Precision Measurement of the Longitudinal Double-spin Asymmetry for Inclusive Jet Production in Polarized Proton Collisions at s √ =200 GeV
STAR Collaboration, L. Adamczyk, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, C. D. Anson, A. Aparin, D. Arkhipkin, E. C. Aschenauer, G. S. Averichev, A. Banerjee, D. R. Beavis, R. Bellwied, A. Bhasin, A. K. Bhati, P. Bhattarai, H. Bichsel, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, W. Borowski, J. Bouchet, A. V. Brandin, S. G. Brovko, S. Bultmann, I. Bunzarov, T. P. Burton, J. Butterworth, H. Caines, M. Calderon de la Barca Sanchez, J. M. Campbell, D. Cebra, R. Cendejas, M. C. Cervantes, P. Chaloupka, Z. Chang, S. Chattopadhyay, H. F. Chen, J. H. Chen, L. Chen, J. Cheng, M. Cherney, A. Chikanian, W. Christie, J. Chwastowski, M. J. M. Codrington, G. Contin, J. G. Cramer, H. J. Crawford, A. B. Cudd, X. Cui, S. Das, A. Davila Leyva, L. C. De Silva, R. R. Debbe, T. G. Dedovich, J. Deng, A. A. Derevschikov, R. Derradi de Souza, S. Dhamija, B. di Ruzza, L. Didenko, C. Dilks, F. Ding, P. Djawotho, X. Dong, J. L. Drachenberg, J. E. Draper, C. M. Du, L. E. Dunkelberger, J. C. Dunlop, L. G. Efimov, J. Engelage, K. S. Engle, G. Eppley, L. Eun, O. Evdokimov, O. Eyser, R. Fatemi, S. Fazio, J. Fedorisin, P. Filip, E. Finch, Y. Fisyak, C. E. Flores, C. A. Gagliardi, D. R. Gangadharan, D. Garand, F. Geurts, A. Gibson, M. Girard, S. Gliske, L. Greiner, D. Grosnick, D. S. Gunarathne, Y. Guo, et al. (261 additional authors not shown)
PPrecision Measurement of the Longitudinal Double-spin Asymmetry for Inclusive JetProduction in Polarized Proton Collisions at √ s = 200 GeV
L. Adamczyk, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, C. D. Anson, A. Aparin, D. Arkhipkin, E. C. Aschenauer, G. S. Averichev, A. Banerjee, D. R. Beavis, R. Bellwied, A. Bhasin, A. K. Bhati, P. Bhattarai, H. Bichsel, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, W. Borowski, J. Bouchet, A. V. Brandin, S. G. Brovko, S. B¨ultmann, I. Bunzarov, T. P. Burton, J. Butterworth, H. Caines, M. Calder´on de la Barca S´anchez, J. M. Campbell, D. Cebra, R. Cendejas, M. C. Cervantes, P. Chaloupka, Z. Chang, S. Chattopadhyay, H. F. Chen, J. H. Chen, L. Chen, J. Cheng, M. Cherney, A. Chikanian, W. Christie, J. Chwastowski, M. J. M. Codrington, G. Contin, J. G. Cramer, H. J. Crawford, A. B. Cudd, X. Cui, S. Das, A. Davila Leyva, L. C. De Silva, R. R. Debbe, T. G. Dedovich, J. Deng, A. A. Derevschikov, R. Derradi de Souza, S. Dhamija, B. di Ruzza, L. Didenko, C. Dilks, F. Ding, P. Djawotho, X. Dong, J. L. Drachenberg, J. E. Draper, C. M. Du, L. E. Dunkelberger, J. C. Dunlop, L. G. Efimov, J. Engelage, K. S. Engle, G. Eppley, L. Eun, O. Evdokimov, O. Eyser, R. Fatemi, S. Fazio, J. Fedorisin, P. Filip, E. Finch, Y. Fisyak, C. E. Flores, C. A. Gagliardi, D. R. Gangadharan, D. Garand, F. Geurts, A. Gibson, M. Girard, S. Gliske, L. Greiner, D. Grosnick, D. S. Gunarathne, Y. Guo, A. Gupta, S. Gupta, W. Guryn, B. Haag, A. Hamed, L.-X. Han, R. Haque, J. W. Harris, S. Heppelmann, A. Hirsch, G. W. Hoffmann, D. J. Hofman, S. Horvat, B. Huang, H. Z. Huang, X. Huang, P. Huck, T. J. Humanic, G. Igo, W. W. Jacobs, H. Jang, E. G. Judd, S. Kabana, D. Kalinkin, K. Kang, K. Kauder, H. W. Ke, D. Keane, A. Kechechyan, A. Kesich, Z. H. Khan, D. P. Kikola, I. Kisel, A. Kisiel, D. D. Koetke, T. Kollegger, J. Konzer, I. Koralt, L. K. Kosarzewski, L. Kotchenda, A. F. Kraishan, P. Kravtsov, K. Krueger, I. Kulakov, L. Kumar, R. A. Kycia, M. A. C. Lamont, J. M. Landgraf, K. D. Landry, J. Lauret, A. Lebedev, R. Lednicky, J. H. Lee, M. J. LeVine, C. Li, W. Li, X. Li, X. Li, Y. Li, Z. M. Li, M. A. Lisa, F. Liu, T. Ljubicic, W. J. Llope, M. Lomnitz, R. S. Longacre, X. Luo, G. L. Ma, Y. G. Ma, D. M. M. D. Madagodagettige