Calculation of the nonperturbative strong coupling from first principles

Abstract

The success of the screened massive expansion is investigated in the framework of a screened momentum-subtraction scheme for the running of the strong coupling in pure Yang-Mills theory. By the exact Slavnov-Taylor and Nielsen identities, a very predictive and self-contained set of stationary conditions are derived for the optimization of the fixed-coupling expansion, yielding explicit analytical one-loop expressions for the propagators, the coupling and the beta function, from first principles. An excellent agreement is found with the lattice data. In the proposed screened renormalization scheme, a monotonic running coupling emerges which saturates in the IR at the finite IR stable fixed point g = 9.40 where the beta function crosses the zero. A simple analytical expression is derived for the leading behavior of the beta in the IR.

Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2

“…. Some of them [12,14,22,26,29] fulfill the relation A(Q 2 ) = 0 at Q 2 = 0, i.e., the same relation that is fulfilled by the coupling A(Q 2 ) considered in this work. For reviews of a variety of holomorphic couplings, cf.…”

“…= 0.1989 is already above the maximum value achievable in our 3δ AQCD framework at that value of αs(M 2 Z ; MS). 29 We recall that the MM scheme is used in the large-volume lattice calculations of the Landau gauge gluon and ghost propagators [43,44], and the scheme is theoretically known at present up to the four-loop level [49][50][51].…”

Thermal extension of the screened massive expansion in the Landau gauge

“…In the last years, a very predictive analytical method has been developed [18][19][20][21] by a mere change of the expansion point of ordinary perturbation theory (PT) for the exact gauge-fixed Becchi-Rouet-Stora-Tyutin (BRST) invariant YM Lagrangian, yielding a screened massive expansion which is safe in the IR while recovering the correct results of ordinary PT in the UV. At oneloop and zero temperature, the screened expansion provides analytical results which are in excellent agreement with the lattice and can be easily continued to Minkowski space [21][22][23][24][25]. Thus the method provides a way to extract dynamical details like masses and damping rates from first principles.…”

Screened massive expansion of the quark propagator in the Landau gauge

“…Its renormalization in the Landau gauge was discussed in Refs. [56,57], where different renormalization schemes were considered and analytical expressions were reported for its beta function. The method has proven to be self-consistent and predictive when optimized by principles of gauge invariance [54,57].…”

“…While in principle the failure of ordinary PT to describe the gluon's infrared mass could be attributed to its break down at low energies, in recent years a new approach to the perturbation theory of pure Yang-Mills (YM) theory has shown that most of the nonperturbative content of the gluon dynamic -at least as far as the two-point functions are concerned -can be absorbed into a shift of the expansion point of the Yang-Mills perturbative series. This approach, termed the screened massive expansion [47][48][49][50][51][52][53][54][55][56][57][58], is a simple extension of ordinary PT, formulated in such a way as to treat the transverse gluons as massive already at tree level while leaving the total action of the theory unchanged. The screened expansion has proven to be self-consistent to one loop -since it is renormalizable and leads to an infraredfinite and moderately small running coupling constant [57] -and predictive when optimized by principles of gauge invariance [54]; it yields two-point functions which are in excellent agreement with the lattice data in the Landau gauge [54,57].…”