I outline some of the most recent developments in the global fit to parton distributions
performed by the MRST collaboration

Martin, AD

Roberts, RG

Stirling, WJ

Thorne, RS

English

arXiv

I outline some of the most recent developments in the global fit to parton distributions performed by the MRST collaboration

Apollo (Cambridge)

arXiv:hep-ph/0507015v1  1 Jul 2005Recent Progress in Parton Distributions andImplications for LHC PhysicsRobert S. Thorne∗, A. D. Martin†, R. G. Roberts∗∗ and W. J. Stirling†∗Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK†Institute for Particle Physics Phenomenology, University of Durham, DH1 3LE, UK∗∗Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, UKAbstract. I outline some of the most recent developments in the global fit to parton distributionsperformed by the MRST collaboration.At present there is a great deal of interest in the importanceof parton distributions forstudies at the LHC. This necessarily involves a certain kinematic range for the partons.The kinematic range for particle production at the LHC is shown in fig. 1. Partondistributions atx ∼ 0.001− 0.01 are vital for understanding the standard productionprocesses at the LHC. However, even smaller (and higher)x partons are required whenone moves away from zero rapidity, e.g. when calculating thetotal production cross-section of the heavy boson. As well as the central values one needs the uncertaintieson the partons, and there has been a lot of work on this [1]–[9]. This uncertainty isshown for the ¯u and d̄ quarks in fig. 2. Central rapidity production ofW,Z Higgs atthe LHC probesx = 0.006, which is ideal for the MRST partons. The current best10-710-610-510-410-310-210-1100100101102103104105106107108109fixedtargetHERAx1,2 = (M/14 TeV) exp(±y)Q = MLHC parton kinematicsM = 10 GeVM = 100 GeVM = 1 TeVM = 10 TeV66y = 40 224Q2    (GeV2 )xFIGURE 1. The kinematic range for particle production at the LHCFIGURE 2. Uncertainty on MRST ¯u andd̄ distributions, along with CTEQ6estimate for the uncertainty due to experimental errors isδσNLOW,Z (expt. pdf) =±2%, butwe note that there is a theoretical uncertainty, which is potentially large due to possibleproblems at smallx. This is because the large rapidityW andZ cross-sections samplevery smallx. However, the ratioσ(W+)/σ(W−) is agold-plated prediction, whereR± =σ(W+)σ(W−) ≃u(x1)d̄(x2)d(x1)ū(x2)≃u(x1)d(x1)and using the MRST2001E partonsδR±(expt. pdf) =±1.4%.Assuming all other uncertainties cancel, this is probably the most accurate SM cross-section test at LHC.This suggests thatσ(W ) or σ(Z) could be used to calibrate other cross-sections, e.g.σ(WH), σ(Z′). As an example we considerW plus Higgs production.σ(WH) is moreprecisely predicted thanσ(W ) because it samples quark pdfs at higherx and scale.However, the ratio shows no improvement in uncertainty, andcan be worse, see fig. 3.This is because partons in different regions ofx are often anti-correlated rather thancorrelated, partially due to sum rules. Similarly, there isno obvious advantage in usingσ(tt̄) as a calibration SM cross-section, except maybe for very particular, and ratherlarge,MH , where the gluon is probed in the same region for both. However, a light(SM or MSSM) Higgs is dominantly produced viagg → H, and the cross-section hasa small pdf uncertainty becauseg(x) at smallx is well constrained by HERA DIS data.The current best MRST estimate, forMH = 120GeV, isδσNLOH (expt pdf) = ±2−3%with less sensitivity to smallx thanσ(W ). This is a much smaller uncertainty than thatfrom higher-order corrections, for example [10],δσNNLLH (scale variation) = ±8%. Inconstrast, the error on predictions for very high-ET jets at the LHC is dominated by theparton uncertainties, because it is sensitive to the relativ ly poorly known high-x gluon.Different approaches to fits generally lead to similar uncertainties for measured quan-tities, but can lead to different central values [9]. For therue uncertainty one mustconsider the effect of assumptions made during the fit and thecorr ctness of fixed orderQCD. The failings of NLO QCD are indicated by some areas wherethe fit quality couldbe improved. There is a good fit to HERA data, but there are someproblems at the high-100 150 200 250 30001234  σ(W)  σ(WH)  σ(WH) / σ(W)pdf uncertainties on W, WH cross sections at LHC (MRST2001E) pdf uncertainty (percent)MH (GeV)FIGURE 3. The uncertainty onW and Higgs productionestQ2 at moderatex, i.e. in dF2/d lnQ2. Also the data require the gluon to be small ornegative at lowQ2 andx, and this is needed by all data (e.g. Tevatron jets), not justlow-Q2, low-x data. Other groups find similar problems with the gluon at lowx. CTEQ havea valence-like input gluon atQ20 = 1.69GeV2 which would marginally prefer to be neg-ative [11]. There is also instability in the physical, gluon-dominated