Diagrammatic approach to meson-meson scattering in the nonrelativistic quark potential model

Journal Article · Wed Jul 01 04:00:00 EDT 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.131· OSTI ID:7206032

Barnes, T ^[1]; Swanson, E S ^[2]

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1. Physics Division and Center for Computationally Intensive Physics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373 (United States) Department of Physics, University of Tennessee, Knoxville, Tennessee 37996-1200 (United States)
2. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

In this paper we use Born-order quark-exchange diagrams in a nonrelativistic potential model to describe low-energy scattering of {ital q{bar q}} mesons. A formalism for evaluating quark Born diagrams is developed, and as a first application we consider meson-meson scattering in channels in which {ital q{bar q}} annihilation is thought to be unimportant. In particular our results are relevant to {ital I}=2 {pi}{pi} and {ital I}=1 {ital KK} elastic scattering. Simple rules for the Born diagrams are given, which allow the evaluation of scattering amplitudes in terms of external meson wave functions by inspection. These techniques are applied to systems having identical quarks, and {pi}{sup +}{pi}{sup +}, K{sup +}K{sup +}, and {rho}{sup +}{rho}{sup +} elastic scattering phase shifts, cross sections, and equivalent potentials are derived as examples. The {ital S}-wave {ital I}=2 {pi}{pi} phase shift for a Gaussian {ital q{bar q}} wave function with conventional quark model parameters {alpha}{sub {ital s}}, {ital m}{sub {ital q}}, and {beta}{sub SHO} is found to be in good agreement with experiment and with Weinberg's PCAC (partial conservation of axial-vector current) result. At higher energies the predicted differential cross sections have the characteristic diffractive features of an exponential {ital t} peak at small angles and vacuum quantum number exchange. The phase of the predicted amplitude however differs from the experimental diffractive amplitude, so these quark Born diagrams cannot be directly identified with the Pomeron'' of diffractive scattering phenomenology.

• DOE Contract Number: AC05-84OR21400; FG05-91ER40627
• OSTI ID: 7206032
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 46:1; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662230 -- Quantum Chromodynamics-- (1992-)
662340* -- Hadron Interactions-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANNIHILATION
BASIC INTERACTIONS
COMPOSITE MODELS
COUPLING CONSTANTS
CROSS SECTIONS
DIFFERENTIAL CROSS SECTIONS
ELECTROMAGNETIC INTERACTIONS
FIELD THEORIES
FUNCTIONS
HADRON-HADRON INTERACTIONS
INTERACTIONS
KAON-KAON INTERACTIONS
MATHEMATICAL MODELS
MESON-MESON INTERACTIONS
PARTIAL WAVES
PARTICLE INTERACTIONS
PARTICLE MODELS
PCAC THEORY
PHASE SHIFT
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM NUMBERS
QUARK MODEL
QUARK-ANTIQUARK INTERACTIONS
S WAVES
SCATTERING
SCATTERING AMPLITUDES
WAVE FUNCTIONS