Abstract
We discuss the accurate determination of matrix elements 〈f |ĥ w|i〉 where neither |i〉 nor |f〉 is the vacuum state and ĥ w is some operator. Using solutions of the Generalized Eigenvalue Problem (GEVP) we construct estimators for matrix elements which converge rapidly as a function of the Euclidean time separations involved. |i〉 and |f〉 may be either the ground state in a given hadron channel or an excited state. Apart from a model calculation, the estimators are demonstrated to work well for the computation of the B* Bπ-coupling in the quenched approximation. They are also compared to a standard ratio as well as to the “summed ratio method” of [1–3]. In the model, we also illustrate the ordinary use of the GEVP for energy levels.
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L. Maiani, G. Martinelli, M. Paciello and B. Taglienti, Scalar densities and baryon mass differences in lattice QCD with Wilson fermions, Nucl. Phys. B 293 (1987) 420 [INSPIRE].
ALPHA collaboration, J. Bulava, M. Donnellan and R. Sommer, The B ∗ Bπ coupling in the static limit, PoS(LATTICE 2010)303 [arXiv:1011.4393] [INSPIRE].
S. Capitani, M. Della Morte, B. Knippschild and H. Wittig, Systematic errors in extracting nucleon properties from lattice QCD, PoS(LATTICE 2010)147.
G.P. Lepage, The analysis of algorithms for lattice field theory, in From actions to answers, T. DeGrand and D. Toussaint eds., World Scientic, Singapore (1989).
M. Lüscher, Computational strategies in lattice QCD, arXiv:1002.4232 [INSPIRE].
S. Hashimoto, Computation of the heavy-light decay constant using nonrelativistic lattice QCD, Phys. Rev. D 50 (1994) 4639 [hep-lat/9403028] [INSPIRE].
M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005)051 [hep-lat/0506008] [INSPIRE].
D.B. Renner, Status and prospects for the calculation of hadron structure from lattice QCD, PoS(LAT2009)018 [arXiv:1002.0925] [INSPIRE].
C. Alexandrou, Hadron structure and form factors, PoS(LATTICE 2010)001 [arXiv:1011.3660] [INSPIRE].
S. Dinter et al., Precision study of excited state effects in nucleon matrix elements, Phys. Lett. B 704 (2011) 89 [arXiv:1108.1076] [INSPIRE].
G. Parisi, R. Petronzio and F. Rapuano, A measurement of the string tension near the continuum limit, Phys. Lett. B 128 (1983) 418 [INSPIRE].
U. Wolff, Asymptotic freedom and mass generation in the O(3) nonlinear σ-model, Nucl. Phys. B 334 (1990) 581 [INSPIRE].
M. Lüscher and P. Weisz, Locality and exponential error reduction in numerical lattice gauge theory, JHEP 09 (2001) 010 [hep-lat/0108014] [INSPIRE].
M. Della Morte and L. Giusti, Symmetries and exponential error reduction in Yang-Mills theories on the lattice, Comput. Phys. Commun. 180 (2009) 819 [arXiv:0806.2601] [INSPIRE].
M. Della Morte and L. Giusti, A novel approach for computing glueball masses and matrix elements in Yang-Mills theories on the lattice, JHEP 05 (2011) 056 [arXiv:1012.2562] [INSPIRE].
U. Wolff, Strong coupling expansion Monte Carlo, PoS(LATTICE 2010)020 [arXiv:1009.0657] [INSPIRE].
R. Sommer, Leptonic decays of B and D mesons, Nucl. Phys. Proc. Suppl. 42 (1995) 186 [hep-lat/9411024] [INSPIRE].
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].
J. Foley et al., Practical all-to-all propagators for lattice QCD, Comput. Phys. Commun. 172 (2005)145 [hep-lat/0505023] [INSPIRE].
C. Morningstar et al., Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD, Phys. Rev. D 83 (2011) 114505 [arXiv:1104.3870] [INSPIRE].
B. Blossier, M. Della Morte, G. von Hippel, T. Mendes and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, JHEP 04 (2009) 094 [arXiv:0902.1265] [INSPIRE].
S. Güsken et al., Nonsinglet axial vector couplings of the baryon octet in lattice QCD, Phys. Lett. B 227 (1989) 266 [INSPIRE].
C. Michael and I. Teasdale, Extracting glueball masses from lattice QCD, Nucl. Phys. B 215 (1983)433 [INSPIRE].
M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [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].
J.J. Dudek, R.G. Edwards, N. Mathur and D.G. Richards, Charmonium excited state spectrum in lattice QCD, Phys. Rev. D 77 (2008) 034501 [arXiv:0707.4162] [INSPIRE].
G. Burdman and J.F. Donoghue, Union of chiral and heavy quark symmetries, Phys. Lett. B 280 (1992)287 [INSPIRE].
M.B. Wise, Chiral perturbation theory for hadrons containing a heavy quark, Phys. Rev. D 45 (1992)2188 [INSPIRE].
T.-M. Yan et al., Heavy quark symmetry and chiral dynamics, Phys. Rev. D 46 (1992) 1148 [Erratum ibid. D 55 (1997) 5851] [INSPIRE].
UKQCD collaboration, G. de Divitiis et al., Towards a lattice determination of the B* B pi coupling, JHEP 10 (1998) 010 [hep-lat/9807032] [INSPIRE].
D. Becirevic, B. Blossier, E. Chang and B. Haas, g(B ∗ Bπ)-coupling in the static heavy quark limit, Phys. Lett. B 679 (2009) 231 [arXiv:0905.3355] [INSPIRE].
H. Ohki, H. Matsufuru and T. Onogi, Determination of B ∗ Bπ coupling in unquenched QCD, Phys. Rev. D 77 (2008) 094509 [arXiv:0802.1563] [INSPIRE].
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Bulava, J., Donnellan, M. & Sommer, R. On the computation of hadron-to-hadron transition matrix elements in lattice QCD. J. High Energ. Phys. 2012, 140 (2012). https://doi.org/10.1007/JHEP01(2012)140
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DOI: https://doi.org/10.1007/JHEP01(2012)140