Parton distributions with theory uncertainties: general formalism and first phenomenological studies

Abstract

We formulate a general approach to the inclusion of theoretical uncertainties, specifically those related to the missing higher order uncertainty (MHOU), in the determination of parton distribution functions (PDFs). We demonstrate how, under quite generic assumptions, theory uncertainties can be included as an extra contribution to the covariance matrix when determining PDFs from data. We then review, clarify, and systematize the use of renormalization and factorization scale variations as a means to estimate MHOUs consistently in deep inelastic and hadronic processes. We define a set of prescriptions for constructing a theory covariance matrix using scale variations, which can be used in global fits of data from a wide range of different processes, based on choosing a set of independent scale variations suitably correlated within and across processes. We set up an algebraic framework for the choice and validation of an optimal prescription by comparing the estimate of MHOU encoded in the next-to-leading order (NLO) theory covariance matrix to the observed shifts between NLO and NNLO predictions. We perform a NLO PDF determination which includes the MHOU, assess the impact of the inclusion of MHOUs on the PDF central values and uncertainties, and validate the results by comparison to the known shift between NLO and NNLO PDFs. We finally study the impact of the inclusion of MHOUs in a global PDF determination on LHC cross-sections, and provide guidelines for their use in precision phenomenology.

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“…Similarly to what happens for experimental uncertainties, such a cancellation would be compensated by the theoretical uncertainty on the total cross section and the associated correlations. While theoretical uncertainties could be included in a fit [37,38], they are not in this study.…”

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“…Since this type of background cannot be modeled in our analysis setup, especially at the 100 TeV LHC, we will ignore the subleading backgrounds from the fake photons. Signal and background processes are simulated at LO, using MadGraph5_aMC@NLO [81,82] with the NNPDF31 PDF set [93] and α s ðM Z Þ ¼ 0.118. For the renormalization and factorization scales, we choose…”

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“…The bin edges are: 20,22,26,28,32,37,43,52,65,85,120,160,190,220,250, 300, 400, 500, 800, 1500 GeV. From figure 7, we observe that the validation of the PineAPPL result remains successful: its difference with respect to the MC result is at most 3 ‰, as usual irrespective of the accuracy of the theory and of the choice of scale.…”

“…Theoretical uncertainties, possibly of comparable size (e.g. from missing higher-order terms in the QCD perturbative expansion), have started to be represented into PDF uncertainties only very recently [25,26].…”

“…• Table 9 collects the 166 parton luminosities contributing to the Z p T distribution measured by the CMS experiment at a centre-of-mass energy of 13 TeV [112]. The bin edges are: 20,22,26,28,32,37,43,52,65,85,120,160,190,220,250, 300, 400, 500, 800, 1500 GeV.…”