Measurement of the Z forward-backward asymmetry with the ATLAS detector and determination of sin 2 æ lep

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1 Measurement of the Z forward-backward asymmetry with the ATLAS detector and determination of sin 2 æ lep ef f èm 2 Z è ATL-PHYS /05/2000 Krzysztof Sliwa 1, Sean Riley 1, and Ulrich Baur 2 1 Tufts University, Medford, Massachusetts 02155, USA 2 State University of New York, Buffalo, NY 14260, USA 1 Introduction The electroweak mixing angle is a fundamental parameter in the Standard Model. Precise measurements of the ective weak mixing angle can be used, together with the top quark mass M top,to put constraints on the Higgs boson mass, similarly to the way it can be done using very high precision W mass measurements - by studying the ects of radiative corrections. At hadron colliders, the ective weak mixing angle (or, to be more precise, the value of sin 2 æ lep ) can be measured indirectly using the forward-backward asymmetry (A FB ) in di-lepton production near the Z pole. At LEP, sin 2 æ lep has been measured with a precision of approximately =2:3 æ 10,4 : LHC experiments will produce very large numbers of Z bosons and, in principle, one could measure the forward-backward asymmetry and, indirectly, sin 2 æ lep with a very small statistical error. The question whether one can measure the ective weak mixing angle at LHC with precision comparable to, or better than, the LEP result has been investigated in the past[1, 2]. The improvement in the precision of determination of sin 2 æ lep by detecting electrons in in the ATLAS detector up to jçj é4.9 is the subject of this note. 2 Past results In order to be able to translate the measurements of A FB into the measurement of sin 2 æ lep, one must understand the ects of higher order QCD and electroweak radiative corrections. The most important factor determining the precision of the sin 2 æ lep measurement are the values of parameters a and b, which relate[3] the A FB and sin 2 æ lep A FB = bèa, sin 2 æ lep è The O(æ) QED corrections as well as the O(æ s ) QCD corrections to the process pp! èæ æ ;Zè! èç + ç, ;e + e, è were calculated[2]. The authors pointed out that the measured asymmetry in pp collisions is smaller than in pçp collisions at Tevatron, and that the asymmetry and the sensitivity to the ective weak mixing angle increases with rapidity of the di-lepton system. For an integrated luminosity of 100 fb,1, they estimated that it should be possible to measure sin 2 æ lep with a statistical precision of =3:9 æ 10,5 :

2 for full rapidity coverage for leptons and =4:4 æ 10,4 : for the more realistic finite lepton rapidity coverage of jy lep j é2.4. With an additional cut on Z rapidity[4], jy Z j é1, they have found that the precision could be improved by an additional 10%. The next-to-leading order QCD and QED radiative corrections were taken into account. Events with di-lepton masses in the range 75 GeV-105 GeV/c 2 were selected as Z candidates for the above estimates. 3 Rapidity coverage of the ATLAS detector for electrons The nominal rapidity coverage used for precision physics (e.g. electron and photon identification) in the ATLAS detector is in the range jyj é2.5, which corresponds to the region equipped with the inner detector and where the electromagnetic calorimeter has the best granularity. Since the sensitivity of the asymmetry measurement increases at large rapidity, we have studied the possibility of detecting one electron in the rapidity range up to jy l j é4.9, whereas the other electron is required to be within jy l j é2.5. Electrons within the rapidity range jyj é2.5 are very well identified, while for those in the region jyj é2.5 the identification is not as good, although possible by using the end-cap and forward calorimeters. Our analysis focuses on two questions: i) how does the increased rapidity coverage for electrons affect the precision of the determination of the weak mixing angle sin 2 æ lep ; ii) what is the minimum jet rejection (e/jet separation) in the forward calorimeter necessary to make a significantly better measurement of sin 2 æ lep possible. The ATLAS forward calorimeter allows, in principle, for identification of electrons up to jy l j é4.9, however, the particle identification capability in the forward region has not been evaluated yet. The results of our study suggest that potential gains in physics reach due to extending the rapidity coverage for one of the electrons up to jy l j é4.9 are very large, indeed. 3.1 Monte Carlo samples We have used PYTHIA 5.7 and JETSET 7.2 to generate the physics processes under study, i.e. production of Z (including properly the æ æ /Z interference terms) and the two dominant backgrounds we had considered - top-antitop pairs and QCD 2-jet production. In Tables I and II we summarize the cross sections, number of generated events (N) and the ective luminosities of signal and background MC samples, respectively. The Monte Carlo samples were generated with mass of the parton-parton system, ^m é50 GeV/c 2, and with ^p t (transverse momentum defined in the rest frame of the hard parton-parton interaction) in the range GeV/c. We have also verified that adding events generated with ^p t in the range 2-10 GeV/c and GeV/c for pp! 2 jet, or Z events above 50 GeV will not affect the results by more than a fraction of 1%. (In the QCD 2-jet production case we have generated two data sets, each normalized to 50 fb,1. The first set has been generated with ^p min t, ^p max t in the range GeV/c; for the other set the ^p min t was GeV/c and GeV/c. When added, the two sets correspond to 100 fb,1.), ^p max t range 3.2 Analysis and selection cuts We have used ATLAS standard cuts to select Z candidates for the measurement of A FB : i) P electron t é 20 GeV/c 2

