Re-evaluation of the LHC potential for the measurement of Mw

a r X i v :0805.2093v 2 [h e p -e x ] 13 J u n 2008June 13,2008Re-evaluation of the LHC potential for the measurement of m W Nathalie Besson,Maarten Boonekamp (CEA-Saclay),Esben Klinkby,Sascha Mehlhase,Troels Petersen (NBI)Abstract We present a study of the LHC sensitivity to the W boson mass based on simulation studies.We find that both experimental and phenomenological sources of systematicuncertainties can be strongly constrained with Z measurements:the lineshape,d σZ /d m ,is robustly predicted,and its analysis provides an accurate measurement of the detector resolution and absolute scale,while the differential cross-section analysis,d 2σZ /d y d p T ,absorbs the strong interaction uncertainties.A sensitivity δm W ∼7MeV for each decay channel (W →e ν,W →µν),and for an integrated luminosity of 10fb −1,appears as a reasonable goal.1IntroductionThe Standard Model(SM),now computed at two-loop precision[1,2],is a very predictive framework. Its most precisely measured parametersαQED,Gµ,and m Z,provide constraints on the W boson and top quark masses,which can be confronted with measurement.Injecting the measured value of the W mass and the measured Z boson couplings,a definite prediction is given for the top quark mass[3]. This prediction,together with the discovery of the top quark at a compatible mass[4,5],has been a major achievement in high energy physics.The measured values of the W boson and top quark masses are now more precise than their quantum predictions,and provide non-trivial constraints on the gauge symmetry breaking sector.In the SM, this translates into limits on the Higgs boson mass[6].Beyond the SM,constraints are given on the contributions of other heavy particles,like supersymmetric particles[7].The W mass has been measured at UA2[8],LEP[6],and the Tevatron[9].The recent measure-ment by the CDF Collaboration gives m W=80.413±0.048GeV,yielding a current world average of m W=80.398±0.025GeV[10].In the SM,the resulting Higgs boson mass uncertainty is about50%. Any further improvement in this measurement will translate into more precise indirect predictions. The present paper discusses the LHC prospects for the W mass measurement.The expected W cross-section at the LHC is about20nb[11].In10fb−1of data,a benchmark for one year of in-tegrated luminosity during thefirst years of stable running,around4×107W events will be selected in each exploitable decay channel(W→eν,µν),providing a combined statistical sensitivity of about 1MeV.Previous estimates[12–14]of the systematic uncertainties affecting this measurement how-ever amount toδm W∼20MeV per experiment,and to a combined uncertainty ofδm W∼15MeV. The main sources are the imperfect determination of the experiments absolute energy scale,and the uncertainties in the W boson kinematical distributions(rapidity,transverse momentum),which in turn stem from proton structure function uncertainties and higher orders QCD effects.The purpose of this paper is to re-investigate the possibilities to measure the W mass with the great-est possible precision.As is known from the Tevatron,the uncertainties can be significantly reduced using Z boson measurements;this approach will be employed here,with modifications and improve-ments suggested by the high Z statistics expected.Although our discussion is general,most of our arguments rely on the expected performance of the ATLAS experiment[15].The paper is structured as follows.Section2summarizes the W massfitting procedure,lists the in-gredients needed to describe the W distributions used in thefit,and gives a general description of how these ingredients can be determined.The sources of uncertainty are then discussed in turn,in Sec-tion3(experimental uncertainties),Section4(theoretical uncertainties),and Section5(backgrounds, underlying event,and effects related to the machine operation).Correlations between these effects are discussed in Section6,and the results are given in Section7.Section8concludes the paper.2General discussionThis section discusses our technical set-up,the W and Z event selection,the massfitting procedure, and the problem of controlling all ingredients entering in the definition of thefitted distributions.22.1W and Z production.Event generation and simulationThroughout this paper,W and Z boson samples,and their distributions and acceptances are computed using the PYTHIA general purpose event generator[16].On top of PYTHIA,the treatment of pho-ton radiation in W and Z decays is done via an interface to PHOTOS[17].The size of the expected samples are computed assuming the NLO W and Z cross-sections,as obtained from RESBOS[18]. These choices are not unique,and the simulation of physics processes