PDF4LHC update +SCET re-weighting update

PDF4LHC update +SCET re-weighting update J. Huston Michigan State University Tevatron Higgs meeting April 18, 2011

PDF4LHC benchmarks/recommendations We ve called these interim. How/when do we want to update them? In the next few months, we ll have NNLO PDFs for all 6 groups represented in these reports. We ll also be able to confront a wide variety of LHC data with predictions from these PDFs, at a reasonable precision level. More benchmarking?

Last meeting: Mar 7 http://indico.cern.ch/ conferencedisplay.py?confid=127425

Chiara Mariotti representing the LHC Higgs Cross Section Working Group

Chiara Mariotti

W lepton asymmetry at the LHC my talk CT10/10W should look similar to CTEQ6.6 here

NMC data: F 2 vs σ l NMC experiment reported both F 2 and differential cross section measurements l Value of R used for low x is inconsistent with current world knowledge l Recent paper by Alekhin, Bluemlein and Moch (arxiv: 1101.5261) pointed this out and showed that in ABKM analysis, the use of R (rather than σ) results in an increase in the predictions for Higgs production at both the Tevatron and LHC correct way of including data is with the cross sections l CTEQ PDFs have always used the NMC values of F 2 l We tried replacing F 2 by the differential cross sections and find little difference in the fit results l Similar to conclusions of MSTW and NNPDF

Results l Blue band is CT10 uncertainty l Green: replace NMC F2 by cross section data l Red: include Run II W electron asymmetry data with various weights l By definition, α s (m Z ) is fixed at 0.118 (world average) m h =160 at 7 TeV m h =160 at Tevatron

Issues regarding jet cross sections from Jet Pair Production in Powheg, arxiv:1012.3380 note that theory/data has a slope not evident with fixed order comparisons (NLO corrected by UE/hadronization) also observed in ATLAS comparisons an effect we need to understand

Correlations (see PDF4LHC note) l l Consider a cross section X(a) i th component of gradient of X is l l l l Now take 2 cross sections X and Y or one or both can be pdf s Consider the projection of gradients of X and Y onto a circle of radius 1 in the plane of the gradients in the parton parameter space The circle maps onto an ellipse in the XY plane The angle φ between the gradients of X and Y is given by If two cross sections/pdf s are very correlated, then cosφ~1 uncorrelated, then cosφ~0 anti-correlated, then cosφ~-1 l The ellipse itself is given by

Correlations among Higgs channels/backgrounds can be used for combination of Higgs channels, subtraction of backgrounds

PDF Errors (in Blackhat+Sherpa ntuples) Better than what is done in MCFM (as far as disk space is concerned); PDF errors are generated on-the-fly through calls to LHAPDF. But then don t store information for individual eigenvectors. for W+n jet NLO analysis that Brian Martin and I are carrying out Suppose I want to calculate the PDF errors for a ratio (say n+1 jet/n jet)

Using correlations to determine PDF uncertainties For each event, calculate the gradient direction (22 eigenvector directions for CTEQ6.6). Keep a running (weighted) determination of this gradient as you cycle through all events. Suppose now you want to understand the cancellation in PDF errors between two cross sections, again like σ n+1jets /σ n jets. Calculate the correlation cosine. Now you can calculate the error on the ratio taking into account the correlation in the errors, while only storing a 22 dimensional array per cross section.

Correlations, continued so very strong correlation (0.8) between the Higgs cross section and the hyperplane formed by the first 11 (of 22) eigenvectors in CTEQ6.6 low number eigenvectors have quadratic χ 2 behavior one interesting angle to calculate is the angle between the gradient for a particular physics process and the hyperplane formed by the first n eigenvectors take gg->higgs (120 GeV) eigenvector cos φ =1 0.028 <=2 0.077 <=3 0.077 <=4 0.534 (4 has impact) <=5 0.551 <=6 0.553 <=7 0.602 <=8 0.604 <=9 0.609 <=10 0.808 <=11 0.808

On to NNLO l CTEQ/TEA is working on first NNLO PDFs, with goal of showing at DIS2011 l NNLO evolution for α s and PDFs provided by HOPPET l Matching coefficients relating PDFs in N f and N f+1 from Smith, van Neerven et al l NNLO Wilson coefficient functions for F 2c (x,q), F Lc (x,q) l Work in progress MSbar masses as input; pole masses in Wilson coefficient functions and PDF evolution verifying cancelllations between classes of diagrams at Q~mc and Q>>mc ACOT reduces to FFNS at Q~m c and to ZM at Q>>m c

Sergey Alekhin

Juan Rojo (NNPDF)

Ronan McNulty (LHCb)

Frank Tackmann

If τ=10 GeV corresponds to p T veto =20 GeV then expect large reduction in cross section and increase in uncertainty. But Monte Carlo seems to suggest that the correspondence is more like 1 to 1. Importance of non-leading logs. Smaller reduction in cross section but still increase in uncertainty.