Don, D. P. Mahapatra, R. Majka, S. Margetis, C. Markert, H. Masui, H. S. Matis, D. McDonald, T. S. McShane, N. G. Minaev, S. Mioduszewski, B. Mohanty, M. M. Mondal, D. A. Morozov, M. K. Mustafa, B. K. Nandi, Md. Nasim, T. K. Nayak, J. M. Nelson, G. Nigmatkulov, L. V. Nogach, S. Y. Noh, J. Novak, S. B. Nurushev, G. Odyniec, A. Ogawa, K. Oh, A. Ohlson, V. Okorokov, E. W. Oldag, D. L. Olvitt Jr., M. Pachr, B. S. Page, S. K. Pal, Y. X. Pan, Y. Pandit, Y. Panebratsev, T. Pawlak, B. Pawlik, H. Pei, C. Perkins, W. Peryt, P. Pile, M. Planinic, J. Pluta, N. Poljak, K. Poniatowska, J. Porter, A. M. Poskanzer, N. K. Pruthi, M. Przybycien, P. R. Pujahari, J. Putschke, H. Qiu, A. Quintero, S. Ramachandran, R. Raniwala, S. Raniwala, R. L. Ray, C. K. Riley, H. G. Ritter, J. B. Roberts, O. V. Rogachevskiy, J. L. Romero, J. F. Ross, A. Roy, L. Ruan, J. Rusnak, O. Rusnakova, N. R. Sahoo, P. K. Sahu, I. Sakrejda, S. Salur, J. Sandweiss, E. Sangaline, A. Sarkar, J. Schambach, R. P. Scharenberg, A. M. Schmah, W. B. Schmidke, N. Schmitz, J. Seger, P. Seyboth, N. Shah, E. Shahaliev, P. V. Shanmuganathan, M. Shao, B. Sharma, W. Q. Shen, S. S. Shi, Q. Y. Shou, E. P. Sichtermann, R. N. Singaraju, M. J. Skoby, D. Smirnov, N. Smirnov, D. Solanki, P. Sorensen, H. M. Spinka, B. Srivastava, T. D. S. Stanislaus, J. R. Stevens, R. Stock, M. Strikhanov, B. Stringfellow, M. Sumbera, X. Sun, X. M. Sun, Y. Sun, Z. Sun, B. Surrow, D. N. Svirida, T. J. M. Symons, M. A. Szelezniak, J. Takahashi, A. H. Tang, Z. Tang, T. Tarnowsky, J. H. Thomas, A. R. Timmins, D. Tlusty, M. Tokarev, S. Trentalange, R. E. Tribble, P. Tribedy, B. A. Trzeciak, O. D. Tsai, J. Turnau, T. Ullrich, D. G. Underwood, G. Van Buren, G. van Nieuwenhuizen, M. Vandenbroucke, J. A. Vanfossen, Jr., R. Varma, G. M. S. Vasconcelos, A. N. Vasiliev, R. Vertesi, F. Videbæk, Y. P. Viyogi, S. Vokal, A. Vossen, M. Wada, F. Wang, G. Wang, H. Wang, J. S. Wang, X. L. Wang, Y. Wang, Y. Wang, G. Webb, J. C. Webb, G. D. Westfall, H. Wieman, S. W. Wissink, R. Witt, Y. F. Wu, Z. Xiao, W. Xie, K. Xin, H. Xu, J. Xu, N. Xu, Q. H. Xu, Y. Xu, Z. Xu, W. Yan, C. Yang, Y. Yang, Y. Yang, Z. Ye, P. Yepes, L. Yi, K. Yip, I.-K. Yoo, N. Yu, Y. Zawisza, H. Zbroszczyk, W. Zha, J. B. Zhang, J. L. Zhang, S. Zhang, X. P. Zhang, Y. Zhang, Z. P. Zhang, F. Zhao, J. Zhao, C. Zhong, X. Zhu, Y. H. Zhu, Y. Zoulkarneeva, and M. Zyzak a r X i v : . [ h e p - e x ] M a y (STAR Collaboration) AGH University of Science and Technology, Cracow, Poland Argonne National Laboratory, Argonne, Illinois 60439, USA University of Birmingham, Birmingham, United Kingdom Brookhaven National Laboratory, Upton, New York 11973, USA University of California, Berkeley, California 94720, USA University of California, Davis, California 95616, USA University of California, Los Angeles, California 90095, USA Universidade Estadual de Campinas, Sao Paulo, Brazil Central China Normal University (HZNU), Wuhan 430079, China University of Illinois at Chicago, Chicago, Illinois 60607, USA Cracow University of Technology, Cracow, Poland Creighton University, Omaha, Nebraska 68178, USA Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic Nuclear Physics Institute AS CR, 250 68 ˇReˇz/Prague, Czech Republic Frankfurt Institute for Advanced Studies FIAS, Germany Institute of Physics, Bhubaneswar 751005, India Indian Institute of Technology, Mumbai, India Indiana University, Bloomington, Indiana 47408, USA Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia University of Jammu, Jammu 180001, India Joint Institute for Nuclear Research, Dubna, 141 980, Russia Kent State University, Kent, Ohio 44242, USA University of Kentucky, Lexington, Kentucky, 40506-0055, USA Korea Institute of Science and Technology Information, Daejeon, Korea Institute of Modern