at the LHC,in particular non-perturbative strong interaction parameters,will obviously need to be adjusted using the forthcoming data.In this analysis,the effects of the corresponding uncertainties are estimated either by changing parameters in these programs,or by distorting the output distributions according to our assumptions. When referring to“fast simulation”,we mean a simplified simulation of the ATLAS detector response using scale factors and Gaussian resolution functions,applied to the generator-level information ob-tained above[19].When referring to“full simulation”,we mean the complete simulation of the ATLAS detector using GEANT4[20].In our discussions below,and in the absence of real physics data, we often treat our fully simulated event samples as data samples,and the fast simulation samples as their Monte-Carlo simulation.The different detector response in fast and full simulation allows to emulate the realistic situation where the imperfect detector simulation is adjusted during data taking.2.2Signal selection andfitting procedureAt hadron colliders,W and Z events can be detected and reconstructed in the eνe,µνµ,ee,andµµfinal states.The hadronic modes suffer prohibitively large background from jet production;τmodes can be detected but theτ-lepton decay produces additional undetected particles in thefinal state,di-luting the information that can be extracted from these modes.In W events,the observables most sensitive to m W are:•The reconstructed lepton transverse momentum,pℓT;•The reconstructed W transverse mass,m W T≡Channel W→lνZ→llFigure2:χ2value as function of the tested value of m W.Each dot represents a comparison between the data and the template distribution obtained for a given m W.The curve is thefitted parabola.The different template distributions are obtained by varying the value of the W boson mass parameter in the event generation.The statistical comparison of the data to the templates can be performed in various ways;throughout this study we will use a simple binnedχ2test.Theχ2quantifying the compatibility of a given template distribution with the data is defined as follows:χ2=∑i (n obs i−n exp i)2•Theoretical inputs:the W rapidity distribution,y W,affects the m W T and pℓT distributions.The trans-verse momentum of the W,p W T,directly affects the pℓT spectrum;its impact is weaker on the m W T spectrum.The y W and p W T distributions depend on the proton structure functions and on higher-order QCD effects.The lepton angular distribution in the W rest frame is of importance for both pℓT and m W T and changes with the W polarization[22].Finally,QED effects(photon radiation in the W decay) shifts the lepton p T downwards.Since the radiated photons are mostly collinear to the charged decay lepton,the impact on electrons and muons is different:the measured muon momentum entirely re-flects the momentum loss by radiation,whereas the electron energy,measured essentially in the EMC, includes most of the radiated energy.•Environmental inputs:these include,among others,backgrounds surviving the W selection,un-derlying event and pile-up effects on reconstructed energies and momenta,random neutron hits in the muon spectrometer(“cavern background”),and the impact of a non-zero beam crossing angle.In all cases,imperfect modelling of these inputs biases the event reconstruction,leading to distorted pℓT and m W T distributions.2.4Propagation of systematic uncertaintiesThe impact of underlying physics mechanisms affecting the W mass determination is estimated by producing template distributions of pℓT and m W T unaware of the effect under consideration,andfitting them to pseudo-data including this effect.The resulting bias(i.e.the difference between the injected andfitted values of m W)gives the corresponding systematic uncertainty.In the simplest case,a physics effect affecting the distributions(for a given value of the W mass)can be summarized by a single parameter.In this case,the induced systematic uncertainty is simply given by:∂m Wδm W=∂m W∂relαi2.5The impact of Z boson measurementsThe LHC will produce a large number of Z events.Their selection is rather straightforward,requir-ing two reconstructed isolated,high-p t leptons(pℓT>20GeV,|ηℓ|<2.5),and low hadronic activity (hadronic recoil smaller than30GeV).For each useful decay mode(Z→ee,µµ)and for∼10fb−1,around3.5×106events should survive selections.This represents a factor10less than the expected W statistics,but the fact that Z events are fully reconstructed largely compensates this deficit.Cross-sections and statistics are summarized in Table1.The precise knowledge of the Z mass and width will allow to determine the lepton energy scale and resolution precisely.Exploiting the energy distribution