3 ^p min t Table I: Monte Carlo signal samples pp! èæ æ ;Zè! e + e,, ^p max t 5-10 GeV GeV GeV çæ BF(mb) 5.56æ10,8 1.75æ10,7 1.25æ10,6 N L (fb,1 ) Table II: Monte Carlo background samples process pp! 2 jets pp! tçt! e + e, ^p min t, ^p max t GeV GeV GeV GeV çæ BF(mb) æ10,1 7.47æ10,9 N L (fb,1 ) 1.83æ10,7 2.27æ10,7 9.72æ10, ii) 85.2 GeV/c 2 ém(e + e, )é97.2 GeV/c 2. To allow a realistic estimate of the precision of the determination of sin 2 æ lep from the measurement of A FB, Ulrich Baur has recalculated[5] the results from the 1998 paper[2] with the extended rapidity coverage for one of the electrons and a narrower Z mass window we have used. We present results for 4 sets of cuts: a) jy l j é2.5 for both electrons b) jy l j é2.5 for both electrons and jy Z j é1.0 c) jy l j é2.5 for one of the electrons, jy l j é4.9 for the other electron d) jy l j é2.5 for one of the electrons, jy l j é4.9 for the other electron and jy Z j é1.0 In Figure 1 we present distributions of rapidity of the di-lepton system. Moving from outside inwards, each contour represents a distribution obtained with a subset of data using more restrictive cuts. The most outside contour corresponds to all di-lepton pairs. Moving inwards, the next contour corresponds to the di-lepton pairs passing the ATLAS standard Z selection cuts. The lepton rapidity coverage extends here to a maximum possible with the ATLAS detector, jy l j é4.9 for both electrons. The next distribution, whose outside contour is shaded light gray, corresponds to a subset of the di-leptons pairs passing the Z selection cuts. Here, the leptons must satisfy the extended lepton rapidity cuts studied in this note, i.e. one of the electrons has its rapidity in the range 2.5é jy l j é4.9, while the other is constrained to remain within jy l j é2.5. Finally, the inner-most (dark-gray) distribution corresponds to the di-lepton pairs passing the Z selection cuts, and with both electrons constrained to remain within jy l j é2.5. (The dark-shaded area is a subset of a lightshaded area). The area shaded in light gray represents the gain in acceptance due to the extended lepton rapidity coverage, as compared to the ATLAS coverage for precision physics. It is interesting to note that the acceptance gain would almost double, if it were possible to detect both electrons in the forward region 2.5é jy l j é4.9. However, extending the rapidity coverage beyond jy l j =4.9 would not result in further significant gains in acceptance, as the Z bosons are mostly produced in the central region, due to their large mass. 3.3 Higher order radiative correction for the cuts used in our analysis In Table III we list the values of the parameters (a,b) recalculated[5] for the cuts used in this analysis. 3