Physics, Lanzhou, China Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA Max-Planck-Institut f¨ur Physik, Munich, Germany Michigan State University, East Lansing, Michigan 48824, USA Moscow Engineering Physics Institute, Moscow Russia National Institute of Science Education and Research, Bhubaneswar 751005, India Ohio State University, Columbus, Ohio 43210, USA Old Dominion University, Norfolk, Virginia 23529, USA Institute of Nuclear Physics PAN, Cracow, Poland Panjab University, Chandigarh 160014, India Pennsylvania State University, University Park, Pennsylvania 16802, USA Institute of High Energy Physics, Protvino, Russia Purdue University, West Lafayette, Indiana 47907, USA Pusan National University, Pusan, Republic of Korea University of Rajasthan, Jaipur 302004, India Rice University, Houston, Texas 77251, USA University of Science and Technology of China, Hefei 230026, China Shandong University, Jinan, Shandong 250100, China Shanghai Institute of Applied Physics, Shanghai 201800, China SUBATECH, Nantes, France Temple University, Philadelphia, Pennsylvania 19122, USA Texas A&M University, College Station, Texas 77843, USA University of Texas, Austin, Texas 78712, USA University of Houston, Houston, Texas 77204, USA Tsinghua University, Beijing 100084, China United States Naval Academy, Annapolis, Maryland, 21402, USA Valparaiso University, Valparaiso, Indiana 46383, USA Variable Energy Cyclotron Centre, Kolkata 700064, India Warsaw University of Technology, Warsaw, Poland University of Washington, Seattle, Washington 98195, USA Wayne State University, Detroit, Michigan 48201, USA Yale University, New Haven, Connecticut 06520, USA University of Zagreb, Zagreb, HR-10002, Croatia (Dated: May 21, 2014)We report a new high-precision measurement of the mid-rapidity inclusive jet longitudinal double-spin asymmetry, A LL , in polarized pp collisions at center-of-mass energy √ s = 200 GeV. The STAR data place stringent constraints on polarized parton distribution functions extracted at next-to-leading order from global analyses of inclusive deep inelastic scattering (DIS), semi-inclusive DIS,and RHIC pp data. The measured asymmetries provide evidence for positive gluon polarization inthe Bjorken- x region x > . PACS numbers: 14.20.Dh, 13.88.+e, 13.87.Ce, 14.70.Dj
A fundamental and long-standing puzzle in QuantumChromodynamics (QCD) concerns how the intrinsic spinsand orbital angular momenta of the quarks, anti-quarks,and gluons sum to give the proton spin of (cid:126) / x accessed by fixed-target experiments,the polarized deep-inelastic scattering (DIS) data used toextract ∆Σ provide only loose constraints on the gluonspin contribution, ∆ G , via scaling violations.The measurement of asymmetries directly sensitive tothe gluon helicity distribution was a primary motivationfor establishing the spin structure program at the Rela-tivisitic Heavy Ion Collider (RHIC). Since the commence-ment of the RHIC spin program, several inclusive jet [7–9] and pion [10–14] asymmetry measurements have beenincorporated into next-to-leading-order (NLO) perturba-tive QCD (pQCD) fits. While these data provide someconstraints on ∆ G , ruling out large positive or negativegluon contributions to the proton spin, they lack the sta-tistical power to distinguish a moderate gluon contribu-tion from zero. The inclusive jet asymmetries presentedhere benefit from nearly a 20-fold increase in the eventsample as well as improved jet reconstruction and cor-rection techniques compared to [9], and provide muchtighter constraints on the gluon polarization.The cross section for mid-rapidity inclusive jet produc-tion in pp collisions at √ s = 200 GeV is well described byNLO pQCD calculations [15, 16] over the transverse mo-mentum range 5 < p T <
