Abstract
We investigate the positivity of double parton distributions with a non-trivial dependence on the parton colour. It turns out that positivity is not preserved by leading-order evolution from lower to higher scales, in contrast to the case in which parton colour is summed over. We also study the positivity properties of the distributions at small distance between the two partons, where they can be computed in terms of perturbative splitting kernels and ordinary parton densities.
Highlights
Parton distribution functions and related quantities are crucial ingredients for computing hadronic cross sections at high energies, and they are the main quantities that describe the structure of hadrons at the level of quarks and gluons
We investigate the positivity of double parton distributions with a non-trivial dependence on the parton colour
In the context of the parton model, double parton distributions (DPDs) in the s channel colour basis are probability densities for finding two partons in a definite colour state. This leads to the expectation that s channel DPDs for unpolarised partons should be non-negative
Summary
Parton distribution functions and related quantities are crucial ingredients for computing hadronic cross sections at high energies, and they are the main quantities that describe the structure of hadrons at the level of quarks and gluons. DPDs have a non-trivial dependence on the polarisation of the partons, and on their colour, and corresponding positivity bounds have been derived in [6]. An important result is that LO DGLAP evolution to higher scales conserves the positivity of PDFs, both in the unpolarised sector [13,14] and in the polarised one [15,16]. Using the results of the recent two-loop calculation in [20], we can investigate to which extent positivity of DPDs in colour space is realised in the small y limit. This is the second goal of our work.
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