQCD collaboration, J. Flynn, A. Jüttner and C. Sachrajda, A numerical study of partially twisted boundary conditions, Phys. Lett. B 632 (2006) 313 [hep-lat/0506016] [INSPIRE].
33. K.G. Wilson, Confinement of Quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].
34. ALPHA collaboration, K. Jansen and R. Sommer, O(a) improvement of lattice QCD with two flavors of Wilson quarks, Nucl. Phys. B 530 (1998) 185 [Erratum ibid. B 643 (2002) 517-518] [hep-lat/9803017] [INSPIRE].
35. M. Lüscher, S. Sint, R. Sommer and P. Weisz, Chiral symmetry and O(a) improvement in lattice QCD, Nucl. Phys. B 478 (1996) 365 [hep-lat/9605038] [INSPIRE].
36. M. Della Morte, R. Hoffmann and R. Sommer, Non-perturbative improvement of the axial current for dynamical Wilson fermions, JHEP 03 (2005) 029 [hep-lat/0503003] [INSPIRE].
37. S. Sint and P. Weisz, Further one loop results in O(a) improved lattice QCD, Nucl. Phys. Proc. Suppl. 63 (1998) 856 [hep-lat/9709096] [INSPIRE].
38. P. Fritzsch, J. Heitger and N. Tantalo, Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD, JHEP 08 (2010) 074 [arXiv:1004.3978] [INSPIRE].
39. P. Fritzsch et al., The strange quark mass and Lambda parameter of two flavor QCD, Nucl. Phys. B 865 (2012) 397 [arXiv:1205.5380] [INSPIRE].
40. M. Della Morte, R. Sommer and S. Takeda, On cutoff effects in lattice QCD from short to long distances, Phys. Lett. B 672 (2009) 407 [arXiv:0807.1120] [INSPIRE].
41. ALPHA collaboration, Non-perturbative quark mass renormalization in two-avor QCD, Nucl. Phys. B 729 (2005) 117 [hep-lat/0507035] [INSPIRE].
42. L. Del Debbio, L. Giusti, M. Lüscher, R. Petronzio and N. Tantalo, QCD with light Wilson quarks on fine lattices. II. DD-HMC simulations and data analysis, JHEP 02 (2007) 082 [hep-lat/0701009] [INSPIRE].
43. PARTICLE DATA GROUP collaboration, Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].
44. J. Bulava, M. Donnellan and R. Sommer, On the computation of hadron-to-hadron transition matrix elements in lattice QCD, JHEP 01 (2012) 140 [arXiv:1108.3774] [INSPIRE].
45. S. Capitani et al., The nucleon axial charge from lattice QCD with controlled errors, Phys. Rev. D 86 (2012) 074502 [arXiv:1205.0180] [INSPIRE].
46. R. Sommer, A new way to set the energy scale in lattice gauge theories and its applications to the static force and αs in SU(2) Yang-Mills theory, Nucl. Phys. B 411 (1994) 839 [hep-lat/9310022] [INSPIRE].
47. 0 and the static potential from the CLS lattices, PoS(LATTICE 2010)233 [arXiv:1012.1141] [INSPIRE].
48. S. Capitani, M. Della Morte, G. von Hippel, B. Knippschild and H. Wittig, Scale setting via the Ω baryon mass, PoS(LATTICE 2011)145 [arXiv:1110.6365] [INSPIRE].
49. UKQCD collaboration, M. Foster and C. Michael, Quark mass dependence of hadron masses from lattice QCD, Phys. Rev. D 59 (1999) 074503 [hep-lat/9810021] [INSPIRE].
50. UKQCD collaboration, C. McNeile and C. Michael, Decay width of light quark hybrid meson from the lattice, Phys. Rev. D 73 (2006) 074506 [hep-lat/0603007] [INSPIRE].
51. P. Boyle, A. Jüttner, C. Kelly and R. Kenway, Use of stochastic sources for the lattice determination of light quark physics, JHEP 08 (2008) 086 [arXiv:0804.1501] [INSPIRE].
52. E. Endress, A. Juttner and H. Wittig, On the efficiency of stochastic volume sources for the determination of light meson masses, arXiv:1111.5988 [INSPIRE].
53. RBC-UKQCD collaboration, P. Boyle et al., K → π form factors with reduced model dependence, Eur. Phys. J. C 69 (2010) 159 [arXiv:1004.0886] [INSPIRE].
54. B. Efron, Bootstrap methods: another look at the jacknife, Ann. Statist. 7 (1979) 1.
55. C. Michael, Fitting correlated data, Phys. Rev. D 49 (1994) 2616 [hep-lat/9310026] [INSPIRE].
56. F.-J. Jiang and B. Tiburzi, Flavor twisted boundary conditions, pion momentum and the pion electromagnetic form-factor, Phys. Lett. B 645 (2007) 314 [hep-lat/0610103] [INSPIRE].
57. NA7 collaboration, S. Amendolia et al., A Measurement of the Space-Like Pion Electromagnetic Form-Factor, Nucl. Phys. B 277 (1986) 168 [INSPIRE].
58. G. Colangelo, S. Dürr and C. Haefeli, Finite volume effects for meson masses and decay constants, Nucl. Phys. B 721 (2005) 136 [hep-lat/0503014] [INSPIRE].
59. F.-J. Jiang and B.C. Tiburzi, Flavor Twisted Boundary Conditions in the Breit Frame, Phys. Rev. D 78 (2008) 037501 [arXiv:0806.4371] [INSPIRE].
60. G. Colangelo, J. Gasser and H. Leutwyler, ππ scattering, Nucl. Phys. B 603 (2001) 125 [hep-ph/0103088] [INSPIRE].
61. J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys. 158 (1984) 142 [INSPIRE].
62. U. Burgi, Charged pion pair production and pion polarizabilities to two loops, Nucl. Phys. B 479 (1996) 392 [hep-ph/9602429] [INSPIRE].
63. U. Burgi, Charged pion polarizabilities to two loops, Phys. Lett. B 377 (1996) 147 [hep-ph/9602421] [INSPIRE].
64. J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M. Sainio, Pion pion scattering at low-energy, Nucl. Phys. B 508 (1997) 263 [Erratum ibid. B 517 (1998) 639] [hep-ph/9707291] [INSPIRE].
65. L. Del Debbio, H. Panagopoulos and E. Vicari, θ dependence of SU(N) gauge theories, JHEP 08 (2002) 044 [hep-th/0204125] [INSPIRE].
66. S. Schaefer, R. Sommer and F. Virotta, Investigating the critical slowing down of QCD simulations, PoS(LAT2009)032 [arXiv:0910.1465] [INSPIRE].
67. ALPHA collaboration, S. Schaefer, R. Sommer and F. Virotta, Critical slowing down and error analysis in lattice QCD simulations, Nucl. Phys. B 845 (2011) 93 [arXiv:1009.5228] [INSPIRE].
68. M. Lüscher and S. Schaefer, Lattice QCD without topology barriers, JHEP 07 (2011) 036 [arXiv:1105.4749] [INSPIRE].
69. M. Lüscher and S. Schaefer, Lattice QCD with open boundary conditions and twisted-mass reweighting, Comput. Phys. Commun. 184 (2013) 519 [arXiv:1206.2809] [INSPIRE].
70. M. Gell-Mann, R. Oakes and B. Renner, Behavior of current divergences under SU(3) x SU(3), Phys. Rev. 175 (1968) 2195 [INSPIRE].