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Register a new userCalculating the pion decay constant from alpha_s(M_Z)
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We revisit the analysis of the improved ladder Schwinger-Dyson (SD) equation for the dynamical chiral symmetry breaking in QCD with emphasizing the importance of the scale ambiguity. Previous calculation done so far naively used one-loop MSbar coupling in the improved ladder SD equation without examining the scale ambiguity. As a result, the calculated pion decay constant f_pi was less than a half of its experimental value f_pi=92.4MeV once the QCD scale is fixed from the high energy coupling alpha_s(M_Z). In order to settle the ambiguity in a proper manner, we adopt here in the present paper the next-to-leading-order effective coupling instead of a naive use of the MSbar coupling. The pion decay constant f_pi is then calculated from high energy QCD coupling strength alpha_s(M_Z)=0.1172 pm 0.0020. Within the Higashijima-Miransky approximation, we obtain f_pi=85--106MeV depending on the value of alpha_s(M_Z) which agrees well with the experimentally observed value f_pi=92.4MeV. The validity of the improved ladder SD equation is therefore ascertained more firmly than considered before.
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We revisit the earlier determination of alpha_s(M_Z) via perturbative analyses of short-distance-sensitive lattice observables, incorporating new lattice data and performing a modified version of the original analysis. We focus on two high-intrinsic-scale observables, log(W_11) and log(W_12), and one lower-intrinsic scale observable, log(W_{12}/u_0^6), finding improved consistency among the values extracted using the different observables and a final result, alpha_s(M_Z)=0.1192(11), 2 sigma higher than the earlier result, in excellent agreement with recent non-lattice determinations and, in addition, in good agreement with the results of a similar, but not identical, re-analysis by the HPQCD Collaboration. A discussion of the relation between the two re-analyses is given, focussing on the complementary aspects of the two approaches.
We study aspects of the pion condensation in two-flavor neutral quark matter using the Nambu--Jona-Lasinio model of QCD at finite density. We investigate the role of electric charge neutrality, and explicit symmetry breaking via quark mass, both of which control the onset of the charged pion $(pi^c)$ condensation. We show that the equality between the electric chemical potential and the in-medium pion mass, $mu_{e}=M_{pi^-}$, as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion condensed phase is of the second order. Moreover, we find that the pion condensate in neutral quark matter is extremely fragile to the symmetry breaking effect via a current quark mass $m$, and is ruled out for $m$ larger than the order of 10 keV.
From soft-collinear effective theory one can derive a factorization formula for the e+e- thrust distribution dsigma/dtau with tau = 1-T that is applicable for all tau. The formula accommodates available O(alpha_s^3) fixed-order QCD results, resummation of logarithms at NNNLL order, a universal nonperturbative soft function for hadronization effects, factorization of nonperturbative effects in subleading power contributions, bottom mass effects and QED corrections. We emphasize that the use of Monte Carlos to estimate hadronization effects is not compatible with high-precision, high-order analyses. We present a global analysis of all available e+e- thrust data measured at Q = 35 to 207 GeV in the tail region, where a two-parameter fit can be carried out for alpha_s(m_Z) and Omega_1, the first moment of the soft function. To obtain small theoretical errors it is essential to define Omega_1 in a short-distance scheme, free of an O(Lambda_QCD) renormalon ambiguity. We find alpha_s(m_Z) = 0.1135 +- (0.0002)_expt +- (0.0005)_Omega_1 +- (0.0009)_pert with chi^2/dof = 0.9.
The pion structure in Minkowski space is described in terms of an analytic model of the Bethe-Salpeter amplitude combined with Euclidean Lattice QCD results for the running quark mass. In the present work, a pion model previously proposed, which allows for a Nakanishi integral representation, is studied in order to verify the sensitivity of the pion electromagnetic form factor to small variations of the quark self-energy. In addition, we extend the previous work, providing the Nakanishi integral representation for the invariants associated with a decomposition of the pion Bethe-Salpeter amplitude.
We summarize a comparison of the two strategies which are currently available in the literature for determining the value of $alpha_s(m_tau)$. We will refer to these as the truncated Operator Product Expansion model and the Duality Violation model. After describing the main features of both approaches, we explain why the former fails to pass crucial tests. The latter, on the other hand, passes all the tests known up to date and, therefore, should be currently considered the only reliable method.
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