Couplings of pions with heavy baryons from light-cone QCD sum rules in the leading order of HQET

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Abstract

The couplings of pions with heavy baryons g2,Σ) and g3,Λ) are studied with light-cone QCD sum rules in the leading order of heavy quark effective theory. Both sum rules are stable. Our results are g2=1.56±0.3±0.3, g3=0.94±0.06±0.2.

Introduction

Important progress has been achieved in the interpretation of heavy hadrons composed of a heavy quark with the development of the heavy quark effective theory (HQET) [1]. HQET provides a systematic expansion of the heavy hadron spectra and transition amplitude in terms of 1/mQ, where mQ is the heavy quark mass. Of course one has to employ some specific nonperturbative methods to arrive at the detailed predictions. Among the various nonpeturbative methods, QCD sum rules is useful to extract the low-lying hadron properties [2].

The couplings of the heavy mesons with pions has been analysed with QCD sum rules 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. The couplings of heavy baryons with soft pions are estimated from QCD sum rules in an external axial field [13]. In this approach the mass difference Δ between the baryons in the initial and final states is approximately taken to be zero.

In this work we employ the light-cone QCD sum rules (LCQSR) in HQET to calculate the couplings g2,3 to the leading order of 1/mQ. The LCQSR is quite different from the conventional QCD sum rules, which is based on the short-distance operator product expansion (OPE). The LCQSR is based on the OPE on the light cone, which is the expansion over the twists of the operators. The main contribution comes from the lowest twist operator. Matrix elements of nonlocal operators sandwiched between a hadronic state and the vacuum defines the hadron wave functions. The LCQSR approach has the advantage that the double Borel transformation is used so that the the continuum contribution is treated in a way better than the external field approach. Moreover, the final sum rule depends only on the value of the wave function at a specific point like ϕπ(u0=12), which is much better known than the whole wave function [10].

Section snippets

Sum rules for the coupling constants

We first introduce the interpolating currents for the heavy baryons:ηΛ(x)=ϵabc[uaT(x)Cγ5db(x)]hvc(x),ηΣ+(x)=ϵabc[uaT(x)Cγμdb(x)]γμtγ5hvc(x),ημΣ++(x)=ϵabc[uaT(x)Cγνub(x)](−gtμν+13γtμγtν)hvc(x),where a, b, c is the color index, u(x), d(x), hv(x) is the up, down and heavy quark fields, T denotes the transpose, C is the charge conjugate matrix, gtμν=gμνvμvν, γtμμv̂vμ, and vμ is the velocity of the heavy hadron.

The overlap amplititudes of the interpolating currents with the heavy baryons is

Determination of the parameters

In order to obtain the coupling constants from (23)–(26) we need the mass parameters Λ̄'s and the coupling constants f's of the corresponding interpolating currents as input. The results are [14]Λ̄Λ=0.8GeVfΛ=(0.018±0.002)GeV3,Λ̄Σ=1.0GeVfΣ=(0.04±0.004)GeV3.For the sum rule (23) and (26) the continuum threshold is ωc=(2.5±0.1) GeV.

We use the wave functions adopted in [10] to compute the coupling constants. Moreover, we choose to work at the symmetric point T1=T2=2T, i.e., u0=12 as traditionally

Numerical results and discussion

We now turn to the numerical evaluation of the sum rules for the coupling constants. Since the spectral density of the sum rule (23)–(26) ρ(s) is either proptional to s2 or s3, the continuum has to be subtracted carefully. We use the value of the continuum theshold ωc determined from the corresponding mass sum rule at the leading order of αs and 1/mQ [14].

The lower limit of T is determined by the requirement that the terms of higher twists in the operator expansion is reasonably smaller than

Acknowledgements

S.-L. Zhu was supported by the National Postdoctoral Science Foundation of China and Y.D. was supported by the National Natural Science Foundation of China.

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