Effective quark operator models of U{sub A}(1) symmetry breaking
- Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208 (United States)
We undertake a systematic investigation of U{sub A}(1) symmetry-breaking, C-, P-, T-, and SU{sub L}(N{sub f}){times}SU{sub R}(N{sub f})-invariant effective fermion operators and their consequences for pseudoscalar and scalar mesons. We construct four types of such operators that exist for any number of flavors N{sub f}{ge}2, two of which can be identified with {close_quote}t Hooft{close_quote}s interaction and the quark self-interaction leading to the Veneziano-Witten meson-interaction term. We isolate the U{sub A}(1) symmetry-breaking effect from the quark mass- and electromagnetic interaction-induced chiral symmetry-breaking effects and quantify it as the deviation from zero of f{sub 0}{sup 2}m{sub U(1)}{sup 2}=f{sub {eta}{sup {prime}}}{sup 2}m{sub {eta}{sup {prime}}}{sup 2}+f{sub {eta}}{sup 2}m{sub {eta}}{sup 2}{minus}f{sub K}{sup 2}(m{sub K{sup +}}{sup 2}+m{sub K{sup 0}}{sup 2})+f{sub {pi}}{sup 2}(m{sub {pi}{sup +}}{sup 2}{minus}m{sub {pi}{sup 0}}{sup 2}), where m{sub {phi}},f{sub {phi}} are the pseudoscalar {phi} meson mass and weak decay constant, respectively. Then we use Dashen{close_quote}s general formula to evaluate the masses and the mixing angle of isoscalar pseudoscalar mesons in the presence of the current quark masses and each one of these four types of U{sub A}(1) symmetry-breaking interactions. We find that both the {close_quote}t Hooft and the Veneziano-Witten interaction push the sum of the {eta}{sup {prime}} and {eta} masses squared upward and the mixing angle to negative values, in accord with empirical evidence. The other two types of U{sub A}(1) symmetry-breaking operators do not influence the pseudoscalar meson spectrum to leading order in N{sub C}, so long as no new higher-order quark condensates are assumed. (Abstract Truncated)
- OSTI ID:
- 531965
- Journal Information:
- Physical Review, D, Vol. 56, Issue 1; Other Information: PBD: Jul 1997
- Country of Publication:
- United States
- Language:
- English
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