from the decay leptons will also allow to de-termine the scale’s energy dependence(i.e,the linearity of the detector response),and the energy dependent resolution function.Once this is achieved,the Z transverse momentum will also serve to scale the measured hadronic recoil to the Z;together with the measured lepton transverse momentum, this defines the missing transverse energy.Finally,“tag and probe”methods[23]will allow to deter-mine the lepton reconstruction efficiency.Although most of the QCD mechanisms affecting W distributions carry significant uncertainty[24], they affect W and Z events in a similar way.This is the case for non-perturbative contributions to the W transverse momentum distributions,but also for parton density(PDF)effects:at the LHC,the W and the Z are essentially sensitive to high-Q2sea partons,and a variation of these parameters will affect the W and Z distributions(in particular y W,y Z)in a correlated way.Hence,the measurement of the Z distributions will help to control the W ones.The simulation of QED radiation in W and Z decays was much improved recently[17,25].Still, the measurement of this process(through e.g.Z→ℓℓγ)will allow to confirm the predictions.Other sources of uncertainty(e.g.backgrounds and underlying event)will also be controlled by auxiliary measurements at the LHC.The following sections attempt to quantify the above arguments.3Experimental uncertaintiesThis section assesses the effect of efficiency and resolution in the reconstruction of leptons and missing transverse energy.3.1Lepton scale and resolutionThe Z boson resonance has been measured very precisely at the lepton colliders during the90’s[3]. The Z boson mass and width can be exploited as an absolute reference to determine as precisely as possible the detector energy scale,its linearity and resolution.The basic method is rather simple,and consists in comparing the position and width of the observed mass peak in reconstructed dilepton events with the Z boson parameters.A shift of the observed po-sition of the mass peak,with respect to the nominal Z peak position,is corrected for by scaling the7detector response,hence determining the detector absolute scale;the additional spread of the mass distribution,as compared to the natural Z boson width,is used to estimate the resolution.The high statistics expected at the LHC,however,imposes a number of refinements.First,the scale obtained as above is averaged over the lepton kinematical spectrum,whereas an energy-dependent scale is needed for a correct description of the Jacobian distributions in W events.Secondly,lepton energy resolution effects induce a small but non-negligible shift in the di-lepton invariant mass distri-bution.This shift needs to be subtracted before converting the scale measured from the Z invariant mass distribution into the scale used to describe the Jacobian distributions in W events.The resulting method has been described in detail in Ref.[26],and is summarized below.3.1.1Average detector scaleWefirst illustrate the energy-independent method,providing an average detector ing the PYTHIA event generator[16],we produce a set of template histograms corresponding to generator-level Z lineshapes.The decay leptons are smeared and decalibrated with different energy scale factors αand resolution functionsσ.For definiteness,we consider calorimeter-like resolution functions√parametrized asσ(E)=a×Figure3:Comparison of a fully simulated Z→ee sample(dots)to an initial template example, produced withα=1and a=0.12,and to the bestfit result.3.1.2Linearity:energy dependent scale and resolutionThe above method can be extended as follows.The data and the templates are classified as a function of the lepton energies.This leads to templates and pseudo-data labeled(i,j),corresponding to the event categories where one lepton falls in bin i,and the other in bin j.The scale factorαi j and the resolution parameter a i j are thenfitted in every bin.In case of small non-linearities of the calorimetry response(i.e.αi j,αi,αj very close to1),we can then derive theαi from theαi j,writing infirst order approximation that the mass peak decalibration results from the decay lepton decalibrations:αi j m12=m4i j =σ2iE2j(6)which can again be solved using least squares,yielding theσi.We thus obtain the energy-dependent resolution function,independently of the form used to produce the templates.9Figure4:Left:reconstructed absolute energy scale,as a function of energy(points with error bars). The full line gives the injected function,representing the effect of non simulated passive material in front of the calorimeter.The dashed line is an empirical functionfitted through the points;the dot-dashed line shows the result of an energy-independent