Correction factors for reactions involvingqq¯annihilation or production

Abstract

In reactions with qq production or qq annihilation, initialand final-state interactions give rise to large corrections to the lowest-order cross sections. We evaluate the correction factor first for low relative kinetic energies by studying the distortion of the relative wave function. We then follow the procedure of Schwinger to interpolate this result with the well-known perturbative QCD vertex correction factors at high energies, to obtain an explicit semiempirical correction factor applicable to the whole range of energies. The correction factor predicts an enhancement for qq in color-singlet states and a suppression for color-octet states, the efFect increasing as the relative velocity decreases. Consequences on dilepton production in the quark-gluon plasma, the Drell-Yan process, and heavy quark production processes are discussed.PACS number(s): 25.75.+r, 24.85. +p, 12.38.Mh, 13.90.+i I. INTRODUCTIONThe possibility of hadron matter going through a phase transition into a deconfined quark-gluon plasma (QGP) state during high-energy heavy-ion collisions makes these collisions the focus of intense experimental and theoretical research [1]. In these collisions, the constituents of the possible QGP or the partons of the colliding nucleons can react at varying energies. Their reaction products such as dileptons and. photons provide the signals and the backgrounds for the detection of the quark-gluon plasma. The magnitudes of the signals depend on the cross sections for dilepton and photon production from the constituents of the plasma. The rates of approach to chemical equilibrium and thermal equilibrium of the plasma depend also on the cross sections for reactions among the constituents.When quarks, antiquarks, and gluons interact, they interact as constituents in the quark-gluon plasma or as partons in the colliding nucleon. However, the lowestorder Feynman diagrams and the next-to-leading-order Feynman diagrams are the same for the basic reaction processes involving q, q, and gluons, whether the reaction takes place in the environment of the quark-gluon plasma or in the environment, of partons in nucleon-nucleon collisions. In these basic reactions of quarks, antiquarks, and gluons, the next-to-leading-order diagrams, including the initialand final-state interactions and gluon radiations, give rise to large corrections to the lowest-order cross sections. It will be useful to develop an analytical semiempirical correction factor for the basic reaction processes over the whole range of relative energies so that in the next level of approximation the basic lowest-order reaction cross sections of quarks, antiquarks, and gluons can be corrected. on the same footing. Additional efFects and refinements such as the plasma screening and temperature can be added on in the future as our theoretical understanding is developed further.For processes involving qq production and annihilation

Effects of parton intrinsic transverse momentum on photon production in hard-scattering processes

“…It represents an effective modification of the strength of the coupling constant at the vertex, as in a vertex correction, due to the initialstate interaction between partons [33][34][35][36]. On the other hand, the vertex correction depends on the relative momentum between the colliding partons [34][35][36], which in turn depends mainly on the longitudinal momenta; the vertex correction is insensitive to the parton transverse momenta. Because of this property, it is reasonable to consider the K-factor to be approximately independent of the parton transverse momentum; that is…”

Signatures of thermal dilepton radiation at ultrarelativistic energies

“…Naively, one might anticipate in-medium corrections to be of order α s or O(T /M ), O(µ q /M ), but theoretically the impact of 'soft' corrections to the finite-temperature qq rates is not very well under control, see, e.g., refs. [39][40][41][42]. For the (closely related) Drell-Yan annihilation process, corrections of similar nature are subsumed in the famous K-factors, which, for modern parton distribution functions (e.g., GRV-94 [43]), are around 1.3-1.5.…”

Relativistic modification of the Gamow factor

“…They have a great influence on the reaction rates or the production cross sections [1][2][3][4][5][6][7][8][9][10][11]. These initial-and final-state interactions lead to a large enhancement of the cross section if the particles are subject to a strong attractive interaction; they can lead to a large suppression under a strong repulsive interaction.…”