Many-body theory of {rho}-{omega} mixing

Journal Article · Fri Mar 01 04:00:00 EST 1996 · Physical Review, C

DOI:https://doi.org/10.1103/PhysRevC.53.1374· OSTI ID:279138

Gao, S; Shakin, C M; Sun, W ^[1]

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1. Department of Physics and Center for Nuclear Theory, Brooklyn College of the City University of New York, Brooklyn, New York 11210 (United States)

We calculate the tensor describing {rho}-{omega} mixing making use of an extended Nambu{endash}Jona-Lasinio (NJL) model that we have developed in recent years. We use the definition of the {rho} and {omega} fields that arises upon a momentum-space bosonization of the extended NJL model. A quantity of interest is the on-shell ({ital q}{sup 2}={ital m}{sub {omega}}{sup 2}) matrix element that describes the coupling of the {rho} and {omega} fields, {l_angle}{rho}{parallel}{ital H}{sub {ital SB}}{parallel}{omega}{r_angle}. That quantity has been determined to be {l_angle}{rho}{parallel}{ital H}{sub {ital SB}}{parallel}{omega}{r_angle}={minus}(4520{plus_minus}600) MeV{sup 2} in a study of the two-pion decay of the {omega} meson. If corrected for an electromagnetic process, the strong interaction contribution is {l_angle}{rho}{parallel}{ital H}{sub {ital SB}}{sup st}{parallel}{omega}{r_angle}={minus}(5130{plus_minus}600) MeV{sup 2}. Our calculation of {l_angle}{rho}{parallel}{ital H}{sub {ital SB}}{sup st}{parallel}{omega}{r_angle} is sensitive to the difference of the current quark masses, {ital m}{sup 0}{sub {ital d}}{minus}{ital m}{sup 0}{sub {ital u}}. Our results may be put into agreement with the data, if we use {ital m}{sup 0}{sub {ital d}}{minus}{ital m}{sup 0}{sub {ital u}}=3.1{plus_minus}0.3 MeV. (That value is reduced to {ital m}{sup 0}{sub {ital d}}{minus}{ital m}{sup 0}{sub {ital u}}=2.7{plus_minus}0.3 MeV, if we use a subtraction scheme that causes the polarization tensor to be equal to zero at {ital q}{sup 2}=0.) The momentum-space bosonization procedure naturally leads to momentum-dependent coupling constants, {ital g}{sub {omega}{ital qq}}({ital q}{sup 2}) and {ital g}{sub {rho}{ital qq}}({ital q}{sup 2}). The value of these constants increases by about a factor of {radical}2, when one goes from {ital q}{sup 2}={ital m}{sub {omega}}{sup 2} (or {ital q}{sup 2}={ital m}{sub {rho}}{sup 2}) to {ital q}{sup 2}=0. (Abstract Truncated)

• OSTI ID: 279138
• Journal Information: Physical Review, C, Journal Name: Physical Review, C Journal Issue: 3 Vol. 53; ISSN PRVCAN; ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOSON EXPANSION
CONFIGURATION MIXING
COUPLING
MASS
MOMENTUM TRANSFER
OMEGA-782 MESONS
QUARK MODEL
RHO-770 MESONS
TENSORS