Damtp1999116
UtccpP72
September 1999
Heavylight decay constants from clover heavy quark action
in QCD with two flavors of dynamical quarks^{†}^{†}thanks: talk presented by H.P. Shanahan
Abstract
We present results on an analysis of the decay constants and with two flavours of sea quark. The calculation has been carried out on 3 different bare gauge couplings and 4 sea quark masses at each gauge coupling, with ranging from 0.8 to 0.6. We employ the Fermilab formalism to perform calculations with heavy quarks whose mass is in the range of the bquark. A detailed comparison with a quenched calculation using the same action is made to elucidate the effects due to the sea quarks.
1 Introduction
An accurate determination of the parameters and , in conjunction with the (future) experimental data on (and ) will provide excellent constraints on and [1]. Their calculation in the quenched approximation, using the plaquette gluon action, has been carried out using a number of different formulations for heavy quarks and the results are converging[2, 3].
A major uncertainty in these results, however, is that they may be susceptible to large corrections due to the effect of sea quarks [4, 5]. The penultimate step in eliminating this uncertainty is to consider the effect of two flavours of sea quark (). Here we present the status of such a study, using the clover action for heavy quark, which we started last year[6].
As the lattice spacings available to us are relatively coarse, we deal with the large mass of quark in the formalism of Ref. [7], which has been previously applied in the quenched calculation of B meson decay constants[8, 9].
In order to reduce discretisation effects, we have employed an RGimproved action in the gluon sector. Since this action was not considered in previous studies of , we repeat the calculation in quenched QCD to compare with full QCD results.
A comparison is also made with preliminary NRQCD results for the decay constants obtained on the same full QCD configurations, presented elsewhere in these proceedings[10].
1.8  2.8 fm  0.835 GeV  
1.95  2.5 fm  1.263 GeV  
2.1  2.6 fm  1.807 GeV  

2 Computational Details
Gauge configurations are computed using the RGimproved gauge action and a tadpoleimproved SW clover fermion action to create the background for two flavours of seaquark. As listed in Table 1, three bare gauge couplings were used. At each bare gauge coupling () runs were made for four sea quark masses () in the range . More details of these gauge configurations are presented in Ref. [11, 12].
At each , propagators for 8 heavy and 2 light valence quark masses were computed. The same tadpoleimproved clover action is employed for both heavy and light quarks. Details of the propagators computation and the choice of smearing can be found in Ref. [6].
The heavy quark masses ranged roughly from charm to bottom. One of the light valence quark masses was chosen so that , which approximately corresponds to the strange quark mass. The other light valence quark mass was chosen equal to the bare sea quark mass parameter. For each , both types of matrix element were fitted as a function of to compute and at zero sea quark mass and finite lattice spacing.
We include the correction to the axial vector current obtained by the following substitution to the heavy quark field [7],
(1) 
Using tadpoleimproved treelevel value for , we find that this correction has a contribution of up to 8% of the original current.
As a definition for the ground state mass of the heavylight meson we used the “HQET” mass definition, as discussed in Ref. [13, 9, 6]. The physical scale of lattice spacing is fixed by the string tension measured for each sea quark mass using .
We made the quenched calculation with the same action at 5 different gauge couplings each on and lattices. The couplings were tuned so that they match the string tensions of full QCD for the four values of finite sea quark mass and the extrapolated zero sea quark mass. For more details see Ref. [11].
3 Results
In Fig. 1 we plot results for for and in the quenched approximation (); sea quark mass is extrapolated to the chiral limit for . A clear increase of 10–20% is seen from two flavours of sea quark.
We also include the preliminary results from NRQCD [10] in Fig. 1, for two values of finite sea quark mass at in full QCD (filled squares), and one value in quenched QCD (open squares). In Fig. 2 we present a similar comparison of the Fermilab and NRQCD approaches for . In both figures we find good consistency of results between the two approaches.
Finally, we plot the ratio in Fig. 3 using the meson mass to set the strange quark mass. We observe only mild variation of the ratio with respect to for even the coarsest of our lattice spacings.
As a preliminary result we quote
(2)  
(3)  
(4) 
The first errors are statistical. The error labelled is due to the ambiguity of using the mass of the or to set the strange quark mass. The central values are determined by assuming the results independent of for the two finer lattice spacings. The resulting systematic error is derived by taking the difference between a constant and a linear fit in for all three points. We should also add an uncertainty due to the choice of scale; our preliminary estimate is 15–20 MeV from comparision of results using the scale determind from .
4 Conclusions
At this point it seems clear that there exists a systematic difference between the and data. Encouragingly enough, the preliminary NRQCD results are also in agreement with the relativistic results in both cases as well. One worrying point is that the quenched results for is approximately 10% larger than the quenched results using the Wilson action[2, 3]. Clearly this effect needs further examination. The ratio appears to be less affected by discretisation effects and is not substantially different from previous quenched calculations. It should be noted that even a systematic error of 10% for this ratio would be of substantial use for phenomenologists. It seems plausible then that a calculation of could be carried out for three flavors of dynamical quarks on a comparatively coarse lattice.
This work is supported in part by the GrantsinAid of Ministry of Education, Science and Culture (Nos. 09304029, 10640246, 10640248, 10740107, 11640250, 11640294, 11740162). SE and KN are JSPS Research Fellows. AAK, HPS and TM are supported by Research for the Future Program of JSPS, and HPS also by the Leverhulme foundation.
References
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