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 {mathcal {O}}(alpha ), {mathcal {O}}(alpha alpha _{S}), {mathcal {O}}(alpha ^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.
Highlights
The photon Parton Distribution Functions (PDFs) corresponds to the flux of emitted photons within the context of the equivalent photon approximation, and as discussed in some of the early work on this [18], the contributions from elastic and inelastic emission to the photon PDF are directly related to the corresponding structure functions (F1e,l2, F1i,n2el ) probed in lepton–proton scattering
First we discuss the effect of a kinematic cut on the photon, as introduced by the lower limit of the integral in Q2 in the expression for xγ (x, Q2), which as discussed in Sect. 2.2 has the effect of introducing an effective cut on the photon PDF at high x during the evolution. This removal of photon contributions at high x is a target mass correction, which is not required to obey the momentum conservation of the partons ordinarily found in DGLAP evolution and introduces small amounts of violation into Eq (14) of O(10−3 %)
Our resultant photon PDF, xγ (x, Q2), based on a similar methodology for the input to that of LUXqed is seen to closely resemble others in the literature, despite several modifications made to take into account our lower starting scale for the evolution and the fact that we use our own PDFs
Summary
We describe how the MMHT framework has been modified to incorporate the QED splitting kernels in DGLAP evolution and the form we take for the input distribution of the photon, and discuss their effect on the final set of partons and the corresponding PDF uncertainties. 2.1 Baseline QCD fit Throughout this paper, in order to meaningfully interpret the effects of including QED effects, we will compare the new partons to a baseline set of PDFs evolved and fit solely with QCD kernels (at, unless explicitly stated, NNLO). This set differs from the most recent public release of partons, MMHT2014 [29]. This more closely corresponds to the set described in [30], where the HERA Run I + II combined cross section data [31] have been included in the fit. We refer to this as the MMHT2015 PDF set and the PDFs with the QED effects included as MMHT2015qed
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