Measurements of Inclusive W/Z Production Cross Sections at CMS and W/Z as a Luminometer
MMEASUREMENTS OF INCLUSIVE W/Z PRODUCTION CROSSSECTIONS AT CMS AND W/Z AS A LUMINOMETER
Jeremy Werner, Princeton University, Princeton, NJ USAon behalf of the CMS Collaboration, CERN, Geneva, Switzerland
Abstract
Leptonic decays of W/Z bosons provide the firstelectroweak precision measurements at the LargeHadron Collider (LHC). The results of measurementsof inclusive W and Z boson production cross sectionsin pp collisions at √ s = 7 TeV are presented [1],based on 2 . − of data recorded by the CompactMuon Solenoid (CMS) detector at the LHC. The mea-surements, performed in the electron and muon de-cay channels, are combined to give σ (pp → W X ) ×B (W → (cid:96)ν ) = 9 . ± .
07 (stat.) ± .
28 (syst.) ± .
09 (lumi.) nb and σ (pp → Z X ) × B (Z → (cid:96) + (cid:96) − ) =0 . ± .
026 (stat.) ± .
023 (syst.) ± .
102 (lumi.) nb,where (cid:96) stands for either e or µ . Theoretical pre-dictions, calculated at the next-to-next-to-leading or-der (NNLO) in QCD using recent parton distributionfunctions (PDFs), are in agreement with the measuredcross sections. Hence copious production of these wellunderstood and clean signatures suggest the use ofW/Z as a “standard candle” for measuring the lumi-nosity at the LHC alongside the current Van der Meer(VdM) separation scan method. INTRODUCTION
Inclusive leptonic decays of W and Z bosons arebenchmark physics processes at hadron colliders.These first electroweak processes studied at the LHCallow validation of high transverse momentum electronand muon reconstruction and identification. In addi-tion, precision measurements of the W/Z are impor-tant in testing the Standard Model more rigorouslythan ever before, constraining the PDF, and poten-tially uncovering signs of new physics that could ap-pear through radiative corrections.The results of the W/Z production cross sectionmeasurements with pp collisions at a center-of-massenergy of 7 TeV provided by the LHC are reported [1].The data were collected from April through August,2010, by the CMS experiment, and correspond to anintegrated luminosity of 2 . ± . − . The consis-tency of the results between the different leptonic de-cay channels and with the NNLO theoretical calcu-lations suggests already considering the use of theseelectroweak boson decays as “Standard Candles forLHC” to calibrate the absolute luminosity alongsidethe Van deer Meer separation scan. Comparison ofthe systematic uncertainties between the two methods is provided.The precision of the cross section measurements waslimited by the systematic uncertainty on the luminos-ity (11%). In the very near future more detailedunderstanding of several of the main systematic bi-ases will substantially reduce the uncertainty of thesemeasurements. The statistical uncertainty will also bereduced by about a factor of 3 once the measurementis performed on the entire 2010 data set, correspond-ing to 36 pb − . Conservative systematic uncertaintyprojections for the measurements using the full 2010data set are provided. CROSS SECTION RESULTS FOR 2.9pb − Results for electron and muon decay channels arereported separately, and then combined assuming lep-ton universality in W and Z decays. The electron andmuon channels are combined by maximizing a likeli-hood that accounts for the individual statistical andsystematic uncertainties and their correlations. Forcross section measurements, correlations are only nu-merically relevant for theoretical uncertainties, includ-ing the PDF uncertainties on the acceptance values.For cross section ratio measurements, the correlationsof lepton efficiencies are taken into account in eachlepton channel, with other experimental uncertaintiesassumed uncorrelated; in the combination of leptonchannels, fully-correlated uncertainty for the accep-tance factor are assumed, with other uncertainties as-sumed uncorrelated.Table 1 summarizes the measured electroweak bosonproduction cross sections, and compares them to theirtheoretical NNLO predictions [3, 4]. The reported Zboson production cross sections pertain to the invari-ant mass range M (cid:96)(cid:96) ∈ (60 , γ ∗ exchange. Each cross section result in the tablecarries an additional uncertainty of 11% from the lu-minosity that is not listed.Table 2 lists the measured W/Z and W + /W − crosssection ratios, which are denoted R W / Z and R + / − , re-spectively. The measured cross section and ratio val-ues are all in agreement with the predictions. As of the publication date of this article the luminosityuncertainty has been reduced to 4%. Since the LHC Lumi Days workshop, this analysis on 36pb − has been completed [2]. a r X i v : . [ h e p - e x ] J un able 1: Summary of the production cross sectiontimes branching ratio measurements and their theo-retical predictions Channel σ × B (nb) NNLO (nb) W eν . ± . ± . . ± . µν . ± . ± . (cid:96)ν . ± . ± . + e + ν . ± . ± . . ± . µ + ν . ± . ± . (cid:96) + ν . ± . ± . − e − ν . ± . ± . . ± . µ − ν . ± . ± . (cid:96) − ν . ± . ± . ee . ± . ± . . ± . µµ . ± . ± . (cid:96)(cid:96) . ± . ± . Table 2: Summary of the cross section ratio measure-ments and their theoretical predictions
