Measurements of W and Z/ γ ∗ cross sections and their ratios in p+p collisions at RHIC
STAR Collaboration, J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, D. M. Anderson, A. Aparin, E. C. Aschenauer, M. U. Ashraf, F. G. Atetalla, A. Attri, G. S. Averichev, V. Bairathi, K. Barish, A. Behera, R. Bellwied, A. Bhasin, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. D. Brandenburg, A. V. Brandin, J. Butterworth, H. Caines, M. Calderón de la Barca Sánchez, D. Cebra, I. Chakaberia, P. Chaloupka, B. K. Chan, F-H. Chang, Z. Chang, N. Chankova-Bunzarova, A. Chatterjee, D. Chen, J. Chen, J. H. Chen, X. Chen, Z. Chen, J. Cheng, M. Cherney, M. Chevalier, S. Choudhury, W. Christie, X. Chu, H. J. Crawford, M. Csanád, M. Daugherity, T. G. Dedovich, I. M. Deppner, A. A. Derevschikov, L. Didenko, X. Dong, J. L. Drachenberg, J. C. Dunlop, T. Edmonds, N. Elsey, J. Engelage, G. Eppley, S. Esumi, O. Evdokimov, A. Ewigleben, O. Eyser, R. Fatemi, S. Fazio, P. Federic, J. Fedorisin, C. J. Feng, Y. Feng, P. Filip, E. Finch, Y. Fisyak, A. Francisco, L. Fulek, C. A. Gagliardi, T. Galatyuk, F. Geurts, A. Gibson, K. Gopal, X. Gou, D. Grosnick, W. Guryn, A. I. Hamad, A. Hamed, S. Harabasz, J. W. Harris, S. He, W. He, X. H. He, Y. He, S. Heppelmann, S. Heppelmann, N. Herrmann, E. Hoffman, L. Holub, Y. Hong, et al. (270 additional authors not shown)
aa r X i v : . [ nu c l - e x ] D ec Measurements of W and Z/γ ∗ cross sections and their ratios in p + p collisions at RHIC J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev,
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D. M. Anderson, A. Aparin, E. C. Aschenauer, M. U. Ashraf, F. G. Atetalla, A. Attri, G. S. Averichev, V. Bairathi, K. Barish, A. Behera, R. Bellwied, A. Bhasin, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. D. Brandenburg, A. V. Brandin, J. Butterworth, H. Caines, M. Calder´on de la Barca S´anchez, D. Cebra, I. Chakaberia,
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P. Chaloupka, B. K. Chan, F-H. Chang, Z. Chang, N. Chankova-Bunzarova, A. Chatterjee, D. Chen, J. Chen, J. H. Chen, X. Chen, Z. Chen, J. Cheng, M. Cherney, M. Chevalier, S. Choudhury, W. Christie, X. Chu, H. J. Crawford, M. Csan´ad, M. Daugherity, T. G. Dedovich, I. M. Deppner, A. A. Derevschikov, L. Didenko, X. Dong, J. L. Drachenberg, J. C. Dunlop, T. Edmonds, N. Elsey, J. Engelage, G. Eppley, S. Esumi, O. Evdokimov, A. Ewigleben, O. Eyser, R. Fatemi, S. Fazio, P. Federic, J. Fedorisin, C. J. Feng, Y. Feng, P. Filip, E. Finch, Y. Fisyak, A. Francisco, L. Fulek, C. A. Gagliardi, T. Galatyuk, F. Geurts, A. Gibson, K. Gopal, X. Gou, D. Grosnick, W. Guryn, A. I. Hamad, A. Hamed, S. Harabasz, J. W. Harris, S. He, W. He, X. H. He, Y. He, S. Heppelmann, S. Heppelmann, N. Herrmann, E. Hoffman, L. Holub, Y. Hong, S. Horvat, Y. Hu, H. Z. Huang, S. L. Huang, T. Huang, X. Huang, T. J. Humanic, P. Huo, G. Igo, D. Isenhower, W. W. Jacobs, C. Jena, A. Jentsch, Y. Ji, J. Jia,
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K. Jiang, S. Jowzaee, X. Ju, E. G. Judd, S. Kabana, M. L. Kabir, S. Kagamaster, D. Kalinkin, K. Kang, D. Kapukchyan, K. Kauder, H. W. Ke, D. Keane, A. Kechechyan, M. Kelsey, Y. V. Khyzhniak, D. P. Kiko la, C. Kim, B. Kimelman, D. Kincses, T. A. Kinghorn, I. Kisel, A. Kiselev, M. Kocan, L. Kochenda, D. D. Koetke, L. K. Kosarzewski, L. Kramarik, P. Kravtsov, K. Krueger, N. Kulathunga Mudiyanselage, L. Kumar, S. Kumar, R. Kunnawalkam Elayavalli, J. H. Kwasizur, R. Lacey, S. Lan, J. M. Landgraf, J. Lauret, A. Lebedev, R. Lednicky, J. H. Lee, Y. H. Leung, C. Li, C. Li,
1. Li, W. Li, X. Li, Y. Li, Y. Liang, R. Licenik, T. Lin, Y. Lin, M. A. Lisa, F. Liu, H. Liu, P. Liu, P. Liu, T. Liu, X. Liu, Y. Liu, Z. Liu, T. Ljubicic, W. J. Llope, R. S. Longacre, N. S. Lukow, S. Luo, X. Luo, G. L. Ma, L. Ma, R. Ma, Y. G. Ma, N. Magdy, R. Majka, D. Mallick, S. Margetis, C. Markert, H. S. Matis, J. A. Mazer, N. G. Minaev, S. Mioduszewski, B. Mohanty, I. Mooney, Z. Moravcova, D. A. Morozov, M. Nagy, J. D. Nam, Md. Nasim, K. Nayak, D. Neff, J. M. Nelson, D. B. Nemes, M. Nie, G. Nigmatkulov, T. Niida, L. V. Nogach, T. Nonaka, A. S. Nunes, G. Odyniec, A. Ogawa, S. Oh, V. A. Okorokov, B. S. Page, R. Pak, A. Pandav, Y. Panebratsev, B. Pawlik, D. Pawlowska, H. Pei, C. Perkins, L. Pinsky, R. L. Pint´er, J. Pluta, J. Porter, M. Posik, N. K. Pruthi, M. Przybycien, J. Putschke, H. Qiu, A. Quintero, S. K. Radhakrishnan, S. Ramachandran, R. L. Ray, R. Reed, H. G. Ritter, O. V. Rogachevskiy, J. L. Romero, L. Ruan, J. Rusnak, N. R. Sahoo, H. Sako, S. Salur, J. Sandweiss, S. Sato, W. B. Schmidke, N. Schmitz, B. R. Schweid, F. Seck, J. Seger, M. Sergeeva, R. Seto, P. Seyboth, N. Shah, E. Shahaliev, P. V. Shanmuganathan, M. Shao, A. I. Sheikh, W. Q. Shen, S. S. Shi, Y. Shi, Q. Y. Shou, E. P. Sichtermann, R. Sikora, M. Simko, J. Singh, S. Singha, N. Smirnov, W. Solyst, P. Sorensen, H. M. Spinka, B. Srivastava, T. D. S. Stanislaus, M. Stefaniak, D. J. Stewart, M. Strikhanov, B. Stringfellow, A. A. P. Suaide, M. Sumbera, B. Summa, X. M. Sun, X. Sun, Y. Sun, Y. Sun, B. Surrow, D. N. Svirida, P. Szymanski, A. H. Tang, Z. Tang, A. Taranenko, T. Tarnowsky, J. H. Thomas, A. R. Timmins, D. Tlusty, M. Tokarev, C. A. Tomkiel, S. Trentalange, R. E. Tribble, P. Tribedy, S. K. Tripathy, O. D. Tsai, Z. Tu, T. Ullrich, D. G. Underwood, I. Upsal,
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G. Van Buren, J. Vanek, A. N. Vasiliev, I. Vassiliev, F. Videbæk, S. Vokal, S. A. Voloshin, F. Wang, G. Wang, J. S. Wang, P. Wang, Y. Wang, Y. Wang, Z. Wang, J. C. Webb, P. C. Weidenkaff, L. Wen, G. D. Westfall, H. Wieman, S. W. Wissink, R. Witt, Y. Wu, Z. G. Xiao, G. Xie, W. Xie, H. Xu, N. Xu, Q. H. Xu, Y. F. Xu, Y. Xu, Z. Xu, Z. Xu, C. Yang, Q. Yang, S. Yang, Y. Yang, Z. Yang, Z. Ye, Z. Ye, L. Yi, K. Yip, Y. Yu, H. Zbroszczyk, W. Zha, C. Zhang, D. Zhang, S. Zhang, S. Zhang,
2. P. Zhang, Y. Zhang, Y. Zhang, Z. J. Zhang, Z. Zhang, Z. Zhang, J. Zhao, C. Zhong, C. Zhou, X. Zhu, Z. Zhu, M. Zurek, and M. Zyzak (STAR Collaboration) Abilene Christian University, Abilene, Texas 79699 AGH University of Science and Technology, FPACS, Cracow 30-059, Poland Alikhanov Institute for Theoretical and ExperimentalPhysics NRC ”Kurchatov Institute”, Moscow 117218, Russia Argonne National Laboratory, Argonne, Illinois 60439 American University of Cairo, New Cairo 11835, New Cairo, Egypt Brookhaven National Laboratory, Upton, New York 11973 University of California, Berkeley, California 94720 University of California, Davis, California 95616 University of California, Los Angeles, California 90095 University of California, Riverside, California 92521 Central China Normal University, Wuhan, Hubei 430079 University of Illinois at Chicago, Chicago, Illinois 60607 Creighton University, Omaha, Nebraska 68178 Czech Technical University in Prague,FNSPE, Prague 115 19, Czech Republic Technische Universit¨at Darmstadt, Darmstadt 64289, Germany ELTE E¨otv¨os Lor´and University, Budapest, Hungary H-1117 Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany Fudan University, Shanghai, 200433 University of Heidelberg, Heidelberg 69120, Germany University of Houston, Houston, Texas 77204 Huzhou University, Huzhou, Zhejiang 313000 Indian Institute of Science Education and Research (IISER), Berhampur 760010 , India Indian Institute of Science Education andResearch (IISER) Tirupati, Tirupati 517507, India Indian Institute Technology, Patna, Bihar 801106, India Indiana University, Bloomington, Indiana 47408 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu 730000 University of Jammu, Jammu 180001, India Joint Institute for Nuclear Research, Dubna 141 980, Russia Kent State University, Kent, Ohio 44242 University of Kentucky, Lexington, Kentucky 