4 x y(e+e-) Figure 1: Rapidity of the di-lepton system for various selection cuts. 3.4 Acceptance, reconstruction iciency, jet rejection factors In our quick study we have not used the full ATLAS simulation to model the detector response, but instead we used the ATLAS Technical Design Report[6] values for electron detection iciencies and jet rejection factors in the jyj é2.5 region, valid for the standard cuts we used in our analysis. In the forward region, 2.5é jy l j é4.9, we have assumed the iciency of electron detection to be æ fwd =0.5. The jet rejection in the forward region, ç fwd, was varied in the range Table IV summarizes the values used. 3.5 Results The precision of the A FB measurement increases, if one allows one of the leptons to be detected in the 2.5é jy l j é4.9 range, for two reasons. First, the forward-backward asymmetry is significantly increased in that region, and second, the statistical error decreases with larger statistics. Measurements of the A FB as a function of jy Z j are shown in Figure 2. Triangles represent the values of A FB measured with both lepton rapidities restricted to jy l j é2.5, while the squares represent the asymmetry measurements with the extended rapidity coverage, when one of the leptons is allowed to be detected in the 2.5é jy l j é4.9 range. Restricting the A FB measurement to the e + e, events with jy Z j é1.0 improves the significance of the measurement slightly, as the gain due to the larger asymmetry for events with larger jy Z j values is partially cancelled by the loss of statistics. As mentioned earlier, the most important factor determining the precision of the sin 2 æ lep relate the A FB and sin 2 æ lep measurement are the values of parameters a and b, which. Our results are summarized in Table V. 4

5 Table III: Parameters a and b in A FB = bèa,sin 2 æ lep ef f è used in our study. æa and æbaretheqcdandqde corrections to parameters a and b; æa and æb are the values of the parameters a and b including radiative corrections. cuts a Born æa qed æa qcd æa b Born æb qed æb qcd æb jy l j é2.5 both e æ jy l j é2.5 both e æ jy Z j é1.0 jy l j é2.5 one e æ jy l j é4.9 the other e æ jy l j é2.5 one e æ jy l j é4.9 the other e æ jy Z j é1.0 Table IV: Electron identification iciency (æ electron ) and e/jet rejection factors (ç) as a function of electron rapidity. We used two values for the jet rejection factor in the central (jçj é2.5) region, ç = 10 5 (nominal ATLAS value) and ç =10 4. jy l j range æ electron e/jet rejection (ç) 10 4è5è 10 4è5è 10 4è5è 10 4è5è 10 4è5è ç fwd 3.6 Discussion of results, remaining challenges As the parameter b increases multifold with the increased rapidity coverage for one of the electrons (2.5é jy l j é4.9), the resulting error on the sin 2 æ lep is significantly reduced, as compared to the standard analysis which requires both leptons within jy l j é2.5. The precision of the determination of the sin 2 æ lep is improved by a factor of 2.9 (4.8), depending on whether the jy Zj é1.0 cut is used (or not used). It is interesting to note that the precision of the analyses with extended rapidity coverage for one of the electrons is better than that obtained with LEP. We find it also very encouraging that our results will remain almost unaffected should the jet rejection factor drop to 10 4 from the nominal 10 5 in the central region, jy l j é2.5. We have assumed the electron identification iciency of 0.5 in the region 2.5é jy l j é4.9. As we require one lepton to be well identified in the central region, one could relax the selection cuts for the second electron in the forward region to achieve such high iciency value. Our study indicates that such a strategy could succeed. We find that the jet rejection factor of ç100 in the forward region (which might be possible to achieve) should be sufficient to allow the measurement of A FB, and what follows, the weak mixing angle sin 2 æ lep with precision of the order of =1:4 æ 10,4 : Obviously, a dedicated study of the forward calorimeter will have to be performed to determine whether an electron identification iciency of ç0.50, and a jet rejection factor of ç10-100, can be achieved in reality. We would like to emphasize the fact that all error estimates quoted in our study are purely statistical. In order to be able to exploit a possibility of measuring sin 2 æ lep with such high precision, the systematic errors have to be comparably small. Quick estimates indicate that three factors are the most important ones: 5

