Abstract
We calculate vector-vector correlation functions at two loops using partially quenched chiral perturbation theory including finite volume effects and twisted boundary conditions. We present expressions for the flavor neutral cases and the flavor charged case with equal masses. Using these expressions we give an estimate for the ratio of disconnected to connected contributions for the strange part of the electromagnetic current. We give numerical examples for the effects of partial quenching, finite volume and twisting and suggest the use of different twists to check the size of finite volume effects. The main use of this work is expected to be for lattice QCD calculations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.
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References
Muon g-2 collaboration, G.W. Bennett et al., Measurement of the positive muon anomalous magnetic moment to 0.7 ppm, Phys. Rev. Lett. 89 (2002) 101804 [Erratum ibid. 89 (2002) 129903] [hep-ex/0208001] [INSPIRE].
Muon g-2 collaboration, G.W. Bennett et al., Measurement of the negative muon anomalous magnetic moment to 0.7 ppm, Phys. Rev. Lett. 92 (2004) 161802 [hep-ex/0401008] [INSPIRE].
Muon g-2 collaboration, G.W. Bennett et al., Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
F. Jegerlehner and A. Nyffeler, The Muon g-2, Phys. Rept. 477 (2009) 1 [arXiv:0902.3360] [INSPIRE].
G. D’Ambrosio, M. Iacovacci, M. Passera, G. Venanzoni, P. Massarotti and S. Mastroianni eds., Proceedings of Workshop on Flavour changing and conserving processes 2015 (FCCP2015) Anacapri Italy (2015), [EPJ Web Conf. 118 (2016) 1].
R.M. Carey et al., The New (g-2) Experiment: A proposal to measure the muon anomalous magnetic moment to ±0.14 ppm precision, FERMILAB-PROPOSAL-0989 (2009).
J-PARC muon g-2/EDM collaboration, H. Iinuma, New approach to the muon g-2 and EDM experiment at J-PARC, J. Phys. Conf. Ser. 295 (2011) 012032 [INSPIRE].
T.P. Gorringe and D.W. Hertzog, Precision Muon Physics, Prog. Part. Nucl. Phys. 84 (2015) 73 [arXiv:1506.01465] [INSPIRE].
C.M. Carloni Calame, M. Passera, L. Trentadue and G. Venanzoni, A new approach to evaluate the leading hadronic corrections to the muon g-2, Phys. Lett. B 746 (2015) 325 [arXiv:1504.02228] [INSPIRE].
T. Blum, Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 91 (2003) 052001 [hep-lat/0212018] [INSPIRE].
M. Della Morte, B. Jager, A. Juttner and H. Wittig, Towards a precise lattice determination of the leading hadronic contribution to (g − 2) μ , JHEP 03 (2012) 055 [arXiv:1112.2894] [INSPIRE].
M. Della Morte and A. Juttner, Quark disconnected diagrams in chiral perturbation theory, JHEP 11 (2010) 154 [arXiv:1009.3783] [INSPIRE].
A. Juttner and M. Della Morte, New ideas for g-2 on the lattice, PoS(LAT2009)143 [arXiv:0910.3755] [INSPIRE].
C. Aubin, T. Blum, M. Golterman and S. Peris, Hadronic vacuum polarization with twisted boundary conditions, Phys. Rev. D 88 (2013) 074505 [arXiv:1307.4701] [INSPIRE].
D. Bernecker and H.B. Meyer, Vector Correlators in Lattice QCD: Methods and applications, Eur. Phys. J. A 47 (2011) 148 [arXiv:1107.4388] [INSPIRE].
RBC/UKQCD collaboration, T. Blum et al., Lattice calculation of the leading strange quark-connected contribution to the muon g − 2, JHEP 04 (2016) 063 [Erratum ibid. 1705 (2017) 034] [arXiv:1602.01767] [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].
G. Bali and G. Endrödi, Hadronic vacuum polarization and muon g − 2 from magnetic susceptibilities on the lattice, Phys. Rev. D 92 (2015) 054506 [arXiv:1506.08638] [INSPIRE].
X. Feng, S. Hashimoto, G. Hotzel, K. Jansen, M. Petschlies and D.B. Renner, Computing the hadronic vacuum polarization function by analytic continuation, Phys. Rev. D 88 (2013) 034505 [arXiv:1305.5878] [INSPIRE].
HPQCD collaboration, B. Chakraborty et al., Strange and charm quark contributions to the anomalous magnetic moment of the muon, Phys. Rev. D 89 (2014) 114501 [arXiv:1403.1778] [INSPIRE].
