Cross sections for 2-to-3 meson-meson scattering

Abstract

We study the processes KK → φ, πD → D * , πD →D * , and the production of ψ(4160) and ψ(4415) mesons in collisions of charmed mesons or charmed strange mesons. The 2-to-1 meson-meson scattering involves a process where a quark and an antiquark from the two initial mesons annihilate into a gluon and subsequently the gluon is 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 ψ(4160) and ψ(4415) generally increase as the colliding mesons go through the cases of DDWe suggest the production of ψ(4160) and ψ(4415) as a probe of hadronic matter that results from the quark-gluon plasma created in ultrarelativistic heavyion collisions. → ψ(4415), and D * + s D * − s → ψ(4415). Both ψ(4160) and ψ(4415) consist of aquark and an antiquark [20,21]. All these reactions are governed by the strong interaction.2The reaction KK → φ was studied in Ref. [22] in a mesonic model. The fifteen reactions that lead to ψ(4160) or ψ(4415) as a final state have not been studied theoretically. Now we study KK → φ, πD → D * , πD →D * , and the fifteen reactions using quark degrees of freedom. The production of J/ψ is a subject intensively studied in relativistic heavy-ion collisions. The ψ(4160) and ψ(4415) mesons may decay into the J/ψ meson. Through this decay the fifteen reactions add a contribution to the J/ψ production in relativistic heavy-ion collisions. This is another reason why we study the fifteen reactions here.This paper is organized as follows. In Sect. II we consider four Feynman diagrams and the S-matrix element for 2-to-1 meson-meson scattering, derive transition amplitudes and provide cross-section formulas. In Sect. III we present transition potentials corresponding to the Feynman diagrams and calculate flavor matrix elements and spin matrix elements. In Sect. IV we calculate cross sections, present numerical results and give relevant discussions. In Sect. V we summarize the present work. II. FORMALISMLowest-order Feynman diagrams are shown in Fig. 1 for the reaction A(q 1q1 ) + B(q 2q2 ) → H(q 2q1 or q 1q2 ). A quark in an initial meson and an antiquark in the other initial meson annihilate into a gluon, and the gluon is then absorbed by a spectator quark or antiquark. The four processes q 1 +q 2 +q 1 →q 1 , q 1 +q 2 + q 2 → q 2 , q 2 +q 1 + q 1 → q 1 , and q 2 +q 1 +q 2 →q 2 in Fig. 1 give rise to the four transition potentials V rq 1q2q1 , V rq 1q2 q 2 , V rq 2q1 q 1 , and V rq 2q1q2 , respectively. Denote by E i and ...

Cross sections for 2-to-1 meson–meson scattering

“…The magnitude is much larger than the peak cross sections of KK → π KK for I=1 and I f πK = 3/2 and for I=1 and I f πK = 1/2 at zero temperature in Refs. [66,67], where I f πK is the total isospin of the final π andK mesons. The case KK → π KK is governed by a process where a gluon is emitted by a constituent quark or antiquark in the initial mesons and subsequently the gluon creates a quark-antiquark pair.…”