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Can \( \overline{\mathrm{MS}} \) parton distributions be negative?
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 24 November 2020

Can \( \overline{\mathrm{MS}} \) parton distributions be negative?

  • Alessandro Candido1,
  • Stefano Forte1 &
  • Felix Hekhorn1 

Journal of High Energy Physics volume 2020, Article number: 129 (2020) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

It is common lore that Parton Distribution Functions (PDFs) in the \( \overline{\mathrm{MS}} \) factorization scheme can become negative beyond leading order due to the collinear subtraction which is needed in order to define partonic cross sections. We show that this is in fact not the case and next-to-leading order (NLO) \( \overline{\mathrm{MS}} \) PDFs are actually positive in the perturbative regime. In order to prove this, we modify the subtraction prescription, and perform the collinear subtraction in such a way that partonic cross sections remain positive. This defines a factorization scheme in which PDFs are positive. We then show that positivity of the PDFs is preserved when transforming from this scheme to \( \overline{\mathrm{MS}} \), provided only the strong coupling is in the perturbative regime, such that the NLO scheme change is smaller than the LO term.

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Authors and Affiliations

  1. Tif Lab, Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, I-20133, Milano, Italy

    Alessandro Candido, Stefano Forte & Felix Hekhorn

Authors
  1. Alessandro Candido
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  2. Stefano Forte
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  3. Felix Hekhorn
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Correspondence to Stefano Forte.

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ArXiv ePrint: 2006.07377

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Cite this article

Candido, A., Forte, S. & Hekhorn, F. Can \( \overline{\mathrm{MS}} \) parton distributions be negative?. J. High Energ. Phys. 2020, 129 (2020). https://doi.org/10.1007/JHEP11(2020)129

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  • Received: 31 July 2020

  • Accepted: 18 October 2020

  • Published: 24 November 2020

  • DOI: https://doi.org/10.1007/JHEP11(2020)129

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Keywords

  • Deep Inelastic Scattering (Phenomenology)
  • QCD Phenomenology
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