analysis,missing the non-linearities.Right: reconstructed energy resolution(points with error bars).The full line is the true resolution function,√of the formσ(E)/E=a/∼800MeV/%,∂relαℓas illustrated in Figure5.In the case of an energy-dependent scale,the uncertainty on m W is obtained by injecting random, energy-dependent decalibrations in the pseudo-data,with a spread corresponding to the result of the analysis of Section3.1.2.With480independent exercises of this type,we obtain a distribution of m f it W as shown on Figure6.The scale-induced W mass uncertainty is given by the spread of this distribu-tion,and isδm W(αℓ)=4MeV.10Figure 5:Left:bias on m W ,m f it W −m true W ,as a function of the relative bias on αℓ,δαℓ=(αf it ℓ−αtrue ℓ)/αtrue ℓ.Right:bias on m W as function of the resolution bias,δσℓ=(σf it ℓ−σtrue ℓ)/σtrue ℓ.Alinear dependence is observed in each case,with ∂m W /∂rel αℓ=800MeV /%and ∂m W /∂rel σℓ=0.8MeV /%.Figure 6:Distribution of m f itW ,for 480exercises with energy-dependent scale parameters randomly drawn within their uncertainties.The true mass is m W =80.33GeV;the systematic uncertainty is ∼4MeV.11The effect of the resolution is studied by varying the resolution parameter in the pseudo-data,fitting to templates withfixed resolution,and collecting the corresponding values of m f it W.This provides the relation between the resolution bias and the resulting bias on m W:∂m WFigure7:Electron(left)and muon(right)ηdistributions at reconstruction level,for W and Z events. This confrontation of measurements is expected to allow to understand the source of any observed non-linearities in terms of magneticfield effects,imperfect alignement,excess of passive material in the detector,etc.It will thus be possible to confront several independent probes of the detector scale;compatibility between these measurements then validates its use for the measurement of m W. This discussion is familiar from the Tevatron m W measurements[9,10].The present analysis,using Z events only,quantifies the precision achievable at the LHC provided all measurements of the scale agree.3.2Lepton reconstruction efficiencyThe observed Jacobian distributions in W events also reflect any p T dependence of the lepton recon-struction efficiency.Any difference between the simulation used to produce the templates and the data will induce a distortion of the spectrum and cause a bias in the massfit.We again take the electron channel as our main example.The ATLAS electron identification largely exploits the shapes of their calorimetric showers[15],which have significant energy dependence. Hence,any selection based on these will have a p T-dependent efficiency which has to be appropri-ately simulated in the templates.Unlike the electrons,no strong p T dependence affects the muon reconstruction efficiency.3.2.1Electron efficiency measurementsElectron reconstruction efficiency can be determined from the data with Z events,using e.g.the so-called“tag and probe”method[23],which we briefly summarize here.Events are selected with one well-identified electron,and an additional high-p T,isolated track.The invariant mass of these two objects is required to be within10GeV from the nominal Z boson mass. Assuming that this selects Z events with enough purity,the identification efficiency is then obtained by computing the fraction of events where the second object is indeed identified as an electron.The efficiency of the isolation criterion is obtained in a similar way.Simulation studies show that the im-pact of backgrounds on the estimation of the efficiency is small compared to the statistical uncertainty.13Figure8:Electron reconstruction efficiency,as determined from fully simulated Z→ee events. For the present study we use about200000fully simulated Z→ee events,from which the efficiency is evaluated.The result is shown in Figure8,together with an empirical function describing main features of the p e T dependence.The following form:ε(p T)=ε0−a exp(−b×p T)(7) correctly describes the efficiency in the p e T range relevant for the analysis.3.2.2Propagation to m W:δm W(ε)The effect of the efficiency uncertainty is estimated as in the previous section.Template distributions are produced at generator level,with varying values of m W,and applying an efficiency factor accord-ing to the bestfit efficiency function obtained above.One hundred independent pseudo-data samples are generated at afixed mass(m W=80.33MeV).Ef-ficiency functions are applied with parameters drawn randomly within their uncertainties,as obtained in the previous section.For each sample of pseudo-data,afit is performed to the W mass.Thefitted mass values are his-togrammed,and the spread of the histogram gives the corresponding systematic