40506-0055 Lawrence Berkeley National Laboratory, Berkeley, California 94720 Lehigh University, Bethlehem, Pennsylvania 18015 Max-Planck-Institut f¨ur Physik, Munich 80805, Germany Michigan State University, East Lansing, Michigan 48824 National Research Nuclear University MEPhI, Moscow 115409, Russia National Institute of Science Education and Research, HBNI, Jatni 752050, India National Cheng Kung University, Tainan 70101 Nuclear Physics Institute of the CAS, Rez 250 68, Czech Republic Ohio State University, Columbus, Ohio 43210 Institute of Nuclear Physics PAN, Cracow 31-342, Poland Panjab University, Chandigarh 160014, India Pennsylvania State University, University Park, Pennsylvania 16802 NRC ”Kurchatov Institute”, Institute of High Energy Physics, Protvino 142281, Russia Purdue University, West Lafayette, Indiana 47907 Rice University, Houston, Texas 77251 Rutgers University, Piscataway, New Jersey 08854 Universidade de S˜ao Paulo, S˜ao Paulo, Brazil 05314-970 University of Science and Technology of China, Hefei, Anhui 230026 Shandong University, Qingdao, Shandong 266237 Shanghai Institute of Applied Physics,Chinese Academy of Sciences, Shanghai 201800 Southern Connecticut State University, New Haven, Connecticut 06515 State University of New York, Stony Brook, New York 11794 Instituto de Alta Investigaci´on, Universidad de Tarapac´a, Arica 1000000, Chile Temple University, Philadelphia, Pennsylvania 19122 Texas A&M University, College Station, Texas 77843 University of Texas, Austin, Texas 78712 Tsinghua University, Beijing 100084 University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan United States Naval Academy, Annapolis, Maryland 21402 Valparaiso University, Valparaiso, Indiana 46383 Variable Energy Cyclotron Centre, Kolkata 700064, India Warsaw University of Technology, Warsaw 00-661, Poland Wayne State University, Detroit, Michigan 48201 Yale University, New Haven, Connecticut 06520 (Dated: November 11, 2020)
Abstract
We report on the W and Z/γ ∗ differential and total cross sections as well as the W + / W − and( W + + W − )/( Z/γ ∗ ) cross-section ratios measured by the STAR experiment at RHIC in p + p collisions at √ s = 500 GeV and 510 GeV. The cross sections and their ratios are sensitive to quarkand antiquark parton distribution functions. In particular, at leading order, the W cross-sectionratio is sensitive to the ¯ d/ ¯ u ratio. These measurements were taken at high Q ∼ M W , M Z andcan serve as input into global analyses to provide constraints on the sea quark distributions. Theresults presented here combine three STAR data sets from 2011, 2012, and 2013, accumulating anintegrated luminosity of 350 pb − . We also assess the expected impact that our W + /W − cross-section ratios will have on various quark distributions, and find sensitivity to the ¯ u − ¯ d and ¯ d/ ¯ u distributions. PACS numbers: 13.38.Be, 13.38.Dg, 14.20.Dh,24.85.+p . INTRODUCTION Since the discovery of the W and Z bosons by the UA1 [1–4] and UA2 [5–8] experimentsin proton-antiproton collisions at the CERN S p ¯ p S facility, a significant amount of workhas been done measuring the properties of the bosons using a variety of collision systems.These probes range from additional proton-antiproton collision measurements by CDF [9–12] and D0 [13–17] at the Fermilab Tevatron, to measurements based on electron-positroncollisions by the ALEPH, DELPHI, L3, and OPAL experiments performed at LEP [18–20]. More recent measurements from ATLAS [21–24] and CMS [25–28] at the LHC, andPHENIX [29, 30] and STAR [31] at the Relativistic Heavy Ion Collider (RHIC) use proton-proton collisions to investigate the properties of the W and Z bosons. Additionally, boththe PHENIX and STAR experiments have used polarized proton collisions to study the W and Z boson spin asymmetries [30, 32–36]. The current study of inclusive W and Z bosonproduction benefits from these previous experiments. Modern measurements not only serveas an excellent benchmark for Standard Model testing, but also as a means by which toconstrain Parton Distribution Functions (PDFs) of the proton.One particular parton distribution of interest is the ¯ d/ ¯ u ratio near the valence region( x ≈ . d/ ¯ u distribution in the proton. TheNuSea experiment found evidence of a larger-than-expected ¯ d/ ¯ u flavor asymmetry, especiallyas x , the fraction of the proton momentum carried by the struck parton, exceeds x ≈ . x and improve on statistics compared to the previous NuSeameasurement, the STAR experiment at RHIC is able to provide new and complementaryinformation about the ¯ d/ ¯ u distribution, from a different reaction channel, W production, ata large momentum scale, Q = M W .RHIC can collide protons up to √ s = 510 GeV. W ± bosons at RHIC are producedthrough u + ¯ d ( d + ¯ u ) fusion, which allows observables to have sensitivity to the sea quarkdistributions. The W + / W − cross section ratio is sensitive to the ¯ d/ ¯ u distribution, as canbe seen from its leading order contribution [41] σ W + σ W − ≈ u ( x ) ¯ d ( x ) + u ( x ) ¯ d ( x ) d ( x )¯ u ( x ) + d ( x )¯ u ( x ) , (1)where x and x are the fractions of the proton momenta carried by the scattering partons.6dditionally, ATLAS has recently used their measured ( W + + W − ) /Z cross-section ratioto investigate the strange quark content of the proton [23], where an enhancement of theproton strange quark contribution is seen. Furthermore, measurements of differential W and Z cross sections have been used to provide further constraints for PDF extractions [23, 42].These quantities measured at STAR serve as complementary measurements to their LHCcounterparts. They probe a higher x region due to the lower center of mass energy of theproton collisions.We report on the measurements of the differential and total W and Z cross sections,as well as the W + /W − and ( W + + W − )/( Z/γ ∗ ) cross-section ratios made by the STARexperiment at RHIC during the 2011, 2012, and 2013 p + p running periods at √ s = 500GeV (2011 data set) and 510 GeV (2012 and 2013 data sets), accumulating a total integratedluminosity of 350 pb − . A summary of these data sets, including their center of mass energiesand integrated luminosities, is listed in Table I. These measurements are derived from studiesof the W +( − ) → e +( − ) + ν (¯ ν ) and Z/γ ∗ → e + e − decay channels for outgoing leptons. Thisexpands on previous STAR results based on the RHIC 2009 p + p data set [31], not only byadding more statistics, but also in several other areas. First, in addition to the total W and Z cross sections, we have measured the differential cross sections dσ W ± /dη e ± and dσ Z/γ ∗ /dy Z as functions of e ± pseudorapidity, η e ± , and Z boson rapidity, y Z , respectively. Second, ameasurement of the lepton pseudorapidity dependence of the W + / W − cross-section ratiobetween − . ≤ η ≤ . W + + W − )/( Z/γ ∗ ) cross-section ratio wasmeasured. These measurements make use of the same apparatus and techniques describedin previous STAR W and Z publications [31, 33–36].Our results are organized into eight additional sections. Section II provides a briefoverview of the STAR subsystems used in this analysis, while Sec. III describes the data andsimulation samples that were used. The details regarding the extraction of the W and Z/γ ∗ signals from the data and the procedures used to estimate the background contributions arediscussed in Secs. IV and V. In Sec. VI we report on the electron and positron detectionefficiencies. The differential and total cross section results are presented in Sec. VII, whilethe W + / W − and ( W + + W − )/ Z cross-section ratios are shown in Sec. VIII. Finally, Sec. IXpresents a summary of the measurements. Throughout the remainder of the paper we willbe using “ Z/γ ∗ ” and “ Z ” interchangeably. 7 I. EXPERIMENTAL SETUP
