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arXiv 1401.1192hep-ph
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分数阶解析微扰理论中的胶子算符

Gluon Propagator in Fractional Analytic Perturbation Theory

Pedro Allendes, Cesar Ayala, Gorazd Cvetič

摘要:

我们考虑了类空动量较低的朗道规范中的胶子传播子,其修整函数$Z(Q^2)$为双圈阶。我们通过分数解析微扰理论(FAPT)模型使修饰函数$Z(Q^2)$中QCD耦合的(非整数)幂解析(全纯),并同时在传播子中引入胶子动力学质量,从而引入非微扰效应,正如前面对戴森-施温格方程的分析所激发的那样。在低类空动量$0.4 \ {\rm GeV} < Q \lesssim 10$ GeV下,所得到的传播子具有与非猝灭晶格数据($N_f=2+1$)相一致的行为.我们的结论是,通过(F)APT处方的耦合功率的非物理朗道奇异性的去除,结合胶子的动力学质量$M \approx 0.62$ GeV的引入,导致传播子在红外区的可接受的行为。

英文摘要:

We consider the gluon propagator in the Landau gauge at low spacelike momenta and with the dressing function $Z(Q^2)$ at the two-loop order. We incorporate the nonperturbative effects by making the (noninteger) powers of the QCD coupling in the dressing function $Z(Q^2)$ analytic (holomorphic) via the Fractional Analytic Perturbation Theory (FAPT) model, and simultaneously introducing the gluon dynamical mass in the propagator as motivated by the previous analyses of the Dyson-Schwinger equations. The obtained propagator has behavior compatible with the unquenched lattice data ($N_f=2+1$) at low spacelike momenta $0.4 \ {\rm GeV} < Q \lesssim 10$ GeV. We conclude that the removal of the unphysical Landau singularities of the powers of the coupling via the (F)APT prescription, in conjunction with the introduction of the dynamical mass $M \approx 0.62$ GeV of the gluon, leads to an acceptable behavior of the propagator in the infrared regime.

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