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.
Highlights
These positivity constraint may have a significant impact on Parton Distribution Functions (PDFs) determination, especially in regions where there are little or no direct constraints coming from experimental data
It is common lore that Parton Distribution Functions (PDFs) in the 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 not the case and next-to-leading order (NLO) MS PDFs are positive in the perturbative regime
Summary
QCD factorization allows expressing physical cross sections σ as convolutions of partonic cross sections with parton distributions fi. The advantage of determining the counterterms in this way, as opposed to performing a direct computation of the current matrix element eq (2.2) is that in operator matrix elements all divergences appear as ultraviolet, while, when computing a structure function for an incoming free parton (or, more generally, a generic partonic cross-section), collinear singularities come from the infrared region of integration over transverse momenta. The universal (i.e. process-independent) nature of the collinear singularities ensure that the renormalization conditions on parton distributions, defined as operator matrix elements eq (2.2) without reference to any specific process, may be determined by the computation of a particular process or set of processes as discussed here. The residue of the collinear pole is universal — it is given by process-independent splitting functions — and this makes it possible to define its subtraction in a way that preserves positivity of the partonic cross section at the regularized level. We turn to hadronic processes, both quark-induced and gluon induced
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
