{"title":"Towards unifying perturbative and Holographic Light-Front QCD via holomorphic coupling","authors":"César Ayala, Gorazd Cvetič","doi":"10.1007/JHEP12(2024)075","DOIUrl":null,"url":null,"abstract":"<p>We construct a QCD coupling <span>\\( \\mathcal{A} \\)</span>(<i>Q</i><sup>2</sup>) in the Effective Charge (ECH) scheme of the canonical part <i>d</i>(<i>Q</i><sup>2</sup>) of the (inelastic) polarised Bjorken Sum Rule (BSR) <span>\\( {\\overline{\\Gamma}}_1^{\\textrm{p}-\\textrm{n}} \\)</span>(<i>Q</i><sup>2</sup>). In the perturbative domain, the coupling <span>\\( \\mathcal{A} \\)</span>(<i>Q</i><sup>2</sup>) practically coincides with the perturbative coupling <i>a</i>(<i>Q</i><sup>2</sup>) [≡ <i>α</i><sub><i>s</i></sub>(<i>Q</i><sup>2</sup>)/<i>π</i>] in the four-loop ECH renormalisation scheme. In the deep infrared (IR) regime, <span>\\( \\mathcal{A} \\)</span>(<i>Q</i><sup>2</sup>) behaves as suggested by the Holographic Light-Front QCD up to the second derivative. Furthermore, in contrast to its perturbative counterpart <i>a</i>(<i>Q</i><sup>2</sup>), the coupling <span>\\( \\mathcal{A} \\)</span>(<i>Q</i><sup>2</sup>) is holomorphic in the entire complex <i>Q</i><sup>2</sup>-plane with the exception of the negative semiaxis, reflecting the holomorphic properties of the BSR observable <i>d</i>(<i>Q</i><sup>2</sup>) [or: <span>\\( {\\overline{\\Gamma}}_1^{\\textrm{p}-\\textrm{n}} \\)</span>(<i>Q</i><sup>2</sup>)] as dictated by the general principles of the Quantum Field Theory. It turns out that the obtained coupling, used as ECH, reproduces quite well the experimental data for <span>\\( {\\overline{\\Gamma}}_1^{\\textrm{p}-\\textrm{n}} \\)</span>(<i>Q</i><sup>2</sup>) in the entire <i>N</i><sub><i>f</i></sub> = 3 regime 0 < <i>Q</i><sup>2</sup> ≲ 5 GeV<sup>2</sup>.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2024 12","pages":""},"PeriodicalIF":5.4000,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP12(2024)075.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of High Energy Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/JHEP12(2024)075","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a QCD coupling \( \mathcal{A} \)(Q2) in the Effective Charge (ECH) scheme of the canonical part d(Q2) of the (inelastic) polarised Bjorken Sum Rule (BSR) \( {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} \)(Q2). In the perturbative domain, the coupling \( \mathcal{A} \)(Q2) practically coincides with the perturbative coupling a(Q2) [≡ αs(Q2)/π] in the four-loop ECH renormalisation scheme. In the deep infrared (IR) regime, \( \mathcal{A} \)(Q2) behaves as suggested by the Holographic Light-Front QCD up to the second derivative. Furthermore, in contrast to its perturbative counterpart a(Q2), the coupling \( \mathcal{A} \)(Q2) is holomorphic in the entire complex Q2-plane with the exception of the negative semiaxis, reflecting the holomorphic properties of the BSR observable d(Q2) [or: \( {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} \)(Q2)] as dictated by the general principles of the Quantum Field Theory. It turns out that the obtained coupling, used as ECH, reproduces quite well the experimental data for \( {\overline{\Gamma}}_1^{\textrm{p}-\textrm{n}} \)(Q2) in the entire Nf = 3 regime 0 < Q2 ≲ 5 GeV2.
期刊介绍:
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