uncertainty.With the efficiency determined using2×105Z boson decays,the efficiency-induced systematic W mass uncertainty is found to beδm W=33MeV.Other functional forms than Eq.7yield the same result. The most sensitive parameter in Equation7is b,the slope in the exponential.It is determined to be b=0.068±0.006,corresponding to a precision of9%;in other words,∂m W/∂rel b∼4MeV/%.To emphasize the importance of this effect,the same pseudo-data samples are compared to templates assuming no p T-dependence in the lepton reconstruction efficiency(i.e.f(p T)=constant).While the same spread is observed,the m f it W distribution indicates an average bias of about450MeV.This bias vanishes,tofirst order,when using the p T-dependent efficiency in the templates.14p T cut<m f it W><δm f it W><m f it W><δm f it W> (εre f=1)(εre f=1)(εre f=f(p T))(εre f=f(p T))Figure9:Left:statistical sensitivity toαE missT ,as a function of the accumulated Z statistics.Right:statistical sensitivity toσE missT.difference(m W=m Z).Assuming that the absolute lepton scale and resolution have been measured beforehand(cf.Sec-tion3.1),one can measure the recoil scale(αrec)and resolution(σrec)in fully reconstructed Z events,where no significant E missT is expected,by comparing the measured hadronic energy E rec,recoilingagainst the Z boson,to the reconstructed di-lepton four-momentum,pℓℓT.Specifically,αrec andσrec are extracted from the peak position and spread of the distribution of E rec/pℓℓT.The results can then be used to correct the observed recoil,and hence E missT,in W events.Figure9shows the expected sensitivity toαrec andσrec.With10fb−1,these parameters can be deter-mined with a statistical precision ofδαrec=5×10−5andδσrec=6×10−4.3.3.2Propagation to m W:δm W(αE missT ),δm W(σE missT)The effect on m W is evaluated by systematically varying the recoil scale,producing corresponding pseudo-data samples as in the previous sections,andfitting each sample to perfectly calibrated tem-plates.We obtain the relation between the m W bias and the recoil scale and resolution in the form of a derivative:∂m W∂relσE missT=−25MeV/%as illustrated in Figure10.InjectingδαE missT =5×10−5,we obtain a systematic uncertainty ofδm W(αE missT )=1MeV.Similarly,wefind the contribution from the resolution to beδm W(σE missT)=1.5MeV.These numbers assume that the Z-based calibration can be transported to the W sample without additional uncertainty;this is discussed further below.3.3.3Further discussionThe E missT calibration can be studied in more detail,using real Z events where one reconstructed leptonis artificially removed.In the case of electrons,the removed calorimetric energy should be properly16Figure 10:Left:Bias on m W ,δm W =m f it W −m true W ,as a function of the bias on the recoil scale,δαE miss T.Right:δm W as function of the resolution bias,δσE miss T .A linear dependence is observed in each case,with ∂m W /∂rel αE miss T =−200MeV /%and ∂m W /∂rel σE miss T=−25MeV /%.Figure 11:Left:electron cluster in a Z →ee event.Right:the same calorimeter region,after thecluster has been removed.The energy in each cell belonging to the electron cluster is replaced by a number drawn from a Gaussian with mean and RMS corresponding to detector noise.replaced by the expected noise.For muons,also,the minimum-ionizing energy depositions in the calorimeters need to be removed and replaced by the expected noise as above.The resulting events mimic W events and have a precisely known missing energy,corresponding to the energy of the re-moved lepton,which can be compared to the result of the E miss Treconstruction algorithm.The lepton removal requires that one can identify and remove the electron signal from the struckcalorimeter cells,while leaving a realistic contribution from noise and hadronic background (see Fig-ure 11).Several approaches can be tried,such as replacing the contents of the electron cluster cells by energy measured away of any high-p T object in the event (e.g.at 90◦in azimuth),or by the average expected electronic and hadronic noise.To determine the E miss Tresolution and possibly correct for biases in its measurement,we consider the reconstructed E miss Tof Z →ℓℓevents before and after the removal of one lepton,and compare the 17Figure12:Transverse view of a)W→ℓνand b)Z→ℓℓevents.The combined transverse momentum of the recoil u,which should match that of the boson,is used to estimate the momentum of the undetected neutrino in the W→ℓνdecay.The Z boson line offlight is represented,which defines the ( ,⊥)coordinate system.The size of the dotted ellipses represent the resolution on the reconstructed objects.difference to the transverse momentum of the removed lepton.A non-zero average value of this dif-ference points to a