Abstract
The determination of |V us | from kaon semileptonic decays requires the value of the form factor f +(q 2 = 0) which can be calculated precisely on the lattice. We provide the one-loop partially quenched chiral perturbation theory expressions both with and without including the effects of staggered quarks for all form factors at finite volume and with partially twisted boundary conditions for both the vector current and scalar density matrix elements at all q 2. We point out that at finite volume there are more form factors than just f + and f − for the vector current matrix element but that the Ward identity is fully satisfied. The size of the finite-volume corrections at present lattice sizes is small. This will help improve the lattice determination of f +(q 2 = 0) since the finite-volume error is the dominant error source for some calculations. The size of the finite-volume corrections may be estimated on a single lattice ensemble by comparing results for various twist choices.
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References
A. Bazavov et al., Determination of |V us | from a lattice-QCD calculation of the K → πℓν semileptonic form factor with physical quark masses, Phys. Rev. Lett. 112 (2014) 112001 [arXiv:1312.1228] [INSPIRE].
V. Cirigliano, G. Ecker, H. Neufeld, A. Pich and J. Portoles, Kaon Decays in the Standard Model, Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001] [INSPIRE].
JLQCD collaboration, T. Kaneko et al., Chiral behavior of kaon semileptonic form factors in lattice QCD with exact chiral symmetry, PoS (LATTICE 2012) 111 [arXiv:1211.6180] [INSPIRE].
P.A. Boyle et al., The kaon semileptonic form factor with near physical domain wall quarks, JHEP 08 (2013) 132 [arXiv:1305.7217] [INSPIRE].
Fermilab Lattice and MILC collaborations, E. Gámiz et al., Kaon semileptonic form factors with N f = 2 + 1 + 1 HISQ fermions and physical light quark masses, PoS (LATTICE 2013) 395 [arXiv:1311.7264] [INSPIRE].
RBC/UKQCD collaboration, P.A. Boyle et al., The kaon semileptonic form factor in N f = 2 + 1 domain wall lattice QCD with physical light quark masses, JHEP 06 (2015) 164 [arXiv:1504.01692] [INSPIRE].
N. Carrasco, P. Lami, V. Lubicz, L. Riggio, S. Simula and C. Tarantino, K → π semileptonic form factors with N f = 2 + 1 + 1 twisted mass fermions, Phys. Rev. D 93 (2016) 114512 [arXiv:1602.04113] [INSPIRE].
S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 77 (2017) 112 [arXiv:1607.00299] [INSPIRE].
Fermilab Lattice and MILC collaborations, E. Gámiz et al., Kaon semileptonic decays with N f = 2 + 1 + 1 HISQ fermions and physical light-quark masses, arXiv:1611.04118 [INSPIRE].
A. Bazavov et al., Kaon semileptonic vector form factor and determination of |V us | using staggered fermions, Phys. Rev. D 87 (2013) 073012 [arXiv:1212.4993] [INSPIRE].
H. Na, C.T.H. Davies, E. Follana, P. Lepage and J. Shigemitsu, D semi-leptonic decay form factors with HISQ charm and light quarks, PoS (LAT2009) 247 [arXiv:0910.3919] [INSPIRE].
HPQCD collaboration, J. Koponen, C.T.H. Davies and G. Donald, D to K and D to pi semileptonic form factors from Lattice QCD, arXiv:1208.6242 [INSPIRE].
C. Bernard, J. Bijnens and E. Gámiz, Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory, Phys. Rev. D 89 (2014) 054510 [arXiv:1311.7511] [INSPIRE].
K. Ghorbani, Chiral and Volume Extrapolation of Pion and Kaon Electromagnetic form Factor within SU(3) ChPT, Chin. J. Phys. 51 (2013) 920 [arXiv:1112.0729] [INSPIRE].
J. Bijnens and J. Relefors, Masses, Decay Constants and Electromagnetic Form-factors with Twisted Boundary Conditions, JHEP 05 (2014) 015 [arXiv:1402.1385] [INSPIRE].
F.J. Jiang and B.C. Tiburzi, Flavor twisted boundary conditions, pion momentum and the pion electromagnetic form-factor, Phys. Lett. B 645 (2007) 314 [hep-lat/0610103] [INSPIRE].
J. Bijnens, CHIRON: a package for ChPT numerical results at two loops, Eur. Phys. J. C 75 (2015) 27 [arXiv:1412.0887] [INSPIRE].
