We summarise recent developments in the path towards the "MMHT19" parton distribution functions. We concentrate on the extraction of the strange quark upon the improvement of theoretical calculations for NNLO charged current cross sections; the effect of an extension of our parameterisation; and the role of correlated uncertainties in some data sets which prove difficult to fit

Bailey, S

Cridge, T

Harland-Lang, L

Martin, A

Nathvani, R

Thorne, R

English

UCL Discovery

Updates of PDFs in the MMHT frameworkR.S. Thorne∗Department of Physics and Astronomy,University College London, WC1E 6BT, UKE-mail: robert.thorne@ucl.ac.ukS. BaileyRudolf Peierls Centre, Beecroft Building,Parks Road, Oxford, OX1 3PU, UKE-mail: shaun.bailey@physics.ox.ac.ukT. CridgeDepartment of Physics and Astronomy,University College London, WC1E 6BT, UKE-mail: t.cridge@ucl.ac.ukL.A. Harland-LangRudolf Peierls Centre, Beecroft Building,Parks Road, Oxford, OX1 3PU, UKE-mail: lucian.harland-lang@physics.oxford.ac.ukA.D. MartinInstitute for Particle Physics Phenomenology,University of Durham, DH1 3LE, UKE-mail: A.D.Martin@durham.ac.ukR. NathvaniDepartment of Physics and Astronomy,University College London, WC1E 6BT, UKE-mail: ricky.nathvani.15@ucl.ac.ukWe summarise recent developments in the path towards the “MMHT19” parton distribution func-tions. We concentrate on the extraction of the strange quark upon the improvement of theoreticalcalculations for NNLO charged current cross sections; the effect of an extension of our parame-terisation; and the role of correlated uncertainties in some data sets which prove difficult to fit.XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS20198-12 April, 2019Torino, Italy∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/arXiv:1907.08147v1  [hep-ph]  18 Jul 2019MMHT – DIS2019 R.S. ThorneThe MMHT2014 PDFs [1] were the last major update in the MRST/MSTW/MMHT family ofPDFs. They included a variety of LHC data in their determination, but at that point the constrainton the PDFs was almost entirely from older fixed target and HERA DIS data, and some Drell-Yanand jet data from Tevatron experiments. Soon after the publication of the MMHT2014 PDFs westudied the effect of including the final HERA total cross section measurements [2], noting onlyminor changes in the central values and uncertainties [3]. The inclusion of a wide variety of newLHC data was considered in [4]. Most new data was fit well, and produced relatively small changesin both the central values and the uncertainties of the PDFs, most notably in the decompositioninto flavours and into valence and sea quarks. A more significant change was induced when theATLAS W,Z data in [5] were included. A relatively good fit could be achieved (∼ 110/61), butthis required a modification of the small-x valence quarks and, in particular, an increase in thestrange quark. This latter change was less pronounced than that found by ATLAS in [5], probablydue to the inclusion of fixed target charged current DIS dimuon production data [6], which is thetraditional type of constraint on the strange quark in global PDF fits and prefers a lower value thanthe ATLAS data.BR(c→ µ) CCFR/NuTeV χ2 ATLAS W,Z χ2 Total χ2MMHT+HERAII 0.090 120.5 3526.3MMHT+HERAII (NNLO dimuon ) 0.102 122.7 3527.3MMHT+HERAII (NNLO VFNS dimuon) 0.101 123.9 3531.3MMHT+HERAII+ATLAS(W,Z) 0.073 127.3 108.6 3684.7MMHT+HERAII+ATLAS(W,Z) (NNLO dimuon ) 0.084 137.8 106.8 3688.4MMHT+HERAII+ATLAS(W,Z) (NNLO VFNS dimuon) 0.086 137.0 106.8 3688.5Npts 126 61 3337Table 1: The branching ratio for charm mesons to muons, and the χ2 values for fit variants before and afterthe inclusion of the data in [5] and the correction to the NNLO dimuon cross sections.However, the full NNLO corrections to heavy flavour charged current DIS have only recentlybeen calculated [7], and all PDF analyses so far have used either NLO cross sections, or NNLOapproximations (as in MMHT), in NNLO PDF extractions. The NNLO corrections are of order−10% in the region x = 0.01 relevant for the main strange quark sensitivity of the ATLAS data.This implies a larger strange quark may be needed to best fit the dimuon data and better potentialcompatibility with the ATLAS data. We have included this full NNLO calculation in a completePDF fit for the first time, and modified our variable flavour number scheme (VFNS) for chargedcurrents to include the calculation, which is for fixed flavour number (this