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1++1^{++} Nonet Singlet-Octet Mixing Angle, Strange Quark Mass, and Strange Quark Condensate

Abstract

Two strategies are taken into account to determine the f1(1420)f_1(1420)-f1(1285)f_1(1285) mixing angle ΞΈ\theta. (i) First, using the Gell-Mann-Okubo mass formula together with the K1(1270)K_1(1270)-K1(1400)K_1(1400) mixing angle ΞΈK1=(βˆ’34Β±13)∘\theta_{K_1}=(-34\pm 13)^\circ extracted from the data for B(Bβ†’K1(1270)Ξ³),B(Bβ†’K1(1400)Ξ³),B(Ο„β†’K1(1270)Ξ½Ο„){\cal B}(B\to K_1(1270) \gamma), {\cal B}(B\to K_1(1400) \gamma), {\cal B}(\tau\to K_1(1270) \nu_\tau), and B(Ο„β†’K1(1420)Ξ½Ο„){\cal B}(\tau\to K_1(1420) \nu_\tau), gave ΞΈ=(23βˆ’23+17)∘\theta = (23^{+17}_{-23})^\circ. (ii) Second, from the study of the ratio for f1(1285)→ϕγf_1(1285) \to \phi\gamma and f1(1285)→ρ0Ξ³f_1(1285) \to \rho^0\gamma branching fractions, we have two-fold solution ΞΈ=(19.4βˆ’4.6+4.5)∘\theta=(19.4^{+4.5}_{-4.6})^\circ or (51.1βˆ’4.6+4.5)∘(51.1^{+4.5}_{-4.6})^\circ. Combining these two analyses, we thus obtain ΞΈ=(19.4βˆ’4.6+4.5)∘\theta=(19.4^{+4.5}_{-4.6})^\circ. We further compute the strange quark mass and strange quark condensate from the analysis of the f1(1420)βˆ’f1(1285)f_1(1420)-f_1(1285) mass difference QCD sum rule, where the operator-product-expansion series is up to dimension six and to O(Ξ±s3,ms2Ξ±s2){\cal O}(\alpha_s^3, m_s^2 \alpha_s^2) accuracy. Using the average of the recent lattice results and the ΞΈ\theta value that we have obtained as inputs, we get /=0.41Β±0.09/ =0.41 \pm 0.09.Comment: 10 pages, 1 table, published versio

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    Last time updated on 03/01/2020