quantityFL(x,Q2)going from LO to NLO to NNLO, seen in fig. 4. The exact NNLO coefficient function[12] has a very large effect, a possible sign of ln(1/x) corrections being required.As an example of the effect assumptions can make to the fit, MRST found only aFL LO , NLO and NNLO00.10.20.30.40.510-510-410-310-210-11F L(x,Q2 )Q2=2 GeV2NLOc fitNNLOc fitLO fit00.10.20.30.40.510-510-410-310-210-1Q2=5 GeV200.10.20.30.40.510-510-410-310-210-11xF L(x,Q2 )Q2=20 GeV200.10.20.30.40.510-510-410-310-210-1xQ2=100 GeV2FIGURE 4. The MRST prediction forFL(x,Q2) at LO, NLO and NNLOMRST 2004 NNLO DIS-type and D0 jet data, αS(MZ)=0.1167 , χ2= 64/82 pts00.510 50 100 150 200 250 300 350 400 4500.0 < | η  | < 0.500.510 50 100 150 200 250 300 350 400 4500.5 < | η | < 1.000.510 50 100 150 200 250 300 350 400 4501.0 < | η | < 1.5-0.500.510 50 100 150 200 250 300 350 400 4501.5 < | η | < 2.0ET (GeV)MRST 2004 NNLO DIS type and D0 jet data, αS(MZ)=0.1167 , χ2= 75/82 pts00.510 50 100 150 200 250 300 350 400 4500.0 < | η  | < 0.500.510 50 100 150 200 250 300 350 400 4500.5 < | η | < 1.000.510 50 100 150 200 250 300 350 400 4501.0 < | η | < 1.5(Data - Theory) / Theory-0.500.510 50 100 150 200 250 300 350 400 4501.5 < | η | < 2.0ET (GeV)FIGURE 5. Change in fit to D0 data with weak correctionsreasonable fit to jet data [13, 14], but needed to use the largesyst matic errors, while theresult is better for CTEQ6 [6] due to different cuts on other data, and a different type ofhigh-x parameterization. However, for the CTEQ6.1M partons, which give a good fit tothe jet data, the gluon is very hard asx → 1. MRST have recently utilised the fact that,under a change of scheme fromMS to DIS schemes, the scheme transformation willdominate the high-x gluon if valence quarks are naturally biggest at highx [15]. Thisallows a high-x gluon in theMS scheme which is determined from the quarks. At NLOtheχ2 for jets reduces from 154 to 116. This prescription works even b tter at NNLO –χ2 for the jets goes from 164 to 117, and the total∆χ2 = −79.Regarding highET jets, there has recently been a calculation of weak corrections [16],which implies thatσQCD → σQCD(1− 23CFαWπ log2(E2T /M2W )). This is a 12% correctionat ET = 450GeV, and the authors question the validity of recent partons due to this. Wehave studied the phenomenological impact, and the movementof bo h CDF and D0 datais relatively small, as shown in fig. 5. The totalχ2 changes by∼ 15 without refitting,which is significant but not a disaster. The correction is more important at higherET , butthere are positive real corrections to be added which dependon the jet definitions.There has also been a study of the inclusion of QED effects by MRST [17]. Theoverall effect is small, but does lead to small isospin violat n becauseupV (x) quarksradiate more photons thandnV (x) quarks. This is in the correct direction to reduce theNuTeV sin2θW anomaly [18], and with current quark masses it is halved. Ourapproachis supported by data on wide-angle photon scattering, i.e.ep → eγX [19] where the finalstate electron and photon have equal and opposite large transverse momentum.A much more important correction is NNLO QCD. The NNLO splitting functions arenow complete [20], but very similar to the average of previous best estimates, so leadto no large change in our previous NNLO partons [21]. The NNLOcorrections improvethe quality of the fit slightly, and reduceαS. However, to perform an absolutely correctNNLO fit we need not only exact NNLO splitting functions, but also require a rigoroustreatment of heavy quark thresholds [22], NNLO Drell-Yan cross-sections [23], and acomplete treatment of uncertainties. All this is in hand, and essentially full NNLOdetermination of partons will appear very soon. Only the NNLO jet cross-section ismissing. This is probably not too important – the NLO corrections themselves are notlarge, except at high rapidities, being∼ 10% at central rapidities. There are also goodNNLO estimates, i.e. the threshold correction logarithms,which are expected to be amajor component of the total NNLO correction [24]. These give a flat 3−4% correction,i.e. smaller than the systematic errors on the data. Hence, the mistakes from ignoringjets in the fits are bigger than the mistakes made at NNLO by notk wing the exacthard cross-section. There is reasonable stability order byo der for (quark-dominated)WandZ cross-sections, but this fairly good convergence is largely uaranteed because thequarks are fit directly to the data. This is much worse for gluon-d minated quantities,e.g.FL(x,Q2), which is unstable at smallx andQ2, as seen in fig. 4.Given this theoretical uncertainty, we devised an approachto look for the safe theoreti-cal regions, i.e. changeQ2cut andxcut , re-fit and see if the quality of the fit to the remainingdata improves and/or the input parameters