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Register a new userFactorization Approach for Inclusive Production of Doubly Heavy Baryon
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We study inclusive production of doubly heavy baryon at a $e^+e^-$ collider and at hadron colliders through fragmentation. We study the production by factorizing nonpertubative- and perturbative effects. In our approach the production can be thought as a two-step process: A pair of heavy quarks can be produced perturbatively and then the pair is transformed into the baryon. The transformation is nonperturbative. Since a heavy quark moves with a small velocity in the baryon in its rest frame, we can use NRQCD to describe the transformation and perform a systematic expansion in the small velocity. At the leading order we find that the baryon can be formed from two states of the heavy-quark pair, one state is with the pair in $^3S_1$ state and in color ${bf bar 3}$, another is with the pair in $^1S_0$ state and in color ${bf 6}$. Two matrix elements are defined for the transformation from the two states, their perturbative coefficients in the contribution to the cross-section at a $e^+e^-$ collider and to the function of heavy quark fragmentation are calculated. Our approach is different than previous approaches where only the pair in $^3S_1$ state and in color ${bf bar 3}$ is taken into account. Numerical results for $e^+e^-$ colliders at the two $B$-factories and for hadronic colliders LHC and Tevatron are given.
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The inclusive gluon production at midrapidities is described in the Color Glass Condensate formalism using the $k_T$ - factorization formula, which was derived at fixed coupling constant considering the scattering of a dilute system of partons with a dense one. Recent analysis demonstrated that this approach provides a satisfactory description of the experimental data for the inclusive hadron production in $pp/pA/AA$ collisions. However, these studies are based on the fixed coupling $k_T$ - factorization formula, which does not take into account the running coupling corrections, which are important to set the scales present in the cross section. In this paper we consider the running coupling corrected $k_T$ - factorization formula conjectured some years ago and investigate the impact of the running coupling corrections on the observables. In particular, the pseudorapidity distributions and charged hadrons multiplicity are calculated considering $pp$, $dAu/pPb$ and $AuAu/PbPb$ collisions at RHIC and LHC energies. We compare the corrected running coupling predictions with those obtained using the original $k_T$ - factorization assuming a fixed coupling or a prescription for the inclusion of the running of the coupling. Considering the Kharzeev - Levin - Nardi unintegrated gluon distribution and a simplified model for the nuclear geometry, we demonstrate that the distinct predictions are similar for the pseudorapidity distributions in $pp/pA/AA$ collisions and for the charged hadrons multiplicity in $pp/pA$ collisions. On the other hand, the running coupling corrected $k_T$ - factorization formula predicts a smoother energy dependence for $dN/deta$ in $AA$ collisions.
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