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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2010.06623 |
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| _version_ | 1866910602681647104 |
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| author | Liu, Wei-Yang Chen, Jiunn-Wei |
| author_facet | Liu, Wei-Yang Chen, Jiunn-Wei |
| contents | We investigate the renormalon ambiguity from bubble-chain diagrams in the isovector unpolarized quasi-parton distribution function (PDF) of a hadron. We confirm the assertion by Braun, Vladimirov and Zhang (arXiv:1810.00048) that the leading IR renormalon ambiguity is formally an $\mathcal{O}(Λ^2_{QCD}/x^2P_z^2)$ effect, with $x$ the parton momentum fraction and $P_z$ the hadron momentum, together with a new $\mathcal{O}(δ(x)Λ^2_{QCD}/P_z^2)$ contribution such that the quark number is conserved. This implies the convergence of the perturbative matching kernel between a quasi-PDF and a PDF would eventually fail for small $x$. However, in both the R-scheme designed to cancel the leading IR renormalon and the typically used RI/MOM scheme in lattice QCD for the same quasi-PDF, we find good convergence in the kernel based on three-loop bubble-chain diagram analyses. These results are encouraging for the quasi-PDF program. However, firm conclusions can only be drawn after the complete higher loop QCD calculations are carried out. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_06623 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Renormalon Effects in Quasi Parton Distributions Liu, Wei-Yang Chen, Jiunn-Wei High Energy Physics - Phenomenology We investigate the renormalon ambiguity from bubble-chain diagrams in the isovector unpolarized quasi-parton distribution function (PDF) of a hadron. We confirm the assertion by Braun, Vladimirov and Zhang (arXiv:1810.00048) that the leading IR renormalon ambiguity is formally an $\mathcal{O}(Λ^2_{QCD}/x^2P_z^2)$ effect, with $x$ the parton momentum fraction and $P_z$ the hadron momentum, together with a new $\mathcal{O}(δ(x)Λ^2_{QCD}/P_z^2)$ contribution such that the quark number is conserved. This implies the convergence of the perturbative matching kernel between a quasi-PDF and a PDF would eventually fail for small $x$. However, in both the R-scheme designed to cancel the leading IR renormalon and the typically used RI/MOM scheme in lattice QCD for the same quasi-PDF, we find good convergence in the kernel based on three-loop bubble-chain diagram analyses. These results are encouraging for the quasi-PDF program. However, firm conclusions can only be drawn after the complete higher loop QCD calculations are carried out. |
| title | Renormalon Effects in Quasi Parton Distributions |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2010.06623 |