Pion nucleon coupling constant , Goldberger - Treiman discrepancy and πN σ term
نویسندگان
چکیده
We start by studying the Goldberger-Treiman discrepancy (GTd) ∆ = (2.259± 0.591)%. Then we look at the πN σ term, with the dimensionless ratio σN/2mN = 3.35%. Finally we return to predicting (via the quark model) the πN coupling constant, with GTd ∆ → 0 as mq → mN/3. Given the recent new value of the πNN coupling constant [1] g πNN/4π = 13.80± 0.12 or gπNN = 13.169± 0.057, (1) along with the observed axial current coupling [2] gA = 1.267± 0.004, (2) combined with the measured pion decay constant [2] fπ = (92.42± 0.26)MeV, (3) the Goldberger-Treiman discrepancy (GTd) is ∆ = 1− mNgA fπgπNN = (2.259± 0.591)%. (4) Here we have used the mean nucleon mass mN= 938.9 MeV and have computed the overall mean square error. To verify this GTd in Eq.(4), we employ the constituent quark loop with imaginary part [3] Imfπ(q ) = 3gπqq 2 4m̂ 8π (
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ar X iv : h ep - p h / 04 06 00 9 v 2 1 1 Ju n 20 04 Pion nucleon coupling constant , Goldberger - Treiman discrepancy and πN σ term
We start by studying the Goldberger-Treiman discrepancy (GTd) ∆ = (2.259± 0.591)%. Then we look at the πN σ term, with the dimensionless ratio σN/2mN = 3.35%. Finally we return to predicting (via the quark model) the πN coupling constant, with GTd ∆ → 0 as mq → mN/3. Given the recent new value of the πNN coupling constant [1] g πNN/4π = 13.80± 0.12 or gπNN = 13.169± 0.057, (1) along with the ob...
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We start by studying the Goldberger-Treiman discrepancy (GTd) ∆ = (2.259± 0.591)%. Then we look at the πN σ term, with the dimensionless ratio σN/2mN = 3.35%. Finally we return to predicting (via the quark model) the πN coupling constant, with GTd ∆ → 0 as mq → mN/3. PACS: 12.39.Ki, 12.39.Mk, 13.25.-k, 14.40.-n Given the recent new value of the πNN coupling constant [1] g πNN/4π = 13.80± 0.12 o...
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