Ad Lucem: QED parton distribution functions in the MMHT framework

Abstract

We present the MMHT2015qed PDF set, resulting from the inclusion of QED corrections to the existing set of MMHT Parton Distribution Functions (PDFs), and which contain the photon PDF of the proton. Adopting an input distribution from the LUXqed formulation, we discuss our methods of including QED effects for the full, coupled DGLAP evolution of all partons with QED at O(α), O(αα S ), O(α 2 ). While we find consistency for the photon PDF of the proton with other recent sets, building on this we also present a set of QED corrected neutron PDFs and provide the photon PDF separated into its elastic and inelastic contributions. The effect of QED corrections on the other partons and the fit quality is investigated, and the sources of uncertainty for the photon are outlined. Finally we explore the phenomenological implications of this set, giving the partonic luminosities for both the elastic and inelastic contributions to the photon and the effect of our photon PDF on fits to high mass Drell-Yan production, including the photon-initiated channel.

A new approach to modelling elastic and inelastic photon-initiated production at the LHC: SuperChic 4

“…In more detail, the structure function receives contributions from: elastic photon emission, for which we use the A1 collaboration [43] fit to the elastic proton form factors; CLAS data on inelastic structure functions in the resonance W 2 < 3.5 GeV 2 region, primarily concentrated at lower Q 2 due to the W 2 kinematic requirement; the HERMES fit [44] to the inelastic low Q 2 < 1 GeV 2 structure functions in the continuum W 2 > 3.5 GeV 2 region; inelastic high Q 2 > 1 GeV 2 structure functions for which the pQCD prediction in combination with PDFs determined from a global fit provide the strongest constraint (we take the ZM-VFNS at NNLO in QCD predictions for the structure functions as implemented in APFEL [45], with the MMHT2015qed_nnlo PDFs throughout, though in the MC the PDF can be set by the user). The inputs we take are as discussed in the MMHT15 photon PDF determination [46], which itself is closely based on that described in [1,2] for the LUXqed set. However, we note that our calculation makes no explicit reference to the partonic content of the proton itself, and as discussed in detail in [3] provides by construction a more precise prediction than the result within collinear factorization that uses such a photon PDF.…”

“…The survival factor is modelled in a rather similar way to the MC implementation. To compare more directly, we have in fact modified the photon PDF to more closely match the MMHT15 photon [46], while we also show the effect of varying the factorization/renormalization scale by a factor of 2 around the central value of μ = M ll to give an estimate of the uncertainty in the prediction in the inclusive case. We can see that broadly the analytic results are in good agreement with the more precise MC implementation, with the approximate treatment of LO collinear factorization framework and the rapidity veto giving a fair description of the overall trends.…”

Collinear electroweak radiation in antenna parton showers

“…Finally, hard processes initiated by vector bosons have been considered for a long time [80,81]. PDF sets with QED corrections have been available for some time [82][83][84][85], and recent progress was made towards PDFs with complete electroweak corrections [86][87][88]. The current shower implementation only allows for the emission of vector bosons from the initial state.…”

NLO QCD+EW predictions for tHj and tZj production at the LHC

“…Second, in order to evaluate flavour-scheme uncertainties, both a 4FS and a 5FS version of the same PDF fit have to be available. Therefore, the only three possible options at the moment are: NNPDF3.0 [41,42], NNPDF3.1 [43,44] and MMHT2014/MMHT2015 [45,46]. All these three sets are accurate up to NNLO in QCD and NLO in QED accuracy and include a photon density based on the LUXqed parameterisation [47,48].…”