E. de Rafael, Moment Analysis of Hadronic Vacuum Polarization — Proposal for a lattice QCD evaluation of g μ − 2, Phys. Lett. B 736 (2014) 522 [arXiv:1406.4671] [INSPIRE].
C.A. Dominguez, K. Schilcher and H. Spiesberger, Theoretical determination of the hadronic g−2 of the muon, Mod. Phys. Lett. A 31 (2016) 1630035 [arXiv:1605.07903] [INSPIRE].
S. Bodenstein, C.A. Dominguez, K. Schilcher and H. Spiesberger, Hadronic contribution to the muon g − 2 factor, Phys. Rev. D 88 (2013) 014005 [arXiv:1302.1735] [INSPIRE].
M. Golterman, K. Maltman and S. Peris, New strategy for the lattice evaluation of the leading order hadronic contribution to (g − 2)μ, Phys. Rev. D 90 (2014) 074508 [arXiv:1405.2389] [INSPIRE].
H. Wittig, Hadronic contributions to the muon g − 2 from lattice QCD, plenary talk at Lattice 2016, Southampton U.K. (2016).
C. Aubin, T. Blum, P. Chau, M. Golterman, S. Peris and C. Tu, Finite-volume effects in the muon anomalous magnetic moment on the lattice, Phys. Rev. D 93 (2016) 054508 [arXiv:1512.07555] [INSPIRE].
A. Francis, B. Jaeger, H.B. Meyer and H. Wittig, A new representation of the Adler function for lattice QCD, Phys. Rev. D 88 (2013) 054502 [arXiv:1306.2532] [INSPIRE].
J. Bijnens and J. Relefors, Connected, Disconnected and Strange Quark Contributions to HVP, JHEP 11 (2016) 086 [arXiv:1609.01573] [INSPIRE].
J. Relefors, Twisted Loops and Models for Form-factors and the Muon g − 2, Ph.D. Thesis, Lund University, Lund Sweden (2016) [ISBN:978-91-7623-975-9].
J. Bijnens, CHIRON: a package for ChPT numerical results at two loops, Eur. Phys. J. C 75 (2015) 27 [arXiv:1412.0887] [INSPIRE].
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].
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, Chiral Logarithms in Quenched M(π) and F(π), Phys. Rev. D 41 (1990) 3233 [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, Chiral perturbation theory for the quenched approximation of QCD, Phys. Rev. D 46 (1992) 853 [hep-lat/9204007] [INSPIRE].
J. Bijnens, G. Colangelo and G. Ecker, The Mesonic chiral Lagrangian of order p 6, JHEP 02 (1999) 020 [hep-ph/9902437] [INSPIRE].
J. Bijnens, G. Colangelo and G. Ecker, Renormalization of chiral perturbation theory to order p 6, Annals Phys. 280 (2000) 100 [hep-ph/9907333] [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.T. Sachrajda and G. Villadoro, Twisted boundary conditions in lattice simulations, Phys. Lett. B 609 (2005) 73 [hep-lat/0411033] [INSPIRE].
J. Bijnens and G. Ecker, Mesonic low-energy constants, Ann. Rev. Nucl. Part. Sci. 64 (2014) 149 [arXiv:1405.6488] [INSPIRE].
J. Bijnens and K. Ghorbani, Finite volume dependence of the quark-antiquark vacuum expectation value, Phys. Lett. B 636 (2006) 51 [hep-lat/0602019] [INSPIRE].
A. Bussone, M. Della Morte, M. Hansen and C. Pica, On reweighting for twisted boundary conditions, Comput. Phys. Commun. 219 (2017) 91 [arXiv:1609.00210] [INSPIRE].
J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
J. Bijnens and P. Talavera, Pion and kaon electromagnetic form-factors, JHEP 03 (2002) 046 [hep-ph/0203049] [INSPIRE].
J. Bijnens, E. Boström and T.A. Lähde, Two-loop Sunset Integrals at Finite Volume, JHEP 01 (2014) 019 [arXiv:1311.3531] [INSPIRE].
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Bijnens, J., Relefors, J. Vector two-point functions in finite volume using partially quenched chiral perturbation theory at two loops. J. High Energ. Phys. 2017, 114 (2017). https://doi.org/10.1007/JHEP12(2017)114
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DOI: https://doi.org/10.1007/JHEP12(2017)114