6 forward-backward asymmetry % rapidity of e + e - system Figure 2: Forward-backward asymmetry in e + e, pairs satisfying the Z selection cuts, as a function of rapidity of the e + e, system, jy Zj. Results obtained with the standard lepton rapidity coverage, with both leptons with rapidities jy l j é2.5 are shown with triangles; while those obtained with the extended rapidity coverage (with one of the leptons with the rapidity of jy l j é4.9) are shown with squares. The first point, jy Zj é1.0, is identical for both sets of cuts. i) Sufficiently good knowledge of the parton distribution functions (PDF s), as it affects the knowledge of the lepton acceptance, as well as the results of radiative correction calculations. ii) Knowledge of the lepton acceptance æ reconstruction iciency as a function of lepton rapidity must reach the level of 0.1%, or better. This may be achievable. CDF[7] has shown that it is possible to achieve precision of about 1%, with the largest contribution being due to uncertainty in the PDF s; iii) Effects of higher order QCD (and EWK) corrections; those can, possibly, be estimated by varying the errors on parameters a and b. It is fair to say that, at present, controlling the systematic errors with the required accuracy remains a challenge. However, it does not seem aprioriimpossible to achieve the desired precision. The most important systematic error is due to the uncertainty in the PDF parametrization. We have tried to estimate the variation of the forward-backward asymmetry with different PDF parametrizations. We have generated several Z samples of events each, using older (MRSD0, EHLQ1, ELHQ2, CTEQ2L, CTEQ2M, CTEQ2F, GRV-L0) and more modern PDF s (MRST, CTEQ3 and CTEQ4). While a very significant variation was observed between datasets obtained with the older parametrizations, results obtained with the modern PDF were identical within the statistical errors (ç1%). The uncertainty in the PDF parametrization should be at least 10 times smaller for this systematic error to be comparable with the statistical error. We hope that, with the new data coming from HERA, CDF and D0, the knowledge of PDF s will improve significantly within the next years, and that it would reach the desired precision by the time LHC experiments 6

7 Table V: Results of our study for the four sets of cut described in section 3.2. cuts e/jet rejection A FB æa FB jy l j é2.5 both e æ (no backgrounds) 0.774% 2.04æ10,4 6.6æ10,4 ç =10 4, % 2.04æ10,4 6.6æ10,4 jy l j é2.5 both e æ (no backgrounds) 1.66% 3.03æ10,4 4.0æ10,4 jy Z j é1.0 ç =10 4, % 3.03æ10,4 4.0æ10,4 jy l j é2.5 one e æ (no backgrounds) 2.02% 1.72æ10,4 1.4æ10,4 jy l j é4.9 the other e æ ç =10 5 ; ç fwd = % 1.72æ10,4 1.4æ10,4 ç =10 4 ; ç fwd = % 1.72æ10,4 1.4æ10,4 ç =10 4 ; ç fwd = % 1.73æ10,4 1.4æ10,4 ç =10 4 ; ç fwd = % 1.76æ10,4 1.4æ10,4 ç =10 4 ; ç fwd = % 2.10æ10,4 1.7æ10,4 ç =10 4 ; ç fwd = % 4.19æ10,4 3.4æ10,4 jy l j é2.5 one e æ (no backgrounds) 3.04% 2.20æ10,4 1.35æ10,4 jy l j é4.9 the other e æ ç =10 5 ; ç fwd = % 2.20æ10,4 1.35æ10,4 jy Z j é1.0 ç =10 4 ; ç fwd = % 2.20æ10,4 1.35æ10,4 ç =10 4 ; ç fwd = % 2.21æ10,4 1.36æ10,4 ç =10 4 ; ç fwd = % 2.29æ10,4 1.41æ10,4 ç =10 4 ; ç fwd = % 2.99æ10,4 1.83æ10,4 ç =10 4 ; ç fwd = % 6.74æ10,4 4.13æ10,4 need them. The LHC data on the lepton asymmetry in W decays will provide additional contraints on the parton distribution functions. It may also be possible, with a careful analysis of the Z sample using multi-dimensional fits, to provide information on the forward-backward asymmetry and the PDF s simultaneously. This problem will certainly be carefully studied in the future. 4 Acknowledgements We thank Dimitri Bourilkov, Fabiola Gianotti and Stephen Haywood for useful discussions and comments on the previous versions of this paper. References 1 P. Fisher, U. Becker and J. Kirkby, Phys. Lett. B356 (1995) U. Baur, S. Keller and W. Sakumoto, Phys. Rev. D57 (1998) 199; hep-ph/ J. Rosner, Phys. Rev. D35 (1987) M. Dittmar, Phys. Rev. D55 (1997) 161; hep-ex/ Calculations were performed by Ulrich Baur, unpublished. 6 Detector and Physics Performance Technical Design Report, CERN/ LHCC/ 99-15, AT- LAS TDR 15, 25 May F. Abe et al, Phys. Rev. D52 (1995)

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