required some minorcorrections to the details of our charged current VFNS). The results of the fit quality are shownin Table 1. We note that when the ATLAS W,Z data are not included the inclusion of the correctNNLO makes little difference to fit quality, though it does raise the preferred value of the branchingratio for c→ µ in the dimuon fit a little, consistent with a smaller charm cross section. The inputvalue of the branching ratio is 0.092±10%, very consistent with these fits. When the ATLAS W,Zdata are added using the standard MMHT treatment of dimuons the fit to the dimuon data deterio-rates a little, but the branching ratio also has to take a very low value of 0.073 to accommodate theraised strange quark. With the full NNLO corrections the dimuon fit actually worsens, but that toATLAS W,Z data improves slightly and the global χ2 changes by less than 5 units. The branchingratio increases back to 0.086, however, demonstrating more genuine compatibility between the fitto dimuon data and to ATLAS data. The effect on s+ s̄ is shown in Fig. 1. With both the old1MMHT – DIS2019 R.S. ThorneMMHT treatment and the corrected NNLO cross section inclusion of the ATLAS W,Z data raisesthe strange quark for x above 0.001 and reduces the uncertainty. However, the rise is a little lesssignificant when the full NNLO is used, with the updated strange central value straying outside theone sigma error band of the fit without ATLAS W,Z data only marginally near x = 0.02.Figure 1: The strange over the light quark average and change in strange on addition of ATLAS W,Z datawithout full NNLO as in MMHT2014 (top), and with full NNLO and the updated VFNS (bottom).With the inclusion of more constraining LHC data we examine the introduction of more freeparameters in our functions for the input PDFs. In [8] we changed our previous parameterisation toone with most PDFs parameterised as A(1−x)ηxδ (1+∑ni=1 aiTi(1−2x12 )), where Ti(1−2x12 )) areChebyshev polynomials. We also examined how many were needed to fit data of a given precision.At the time it was concluded that 4 (at most) was sufficient. However, for (d̄− ū)(x,Q20) by defaultwe still used the old input form with only 4 parameters in total. We now try putting this distributionon an equal footing with the other PDFs by using Chebyshev polynomials, i.e.(d̄− ū)(x,Q20) = A(1− x)ηsea+2xδ (1+ γx+∆x2)→ A(1− x)ηsea+2xδ (1+∑mi=1 aiTi(1−2x12 )),where we first choose m = 4. This improves the global fit by about 10 units and eases tensionbetween ATLAS W,Z data and E866 Drell Yan ratio data [9].However, from the studies in [8] it was clear that once PDF precision of greater than 1%was possible 5 or 6 polynomials would be required. Hence we extend the parameterisation foruV ,dV ,sea,(d̄− ū) and (s+ s̄) sequentially to the form with n = 6 (though for (s+ s̄) the small-xpower and two coefficients remain tied to the sea). The gluon parameterisation is of a different2MMHT – DIS2019 R.S. Thorneform, with two separate terms, but here we increase the free parameters from 7 to 9. Comparedto MMHT2014, this increases our number of free parameters in total from 36 to 50. The mainimprovements in the fit χ2 (to essentially the same data as in [4]) are after the extension to 6polynomials of (d̄− ū)(x,Q20), from additionally extending dV (x,Q20) (uV (x,Q20) is not significant),and g(x,Q20) (sea(x,Q20) and s+(x,Q20) are not significant). The improvements to individual datasets are shown in Table 2. There is a reduction in tension between DY ratio data and LHC data,and an improvement in LHC lepton asymmetry data, and some fixed target deuteron data. Theimprovement due to the gluon is spread over data sets and due only partially to HERA data.Data set −∆χ2 (d̄− ū) −∆χ2 (d̄− ū),dV −∆χ2 AllTotal 17.6 34.0 48.9BCDMS F p2 -4.6 -3.3 -2.7BCDMS Fd2 -2.7 4.9 8.5NMC Fn2 /Fp2 6.5 6.1 6.0NuTeV FN3 -0.3 1.7 3.2E866 σ(pd)/σ(pp) 8.2 10.1 11.0NuTeV dimuon 0.7 1.0 3.0HERA I+II σ(e+p) 920 GeV 1.1 1.7 4.6CMS pp→ l+l− 0.7 1.8 3.1D0 σ(e+)−σ(e−) -1.2 -3.4 -1.4CMS 8 TeVσ(l+)−σ(l−) 4.4 5.0 4.6ATLAS 7 TeV W,Z -0.5 2.2 4.3CMS 7 TeV jets -0.5 0.2 3.2Table 2: The χ2 improvement for various data sets when extra parameters are added.When determining the PDF uncertainties we go from 25 eigenvector pairs in MMHT2014 to30, one extra parameter for each PDF other than the light sea (and s− s̄). 20 parameters are fixed attheir best fit values – any extra eigenvectors would be highly non-quadratic and lead to very littleextra uncertainty. The mean tolerance T = 3.31, similar to MMHT2014. 