We have the re-weighting numbers

My minutes of the Feb meeting The talks can be found at the website below, along with the introductory questions. http://indico.cern.ch/conferencedisplay.py?confid=128018 Frank Tackmann gave the first talk outlining the SCET prescription for identifying and resumming the logs introduced by the imposition of a jet veto on a (gg->) Higgs analysis. The application of a jet veto (or the binning of the inclusive Higgs events according to the number of jets) introduces a new scale into the calculation (pt_jetveto) and a new series of logs (log(pt_jetveto/m_higgs) that have to be resummed. Fixed order calculations, even at NNLO, only account for the effects of the first few terms. The parton showers in programs like Pythia, etc resum the leading logs for this ratio. The calculation that Frank presented is at NNLO and NNLL, i.e. it resums the next-to-next-toleading logs. The phase space corresponding to a single jet is difficult to implement in their resummation calculation, so beam-thrust is used as a stand-in, with a correspondence given between particular values of beam thrust and the pt of a jet veto. One can compare the double logs for the two cases; in order to get the expressions to agree, one needs a correspondence between the beam thrust and the pt of the jet veto of tau_cut/ m_h~[pt_jetveto/m_h]^(sqrt(2)). This correspondence has been confirmed at NNLO down to a pt_jetveto of 20 GeV.

Minutes, continued Thus, a beam thrust of 10 GeV corresponds to a jet veto at 20 GeV. The imposition of a beam thrust cut of 10 GeV leads to a significant reduction of the cross section in their NNLO+NNLL calculation, of the order of a factor of 2 over the NNLO value, and an expansion of scale uncertainty, dominated by the uncertainties of the soft and beam scales. They did some preliminary checks for this correspondence using Pythia, but instead found that the correspondence was closer to one-to-one. This is a critical point, as an equal correspondence would lead to smaller cross section corrections, while still calling for an increased scale uncertainty. It could be that subleading effects in the initial state showers in the Monte Carlo are different for the two observables. For an inclusive Higgs(->WW) analysis, as performed either at the Tevatron or LHC, it should be possible to recover the original scale uncertainty, since no actual events are thrown away. In order to compare directly to the usual division into 0,1 and >=2 jet bins, a similar resummation needs to be carried out on the Higgs + 1 jet final state This work is in progress.

Minutes, continued Jianming then gave a talk representing the ATLAS analyses. ATLAS uses MC@NLO, supplemented with HNNLO, to understand the impacts of higher order corrections on Higgs cross sections and acceptances. A significant amount of the cross section gain from NLO and NNLO corrections is from real radiations, leading to an increase in jet activity. Most of the increase in cross section in going to higher order disappears after the application of a jet veto. The crucial point is that there is good agreement for the jet veto efficiencies between MC@NLO and the NNLO calculation, i.e. the parton shower simulates NNLO reasonably well. Another way of stating this is that NNLO simulates the parton shower reasonably well, i.e. the leading logs resummed in the parton shower seem to not have much of an impact on the jet veto efficiency over the fixed order result. This implies that the large effects observed in the efficiency determined by the SCET calculation then would come from sub-leading logs, and the leading logs are not so important. If this were true, most people would consider this surprising. Si Xie then gave a talk representing CMS. They re-weight all Monte Carlo Higgs predictions to reference pt spectra provided by HqT. They correct the HWW jet veto efficiency by the ratio of the efficiency measured in data to the efficiency predicted by Monte Carlo. This is mainly to cover experimental effects, i.e. in the jet energy scale, rather than because of similarities in physics between the two cases (Z and Higgs). In the end, they see a good overlap in the cross section prediction bands versus pt_jetveto for MC@NLO and HqT.

Minutes, continued So the SCET predictions indicate that (1) there is a significant reduction in the Higgs cross section (over that predicted by fixed order/parton shower) upon application of a jet veto, as well as a significant increase in the scale uncertainty. The problem is that this level of decrease is not observed in Monte Carlo. This calls into question then whether the increase in scale uncertainty is also present. It is difficult to validate this with Z (+ vetoed jets) as the effect is much smaller in this case. It was felt that a color singlet final state, initiated by gg, would be an ideal testing ground (although George Sterman felt that any process, such as dijet production, might be suitable to test the impact of the double logs). One possibility is diphoton production which proceeds through a number of subprocesses, including a gg initial state. Lance also suggested WW production, which has a fraction of its cross section induced by a gg initial state. Other possibilities include photon + jet and/or Z+jet, which proceed primarily through gq initial states: one could measure the beam thrust for the event outside of the photon/z and the lead jet, for example using the "1-jettiness" as a generalization of beam thrust. So we have a quandry: the SCET calculation at NNLO and NNLL predicts larger effects, using the beam thrust variable as a stand-in for the jet veto, than observed with parton showers, using the jet veto directly. If the SCET calculation is correct, then this implies that either the sub-leading logs are particularly important and/or the beam thrust variable does not map onto the jet veto pt using the correspondence of the double log terms.

Barring confirmation from tests in data, we should carry out tests in Monte Carlo. For example, Massimiliano suggested comparing MC@NLO (with hadronization switched off) to the SCET predictions truncated to NLL+NLO (the presumed accuracy of MC@NLO). Giampiero, in addition, suggests to try without the pi^2 resummation. The SCET authors advocate reweighting the partonic beam thrust spectrum in the Monte Carlo to the partonic NNLL+NNLO results and then to use the reweighted sample to analyze jets with a standard pt_jetveto cut. This translation does not rely on the correspondence discussed above and is a better way to test the order of effects from the restriction in phase space. This should be the next step to be carried out by interested parties. After the meeting, a question was raised by John Collins about whether the spin correlation effects discussed in arxiv:1011.3918 might skew the MC/SCET comparison (they are absent in current Monte Carlos). Massimiliano and Stefano Catani replied that the effects are small for gg->higgs due to the spinless nature of the Higgs.