The Solenoidal Tracker At RHIC (STAR) detector [43] and its subsystems have beenthoroughly described in similar STAR analyses [31, 33–36]. The presented analysis utilizesseveral subsystems of the STAR detector. Charged particle tracking, including momentumreconstruction and charge sign determination, is provided by the Time Projection Chamber(TPC) [44] in combination with a 0.5 T magnetic field. The TPC lies between 50 and 200cm from the beam axis and covers pseudorapidities | η | < . < φ < π .Surrounding the TPC is the Barrel Electromagnetic Calorimeter (BEMC) [45], which is alead-scintillator sampling calorimeter. The BEMC is segmented into 4800 optically isolatedtowers covering the full azimuthal angle for pseudorapidities | η | <
1, referred to in this paperas the mid-pseudorapidity region.A second lead-scintillator based calorimeter is located at one end of the STAR TPC,the Endcap Electromagnetic Calorimeter (EEMC) [46]. The EEMC consists of 720 towersextending the particle energy deposition measurements to a pseudorapidity of 1 . < η < .
0, referred to as the intermediate pseudorapidity region, while maintaining full azimuthalcoverage. Included within the EEMC is the EEMC Shower Maximum Detector (ESMD) [46],which is used to discriminate amongst isolated electron or positron (signal) events and widershowers typically seen from jet-like events (background). This discrimination is determinedby measuring the transverse profile of the electromagnetic shower. The ESMD consists ofscintillator strips organized into orthogonal u and v planes.Finally, the Zero Degree Calorimeter (ZDC) [43] is used to determine and monitor theluminosity. III. DATA AND SIMULATION
We present results based on measuremnts made in the mid- ( | η e | < .
0) and intermediatepseudorapidity ( 1 . < η e < . p + p runningperiods (Table I). Due to insufficient statistics collected in the intermediate pseudorapidityrange during the 2011 running period, measurements made in this region only combined thedata taken during the 2012 and 2013 running periods.8 ABLE I. Summary of data sets used in this analysis.Data Sample √ s (GeV) L (pb − )2011 500 25 ± ± ± Before combining the mid-pseudorapidity 2011 data set (taken at √ s = 500 GeV) withthe mid-pseudorapidity 2012 and 2013 data sets (taken at √ s = 510 GeV), we studied howthe W and Z fiducial cross sections changed between the two center of mass energies. Thestudy was performed using the FEWZ [47] theory code with the CT14 PDF set [48], andcalculated a 4.7%, 5.4%, and 6% larger W + , W − , and Z cross section, respectively, for thehigher center of mass energy. To account for these differences, we scaled our measured 2011 W and Z fiducial cross sections by the ratio of the cross sections at √ s = 510 GeV to thecross sections at √ s = 500 GeV, computed from the FEWZ-CT14 study, for each of ourlepton pseudorapidity and Z rapidity data bins. These corrections ( ≈ − W +( − ) and Z/γ ∗ bosons were detected via the leptonic decay channels W +( − ) → e +( − ) + ν (¯ ν ) and Z/γ ∗ → e + + e − . Events that pass a calorimeter trigger, which required a transverseenergy, E T , covering a region of ≈ . × . φ × ∆ η , to be greater than 12 (10) GeVin the BEMC (EEMC), constitute our initial W/Z decay candidate sample. This sample ofevents is later refined by applying additional selection criteria, as discussed in Sec. IV.In order to determine detector efficiencies and estimate background contributions fromelectroweak processes, Monte Carlo (MC) samples for
Z/γ ∗ → e + e − , W → eν , and W → τ ν were generated. All samples were produced using PYTHIA 6.4.28 [51] and the “Perugia 0”tune [52]. The event distributions were then passed through a GEANT 3 [53] model of theSTAR detector, after which they were embedded into STAR zero-bias data to account forpile-up tracks in the TPC volume. The pile-up tracks can be caused by another collisionfrom the same bunch crossing as the triggered event, or a collision that occurred in an9arlier or later bunch crossing. The zero-bias events were obtained during bunch crossingsthat were recorded with no cuts applied. Finally, the MC samples were weighted with theintegrated luminosity of the respective STAR data set. The same reconstruction and analysisalgorithms were used on both the MC and data samples. IV. W AND
Z/γ ∗ RECONSTRUCTION W and Z/γ ∗ candidate events were identified and reconstructed using well-establishedselection cuts used in past STAR measurements [31, 33–36]. Candidate events that trig-gered the electromagnetic calorimeters are required to have their collision vertex along thebeam axis within 100 cm of the center of STAR. The vertex was reconstructed using tracksmeasured in the TPC. The reconstructed vertices had a distribution along the beam axisthat was roughly Gaussian with an RMS width of about 40 cm.In addition to the conditions discussed above, a candidate electron or positron track atmid-pseudorapidity (intermediate pseudorapidity) with an associated reconstructed vertexwas also required to have transverse momentum, p T , larger than 10 (7) GeV. To help ensurethat the track and its charge sign are well reconstructed, and to remove pile-up tracks whichmay have accidentlly been associated with a vertex, we implemented several TPC relatedrequirements. First, we required that the reconstructed track has at least 15 (5) TPC hitpoints. Secondly, the number of hit points used in the track fitting needed to be more than51% of the possible hit points. Finally, in the mid-pseudorapidity range we required thatthe first TPC hit point has a radius (with respect to the beam axis) less than 90 cm, whilethe last TPC hit point had a radius greater than 160 cm. A modified cut was applied totracks in the intermediate pseudorapidity region, where the first TPC hit point was requiredto have a radius smaller than 120 cm.The transverse energy of the e ± decay candidates, E eT , was determined from the largesttransverse energy 2 × V.1. Electron and Positron Isolation Cuts
Electrons and positrons originating from W and Z decays should be relatively isolatedfrom other particles in η − φ space, resulting in isolated transverse energy deposition inthe BEMC and EEMC calorimeters. Jet-like events can be reduced by employing severalisolation cuts. The first cut requires the ratio of the e ± candidate’s E eT and the total E T from a 4 × e ± candidate 2 × e ± candidate’s E eT to the transverse energy, E ∆ R< . T , within a cone of radius ∆ R = p η + φ < . E ∆ R< . T was determined by summing the BEMC and EEMC E T and the TPC track p T within the cone. The e ± candidate track was excluded from the sum of TPC track p T toavoid double-counting in E ∆ R< . T . The final isolation cut only applies to the EEMC and inparticular the ESMD. The ESMD can be used to discriminate between isolated e ± , whichcould come from W and Z decays, and QCD/jet-like events by measuring the transverseprofile of the electromagnetic shower in the two ESMD layers. The transverse profile ofthe electromagnetic shower resulting from isolated e ± will be narrower than the profilesproduced from QCD and jet-like backgrounds. TPC tracks were extrapolated to the ESMD,where the central strip in each direction was defined as the nearest strip pointed to by thetrack. A ratio, R ESMD , was formed with a numerator equal to the total energy depositedin the ESMD strips that were within 1.5 cm of the central strips, and a denominator equalto the total energy deposited in the strips that were within 10 cm of the central strips. Forthis analysis, we required this ratio to be larger than 70%.
