Quark model calculation of [eta][r arrow][ital l][sup +][ital l[minus]] to all orders in the bound-state relative momentum

Journal Article · Sun Feb 28 23:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.1942· OSTI ID:6887683

Margolis, B ^[1]; Ng, J ^[2]; Phipps, M ^[1]; Trottier, H D ^[2]

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1. Physics Department, McGill University, 3600 University Street, Montreal, Quebec, H3A 2T8 (Canada)
2. TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3 (Canada)

We analyze the electromagnetic amplitude for the leptonic decays of pseudoscalar mesons in the quark model, with particular emphasis on [eta][r arrow][ital l][sup +][ital l[minus]] ([ital l]=[ital e],[mu]). We evaluate the electromagnetic box diagram for a quark-antiquark pair with an arbitrary distribution of relative three-momentum [bold p]: the amplitude is obtained to [ital all] [ital orders] in [bold p]/[ital m][sub [ital q]], where [ital m][sub [ital q]] is the quark mass. We compute [ital B][sub [ital P]][equivalent to][Gamma]([eta][r arrow][ital l][sup +][ital l[minus]])/[Gamma]([eta][r arrow][gamma][gamma]) using a harmonic oscillator wave function that is widely used in nonrelativistic (NR) quark model calculations, and with a relativistic momentum space wave function that we derive from the MIT bag model. We also compare with a quark model calculation in the limit of extreme NR binding due to Bergstroem. Numerical calculations of [ital B][sub [ital P]] using these three parametrizations of the wave function agree to within a few percent over a wide kinematical range. Our results show that the quark model leads in a natural way to a negligible value for the ratio of dispersive to absorptive parts of the electromagnetic amplitude for [eta][r arrow][mu][sup +][mu][sup [minus]] (unitary bound). However we find substantial deviations from the unitary bound in other kinematical regions, such as [eta],[pi][sup 0][r arrow][ital e][sup +][ital e[minus]]. Using the experimental branching ratio for [eta][r arrow][gamma][gamma] as input, these quark models yield [ital B]([eta][r arrow][mu][sup +][mu][sup [minus]])[approx]4.3[times]10[sup [minus]6], within errors of the recent SATURNE measurement of 5.1[plus minus]0.8[times]10[sup [minus]6], and [ital B]([eta][r arrow][ital e][sup +][ital e[minus]])[approx]6.3[times]10[sup [minus]9].

• OSTI ID: 6887683
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:5; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662350* -- Decays of Mesons-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BASIC INTERACTIONS
BOSONS
BRANCHING RATIO
COMPOSITE MODELS
DECAY
ELEMENTARY PARTICLES
ETA MESONS
FUNCTIONS
HADRONS
INTERACTIONS
LEPTONIC DECAY
MATHEMATICAL MODELS
MATHEMATICS
MESONS
NUMERICAL ANALYSIS
PARTICLE DECAY
PARTICLE MODELS
PSEUDOSCALAR MESONS
QUARK MODEL
RADIATIVE DECAY
WAVE FUNCTIONS
WEAK INTERACTIONS
WEAK PARTICLE DECAY