New mass and mass-mixing angle relations for pseudoscalar mesons

Abstract

We study the origins of the inaccuracies of Schwinger's nonet mass, and the Sakurai mass-mixing angle, formulae for the pseudoscalar meson nonet, and suggest new versions of them, modified by the inclusion of the pseudoscalar decay constants. We use these new formulae to determine the pseudoscalar decay constants and mixing angle. The results obtained, f 8 /f π = 1.185± 0.040, f 9 /f π = 1.095 ± 0.020, f η /f π = 1.085 ± 0.025, f η ′ /f π = 1.195 ± 0.035, θ = (−21.4 ± 1.0) o , are in excellent agreement with experiment.

Two analytical constraints onη−η′mixing

“…We will not compare our prediction with the results from the two-mixing-angle schemes [4,5,8,12] since different mixing schemes are employed. Our result for the ratio f 8 /f π being 0.94±0.07 is smaller than the prediction from Chiral perturbation theory (ChPT) f 8 /f π = 1.28 [2,8] and most phenomenological analyses [1,3,9,12,13], but is larger than the result given in Ref. [5] f 8 /f π = 0.71.…”

“…The recent experimental measurements on the productions of η and η ′ from the CLEO collaboration [15] and L3 collaboration [16] have stimulated more phenomenological studies on this issue [11][12][13][14]. The theoretical analyses are usually model dependent, and the predictions for θ vary from −12 • [4,13] to −20 • [2,9]. Besides the mixing angle θ, another two parameters f 8 and f 1 , the decay constants of η 8 and η 1 , are usually introduced.…”

ηandη′mesons and dimension 2 gluon condensate⟨A2⟩

“…Thus, introducing only the anomalous shift of the η 0 mass still yields the usual Schwinger relation, as noted by Ref. [51] in a different approach. The pion remains decoupled from the etas as long as one stays in the isospin limit; i.e., after one adds the anomalous contributionM 2 A (35) to Eq.…”

“…(29). The usual Schwinger formula is known to be satisfied well for the vector and tensor nonets, but not for the pseudoscalar nonet [51]. Equation (38) reduces to the usual Schwinger pseudoscalar-meson relation for the limit of no anomaly, 3β → 0, but also for just X → 1, the limit of no influence of the flavor symmetry breaking on the anomalous mass shifts.…”

$\delta$ -pairing forces and collective pairing vibrations

“…This value is in contrast to the experimentally still inaccurately determined mixing angle θ P , which has been subject of several investigations [1,2,3,4,5,6,7,8,9,10,11,12] and was found to be between −9 and −20…”