Renormalization group summation of Laplace QCD sum rules for scalar gluon currents

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• 作者：Farrukh Chishtie^a ; ^{fchishti@uwo.ca" class="auth_mail" title="E-mail the corresponding author} ; T.G. Steele^b ; ^{Tom.Steele@usask.ca" class="auth_mail" title="E-mail the corresponding author} ; D.G.C. McKeon^c ; ^d ; ^{dgmckeo2@uwo.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Sum rules ; Renormalization group ; Scale dependence
• 刊名：Physics Letters B
• 出版年：2016
• 出版时间：10 March 2016
• 年：2016
• 卷：754
• 期：Complete
• 页码：43-48
• 全文大小：416 K

文摘

We employ renormalization group (RG) summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316000125&_mathId=si1.gif&_user=111111111&_pii=S0370269316000125&_rdoc=1&_issn=03702693&md5=2b4251db96d393c0a96c8ce5518b40f9" title="Click to view the MathML source">μ²class="mathContainer hidden">class="mathCode">${\mu }^2$ once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.