IV.2. W ± Candidate Event Selection
Differences in the event topologies between leptonic W decays and QCD or Z decays canbe used to select W → eν candidate events. A ~p balT vector can be constructed which is thevector sum of the decay e ± transverse momentum, ~p eT , plus the sum of ~p T vectors for jetsreconstructed outside of a cone radius ∆ R = 0 .
7. Using towers with E T > . p T > . k T algorithm [54] inwhich the resolution parameter was set to 0 .
6. Reconstructed jets were required to have p T > . W candidates will possess a large missing transverse momentum, due to the11ndetected neutrino, which leads to a large imbalance when computing ~p balT . In contrast, Z → e + e − and QCD backgrounds, such as dijets, do not produce such a large ~p balT . Therefore,using the ~p balT vector we define a scalar signed- p T balance quantity as (cid:0) ~p eT · ~p balT (cid:1) / | ~p eT | andrequire it to be larger than 16 (20) GeV for e ± candidates detected in the BEMC (EEMC).In addition to the signed- p T balance cut, the total transverse energy opposite the candidateelectron or positron in the BEMC ( | ∆ φ − π | < .
7) was required not to exceed 11 GeV.This further helped to remove QCD dijet background events where a sizable fraction of theenergy of one of the jets was not observed due to detector effects. Due to the effectivenessof the R ESMD cut, the cut on the transverse energy opposite of the candidate electronor positron was not needed in the EEMC. The charge-sign associated with the leptoncandidates is determined based on the curvature of their tracks measured in the TPC andSTAR’s magnetic field. The yield for a particular charge-sign in the BEMC is determinedby fitting the Q e · E eT /p T distribution between ± .
0, where Q e is the charge-sign of the e ± candidate determined from the curvature of its reconstructed track. Figure 1 shows the E eT distributions for the e ± decay candidates from the studied W ± bosons decay channels,measured in the BEMC. The Jacobian peak in these distributions can clearly be seen between30 GeV and 40 GeV. The electron and positron yields in the EEMC are also determined byfitting the Q e · E eT /p T distribution. Figure 2 shows the signed- p T balance distribution for e + (left panel) and e − (right panel) W ± decay candidates in the EEMC. Final W candidatesin the BEMC and EEMC are required to fall within the range 25 GeV < E eT <
50 GeV.The details of the fits used to extract the e ± yields and background estimates for thesedistributions will be discussed in Sec. V. IV.3. Z Candidate Event Selection Z → e + e − candidate events can be selected by finding isolated e + e − pairs. The isolated e ± candidates were found using the isolation criteria discussed in Sec. IV.1, with a slightmodification to some of the isolation requirement values. For the e ± candidates the ratio E eT to the energy in the surrounding 4 × E eT /E ∆ R> . T wasrequired to be greater than 88%. In addition to the isolation cuts, Z decay e ± candidateswere also required to have a p T >
15 GeV, | η e | < .
0, and a charge-weighted E eT /p T satisfying | Q e · E eT /p T | ≤ .
0. Finally, by reconstructing the invariant mass of the e + e − pairs, a fiducialcut was placed around the Z mass covering the range 70 GeV ≤ m e + e − ≤
110 GeV. The12
10 20 30 40 50 60 (GeV) Te E05001000150020002500 E v en t s / G e V = 500/510 GeVsSTAR p+p Candidates + e | < 1.0 e η | (a) 0 10 20 30 40 50 60 (GeV) Te E0200400600800100012001400 E v en t s / G e V STAR Data (2011+2012+2013) (MC) ν e → W (MC) ν τ → WData-driven QCDSecond EEMC ee (MC) → Z Candidates - e (b) FIG. 1. Signal and background E eT distributions for positron (a) and electron (b) candidates inthe BEMC. The background contributions are shown as stacked histograms, where the solid blueand brown diagonal histograms correspond to the electroweak residual backgrounds from Z → ee and W → τ ν decay channels, respectively. The vertical cyan and diagonal green histogramscorrespond to the residual QCD contributions estimated from the data driven and second EEMCmethods, respectively. The red dashed histogram shows the W → eν signal along with all estimatedbackground contributions and is compared to the data, the black markers. The vertical error baron the data represents the statistical uncertainty and the horizontal bar shows the bin width. reconstructed invariant mass distribution is shown in Fig. 3 (a), where the Z/γ ∗ → e + e − MC distribution is also shown for comparison. One can clearly see the Z signal peak aroundthe mass of the Z near 91 GeV. Figure 3 (b) shows the number of Z candidates plottedagainst the reconstructed Z -boson rapidity. Good agreement is found between the data andMC distributions. 13 − Balance (GeV) T Signed-p E v en t s / G e V STAR (2012+2013) (MC) ν e → W = 500/510 GeVsSTAR p+p Candidates + e < 1.5 η (a) 20 − Balance (GeV) T Signed-p E v en t s / G e V (MC) ν τ → WData-driven QCD ee (MC) → Z Candidates - e (b) FIG. 2. Signal and background signed- p T balance distributions for positron (a) and electron (b)candidates in the EEMC. The background contributions are shown as stacked histograms, wherethe solid blue and brown diagonal histograms correspond to the electroweak residual backgroundsfrom Z → ee and W → τ ν decay channels, respectively. The vertical cyan histograms correspond tothe residual QCD contributions estimated from the data driven method. The red dashed histogramshows the W → eν signal along with all estimated background contributions and is compared to thedata, the black markers. The vertical error bar on the data represents the statistical uncertaintyand the horizontal bar shows the bin width. V. SIGNAL AND BACKGROUND ESTIMATESV.1. W Signal and Background Estimation
The e ± yields were determined by fitting the charge-weighted E eT /p T distribution. Thefits were done for each of the eight pseudorapidity bins, separately for each of the three datasets. Following the fit procedures used in Ref. [36], the distributions were fitted using twodouble-Gaussian template shapes, determined from MC. To adequately describe the data,one Gaussian function was used to determine the E eT /p T distribution from the W → eν
20 40 60 80 100 120 140 (GeV) - e + e m020406080100120140 E v en t s / G e V STAR (2011+2012+2013) (MC) - e + e → * γ Z/ |< 1.0 e η | (a) 1 − − Z y020406080100120140160180200 E v en t s = 500/510 GeVsSTAR p+p < 110 GeV - e + e
70 GeV < M (b)
FIG. 3. Panel (a) shows the distribution of the reconstructed invariant mass from Z decay can-didates compared to Z/γ ∗ → e + e − MC distribution. Panel (b) shows the number of Z candidateevents plotted against the reconstructed rapidity and compared to the MC distribution. The reddashed histogram shows the Z → e + e − MC signal and is compared to the data, the black markers.The vertical error bar on the data represents the statistical uncertainty and the horizontal barshows the bin width. The asymmetry in the MC between negative and positive y Z in (b) can beattributed to the rapidity asymmetry in the efficiencies, seen in Fig. 6 (d), since these events havenot yet been corrected for detector and cut efficiencies. signal, while the other Gaussian function was used to describe the tails. The former resultedin a narrower distribution than the latter. The amplitudes were fitted to the data, using thelog-likelihood method, along with the width and peak position of the narrower Gaussian ineach of the templates. The remaining parameters were fixed based on the MC fit. Figure 4shows the fit result for the 0 . ≤ η e ≤ .
25 pseudorapidity bin from the 2013 data set. Thered dashed line represents the fit to the positron distribution, while the blue solid line showsthe fit to the electron distribution. This fit result is representative of the fits performedin the other pseudorapidity bins and other data sets. The positron and electron yields15ere determined by integrating the respective double-Gaussian function derived from thefour-Gaussian function total fit. − − − − Te /p Te (E • e Q050100150 E v en t s STAR (2013) Fit + e Fit - e < 0.25 e η FIG. 4. A four-Gaussian function fit to measured 0 . < η e < .
