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Parton distributions incorporating QED contributions
A. D. Martin, R. G. Roberts, W. J. Stirling, R. S. Thorne
TL;DR
Previous investigations generally evolved QCD-only partons with QED effects rather than determining a new QED-corrected set through a global fit. The authors perform a global parton analysis of hard-scattering data using QED-modified DGLAP evolution and QED-corrected starting distributions. Quark and gluon distributions remain extremely similar to standard MRST distributions, while the photon distribution exceeds sea quarks at the highest x values.
Problem
Previous investigations generally evolved QCD-only partons with QED effects rather than determining a new QED-corrected set through a global fit.
Source: §1 · p. 2Method
The authors perform a global parton analysis of hard-scattering data using QED-modified DGLAP evolution and QED-corrected starting distributions.
Source: §1 · pp. 2–3Results
Quark and gluon distributions remain extremely similar to standard MRST distributions, while the photon distribution exceeds sea quarks at the highest x values.
Source: §4 · p. 8Takeaways & Limitations
Different QED evolution of up- and down-type quarks introduces isospin violation, and the analysis generates proton and neutron photon distributions.
Source: §1 · p. 3, §4 · p. 8The analysis notes that different factorisation scales could, in principle, be introduced for QCD and QED collinear-divergence subtraction.
Source: §2 · p. 3
Abstract
from arXiv · showhide
We perform a global parton analysis of deep inelastic and related hard-scattering data, including ${\cal O}(\alpha_{\rm QED})$ corrections to the parton evolution. Although the quality of the fit is essentially unchanged, there are two important physical consequences. First, the different DGLAP evolution of u and d type quarks introduces isospin violation, i.e. $u^p \neq d^n$, which is found to be unambiguously in the direction to reduce the NuTeV $\sin^2\theta_W$ anomaly. A second consequence is the appearance of photon parton distributions $\gamma(x,Q^2)$ of the proton and the neutron. In principle these can be measured at HERA via the deep inelastic scattering processes $e N \to e\gamma X$; our predictions are in agreement with the present data.
1 Introduction
QED collinear effects can be incorporated into hadron parton distributions by modifying DGLAP evolution and generating a photon distribution. The paper performs a global fit with these corrections, whose evolution effects are small overall but introduce isospin violation and a potentially measurable photon distribution.
1 Introduction
- QED collinear logarithms are absorbed into parton distributions, modifying DGLAP evolution as emitted photons carry away quark momentum and generating a proton photon distribution.This gives a consistent treatment of this part of the electroweak correction in hard-scattering processes with initial-state hadrons.Source: §1 · p. 2
- QED effects have a small impact on most quark and gluon evolution compared with NNLO QCD contributions, while gluon evolution is largely unaffected.The passage attributes the smaller effect to the absence of the large logarithms that accumulate at higher QCD orders.Source: §1 · p. 2
- The paper addresses the lack of a consistent global determination of QED-corrected partons by fitting a new set to data rather than evolving QCD-only partons.The authors report that previous investigations generally began with standard QCD-only partons.Source: §1 · p. 2
- Different QED evolution of up- and down-type quarks introduces isospin violation, with a direction relevant to the NuTeV sin^2 θW measurement.The photon distribution may also be measurable in ep collisions at HERA through wide-angle Compton scattering.Source: §1 · p. 3
2 DGLAP formalism including QED effects
The section introduces proton parton evolution equations that include QED effects alongside QCD at leading order. It also notes momentum conservation and the possibility of separating the QCD and QED factorization scales.
2 DGLAP formalism including QED effects
- The factorized QED collinear divergences lead to proton parton evolution equations at leading order in both αS and α.The supplied equation fragments include terms involving Pqg and Pgg.Source: §2 · p. 3
- The formalism states that momentum is conserved.The accompanying equation fragment does not provide enough readable detail to specify its full expression.Source: §2 · p. 3
- Separate factorization scales for QCD and QED collinear subtraction are raised as a possibility.The passage is incomplete and does not state the full treatment of that possibility.Source: §2 · p. 3
F (QCD), µ2
The fit accounts for proton–neutron isospin breaking, but the additional freedom can substantially increase the number of poorly determined parameters. The authors therefore restrict starting-scale isospin violation to valence quarks; sea quarks and gluons begin symmetric, with only weak violation from evolution.
F (QCD), µ2
- For DIS, the conventional choice is to set the factorization scale µF^2 equal to Q^2.The authors set aside the extra complication of separate QCD and QED factorization scales.Source: F (QCD), µ2 · p. 3
- A fully independent proton–neutron fit could more than double the parameters, many of which would be poorly determined.Isospin breaking in the distributions makes evolution and fitting significantly more complex.Source: F (QCD), µ2 · p. 4
- At the starting scale, isospin violation is assumed to reside only in valence quarks because QED radiation is dominated by high-x quarks.This is the simpler approximation adopted to retain the essential physics.Source: F (QCD), µ2 · p. 4
- The starting sea-quark and gluon distributions are taken to be isospin symmetric, although evolution violates that symmetry weakly.The passage identifies these starting distributions as S^p = S^n and g^p = g^n.Source: F (QCD), µ2 · p. 4
3 The starting distributions
The starting distributions model photon emission from valence quarks and impose a small, momentum-conserving isospin difference between proton and neutron valence inputs. The resulting differences have the expected direction at high x, while alternative starting-distribution models give similar features and are more sensitive to quark-mass choices.
