Abstract
Building upon the most recent CT18 global fit, we present a new calculation of the photon content of the proton based on an application of the LUX formalism. In this work, we explore two principal variations of the LUX ansatz. In one approach, which we designate "CT18lux," the photon PDF is calculated directly using the LUX formula for all scales, $\mu$. In an alternative realization, "CT18qed," we instead initialize the photon PDF in terms of the LUX formulation at a lower scale, $\mu\! \sim\! \mu_0$, and evolve to higher scales with a combined QED+QCD kernel at $\mathcal{O}(\alpha),~\mathcal{O}(\alpha\alpha_s)$ and $\mathcal{O}(\alpha^2)$. While we find these two approaches generally agree, especially at intermediate $x$ ($10^{-3}\lesssim x\lesssim0.3$), we discuss some moderate discrepancies that can occur toward the end-point regions at very high or low $x$. We also study effects that follow from variations of the inputs to the LUX calculation originating outside the pure deeply-inelastic scattering (DIS) region, including from elastic form factors and other contributions to the photon PDF. Finally, we investigate the phenomenological implications of these photon PDFs for the LHC, including high-mass Drell-Yan, vector-boson pair, top-quark pair, and Higgs associated with vector-boson production.
Highlights
With the steady accumulation of copious experimental data at the LHC, we have entered into a high-precision era for hadron-collider physics
To perform consistent higher-order calculations with EW corrections included in the initial state of parton-scattering processes at the LHC, it is necessary to employ a set of parton distribution functions (PDFs) in which the photon appears as an active, partonic constituent of the proton
IV, we present the result of the DGLAPdriven CT18qed and compare various photon-PDF sets to different choices of the input scale, μ0, where the photon PDF is provided by the LUX master formula
Summary
With the steady accumulation of copious experimental data at the LHC, we have entered into a high-precision era for hadron-collider physics. The MMHT2015qed PDF set was released a number of years ago These PDFs were generated in a global fit by adopting the LUX formalism at a low starting scale, μ0 1⁄4 1 GeV, for the photon PDF, and evolving to higher scales using QED-corrected DGLAP evolution equations [28]. As we shall discuss in greater detail below, implementation of the LUX formalism, which involves integrations of the proton’s unpolarized electromagnetic structure functions, F2;L, over broad Q2, can be sensitive to higher-twist (i.e., twist-4) and other nonperturbative QCD contributions These effects are unsuppressed at low Q2 and must be explicitly modeled; this is necessary for both theoretical accuracy and uncertainty quantification, for which an estimate of the possible model and parametric dependence is important. In Appendix B, we detail the physical factorization and MS-conversion terms that appear in the LUX formalism
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