25 BEMC Q e · E eT /p T distributionusing the log-likelihood method. The colored lines show individual e + (red dashed) and e − (solidblue) double-Gaussian distributions resulting from the four-Gaussian fit. Two main sources which lead to misidentified W candidates in W → eν decays are fromelectroweak and partonic processes [31, 33–36]. A combination of MC samples and datawas used to estimate these backgrounds. The background estimation procedure we usedfollows the same procedure detailed in Ref. [36]. We then applied the estimated backgroundfractions to the yields found from the fits discussed above.Two sources of electroweak backgrounds in W decay are from W → τ ν and Z → e + e − ,where one of the Z decay particles goes undetected due to either detector inefficiencies oracceptance effects. The contribution of these processes to the W → eν yield was estimatedusing MC samples described in Sec. III.The residual QCD dijet background is mainly due to one of the jets pointing to a region16utside of the STAR acceptance. For the mid-pseudorapidity region (BEMC) this back-ground had two contributions [31, 34, 36]. The first contribution, referred to as the “secondEEMC” background, uses the instrumented EEMC in the pseudorapidity region 1 . < η < e ± candidates that have an opposite-side jet frag-ment outside the detector region − < η < − .
1. The second contribution, referred to asthe “data-driven QCD” background, estimates the QCD background where one of the dijetfragments escapes through the uninstrumented regions at | η | >
2. This procedure looks atevents that pass all W selection criteria, but fail the signed- p T balance requirement. Thebackground distribution was determined by normalizing the E T distribution to the W candi-date E eT distribution between 16 GeV and 20 GeV after all other background contributionsand the W MC signal were removed. Both of these procedures are detailed in Ref. [31].Figure 1 shows the measured W + and W − yields as a function of E eT over the integratedBEMC pseudorapidity range ( | η e | <
1) along with the various estimated background con-tributions and the MC signal distribution for the combined 2011, 2012, and 2013 data sets.The systematic uncertainty associated with the data-driven QCD method was estimated byvarying the signed- p T balance cut value and the E T window used to normalize the QCDbackground. The signed- p T balance cut was varied between 5 GeV and 25 GeV, while the E T normalization window was varied between 16 GeV and 23 . p T balance cut, which are dominated by dijet events, are used to estimate the QCDbackground where dijets escape detection at | η | >
2. However, dijet events selected usingthis method, contain jets that were detected in the region − < η <
2. To account for thedifference in the dijet cross sections, a PYTHIA study looking at hard partonic processes wascarried out comparing the dijet cross section distributions in the regions | η | < | η | > ∼ W yields, and the background to signal ratio foreach process is listed in Table II.The EEMC measurements have a greater likelihood of having the charge-sign misidenti-fied compared to the BEMC. Intermediate pseudorapidity tracks miss the outer radius of theTPC and thus tracking resolution is degraded resulting in broader charge-weighted E eT /p T distributions and larger charge contamination compared to distributions measured at mid-pseudorapidity. It was found that the data could be well described using a two-Gaussian17unction where each Gaussian function described the particular charge’s E eT /p T distribution.As a result the charge separated yield was determined by fitting the EEMC E eT /p T distri-bution with a two-Gaussian function using the log-likelihood method and integrating overthe resulting single Gaussian functions for each e ± yield. The results of this fit are shown inFig. 5. The electron and positron contributions resulting from the two-Gaussian total fit areshown as the blue solid and red dashed lines, respectively. A systematic uncertainty of about3% was estimated by varying the two-Gaussian fitting limits by ± .
3. The estimation ofbackground contributions in the EEMC followed a procedure similar to the one used for theBEMC. The determined background fractions were then applied to the yields determinedfrom the E eT /p T fit. The dominant background sources again resulted from electroweak( W → τ ν and Z → e + e − ) and the hard partonic processes. The residual electroweak decaycontamination was determined from MC samples, while the QCD background was estimatedusing only the data-driven QCD method. The residual QCD backgrounds were estimatedusing the ESMD, where the isolation parameter R ESMD was required to be less than 0 . W candidate signed- p T balance distribution between − W + and W − yields as a function ofsigned- p T balance, along with the estimated backgrounds and MC signal distribution forthe combined 2012 and 2013 data sets. The data-driven QCD systematic uncertainty wasdetermined by varying the R ESMD cut value between 0 . .
55. Furthermore the signed- p T balance window, which was used to normalize the QCD background, was varied between − . . TABLE II. Combined 2011, 2012, and 2013 background to signal ratio for W + and W − between25 GeV < E eT <
50 GeV and | η e | < W → τ ν (%) Z → e + e − (%) Data-driven QCD (%) Second EEMC QCD(%)B/S ( W + ) 2 . ± . . ± . . ± . ± . . ± . W − ) 2 . ± . . ± . . ± . ± . . ± . − − − Te /p Te (E • Q E v en t s STAR (2012+2013) Fit + e Fit - e = 510 GeVsSTAR p+p < 1.5 e η FIG. 5. Double Gaussian fit to measured EEMC Q e · E eT /p T distribution using the log-likelihoodmethod. The colored lines show individual e + (red dashed) and e − (solid blue) Gaussian distribu-tions resulting from the double-Gaussian fit.TABLE III. Combined 2012 and 2013 background to signal ratio for W + and W − for 25 GeV < E eT <
50 GeV, R ESMD > .
7, and signed- p T balance >
20 GeV in 1 . < η e < .
5. Not shown inthe table is the 3% uncertainty associated with the fit to the charge-weighted W yields.Background W → τ ν (%) Z → e + e − (%) Data-driven QCD (%)B/S ( W + ) 3 . ± . . ± . . ± . ± . W − ) 2 . ± . . ± . . ± . ± . V.2. Z Signal and Background Estimation
Due to the requirement of having a pair of oppositely charged, high- E T , and isolated e + and e − , the background in Z → e + e − is expected to be small. The background wasestimated by comparing the number of lepton pairs with the same-charge sign, which passed19ll Z candidate selection criteria, to those which had opposite-charge sign. This backgroundwas found to be just under 4% in our combined data sets. Background corrections wereapplied to each rapidity bin for each of the three data sets by subtracting the number ofsame-charge sign events which passed the Z candidate criteria from the number of opposite-charge sign Z candidates. VI. EFFICIENCIES
The measured fiducial cross sections can be written as σ fidW = N obsW − N bkgdW L · ε W , (2)where N obsW is the number of observed W candidates within the defined kinematic accep-tance that meet the selection criteria specified in Sec. IV. N bkgdW is the total number ofbackground events within the defined kinematic acceptance, as described in Sec V. L is thetotal integrated luminosity, and ε W is the efficiency that needs to be applied to correct fordetector and cut effects. Equation 2 also describes the Z fiducial cross section, σ fidZ , withthe replacement of W related quantities with the Z related quantities.The W and Z efficiencies were computed in the same manner as in Ref. [31]. The ef-ficiencies were defined as the ratios between the number of W ( Z ) boson decay candidatessatisfying selection criteria to all those W ( Z ) bosons falling within the STAR fiducial ac-ceptance.The W candidate efficiencies for each of the three data sets are plotted in Fig. 6 (a)for positron and (b) electron candidates as a function of pseudorapidity. Comparing the W efficiencies between the three data sets, one can clearly see a larger efficiency for the2011 data set. This is due primarily to a lower instantaneous luminosity relative to the2012 and 2013 data sets. The higher instantaneous luminosity leads to larger pile-up inthe TPC, resulting in less efficient track reconstruction. The 2013 data set used a newtrack reconstruction algorithm which resulted in a more efficient track reconstruction. Thiscounteracted much of the efficiency loss that would come with increasing the instantaneousluminosity, allowing for efficiencies that are comparable to those found in the 2012 data set.The positron and electron efficiencies amongst each data set are comparable as can be seenin Fig. 6 (c), which plots the ratio ε W − /ε W + as a function of pseudorapidity. The relativelysmall offset from one shows that the efficiency corrections will have a small effect to the20 fidW + /σ fidW − measurement. Figure 6 (d) shows the Z efficiencies computed for the three datasets as a function of rapidity. The Z efficiencies are overall lower than the W efficiencies,since for Z candidates we required two reconstructed tracks.There were two sources of systematic uncertainties associated with the efficiencies, theestimation of which was based on a previous STAR analysis [31]. The first is associated withTPC track reconstruction efficiency for W or Z candidates. Based on past analyses, theuncertainty of 5% and 10% was used for the W and Z tracking efficiency, respectively. Thesecond systematic uncertainty is related to how well the BEMC and EEMC energy scalesare known. This systematic uncertainty was propagated to the efficiencies by varying theBEMC and EEMC energy scale by its gain uncertainty of 5%. However, when evaluatingthe cross-section ratios (Sec. VIII) many of these systematic uncertainties either partiallyor completely cancel. − − e η e + ε (a) ) -1 -1 − − e η e - ε (b) ) -1 − − e η e + ε / e - ε (c) − − Z y00.20.40.60.81 - e + e ε (d)|< 1.0 e η | FIG. 6. Individual data set efficiencies for: positron (a) and electron (b) W ± decay candidates plot-ted as a function of pseudorapidity. Panel (c) shows the e − /e + efficiency ratio vs. pseudorapidity.Panel (d) shows the efficiency for Z decay candidates vs. rapidity. II. W AND Z CROSS SECTIONSVII.1. W and Z Differential Cross Sections
Using the selected W and Z candidates discussed in Sec. IV, correcting them for back-ground contamination following Sec. V, and finally applying the efficiency corrections com-puted in Sec. VI, Eq. 2 can be used to compute the differential cross sections dσ fidW ± /dη e ± and dσ fidZ /dy Z . The measured differential cross sections dσ fidW + /dη e + and dσ fidW − /dη e − wereobtained in nine pseudorapidity bins, that cover the range − . < η e < .