change dramatically [25]. RaisingQ2cut from2GeV2 in steps, there is a slow, continuous and significant improvement for higherQ2up to> 10GeV2. Raisingxcut from 0 to 0.005, there is a continuous improvement, and ateach step the moderatex gluon becomes more positive. This led to the MRST2003 con-servative partons, which should be the most reliable methodof parton determination, butareonly applicable for a restricted range ofx andQ2. We also have NNLO conservativepartons, with similar cuts and improvement in fit quality, but the change in the partons isconsiderably less in this case because NNLO includes important theoretical correctionslacking at NLO. The variation in predictions with the cuts indicates the range of possibletheoretical errors. There is a large change inσW at the LHC since this is sensitive to thelow x region. The prediction is much more stable at NNLO, and LHC uncertainties are∼ 3−4% including the theoretical uncertainty. Hence,σW is a good candidate for lumi-nosity determination. CTEQ have repeated this type of analysis and see a similar type ofbehaviour with cuts [11], although much less dramatic. Withconservative cuts on datatheir input gluon again marginally prefers to have a negative component, confirming thata negative/small gluon at lowx andQ2 is not due to the data at lowx andQ2. They alsofind that the prediction forσW at the LHC moves down, but only a little, as more cutsare imposed. However, the loss of data with more cuts leads tolarger errors, and theχ2profile is very flat indeed in the downwards direction, as seenin fig. 6. There is not reallyany inconsistency with MRST. If one is cautious about the accura y of theory at lowxandQ2, the conclusion that the uncertainty is large on smallx-sensitive quantities holds.CTEQ claim no reason to be cautious. This theoretical uncertainty is not so much of anissue at NNLO though, as discussed above.In conclusion, we determine the parton distributions and predict cross-sections byperforming global fits, and the fit quality using NLO or NNLO QCD is fairly good.There are various ways of looking at uncertainties due to errrs on data, and theyare 1− 5% for most LHC quantities. Ratios often do not reduce uncertainties. QEDcorrections are small, but introduce important isospin asymmetry. The uncertainty fromusing different approaches is often comparable to or even larger than deriving from theFIGURE 6. CTEQχ2 profile forσW [11], where the wide profile is for conservative cutserrors on the data. For example, a model for the input form of the gluon can solve theapparent high-ET jet problem. Errors from higher orders/resummation are potentiallylarge. Conservative cuts onx andQ2 allow an improved fit to the remaining data, andaltered partons. CTEQ see some effects from this type of study, but these are muchsmaller. NNLO is much more stable than NLO, and more theoretically reliable. ForMRST full NNLO fits are imminent, and should become the new standard.REFERENCES1. M. Botje,Eur. Phys. J.C14 285 (2000).2. W. T. Giele, S. Keller and D. A. Kosower,hep-ph/0104052.3. S. I. Alekhin,Phys. Rev.D68 014002 (2003).4. CTEQ Collaboration: D. Stumpet al., Phys. Rev.D65 014012 (2002).5. CTEQ Collaboration: J. Pumplinet al., Phys. Rev.D65 014013 (2002).6. CTEQ Collaboration: J. Pumplinet al., JHEP 0207:012 (2002).7. H1 Collaboration: C. Adloffet al., Eur. Phys. J.C30 1 (2003).8. ZEUS Collaboration: S. Chekanovet al., hep-ph/0503274.9. A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne,Eur. Phys. J.C28 455 (2003).10. S. Catani,D. de Florian and M. Grazzini, JHEP 0307:028 (2003).11. J. Huston, J. Pumplin, D. Stump and W. K. Tung,hep-ph/0502080.12. S. Moch, J. A. M. Vermaseren and A. Vogt,Phys. Lett.B606 123 (2005);hep-ph/0504242.13. D0 Collaboration: B. Abbottet al., Phys. Rev. Lett.86 1707 (2001).14. CDF Collaboration: T. Affolderet al., Phys. Rev.D64 032001 (2001).15. A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, Phys. Lett.B604 61 (2004).16. S. Moretti, M. R. Nolten and D. A. Ross,hep-ph/0503152.17. A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, Eur. Phys. J.C39 155 (2005).18. G. P. Zelleret al., Phys. Rev. Lett.88 091802 (2002).19. ZEUS collaboration: S. Chekanovet al., Phys. Lett.B595 86 (2004).20. S. Moch,et al., Nucl. Phys.B688 101 (2004);Nucl. Phys.B691 129 (2004).21. A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, Phys. Lett.B531 216 (2002).22. R. S. Thorne,hep-ph/0506251, these proceedings.23. C. Anastasiou,et al, Phys. Rev. Lett.91, 182002 (2003);Phys. Rev.D69, 094008 (2004).24. N. Kidonakis and J. F. Owens,Phys. Rev.D63 054019 (2001).25. A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, Eur. Phys. J.C35 325 (2004).

Recent progress in parton distributions and implications for LHC physics

Abstract

Similar works

Full text

Available Versions

Apollo (Cambridge)