MILC collaboration, A. Bazavov et al., Lattice QCD ensembles with four flavors of highly improved staggered quarks, Phys. Rev. D 87 (2013) 054505 [arXiv:1212.4768] [INSPIRE].
J. Relefors, Twisted Loops and Models for Form-factors and the Muon g − 2, Ph.D. Thesis, Lund University, Sweden (2016), ISBN 978-91-7623-975-9.
S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys. 158 (1984) 142 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].
J. Gasser and H. Leutwyler, Low-Energy Expansion of Meson Form-Factors, Nucl. Phys. B 250 (1985) 517 [INSPIRE].
J. Gasser and H. Leutwyler, Spontaneously Broken Symmetries: Effective Lagrangians at Finite Volume, Nucl. Phys. B 307 (1988) 763 [INSPIRE].
S.R. Sharpe and N. Shoresh, Partially quenched chiral perturbation theory without Phi0, Phys. Rev. D 64 (2001) 114510 [hep-lat/0108003] [INSPIRE].
S.R. Sharpe, Quenched chiral logarithms, Phys. Rev. D 46 (1992) 3146 [hep-lat/9205020] [INSPIRE].
C.W. Bernard and M.F.L. Golterman, Partially quenched gauge theories and an application to staggered fermions, Phys. Rev. D 49 (1994) 486 [hep-lat/9306005] [INSPIRE].
P.H. Damgaard and K. Splittorff, Partially quenched chiral perturbation theory and the replica method, Phys. Rev. D 62 (2000) 054509 [hep-lat/0003017] [INSPIRE].
W.-J. Lee and S.R. Sharpe, Partial flavor symmetry restoration for chiral staggered fermions, Phys. Rev. D 60 (1999) 114503 [hep-lat/9905023] [INSPIRE].
C. Aubin and C. Bernard, Pion and kaon masses in staggered chiral perturbation theory, Phys. Rev. D 68 (2003) 034014 [hep-lat/0304014] [INSPIRE].
C. Aubin and C. Bernard, Pseudoscalar decay constants in staggered chiral perturbation theory, Phys. Rev. D 68 (2003) 074011 [hep-lat/0306026] [INSPIRE].
P.F. Bedaque, Aharonov-Bohm effect and nucleon nucleon phase shifts on the lattice, Phys. Lett. B 593 (2004) 82 [nucl-th/0402051] [INSPIRE].
C.T. Sachrajda and G. Villadoro, Twisted boundary conditions in lattice simulations, Phys. Lett. B 609 (2005) 73 [hep-lat/0411033] [INSPIRE].
H. Na, C.T.H. Davies, E. Follana, G.P. Lepage and J. Shigemitsu, The D → K, lν Semileptonic Decay Scalar Form Factor and |V cs | from Lattice QCD, Phys. Rev. D 82 (2010) 114506 [arXiv:1008.4562] [INSPIRE].
JLQCD collaboration, T. Kaneko et al., Chiral behavior of light meson form factors in 2+1 flavor QCD with exact chiral symmetry, PoS (LATTICE 2015) 325 [arXiv:1601.07658] [INSPIRE].
J. Bijnens and P. Talavera, K(l3) decays in chiral perturbation theory, Nucl. Phys. B 669 (2003) 341 [hep-ph/0303103] [INSPIRE].
Fermilab Lattice and MILC collaborations, A. Bazavov et al., B- and D-meson decay constants from three-flavor lattice QCD, Phys. Rev. D 85 (2012) 114506 [arXiv:1112.3051] [INSPIRE].
Fermilab Lattice and MILC collaborations, A. Bazavov et al., in preparation.
MILC collaboration, A. Bazavov et al., Properties of light pseudoscalars from lattice QCD with HISQ ensembles, PoS (LATTICE 2011) 107 [arXiv:1111.4314] [INSPIRE].
MILC collaboration, A. Bazavov et al., work in progress.
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ArXiv ePrint: 1702.03416
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Bernard, C., Bijnens, J., Gámiz, E. et al. Twisted finite-volume corrections to K l3 decays with partially-quenched and rooted-staggered quarks. J. High Energ. Phys. 2017, 120 (2017). https://doi.org/10.1007/JHEP03(2017)120
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DOI: https://doi.org/10.1007/JHEP03(2017)120