Matrix elements of heavy-light mesons from a fine lattice
A. Ali Khan, A. Al-Haydari, V. Braun, S. Collins, M. Goeckeler, G.N. Lacagnina, M. Panero, A. Schaefer, G. Schierholz
aa r X i v : . [ h e p - l a t ] J a n Matrix elements of heavy-light mesons from a finelattice
A. Ali Khan ∗ ,A. Al-Haydari a , V. M. Braun b , S. Collins b , M. Göckeler b ,G. N. Lacagnina c , M. Panero b , d , A. Schäfer b , and G. Schierholz b , e a Department of Physics, Faculty of Science, Taiz University, Taiz, Yemen Republic b Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany c INFN, Sezione di Milano, 20133 Milano, Italy d Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland e Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany
We performed a calculation of matrix elements of heavy mesons on a quenched lattice, generatedwith Wilson gauge fields at b = . ×
80 and a lattice spacing a − ≃ r = . O ( a ) improved Wilson fermion action and improved currents.We have calculated the charmonium spectrum as well as form factors of semileptonic decays ofpseudoscalar heavy-light mesons containing a c or a b quark to pseudoscalar light mesons througha vector current: h P ( p ) | V m | H ( p H ) i = m H − m P q q m f ( q ) + (cid:18) p m H + p m − m H − m P q q m (cid:19) f + ( q ) , where p and m P are the momentum and the mass of the light meson respectively, and p H and m H the momentum and the mass of the heavy meson respectively. q = p H − p is the momentumtransfer. V m denotes a local vector current. A comparison with other lattice calculations for thedecay B → p l n is shown in Figure 1.For the decay constant of the J / y meson we find a preliminary value of f V = ( ) MeV, usingthe definition h | V j | J / y i = f V m J y e j ( l ) , where e j ( l ) is the polarization vector of the J / y . We obtain the following values for masssplittings of charmonium states: D M ( J / y − h c ) = ( ) MeV and D M ( c c − J / y ) = ( ) MeV, where the errors are only statistical. ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ eavy-light mesons from a fine lattice
A. Ali Khan q [GeV ]048 Figure 1:
The solid lines denote our results for the form factors ( f + : upper line, f : lower line) of the decay B → p l n . The dashed lines denote our error bounds. The squares denote f + , circles denote f from otherrecent lattice calculations (red: quenched, [2], green: N f = +
1, [3], magenta: N f = +
1, [4]) . The details of our calculation of the matrix elements and the results for the form factors at q = J / y is lower than the result of 399(4) MeV from quenched anisotropiclattices of [7] and of 413(40) MeV from lattices with N f = Acknowledgement:
We thank J. Simone for useful discussions.
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