O(αs) corrections to the correlator of finite mass baryon currents

We present analytical next-to-leading order results for the correlator of baryonic currents at the three loop level with one finite mass quark. We obtain the massless and the HQET limit of the correlator from the general formula as particular cases. We also give explicit expressions for the moments of the spectral density. Baryons are an important source of information on QCD interactions. Massive baryons containing a heavy quark form a rich family of particles with many properties experimentally measured [1]. The prominent object of a QCD analysis of the properties of baryons is the correlator of two baryonic currents and the spectral density associated with it. Calculations beyond the leading order have not been done for many interesting cases. The massless case has been known since long ago [2]. We report on the results of calculating the αs corrections to the correlator of two baryonic currents with one finite mass quark and two massless quarks. We give analytical results and discuss the order of magnitude of the αs corrections. The massless and HQET limits are obtained as special cases. We finally present explicit results on the moments of the spectral density associated with the correlator. The discussion of the impact of our new correlator result on baryon phenomenology will be left to future publications. In the present paper we limit ourselves to the simplest case with a three-quark current of the form j = ǫΨa(u T b Cdc) (1) where Ψ is a finite mass quark with mass parameter m, u and d are massless quarks and C is the charge conjugation matrix. ǫ is the totally antisymmetric tensor and a, b, c are color indices for the SU(3) color group. Other baryonic currents with any given specified quantum numbers are obtained from the current in Eq. (1) by inserting the appropriate Dirac matrices. Such additions introduce no principal complication into our method of calculation. The correlator of two baryonic currents is expanded as