bias in the E missTreconstruction.Rather than projecting this difference on conventional X and Y axes in the transverse plane,it is best to consider the natural frame of the event,with axes parallel( )and perpendicular(⊥)to the Z bo-son transverse momentum.Imperfect calibration of the E missT reconstruction will show up as biasesin these distributions,which can then subsequently be corrected for within statistics.The axes are illustrated in Figure12.This method is tried on a fully simulated sample of Z→ee events,with results illustrated in Fig-ure13.As can be seen in this example,a bias is observed in the E missT reconstruction along the Zline offlight.No bias is observed along the other axes.In this example,the calibration is thus cor-rect on average,but the E missTreconstruction does not respond perfectly to the event-by-event topology.As this discussion illustrates,E missT reconstruction is a very difficult experimental algorithm to control,especially to the level of precision desired here.Therefore,we cannot claim at present that the sensitiv-ity quoted in the previous section will indeed be reached.Instead,lacking the proof that the statisticalenhancement can be fully exploited,we assume an overall uncertainty ofδm W(E missT )=5MeV.Thisnumber is a factor3higher than the purely statistical sensitivity,and a factor three smaller than the sys-tematic uncertainty obtained in the recent CDF measurement[10]based on an integrated luminosity of200pb−1and about8000Z events for calibration of the hadronic recoil.18Figure13:Top:resolution on E missT,projected onto the(X,Y)coordinate system,for unmodified,fullysimulated Z→ee events.Bottom: E missT resolution in the( ,⊥)coordinate system.The absence ofbias along the X and Y axes show that the overall calibration is correct on average,but the observed bias along the -axis,corresponding to the Z line offlight,indicates imperfect calibration of the response to the event-by-event topology.194Theoretical uncertaintiesWe discuss below the uncertainties related to imperfect physics modeling of W production.The correlation of the mass measurement with the W width,the impact offinal state radiation,and biases in the pℓT and m W T distributions induced by p W T and y W distortions are discussed in turn.4.1W boson width:δm W(ΓW)A change in the W widthΓW affects the Jacobian peak,and can cause a bias in the W mass measure-ment.To assert the size of this effect,samples with the same W mass but W widths varying in the range1.7−2.5GeVwere produced and subsequentlyfitted.The relation betweenΓW and m W in the fit is linear,with a slope depending on the distribution used in the massfit.If the W transverse mass is used,wefind:∂m W=1.2MeV/%∂relΓWThe intrinsic width of the W resonanceΓW has been measured to be2.141±0.041GeV,while the SM prediction is2.0910±0.0015GeV[28].It should be taken into account that the LHC data can be expected to improve the precision on the W width as well as on m W.Earlier measurements of ΓW[29,30]are affected by the same systematic uncertainties as those discussed in this paper.Hence, anticipating on our results,we assume that an improvement by a factorfive should be achievable, respectively leavingδm W(ΓW)=1.3and0.5MeV for the m W T and pℓTfits.4.2QEDfinal state radiation:δm W(QED)Final state radiation causes significant distortions of the naive,lowest order p T spectrum of the W decay leptons.We estimate the stability of the theoretical calculation below,using the PHOTOS pro-gram[17]as a benchmark.The numerical importance offinal state radiation is illustrated in Figure14,which displays the dis-tribution of the measured lepton energy fraction(relative to their energy in the absence of FSR).For electrons,measured via calorimetric energy clusters,most of the(collinearly radiated)photon energy is collected in the cluster.The momentum of muons tracks,on the contrary,is measured indepen-dently of any photon radiation.The average values of the distributions lie at about99%of the original value,meaning that ignoring the effect entirely would cause a bias on the W mass of about800MeV. The theoretical stability of the calculation is thus of critical importance.In recent versions of PHOTOS,it is possible to switch between several theoretical assumptions.In par-ticular,W and Z boson decays can be simulated with photon emission up to O(α),O(α2),O(α4),or with photon emission exponentiation[31].To study the model differences,we have generated about 106events for each setting,and for each production and decay channel(W→ℓν,Z→ℓℓ,forℓ=e,µ).The average values of the energy fractions discussed above are shown in Figure15,for successive theoretical refinements.The different average values for electrons and muons reflect the different20。