Abstract
We study the processes K{bar{K}} rightarrow phi , pi D rightarrow D^*, pi {bar{D}} rightarrow {bar{D}}^*, and the production of psi (3770), psi (4040), psi (4160), and psi (4415) mesons in collisions of charmed mesons or charmed strange mesons. The process of 2-to-1 meson–meson scattering involves a quark and an antiquark from the two initial mesons annihilating into a gluon and subsequently the gluon being absorbed by the spectator quark or antiquark. Transition amplitudes for the scattering process derive from the transition potential in conjunction with mesonic quark–antiquark wave functions and the relative-motion wave function of the two initial mesons. We derive these transition amplitudes in the partial wave expansion of the relative-motion wave function of the two initial mesons so that parity and total-angular-momentum conservation are maintained. We calculate flavor and spin matrix elements in accordance with the transition potential and unpolarized cross sections for the reactions using the transition amplitudes. Cross sections for the production of psi (4040), psi (4160), and psi (4415) relate to nodes in their radial wave functions. We suggest the production of psi (4040), psi (4160), and psi (4415) as probes of hadronic matter that results from the quark–gluon plasma created in ultrarelativistic heavy-ion collisions.
Highlights
The reactions π π → ρ and π K → K ∗ have been studied in Ref. [39] via a process where a quark in an initial meson and an antiquark in another initial meson annihilate into a gluon and subsequently the gluon is absorbed by the other antiquark or quark
We study K K → φ, π D → D∗, π D → D ∗, and the twenty-one reactions using quark degrees of freedom
Using the process where one quark annihilates with one antiquark to create a gluon and subsequently the gluon is absorbed by a spectator quark or antiquark, we have studied 2-to-1 meson–meson scattering
Summary
The resulting cross sections in vacuum agree with the empirical data Since these two reactions take place in hadronic matter that is created in ultrarelativistic heavy-ion collisions at the Relativistic Heavy. The ψ(3770), ψ(4040), ψ(4160), and ψ(4415) mesons may decay into the J/ψ meson Through this decay the twenty-one reactions add a contribution to the J/ψ production in relativistic heavy-ion collisions. 2 we consider four Feynman diagrams and the S-matrix element for 2-to meson–meson scattering, derive transition amplitudes and provide cross-section formulas. Let χSSz stand for the spin wave function of mesons A and B, which has the total spin S and its z component Sz. The Clebsch–Gordan coefficients (SA SAz SB SBz |S Sz ) couple χSSz to χSA SAz χSB SBz , Smax.
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