Abstract
We present a strategy how to match the full set of components of the heavy-light axial and vector currents in Heavy Quark Effective Theory (HQET), up to and including 1/m h -corrections, to QCD. While the ultimate goal is to apply these matching conditions non-perturbatively, in this study we first have implemented them at tree-level, in order to find good choices of the matching observables with small \( \mathcal{O}\left( {{1 \left/ {{m_{\mathrm{h}}^2}} \right.}} \right) \) contributions. They can later be employed in the non-perturbative matching procedure which is a crucial part of precision HQET computations of semileptonic decay form factors in lattice QCD.
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E. Lunghi and A. Soni, Possible evidence for the breakdown of the CKM-paradigm of CP-violation, Phys. Lett. B 697 (2011) 323 [arXiv:1010.6069] [INSPIRE].
A. Lenz, U. Nierste, J. Charles, S. Descotes-Genon, H. Lacker et al., Constraints on new physics in \( B-\overline{B} \) mixing in the light of recent LHCb data, Phys. Rev. D 86 (2012) 033008 [arXiv:1203.0238] [INSPIRE].
C. Tarantino, Flavor Lattice QCD in the Precision Era, PoS(ICHEP2012)023 [arXiv:1210.0474] [INSPIRE].
J.L. Rosner and S. Stone, Leptonic decays of charged pseudoscalar mesons - 2012, arXiv:1201.2401 [INSPIRE].
ALPHA collaboration, J. Heitger and R. Sommer, Nonperturbative heavy quark effective theory, JHEP 02 (2004) 022 [hep-lat/0310035] [INSPIRE].
M. Della Morte, P. Fritzsch and J. Heitger, Non-perturbative renormalization of the static axial current in two-flavour QCD, JHEP 02 (2007) 079 [hep-lat/0611036] [INSPIRE].
B. Blossier, M. della Morte, N. Garron and R. Sommer, HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation, JHEP 06 (2010) 002 [arXiv:1001.4783] [INSPIRE].
ALPHA collaboration, B. Blossier et al., HQET at order 1/m: II. Spectroscopy in the quenched approximation, JHEP 05 (2010) 074 [arXiv:1004.2661] [INSPIRE].
ALPHA collaboration, B. Blossier et al., HQET at order 1/m: III. Decay constants in the quenched approximation, JHEP 12 (2010) 039 [arXiv:1006.5816] [INSPIRE].
ALPHA collaboration, B. Blossier et al., Parameters of Heavy Quark Effective Theory from N f = 2 lattice QCD, JHEP 09 (2012) 132 [arXiv:1203.6516] [INSPIRE].
F. Bernardoni, B. Blossier, J. Bulava, M. Della Morte, P. Fritzsch et al., B-physics from HQET in two-flavour lattice QCD, PoS(LATTICE2012)273 [arXiv:1210.7932] [INSPIRE].
F. Bernardoni, B. Blossier, J. Bulava, M. Della Morte, P. Fritzsch et al., B-physics with N f = 2 Wilson fermions, PoS(LATTICE2013)381 [arXiv:1309.1074] [INSPIRE].
F. Bahr, F. Bernardoni, A. Ramos, H. Simma, R. Sommer et al., B → π form factor with 2 flavours of O(a) improved Wilson quarks, PoS(LATTICE2012)110 [arXiv:1210.3478] [INSPIRE].
ALPHA collaboration, F. Bahr et al., |V ub | determination in lattice QCD, PoS(ICHEP2012)424 [arXiv:1211.6327] [INSPIRE].
ALPHA collaboration, work in progress.
M. Lüscher, R. Narayanan, P. Weisz and U. Wolff, The Schrödinger functional: A renormalizable probe for non-Abelian gauge theories, Nucl. Phys. B 384 (1992) 168 [hep-lat/9207009] [INSPIRE].
S. Sint, On the Schrödinger functional in QCD, Nucl. Phys. B 421 (1994) 135 [hep-lat/9312079] [INSPIRE].
S. Sint, One loop renormalization of the QCD Schrödinger functional, Nucl. Phys. B 451 (1995) 416 [hep-lat/9504005] [INSPIRE].
ALPHA collaboration, M. Kurth and R. Sommer, Renormalization and O(a) improvement of the static axial current, Nucl. Phys. B 597 (2001) 488 [hep-lat/0007002] [INSPIRE].
D. Hesse and R. Sommer, A one-loop study of matching conditions for static-light flavor currents, JHEP 02 (2013) 115 [arXiv:1211.0866] [INSPIRE].
L. Maiani, G. Martinelli and C.T. Sachrajda, Nonperturbative subtractions in the heavy quark effective field theory, Nucl. Phys. B 368 (1992) 281 [INSPIRE].
R. Sommer, Introduction to Non-perturbative Heavy Quark Effective Theory, arXiv:1008.0710 [INSPIRE].
C.T. Sachrajda and G. Villadoro, Twisted boundary conditions in lattice simulations, Phys. Lett. B 609 (2005) 73 [hep-lat/0411033] [INSPIRE].
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].
S. Sint and P. Weisz, Further results on O(a) improved lattice QCD to one loop order of perturbation theory, Nucl. Phys. B 502 (1997) 251 [hep-lat/9704001] [INSPIRE].
ALPHA collaboration, D. Guazzini, H.B. Meyer and R. Sommer, Non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and the B ∗ − B mass splitting, JHEP 10 (2007) 081 [arXiv:0705.1809] [INSPIRE].
E. Eichten and B.R. Hill, An Effective Field Theory for the Calculation of Matrix Elements Involving Heavy Quarks, Phys. Lett. B 234 (1990) 511 [INSPIRE].
M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005) 051 [hep-lat/0506008] [INSPIRE].
M. Lüscher and P. Weisz, O(a) improvement of the axial current in lattice QCD to one loop order of perturbation theory, Nucl. Phys. B 479 (1996) 429 [hep-lat/9606016] [INSPIRE].
ALPHA collaboration, P. Korcyl, in preparation.
ALPHA collaboration, P. Korcyl, Fixing the parameters of Lattice HQET including 1/m b terms, PoS(Beauty2013)071 [arXiv:1307.5080] [INSPIRE].
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ArXiv ePrint: 1312.1566
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Morte, M.D., Dooling, S., Heitger, J. et al. Matching of heavy-light flavour currents between HQET at order 1/m and QCD: I. Strategy and tree-level study. J. High Energ. Phys. 2014, 60 (2014). https://doi.org/10.1007/JHEP05(2014)060
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DOI: https://doi.org/10.1007/JHEP05(2014)060