Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Light mesons
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ELEMENTARY PARTICLES AND FIELDS Theory
Quark–Antiquark States and Their Radiative Transitions in Terms of the Spectral Integral Equation: Light Mesons* V. V. Anisovich, L. G. Dakhno, M. A. Matveev, V. A. Nikonov, and A. V. Sarantsev Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, 188350 Russia Received November 18, 2005; in final form, April 7, 2006
Abstract—We continue the investigation of mesons in terms of the spectral integral equation initiated before for the b¯b and c¯ c systems; we consider the light-quark (u, d, s) mesons with masses M ≤ 3 GeV. The calculations have been performed for the mesons lying on linear trajectories in the (n, M 2 ) planes, where n is the radial quantum number. Our consideration relates to the q q¯ states with one component in the flavor space, with the quark and antiquark masses equal to each other, such as π(0−+ ), ρ(1−− ), ω(1−− ), φ(1−− ), a0 (0++ ), a1 (1++ ), a2 (2++ ), b1 (1+− ), f2 (2++ ), π2 (2−+ ), ρ3 (3−− ), ω3 (3−− ), φ3 (3−− ), π4 (4−+ ) at n ≤ 6. We obtained the wave functions and mass values of mesons lying on these trajectories. The corresponding trajectories are linear, in agreement with data. We have calculated the two-photon decays π, a0 (980), a2 (1320), f2 (1285), f2 (1525) and radiative transitions ρ, ω → γπ, which agree qualitatively with the experiment. On this basis, we extract the singular part of the interaction amplitude, which corresponds to the so-called “confinement interaction.” The description of the data requires the presence of the strong t-channel singularities for both scalar and vector exchanges. PACS numbers: 11.10.St, 11.15.Tk, 11.55.Fv, 12.39.Ki, 13.40.Hq DOI: 10.1134/S1063778807030040
1. INTRODUCTION
¯ systems in the nonrelativistic to the study of QQ approach.
The present paper continues the investigation of the quark–antiquark states within the spectral integral equation; before, we investigated the b¯b [1] and c¯ c [2] systems, with the use of the information on the radiative decays [3]. Along this line, the investigation of light-quarks q q¯ states is of a particular interest, for the highly excited systems of light quarks are formed at large distances, where the long-distance color forces, or “confinement forces,” work. Just the determination of the strong singularities of the amplitude, which provide the quark confinement, is the main purpose of our investigation.
The spectral integral method used in the analysis of the quark–antiquark systems is a direct generalization of the dispersion N/D method [9] for the case of separable vertices. In the framework of this method, we have analyzed the two-nucleon systems and their interaction with an electromagnetic field [10], in particular, the electric form factors of the deuteron and deuteron photodisintegration amplitude [11]. In this method, there was no problem with the description of the high-spin particles. The method has been generalized [12] aiming to describe the quark–antiquark systems. As a result, the equation was written for the quark wave function, its
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