5. Figure 7 showsthe results for the combined data sets, where the statistical uncertainty is given by the errorbars and the total systematic uncertainties are represented by the boxes surrounding therespective data points. These boxes do not represent a horizontal uncertainty. The bottompanel of Fig. 7 modifies the range of the vertical scale to see better the trend of the W − differential cross section. Using FEWZ [47] in combination with LHAPDF [55], the differ-ential cross sections were evaluated using several PDF sets: CT14MC2nlo [56], CJ15 [57],MMHT2014 [58], NNPDF 3.1 [59], and JAM19 [60]. The CT14MC2nlo PDF set contains1000 replicas and the uncertainty used in the PDF band represents the RMS value in thequantity evaluated from the 1000 replicas. The JAM19 PDF set typically yields smaller val-ues for W − compared to our measurements. This will result in larger W + /W − cross-sectionratios compared to our measured values. Table IV lists the W ± differential cross sectionsand their associated uncertainties that are shown in Fig. 7. Figure 8 shows the combined2011, 2012, and 2013 measured Z differential cross section, dσ fidZ /dy Z , as a function of therapidity. The Z differential cross section was binned in five equally spaced Z rapidity bins.The statistical uncertainties are represented by the error bars, while the total systematicuncertainties are displayed as boxes around the data points. These boxes represent only avertical uncertainty. The experimental results are compared to theory calculations done us-ing FEWZ [47] for several different PDF sets (CT14MC2nlo [56], CJ15 [57], MMHT14 [58],NNPDF3.1 [59], and JAM19 [60]). The cross section values, shown in Fig. 8, are providedin Table V. 22 .5 − − − e η ( pb ) e η / d W f i d σ d W+W-CT14MC2nloCJ15MMHT2014NNPDF3.1JAM19 = 510 GeVs, -1 STAR p+p, L = 350 pb ν e → W < 50 GeV Te
25 GeV < E − − − e η ( pb ) - e η / d - W f i d σ d FIG. 7. The measured dσ fidW + /dη e + (closed circle markers) and dσ fidW − /dη e − (closed triangle markers)for the combined data sets (2011-2013) are plotted as a function of η e . The bottom panel shows dσ fidW − /dη e − when zooming in on the vertical axis. FEWZ [47] was used to compare various NLOPDF sets (CT14MC2nlo [56], CJ15 [57], MMHT14 [58], NNPDF3.1 [59], and JAM19 [60]) to themeasured differential cross sections. VII.2. W and Z Total Cross Sections
The total fiducial cross sections can be obtained by integrating the differential crosssections. Table VI lists the values for the measured fiducial cross sections: σ fidW + , σ fidW − , and σ fidZ . From these, the total cross sections σ totW ± · B ( W → eν ) and σ totZ/γ ∗ · B ( Z/γ ∗ → e + e − )can be calculated according to the relations σ totW ± · B ( W → eν ) = σ fidW ± A W ± (3) σ totZ · B ( Z → e + e − ) = σ fidZ A Z , (4)where A is a kinematic correction factor for the respective boson. The kinematic correctionfactor, which is needed to account for the incomplete STAR kinematic acceptance, wasdetermined for the W + , W − , and Z bosons by using FEWZ in combination with LHAPDF23 ABLE IV. Combined (2011,2012, and 2013) results for differential cross sections, dσ fidW ± /dη e ,binned in e ± pseudorapidity bins, requiring that − < η e < . < E eT <
50 GeV. Thecolumns labeled “Stat.” and “Eff.” represent the statistical uncertainty and the systematic uncer-tainty estimated from the efficiencies, respectively. The later is dominated by the 5% uncertaintyin the tracking efficiency, which is common to all the measurements. The column “Sys.” includesall remaining systematic uncertainties, with the exception of the luminosity. The 9% uncertaintyassociated with the luminosity measurement is not included in the table. η e Range < η e + > dσ fidW + /dη e + (pb) Stat. (pb) Sys. (pb) Eff. (pb) − . − . − .
88 16 . . . . − . − . − .
64 29 . . . . − . − . − .
37 35 . . . . − .
25, 0 . − .
12 40 . . . . .
00, 0 .
25 0 .
13 41 . . . . .
25, 0 .
50 0 .
37 37 . . . . .
50, 0 .
80 0 .
64 26 . . . . .
80, 1 .
00 0 .
89 17 . . . . .
00, 1 .
50 1 .
20 4 . . . . η e Range < η e − > dσ fidW − /dη e − (pb) Stat. (pb) Sys. (pb) Eff. (pb) − . − . − .
89 8 . . . . − . − . − .
65 7 . . . . − . − . − .
38 7 . . . . − .
25, 0 . − .
12 6 . . . . .
00, 0 .
25 0 .
12 6 . . . . .
25, 0 .
50 0 .
38 6 . . . . .
50, 0 .
80 0 .
65 8 . . . . .
80, 1 .
00 0 .
88 8 . . . . .
00, 1 .
50 1 .
25 5 . . . . and an assortment of PDF sets. FEWZ was used with the CT14MC2nlo [56] PDF, tocompute fiducial W ± and Z cross sections, ( σ fidW ± ,Z ) F EW Z , in a kinematic region that mimicsthe STAR detector. Cross sections were also computed using the full leptonic kinematic24 .5 − Z y012345 ( pb ) Z / d y Z f i d σ d STAR (2011+2012 + 2013)JAM19CT14MC2nloCJ15MMHT2014NNPDF3.1 = 510 GeVs, -1 STAR p+p, L = 350 pb - + e + e → * γ / Z > 15 GeV Te | < 1.0, p e η | < 110 GeV ee
70 GeV < M
FIG. 8. The measured dσ fidZ /dy Z for the combined data sets (2011-2013) is plotted against the Z rapidity, and compared to theory calculations done using FEWZ [47] for several different NLOPDF sets (CT14MC2nlo [56], CJ15 [57], MMHT14 [58], NNPDF3.1 [59], and JAM19 [60]). acceptance, ( σ totW ± ,Z ) F EW Z . The kinematic correction factor was then defined as B · A b = (cid:16) σ fidb (cid:17) F EW Z / (cid:0) σ totb (cid:1) F EW Z , (5)where b represents the respective boson, W ± or Z , and B is the corresponding the branch-ing ratio, W → eν or Z → e + e − . The kinematic correction factors calculated using theCT14MC2nlo PDF set are listed in Table VII, along with their evaluated uncertainties.We considered two contributions to the kinematic correction factor uncertainty. The firstcontribution, δA P DF , was on the CT14MC2nlo PDF set itself. To estimate this A W ± and A Z were computed for each replica. A Gaussian fit was made to each boson’s kinematiccorrection factor distribution and the Gaussian width was taken as the uncertainty. Thesecond contribution, δA α s , assessed the effect of changing the α s used in the PDF sets. Thiswas estimated by computing the kinematic correction factor using the NNPDF3.1 [59] PDFset with three different α s values (0.116, 0.118, and 0.120). The average difference from α s =0.118 was used as an uncertainty. Table VII summarizes the two uncertainty contributions25 ABLE V. Combined (2011,2012, and 2013) results for the differential cross section, dσ fidZ /dy Z ,binned in rapidity bins, requiring that | η e | < | y Z | < p eT >
15 GeV, and 70 GeV < M Z <
110 GeV. The columns labeled “Stat.” and “Eff.” represent the statistical uncertainty and thesystematic uncertainty estimated from the efficiencies, respectively. The later is dominated by the10% uncertainty in the tracking efficiency, which is common to all the measurements. The 9%uncertainty associated with the luminosity measurement is not included in the table. < y Z > dσ fidZ /dy Z (pb) Stat. (pb) Eff. (pb) − .
