{"title":"Renormalon-based resummation of Bjorken polarised sum rule in holomorphic QCD","authors":"","doi":"10.1016/j.nuclphysb.2024.116668","DOIUrl":null,"url":null,"abstract":"<div><p>Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) <span><math><msubsup><mrow><mover><mrow><mi>Γ</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>1</mn></mrow><mrow><mi>p</mi><mo>−</mo><mi>n</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> leads to the corresponding BSR characteristic function that allows us to evaluate the leading-twist part of BSR. In our previous work <span><span>[1]</span></span>, this evaluation (resummation) was performed using perturbative QCD (pQCD) coupling <span><math><mi>a</mi><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>≡</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>/</mo><mi>π</mi></math></span> in specific renormalisation schemes. In the present paper, we continue this work, by using instead holomorphic couplings [<span><math><mi>a</mi><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>↦</mo><mi>A</mi><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>] that have no Landau singularities and thus require, in contrast to the pQCD case, no regularisation of the resummation formula. The <span><math><mi>D</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>D</mi><mo>=</mo><mn>4</mn></math></span> terms are included in the Operator Product Expansion (OPE) of inelastic BSR, and fits are performed to the available experimental data in a specific interval <span><math><mo>(</mo><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>min</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>max</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math></span> where <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>max</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>4.74</mn><mspace></mspace><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We needed relatively high <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>min</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>≈</mo><mn>1.7</mn><mspace></mspace><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> in the pQCD case since the pQCD coupling <span><math><mi>a</mi><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> has Landau singularities at <span><math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≲</mo><mn>1</mn><mspace></mspace><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. Now, when holomorphic (AQCD) couplings <span><math><mi>A</mi><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> are used, no such problems occur: for the 3<em>δ</em>AQCD and 2<em>δ</em>AQCD variants the preferred values are <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>min</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>≈</mo><mn>0.6</mn><mspace></mspace><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. The preferred values of <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> in general cannot be unambiguously extracted, due to large uncertainties of the experimental BSR data. At a fixed value of <span><math><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mover><mrow><mrow><mi>MS</mi></mrow></mrow><mo>‾</mo></mover></mrow></msubsup><mo>(</mo><msubsup><mrow><mi>M</mi></mrow><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math></span>, the values of the <span><math><mi>D</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>D</mi><mo>=</mo><mn>4</mn></math></span> residue parameters are determined in all cases, with the corresponding uncertainties.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324002347/pdfft?md5=842e663826ba637998a3b3b4e949dc52&pid=1-s2.0-S0550321324002347-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0550321324002347","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract
Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) leads to the corresponding BSR characteristic function that allows us to evaluate the leading-twist part of BSR. In our previous work [1], this evaluation (resummation) was performed using perturbative QCD (pQCD) coupling in specific renormalisation schemes. In the present paper, we continue this work, by using instead holomorphic couplings [] that have no Landau singularities and thus require, in contrast to the pQCD case, no regularisation of the resummation formula. The and terms are included in the Operator Product Expansion (OPE) of inelastic BSR, and fits are performed to the available experimental data in a specific interval where . We needed relatively high in the pQCD case since the pQCD coupling has Landau singularities at . Now, when holomorphic (AQCD) couplings are used, no such problems occur: for the 3δAQCD and 2δAQCD variants the preferred values are . The preferred values of in general cannot be unambiguously extracted, due to large uncertainties of the experimental BSR data. At a fixed value of , the values of the and residue parameters are determined in all cases, with the corresponding uncertainties.
期刊介绍:
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.