Some Results on Vector and Tensor Meson Mixing in a Generalized QCD-like Theory

Early papers on ω \omega - ϕ \phi mixing include J. J. Sakurai, Phys. Rev. Lett. 9

1964

Earlier work this paper cites.

M. Gell-Mann, Phys. Rev. 125

1964

Earlier work this paper cites.

S. Coleman and H. J. Schnitzer, Phys. Rev. 134

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Earlier work this paper cites.

T. Appelquist and J. Carazzone, Phys. Rev. D 11

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Earlier work this paper cites.

S. Okubo, op. cit

1977

Earlier work this paper cites.

T. Appelquist and H. D. Politzer, Phys. Rev. Lett. 34

1984

Cited alongside, same era.

In addition to the papers on vector and tensor meson mixing cited above, others from the large literature include H. Lipkin, Nucl. Phys. B 244

1992

Cited alongside, same era.

The fitted values of θ V , p ​ h \theta_{V,ph} (and θ T , p ​ h \theta_{T,ph} ) in [ 1 ] are fixed constants. It may be noted that the 2000 paper of Benyaoun et al. [ 7 ] discussed an effective energy-dependent θ V , p ​ h \theta_{V,ph}

2000

Cited alongside, same era.

By “hard” mass, we mean here the mass that the quark would have if one turned off color SU(3) c

2005

Cited alongside, same era.

For our work we do not need precise values of the hard m u m_{u} and m d m_{d} masses, aside from the fact that they are a few MeV and that m d / m u ∼ 2 m_{d}/m_{u}\sim 2 ; for the s s quark running mass, evaluated at a reference scale of 4 GeV, a combination of lattice measurements in G. Colangelo et al., Eur. Phys. J. C 71

Cited in the paper.

In our discussion of meson mixing, we rely on the empirical fact that QCD conserves P, C, and CP. This is automatic if m q = 0 m_{q}=0 , since then the CP-violating angle θ ¯ C ​ P ​ V = θ C ​ P ​ V − arg ⁡ ( det ⁡ ( M u ) ) − arg ⁡ ( det ⁡ ( M d ) ) \bar{\theta}_{CPV}=\theta_{CPV}-{\rm arg}({\rm det}(M_{u}))-{\rm arg}({\rm det}(M_{d})) can be rotated away, where θ C ​ P ​ V \theta_{CPV} is the coefficient of the instanton-induced topological term g s 2 ​ ( 32 ​ π 2 ) − 1 ​ G μ ​ ν a ​ G ~ a ​ μ ​ ν g_{s}^{2}(32\pi^{2})^{-1}G^{a}_{\mu\nu}\tilde{G}^{a\mu\nu} in the QCD Lagrangian. For m q ≠ 0 m_{q}\neq 0 , we implicitly assume a solution of the strong CP problem

Cited in the paper.

The determination of the value of N f , c ​ r N_{f,cr} separating the interval of smaller N f N_{f} with S χ \chi SB from the interval of larger N f < ( 11 / 2 ) ​ N c N_{f}<(11/2)N_{c} where the theory is still asymptotically free but does not have S χ \chi SB has been the subject of intensive study recently using lattice methods. See, e.g., T. Appelquist, G. T. Fleming, and E. T. Neil, Phys. Rev. Lett. 100

Cited in the paper.

Although electromagnetic interactions are a small perturbation, their presence, together with vacuum alignment arguments, implies the absence of charge-violating quark condensates such as ⟨ u ¯ ​ d ⟩ \langle\bar{u}d\rangle , ⟨ u ¯ ​ s ⟩ \langle\bar{u}s\rangle , etc

Cited in the paper.

Here and below, e.g., when using the Gell-Mann Okubo mass relation and giving various quark model formulas, we follow the common practice of using the squared masses of the mesons rather than the masses themselves, because for bosons it is the squared masses that appear in effective Lagrangians

Cited in the paper.

As an auxiliary part of a global fit to the η \eta - η ′ \eta^{\prime} mixing and η ′ \eta^{\prime} -gluonium mixing, a recent value of θ V , p ​ h \theta_{V,ph} was reported in F. Ambrosino et al. (KLOE Collab.), JHEP 0907

Cited in the paper.

C. J. Morningstar and M. J. Peardon, Phys. Rev. D 60

2006

Later among the works it cites.

Particle Data Group, K. Nakamura et al., Journal of Physics G 37

2010

Later among the works it cites.

S. Weinberg, Phys. Rev. D 11

2010

Later among the works it cites.

H. Y. Cheng and K. C. Yang, Phys. Rev. D 76

Original

2011

Closest in time.