Channel σ × B (nb) NNLO (nb) R W / Z e . ± . ± . . ± . µ . ± . ± . (cid:96) . ± . ± . R + / − e . ± . ± . . ± . µ . ± . ± . (cid:96) . ± . ± . Summaries of the measurements are given in Fig-ures 1, 2, 3, and 4, illustrating the consistency of themeasurements in the electron and muon channels, aswell as the confirmation of theoretical predictions com-puted at the NNLO in QCD with state-of-the-art PDFsets. For each reported measurement, the statisticalerror is represented in black and the total experimen-tal uncertainty, obtained by adding in quadrature thestatistical and systematic uncertainties, in dark blue.For the cross section measurements, the luminosity un-certainty is added linearly to the experimental uncer-tainty, and is represented in green. The dark-yellowvertical line represents the theoretical prediction, andthe light-yellow vertical band is the theoretical uncer-tainty, interpreted as a 68% confidence interval.Figure 1: Summary of the W boson production crosssection times branching ratio measurements Figure 2: Summary of the Z boson production crosssection times branching ratio measurementsFigure 3: Summary of the R W / Z cross section ratiomeasurementsFigure 4: Summary of the R + / − cross section ratiomeasurements PROJECTED PRECISIONS FOR A36 PB − ANALYSIS
The overall uncertainty on the W/Z cross sectionresults will be substantially reduced when measure-ments are made on the full 36 pb − dataset, due tolarger event yields, more detailed understanding, andimprovements in analysis techniques. Table 3 com-pares the statistical and (non-luminosity) systematicerrors reported for the 2.9 pb − analysis to conserva-tive predictions for the 36 pb − analysis in the electronnd muon channels. The reduction suggests using elec-troweak boson decays as a luminometer will be com-petitive with VdM scans. This will further be exploredin the following section.Table 3: Production Cross Section Uncertainties andtheir Projections for the Electron and Muon Channels ∆ σ/σ W → e ν Z → ee(%) 2.9 pb −
36 pb − −
36 pb − Stat 0.6 0.2 3.8 1.1Syst 5.1 4.0 6.2 4.2Total 5.1 4.0 7.3 4.3 W → µν Z → µµ −
36 pb − −
36 pb − Stat 0.7 0.2 3.1 0.9Syst 3.1 2.2 2.3 2.1Total 3.4 2.2 3.9 2.3
COMPARISONS OF W/Z VS. VANDER MEER SCAN CALIBRATION
Luminosity at CMS is calibrated via Van der Meerscans [5], where horizontal and vertical beam separa-tion scans are performed to measure the beam sizes.The beam sizes along with the other known machineparameters determine the luminosity. The consistencyof the results obtained for the cross section measure-ments in addition to the copious signal yields and pre-cisely known cross sections, suggest the possibility ofinverting the cross section measurements to insteaduse the signal yield to calibrate the luminosity. Thiscan be demonstrated with Z bosons. Table 4 com-pares the current (with 2.9 pb − ) and projected (36pb − ) systematic uncertainties of a luminosity cali-bration using either Z bosons (combined electron andmuon channels) or VdM scans.Table 4: Luminosity Calibration Systematic Uncer-tainties and their Projections VdM Scan Z → (cid:96)(cid:96) −
36 pb − −
36 pb − ∆ L / L (%) 11 4 6 4-5 The dominant systematic uncertainty on the VdMscans is the beam current measurement. On the otherhand, the dominant systematic uncertainty on the Zbased calibration comes from the PDF [7]. Table 4shows that calibrating the luminosity using Z bosonsis competitive with the separation scans. It indicatesa Z decay based luminosity calibration with a preci-sion of 4-5% should be possible on a daily basis if theLHC provides CMS with approximately 30-40 pb − of collisions per day. Still, continued improvement ofthe VdM scans (in particular reducing the uncertainty on the beam current measurement) is advocated sincescans can be used to constrain the proton PDF. Z YIELD STABILITY FORLUMINOSITY CALIBRATION
Although VdM scans currently provide the pri-mary method to calibrate the luminosity, W/Z bosonscould be used as a cross check in the coming peri-ods of data taking. The signal yield must be con-tinuously validated to use these decays for calibra-tion. Irregularities in the signal yield can be un-covered using a Kolmogrov-Smirnov omnibus test [6].These tests yield the significance or probability valueof an observed or claimed deviation in a given fre-quency distribution from the expected distribution. InKolmogrov-Smirnov tests, the empirical distributionfunction (EDF) of the signal yield is plotted vs. anorthogonal variable. The orthogonal variable could bethe separation scan based luminosity or the yield of an-other signal. The EDF is just the fractional yield of thesignal. This frequency distribution is then comparedto the expected distribution (e.g. the yield increasinglinearly with luminosity). The maximal vertical differ-ence between the observed and expected distributionsdetermines a probability . Such a test is shown in Fig-ure 5 where the EDF of the Z → ee yield observed atCMS is plotted vs. the scan based luminosity for 36pb − . The data is shown in black, while the expecteddistribution is in green. The maximal difference be-tween the 2 distributions is labeled on the plot as D stat and the corresponding probability value is labelled as P KS . The observed distribution agrees well with theexpectation and the high probability value indicates astable signal yield, consistent with the hypothesis thatthe yield increases linearly with luminosity.Figure 5: The Z → ee EDF vs. scan based luminosityther useful checks include plotting the signal yieldvs. blocks of fixed integrated luminosity. One can thenverify that this distribution is flat, having its pointsagreeing within errors. Such a plot is shown in Fig-ure 6, where the Z → ee yield observed at CMS isplotted in 2.4 pb − luminosity blocks with about 4%relative statistical error per point. The data is shownin black while the corresponding statistical error bandis plotted in yellow. The distribution is flat and theyield was stable during data taking.Figure 6: The Z → ee yield vs. blocks of fixed inte-grated luminosity CONCLUSIONS