74 0 . . . − .
41 1 . . . .
02 2 . . . .
37 2 . . . .
71 0 . . . σ fidW + . . . . σ fidW − . . . . σ fidZ . . . . and the final uncertainty associated with A W ± ,Z , which was propagated to the total crosssection as a systematic uncertainty.The total W ± and Z cross sections were computed from the measured fiducial cross sec-tions following Eqs. 3 and 4, and are shown in Fig. 9. The top panel displays the W + and W − total cross sections, while the bottom panel shows the Z total cross section. Included forcomparison are curves produced with FEWZ using the CT14MC2nlo [56] PDF set, as wellas PHENIX [29, 30] and previous STAR [31] results at √ s = 500 and 510 GeV, and LHCdata [22, 23, 28, 61] at larger √ s = 7 and 13 TeV. There is good agreement between this W ± ABLE VII. Kinematic correction factors needed to compute the total cross sections and theiruncertainties.Contrib. δA W + (%) δA W − (%) δA Z (%) δA P DF . . . δA α s . . . . . . A W + A W − A Z . ± .
01 0 . ± .
01 0 . ± . cross section measurement and those from previous STAR [31] and PHENIX [29, 30] analy-ses, which makes it difficult to distiguish them in the figure. As a result we have included inthe figure a panel highlighting this region. Table VIII lists the values of the combined 2011,2012, and 2013 total cross sections and their associated uncertainties. Figure 10 comparesthe new STAR total cross section results to CT14MC2nlo by plotting the ratio of STARcross sections to the CT14MC2nlo cross sections for each boson. The error bars in the figurerepresent the total STAR measurement uncertainties and the CT14MC2nlo PDF uncertain-ties added in quadrature. The CT14MC2nlo PDF uncertainties used for W + , W − , and Z cross sections were 5.9%, 7.4%, and 7.0%, respectively. TABLE VIII. STAR total cross sections calculated from the combined 2011, 2012, and 2013 datasets. The columns labeled “Stat.” and “Eff.” represent the statistical uncertainty and the sys-tematic uncertainty estimated from the efficiencies, respectively. The column “Sys.” includes allremaining systematic uncertainties, with the exception of the luminosity. The 9% uncertaintyassociated with the luminosity measurement is not included in the table.Cross Section (pb) Stat. (pb) Sys. (pb) Eff. (pb) σ totW + · B ( W + → e + ν ) 143 . . . . σ totW − · B ( W − → e − ¯ ν ) 41 . . . . σ totZ · B ( Z → e + e − ) 8 . . . . IG. 9. The measured total W ± and Z cross sections for the combined STAR data sets (2011-2013). For clarity the PHENIX measurements are plotted at -5 GeV from √ s = 510 GeV ( W → µ )and 500 GeV ( W → e ), respectively. The inset plot in the upper panel highlights the STAR andPHENIX results ( √ s ∼
500 GeV). For the Z cross section, the STAR data uses a mass windowof 70 GeV < m e + e − <
110 GeV, CT14MC2nlo and CMS use 60 GeV < m e + e − <
120 GeV, andATLAS uses 66 GeV < m e + e − <
116 GeV. The dashed lines in the figure show the respective W ± and Z cross section curves computed using FEWZ and the CT14MC2nlo [56] PDF. VIII. CROSS-SECTION RATIOS
Equation 2 can also be used to compute the cross-section ratios σ fidW + /σ fidW − and σ fidW /σ fidZ .A benefit to measuring the cross-section ratios rather than the absolute cross sections isthat several systematic uncertainties are reduced or canceled. For example, the luminosityuncertainty in the cross-section ratios is canceled, while the tracking efficiency uncertaintyis reduced in the W/Z (5%) measurement and canceled in the W + /W − measurement.28 − C T M C l o t o t σ / S T A R t o t σ ν + e → + W ν - e → - W - e + e → * γ Z/ = 510 GeVs, -1 STAR p+p, L = 35 pb
FIG. 10. Ratio of the STAR calculated total cross sections to the total cross sections found usingthe CT14MC2nlo PDF set [48] versus the decay boson’s charge. These comparisons place a masswindow of 70 GeV < m e + e − <
110 GeV on the Z cross section. The error bars shown here are thetotal uncertainties including contributions from the efficiency, luminosity, and PDF uncertainties. VIII.1. W Cross-Section Ratio
The W + /W − ratio is presented in eight pseudorapidity bins in the mid-pseudorapidityregion ( | η e | < . < η e < . W + /W − cross-section ratio was computed separately for eachof the three data sets in the mid-pseudorapidity region, while the W + /W − cross-sectionratio in the intermediate pseudorapidity region covered by the EEMC was computed fromthe combined 2012 and 2013 data sets.Figure 11 shows a comparison of the W + /W − cross-section ratios for each data setmeasured in the mid-pseudorapidity region as a function of pseudorapidity, where the errorbars represent statistical uncertainties only. From the figure one can see consistency amongst29he data sets and improvement in the statistical precision with each year. These values areplotted with an offset in η e for clarity.Systematic uncertainties for the backgrounds were computed, as described in Sec. V,for the pseudorapidity dependent W + and W − distributions. These uncertainties werethen propagated to the W + /W − cross-section ratios, which lead to about ∼ .
5% (4%)average uncertainty on the W + /W − cross-section ratio measured in the mid- (intermediate)pseudorapidity regions. The efficiency uncertainties due to the energy scale, discussed inSec. VI were then propagated to the W + /W − ratios measured in the mid- (intermediate)pseudorapidity region, which contributed 1 .