3 The starting distributions
- The starting photon distribution is modeled as leading-log one-photon emission from valence constituent quarks.The authors characterize this as a model and argue that O(α) photon inputs negligibly affect quark and gluon evolution.Source: §3 · p. 4
- The valence difference is modeled by a small function with vanishing zeroth moment and a first moment chosen to conserve momentum.The chosen function is intended to have a valence-like shape as x approaches 0 and 1; ε is fixed by momentum conservation.Source: §3 · p. 5
- For the new NLO fit, the momentum-fraction difference used to set ε is 0.0746, giving ε = 0.0325.The denominator is the proton's valence up momentum fraction minus twice its valence down momentum fraction.Source: §3 · p. 5
- The starting-scale neutron-to-proton valence ratios depart from unity in the expected direction: fewer high-x up quarks in the proton and more down quarks.The passage attributes the pattern to increased photon radiation and identifies the excess down quarks relative to neutron up quarks.Source: §3 · p. 5, Figure 1 · p. 6
- Alternative physically motivated input models yield very similar distributions and asymmetries, while results are more sensitive to quark-mass choices.The passage says the essential features remain identical across the alternative models it discusses.Source: §3 · p. 6
4 Global analysis including QED effects
The global NLO and NNLO fits include QED-corrected evolution, with separate proton and neutron DGLAP equations and isospin-violating valence starting distributions. Fit quality changes little overall, while the resulting valence isospin violation shifts the NuTeV sin²θ_W measurement downward.
Fit quality
- The NLO QED fit has χ² about 15 higher than the standard NLO fit, while the NNLO QED fit is 3 units lower than the standard NNLO fit.The NLO increase reflects tension involving gluon momentum and αS; the authors say it is not evidence that QED effects should be ignored.Source: §4 · p. 7
Fit procedure
- The fits use the same input data as the standard MRST study and separate DGLAP evolution for protons and neutrons, with isospin violation confined to valence starting distributions.The sea quarks and gluon are assumed isospin symmetric at the starting scale; the fit strategy also assumes the input data have not had incoming-quark photon-emission corrections applied.Source: §4 · p. 7
Fit quality
- The QED fit slightly improves descriptions of CCFR F3, BCDMS deuterium, and E866 hydrogen/deuterium data, but the changes are too small to support definite conclusions.The authors identify all three datasets as sensitive to QED-induced isospin violation.Source: §4 · p. 8
Mass prescription
- Using 300 MeV constituent quark masses gives ε=0.0074 rather than ε=0.0325 and improves the NLO χ² by only about 2 units, leaving no clear global-fit preference between mass prescriptions.At NNLO the improvement is even smaller; the authors favor current masses because photon radiation is perturbative.Source: §4 · p. 8
Parton distributions
- At Q²=20 GeV², the photon distribution exceeds the sea quarks at the highest x, while the neutron photon distribution is smaller at large x and similar to the proton at very small x.The proton and neutron distributions are shown in Figures 2 and 3; Figure 4 illustrates the valence-quark isospin difference.Source: §4 · p. 8, Figure 2 · p. 9, Figure 3 · p. 10
NuTeV implications
- At Q²=2 GeV², QED-induced isospin violation shifts measured sin²θ_W by −0.0018, and the shift reaches −0.0029 at Q²=20000 GeV².The authors estimate acceptance cuts may reduce the observed effect by 10–20%; constituent quark masses could reduce it by up to about a factor of four.Source: §4 · pp. 11–12
5 Measuring the photon parton distribution, γ(x, Q2)
Wide-angle Compton scattering in ep → eγX offers a direct way to probe the proton photon distribution; the predicted cross section agrees with ZEUS data, supporting the analysis and its current-quark-mass choice.
5 Measuring the photon parton distribution, γ(x, Q2)
- Wide-angle ep → eγX scattering probes γp by convoluting it with the QED Compton subprocess eγ → eγ.The schematic includes an s-channel diagram and an additional contribution from a virtual u-channel electron.Source: §5 · p. 12, Figure 5 · p. 13
- The ZEUS measurement applies cuts of 5 < Eγ_T < 10 GeV, −0.7 < ηγ < 0.9, Q2 > 35 GeV2, Ee′ > 10 GeV, and 139.8° < θe′ < 171.8°.Source: §5 · p. 13
- PYTHIA and HERWIG underestimate the measured rate by factors of 2 and 8, respectively, and do not reproduce all reported kinematic distributions.Source: §5 · p. 13
- The predicted cross section agrees well with ZEUS data, supporting the analysis and its choice of current quark masses for the initial photon distribution.Using constituent quark masses instead gives a prediction of 3.6 pb, in disagreement with the measured value.Source: §5 · p. 14
- The reported measurement samples xγ in a fairly narrow range centered on approximately 0.005; the paper suggests extending it to measure γp as a function of xγ.Source: §5 · p. 14