Infinite momentum frame calculation of semileptonic heavyΛb→Λctransitions including HQET improvements

Abstract

We calculate the transition form factors that occur in heavy ⌳-type baryon semileptonic decays such as, e.g., in ⌳ b →⌳ c ϩ ϩl Ϫ ϩ l . We use Bauer-Stech-Wirbel-type infinite momentum frame wave functions for the heavy ⌳-type baryons which we assume to consist of a heavy quark and a light spin-isospin zero diquark system. The form factors at q 2 ϭ0 are calculated from the overlap integrals of the initial and final ⌳-type baryon states. To leading order in the heavy mass scale the structure of the form factors agrees with the HQET predictions including the normalization at zero recoil. The leading order dependence of the form factors is extracted by scaling arguments. By comparing the model form factors with the HQET predictions at O(1/m Q ) we obtain a consistent set of model form factors up to O(1/m Q ). With our preferred choice of parameter values we find that the contribution of the nonleading form factor is practically negligible. We use our form factor predictions to compute rates, spectra, and various asymmetry parameters for the semileptonic decay ⌳ b →⌳ c ϩ ϩl Ϫ ϩ l .

Exclusive/inclusive ratio of semileptonicΛbdecays

“…In the mesonic sector Neubert and Rieckert [6] analyzed an infinite momentum frame model and found that O(1/m Q ) effects raise the B → D and B → D * rates by 15.7% and 0.5%, respectively, resulting in a rise of 4.4% for the total D + D * rate. Using a similar infinite momentum frame model König et al find that the O(1/m Q ) effects raise the semileptonic Λ b → Λ c rate by 3% [7] which is quite close to the 4.4% found in [6] in the bottom meson case. Judging from these model calculations our leading order comparison of the mesonic and baryonic rates and the conclusions drawn from it do not seem to be much affected by O(1/m Q ) corrections.…”

“…The form factor function η(x) results from the nonlocal contribution of the kinetic energy term of the 1/m Q corrected HQET Lagrangian. It has been calculated in two different model approaches and has found to be negligibly small [7,13]. Therefore, we can safely drop its contribution in the following.…”

Note on the slope parameter of the baryonic Λb→Λc Isgur–Wise function

“…The Skyrme model predicts ρ 2 ≃ 1.3 [29]. In the infinite momentum frame model one has ρ 2 = 1.44 [18] and in the relativistic three quark model one finds ρ 2 = 1.35 [19]. For the baryonic sum rule results, radiative corrections to ρ 2 and 1/m Q corrections to the form factors are not expected to be large enough to solve the discrepancy between the large experimental central value for ρ in [2] and the small QCD sum rule results [3,4].…”

“…In the heavy baryon sector the masses of heavy baryons and the IW functions describing their weak transitions were calculated in Refs. [3,4,13,14] and [15,16,17,18,19], respectively. In Ref.…”

Choice of heavy baryon currents in the relativistic three-quark model

“…2 we depict our model predictions for the ω-dependence of the form factor ζ(ω). We compare our prediction for ζ(ω) with results from the simple quark model [22], QCD sum rules [21], the infinite momentum frame quark model [23,24], the dipole model [23] and the MIT bag model [25]. In Fig.…”