5% (9%) to the total systematic uncertainty.An additional uncertainty that was studied is related to the difference in the η e + and η e − distributions in the intermediate pseudorapidity measurement. For measurements in themid-pseudorapidity region these differences were negligible. However, in the intermediatepseudorapidity range the means of the two η e distributions differ by about 0.05. FEWZwas used to investigate how the W + /W − cross-section ratio changes over this range usingthe CT14MC2nlo [56], MMHT14 [58], and NNPDF3.1 [59] NLO PDF sets. Based on thisstudy, an uncertainty of 9% was estimated and applied to the intermediate W + /W − cross-section ratio. Figure 12 shows the W + /W − cross-section ratios for the combined datasets plotted against the pseudorapidity. These measurements are also compared to NLOpredictions using two theory frameworks (FEWZ [47] and CHE [62]), and various PDFinputs (CT14MC2nlo [56], MMHT14 [58], BS15 [63], CJ15 [57], JAM19 [60], and NNPDF3.1 [59]). The hatched uncertainty band represents the uncertainty associated with usingthe CT14MC2nlo PDF set within the FEWZ framework. The PDF sets are found to beconsistent within the precision of the measured data. The results shown in Fig. 12 are listedin Table IX. VIII.2. W Cross-section Ratio PDF Impact
Ultimately, the results we presented are intended to be included in future global analysesto constrain PDF quark distributions. However, in the meantime we can assess the impactof these measurements through a PDF reweighting procedure. The W + /W − cross-sectionratio results discussed in Sec. VIII.1 were used to reweight the CT14MC2nlo [56] PDF set30 − − e η W - f i d σ / W + f i d σ ) -1 -1 -1 = 510 GeVsSTAR p+p ν e → W < 50 GeV Te
25 GeV < E
FIG. 11. Ratio of fiducial cross sections for production of W + and W − bosons plotted against thedecay charged lepton pseudorapidity, η e , for each of the three data sets: 2011 (black circle), 2012(blue square), and 2013 (red triangle). For clarity, positions of the data points for the 2011, 2012,and 2013 data sets within each bin are offset by -0.03, 0.0, and 0.03. The error bars correspond tothe statistical uncertainty associated with the cross-section ratio. using the procedure discussed in Ref. [64]. FEWZ was used to evaluate the W ± fiducial crosssections needed as input to evaluate the W + /W − cross-section ratio for each of the 1000CT14MC2nlo replicas. The result of this reweighting with the new STAR data is shown inFig. 13 as a function of pseudorapidity. The red band is the reweighted distribution and theCT14MC2nlo uncertainties are given by the blue hatched band. The impact of the STARdata on various PDF central distributions is assessed by investigating the difference betweenthe reweighted PDF distribution ( P DF rw ) and the nominal CT14MC2nlo PDF distribution( P DF nw ), normalized to the nominal PDF uncertainty ( δP DF nw ). Figure 14 shows thequantity ( P DF rw − P DF nw ) / ( δP DF nw ) (the blue solid line), plotted as a function of x atthe scale Q = 100 GeV, for several PDF distributions (¯ u − ¯ d , ¯ d/ ¯ u , ¯ d , and ¯ u ). The hatchedbands in Fig. 14 represent the ratio between the reweighted and nominal PDF uncertainties, ± ( δP DF rw /δP DF nw ), which are enclosed by blue dashed lines and can be used to assess31 − − e η W - f i d σ / W + f i d σ STAR (2011+2012+2013)CT14MC2nlo (FEWZ)NNPDF3.1 (FEWZ)MMHT2014 (FEWZ)CJ15 (FEWZ)BS15 (CHE)JAM19 (FEWZ) = 510 GeVs, -1 STAR p+p, L = 350 pb ν ± e → ± W < 50 GeV Te
25 GeV < E
FIG. 12. The combined (2011,2012, and 2013) results for the ratio of the fiducial cross sections forthe production of W + and W − bosons plotted against the decay charged letpon pseudorapidity, η e . The error bars represent the statistical uncertainty, whereas the rectangular boxes representthe systematic uncertainty for the respective data point. These measurements are compared tovarious theory predictions displayed in the legend.TABLE IX. The combined (2011, 2012, and 2013) results for the ratio of the fiducial cross sectionsfor production of W + and W − bosons in bins of the decay charged lepton pseudorapidity. < η e > σ fidW + /σ fidW − Stat. Sys. − .
88 1 . . . − .
64 3 . . . − .
37 4 . . . − .
12 5 . . . .
13 6 . . . .
37 5 . . . .
64 3 . . . .
88 2 . . . .
23 0 . . . the change in the PDF uncertainty. The black lines represent ± δP DF nw uncertainties from32he solid blue line. The difference between the solid black and dashed blue lines shows thechange in uncertainty. On the other hand deviations of the solid blue line from zero representchanges in the central value of the nominal PDF set. From Fig. 14, a clear but modestreduction in the uncertainty is seen in all of the distributions. Furthermore, all distributionsshow some modification to the nominal PDF’s central values, which are generally withinthe one-sigma level. The change in the ¯ d/ ¯ u ratio is negative over the x range of 0 . − . d/ ¯ u comparedto the nominal PDF set. While at x > .
2, the change is slightly positive indicating thatthe reweighted PDF prefers a larger ¯ d/ ¯ u than the nominal PDF. − − e η - W f i d σ / + W f i d σ STAR (2011+2012+2013)CT14MC2nlo CT14MC2nlo Reweighted = 510 GeVs, -1 STAR p+p, L = 350 pb ν ± e → ± W < 50 GeV Te
25 GeV < E
FIG. 13. The combined results for the ratio of the fiducial cross sections for the production of W + and W − bosons compared to the predictions from the original and reweighted CT14MC2nloPDF [56] predictions. The error bars on the STAR data represent the quadrature sum of thestatistical and systematic uncertainties. The blue hatched band represents the CT14MC2nlo PDFuncertainty, while the red band shows the reweighted CT14MC2nlo PDF uncertainty after fittingthe STAR data. − − ) n w P D F δ ) / ( n w - P D F r w ( P D F d-u u/d − − ) n w P D F δ ) / ( n w - P D F r w ( P D F d u FIG. 14. The impact of STAR W + /W − data on ¯ u − ¯ d , ¯ d/ ¯ u , ¯ d , and ¯ u PDF distributions at Q = 100GeV. The solid blue line shows the difference between the reweighted and nominal CT14MC2nloPDF central value, normalized by the nominal PDF uncertainty. The hatched bands representthe ratio between the reweighted and nominal PDF uncertainties. The black lines represent thenominal PDF uncertainties from the solid blue line. VIII.3. ( W + + W − ) / Z Cross-Section Ratio
The σ fidW /σ fidZ cross-section ratio was formed using Eq. 2 and adding the W + and W − fiducial cross sections in the central pseudorapidity region ( | η e | < W cross sections were evaluated as discussed in Sec. VIII.1, with the ex-ception of the track reconstruction uncertainty, and were propagated to the ( W + + W − ) /Z cross-section ratio measurement. The systematic uncertainty associated with the track re-construction efficiency was estimated at 5% due to partial cancellation.The measured σ fidW /σ fidZ cross-section ratio for the combined 2011, 2012 and 2013 datasets was found to be 25 . ± . (stat.) ± . (syst.) , and is shown in Fig. 15. The ( W + + W − ) /Z cross-section ratio is compared to NLO evaluations using the FEWZ framework and severalinput PDF sets. This measurement is consistent with the FEWZ predictions for all PDFsets investigated and will allow us to further constrain the sea quark PDFs. The uncertainty34ssociated with the W/Z cross-section ratio calculated from CT14MC2nlo replicas was es-timated to be 2.5% (blue hatched band), based on the distribution’s RMS. Also included isthe ( W + + W − ) /Z cross-section ratio computed from the W and Z fiducial cross sectionsfrom the 2009 STAR p + p data set [31]. The error bars represent the statistical uncertainties,while the boxes represent the total systematic uncertainties. Z f i d σ / W f i d σ STAR (2011+2012+2013)STAR PRD 85, 092010MMHT2014CT14MC2nlo NNPDF3.1CJ15JAM19 = 510 GeVs, -1 STAR p+p, L = 350 pb|< 1) e η (| ν e → W > 15 GeV) eT | < 1, p e η | < 1, | Z (|y - e + e → * γ Z/ < 50 GeV Te
25 GeV < E < 110 GeV - e + e
70 GeV < M
FIG. 15. The measured ( W + + W − ) /Z (red circle marker) for the combined data sets (2011-2013). Compared to this measurement is the ( W + + W − ) /Z computed from the STAR 2009 dataset [31](black square marker), and evaluations using the FEWZ framework [47] and several inputNLO PDF sets (MMHT14 [58], CT14MC2nlo [56], NNPDF3.1 [59], CJ15 [57], and JAM19 [60]). IX. SUMMARY
STAR has measured the W and Z total and differential cross sections, along with the W + /W − and ( W + + W − ) /Z cross-section ratios in p + p collisions at center of mass energiesof 500 GeV and 510 GeV at RHIC, using the total luminosity of 350 pb − . These measure-ments not only provide additional high Q data to be used in future global analyses to help35onstrain PDFs, but also serve as complementary measurements to other experiments. Inparticular, our total and differential W and Z cross sections along with the ( W + + W − ) /Z cross-section ratio, will complement LHC’s W and Z production program by providing dataat lower √ s and sensitivity at larger x . Our W + /W − cross-section ratio measurement, whichis particularly sensitive to the ¯ d/ ¯ u sea quark distribution [65] (Eq. 1), provides an alterna-tive method to study the ¯ d/ ¯ u distribution which is complementary to the measurementsperformed by the NuSea and SeaQuest experiments.Using our pseudorapidity dependent W + /W − cross-section ratio results in a PDFreweighting study, we find sensitivity to the sea quark distributions. Our study showsmodest improvement in the uncertainties of several distributions, in particular the ¯ d/ ¯ u and¯ u − ¯ d distributions, as well as a change in the central values.Overall we find good agreement between our measurements and the current PDF distri-butions. Inclusion of these data into future global fits will help to constrain the PDFs. X. ACKNOWLEDGMENTS
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