How the axial anomaly controls flavor mixing among mesons

Giacosa, Francesco; Koenigstein, Adrian; Pisarski, Robert D.

doi:10.1103/PhysRevD.97.091901

Title: How the axial anomaly controls flavor mixing among mesons

Journal Article · Tue May 22 00:00:00 EDT 2018 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.97.091901· OSTI ID:1438293

Giacosa, Francesco; Koenigstein, Adrian; Pisarski, Robert D.

Here, it is well known that, because of the axial anomaly in QCD, mesons with J^P = 0^– are close to SU(3)_V eigenstates; the η'(958) meson is largely a singlet, and the η meson an octet. In contrast, states with J^P = 1^– are flavor diagonal; e.g., the Φ(1020) is almost pure ¯ss. Using effective Lagrangians, we show how this generalizes to states with higher spin, assuming that they can be classified according to the unbroken chiral symmetry of G_fl = SU(3)_L × SU(3)_R. We construct effective Lagrangians from terms invariant under G_fl and introduce the concept of hetero- and homochiral multiplets. Because of the axial anomaly, only terms invariant under the Z(3)_A subgroup of the axial U(1)_A enter. For heterochiral multiplets, which begin with that including the η and η'(958), there are Z(3)_A invariant terms with low mass dimension which cause states to mix according to SU(3)_V flavor. For homochiral multiplets, which begin with that including the Φ(1020), there are no Z(3)_A invariant terms with low mass dimension, and so states are diagonal in flavor. In this way, we predict the flavor mixing for the heterochiral multiplet with spin 1 as well as for hetero- and homochiral multiplets with spin 2 and spin 3.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704

OSTI ID:: 1438293

Alternate ID(s):: OSTI ID: 1462430

Report Number(s):: BNL-207869-2018-JAAM; PRVDAQ; 091901

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 97 Journal Issue: 9; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 26 works

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