27 eigenvector directionsare constrained primarily by LHC data sets, largely 7 TeV ATLAS W,Z data and CMS W data.E866 Drell Yan asymmetry is vital for constraining d̄− ū. Tevatron data of various types are theprimary constraint for 8 eigenvectors, and fixed target DIS data still constrains 12 eigenvectors(mainly high-x quarks). Hence, a fully global fit is necessary for full constraint. Some of theresulting PDFs are shown in Figs. 2 and 3. There is a significant change in the shape of thedV distribution. The uncertainty at both large and small x increases due to the extra freedom.dV interplays with (d̄ − ū), also shown in Fig. 2, and the latter becomes flatter over the rangex = 0.01−0.1. The gluon, shown in Fig.3, stays well within previous uncertainties, except at veryhigh x where the uncertainty is huge and larger with the new parameterisation. ū, also shown inFig. 3, is generally a little smaller, due to the increase in (s+ s̄) already discussed, and again hasincreased uncertainty at x > 0.6. We note that despite more freedom in (d̄− ū) the parameterisationstill leads to a very quick approach to 0 at low x. This is likely unphysical, and we have recentlytried parameterising d̄/ū instead, using the same number of parameters. Results are preliminary,but a small decrease in χ2 occurs, with a greater uncertainty as x→ 0 (though d̄/ū→ 1 to very3MMHT – DIS2019 R.S. Thornegood accuracy), and with a ratio of d̄/ū < 1 at low x, but only at about one sigma level.Figure 2: The NNLO down valence (left) and d̄− ū (right) for the fits with extended parameterisation.Figure 3: The NNLO gluon (left) and ū (right) for the fits with extended parameterisation.As well as these main results on the way to presenting the new updated “MMHT2019” PDFs,we note some other recent developments. In a previous study [10] we found difficulty in fittingATLAS 7 TeV inclusive jet data [11], even with full NNLO [12]. To alleviate this we investigateddecorrelation of some systematic uncertainties between rapidity bins, finding dramatic improve-ment is we consider just two uncertainties, and little sensitivity of the gluon to the decorrelationprocedure. This led to more sophisticated proposals for similar methods in [13]. We have alsorecently tried fitting to more than one of the top quark differential distributions in [14], which ispossible due to the knowledge of statistical correlations between distributions[15], again using fullNNLO [16]. We see a similar picture, i.e. one can fit some individual distributions well, but not si-multaneously. This is due to inconsistencies in the required shifts related to correlated systematics(the same result is noted and studied in [15] and by the CT collaboration). In this case the im-portant systematics are all related to Monte Carlo generation, and not obviously as well correlatedas presented. Significant improvement can be achieved on relaxation of correlations. However, inthis case the gluon is more sensitive to the details of the treatment, and some distributions requiredecorrelation within that particular distribution to enable a good fit. More details will be presentedin the future.We also note that we have completed the study of the inclusion of QED effects and the photonparton distribution [17]. We use essentially the PDFs of [3] as a baseline and use the LUX [18, 19]procedure for the input photon, making it fully consistent with the MMHT framework, includingthe production of the photon PDF in the neutron. We also examine the impact on high-mass Drell-Yan data, noting that the photon initiated contributions are sometimes smaller than the QED effectson quark evolution. We have made grids available, and in particular have separated the elastic andinelastic contributions to the photon PDF.4MMHT – DIS2019 R.S. ThorneAcknowledgementsLHL thanks the Science and Technology Facilities Council (STFC) for support via grant awardST/P004547/1. RST and TC thank the Science and Technology Facilities Council (STFC) forsupport via grant awards ST/P000274/1. RN thanks the Spreadbury Fund. SB thanks the STFC.References[1] L. A. 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Updates of PDFs using the MMHT framework

https://discovery.ucl.ac.uk/id/eprint/10086824/1/paper_1907.08147.pdf

Updates of PDFs using the MMHT framework

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