50 GeV/ c [7]. The NLO pQCDcalculations indicate that mid-rapidity jet production atRHIC is dominated by quark-gluon ( qg ) and gluon-gluon( gg ) scattering, which together account for 60 −
90% ofthe total yield for the jet transverse momenta studiedhere. The qg and gg scattering cross sections are verysensitive to the longitudinal helicities of the participat-ing partons, so the inclusive jet longitudinal double-spinasymmetry, A LL , provides direct sensitivity to the gluonpolarization in the proton. A LL is defined as: A LL = σ ++ − σ + − σ ++ + σ + − , (1)where σ ++ ( σ + − ) is the differential cross section when thebeam protons have the same (opposite) helicities.The data presented here were extracted from an inte-grated luminosity of 20 pb − recorded in the year 2009with the STAR detector [17] at RHIC. The polarizationwas measured independently for each of the two counter- rotating proton beams (hereafter designated blue (B) andyellow (Y)) and for each fill using Coulomb-nuclear inter-ference proton-carbon polarimeters [18], calibrated via apolarized atomic hydrogen gas-jet target [19]. Averagedover RHIC fills, the luminosity-weighted polarization val-ues for the two beams were P B = 0 .
574 and P Y = 0 . .
5% relative uncertainty on the product P B P Y [20]. The helicity patterns of the colliding beam buncheswere changed between beam fills to minimize system-atic uncertainties in the A LL measurement. SegmentedBeam-Beam Counters (BBC) [21], symmetrically locatedon either side of the STAR interaction point and cover-ing the pseudo-rapidity range 3 . < | η | < .
0, measuredthe helicity-dependent relative luminosities and served aslocal polarimeters.The STAR subsystems used to measure jets arethe Time Projection Chamber (TPC) and the Bar-rel (BEMC) and Endcap (EEMC) ElectromagneticCalorimeters [17]. The TPC provides tracking forcharged particles in the 0.5 T solenoidal magnetic fieldwith acceptance of | η | < . π in the azimuthal an-gle φ . The BEMC and EEMC cover a fiducial area of − . < η < . < φ < π , and provide triggeringand detection of photons and electrons.Events were recorded if they satisfied the jet patch (JP)trigger condition in the BEMC or EEMC. The JP triggerrequired a ∆ η × ∆ φ = 1 × . . . η , resulted in a 37% increase in jet ac-ceptance compared to previous data [9]. Upgrades in thedata acquisition system allowed STAR to record eventsat much higher rates as well.The analysis procedures were similar to those in [9] ex-cept where noted below. The inputs to the jet finder werethe charged particle momenta measured by the TPC andthe neutral energy depositions observed by the calorime-ter towers. Jets were reconstructed using the anti- k T al-gorithm [22], as implemented in the FastJet package [23],with a resolution parameter R = 0.6. This is a changefrom the mid-point cone algorithm [24] that was usedin previous STAR inclusive jet analyses [7–9]. Anti- k T jets are less susceptible to diffuse soft backgrounds fromunderlying event and pile-up contributions, which pro-vides a significant reduction in the trigger bias describedbelow.Most frequently, charged hadrons deposit energyequivalent to a minimum ionizing particle (MIP) in thecalorimeter towers. Because the TPC reconstructs themomentum of all charged particles, the inclusion of towerenergy from charged hadrons results in an overestima-tion of the jet momentum. Fluctuations in the de-posited tower energy when charged hadrons interact withcalorimeter materials further distort the jet momentumand degrade the jet momentum resolution. In previousSTAR jet analyses [7–9], this hadronic energy was ac-counted for by subtracting energy corresponding to aMIP from the energy deposited in any BEMC or EEMCtower with a charged track passing through it, and thenusing simulations to estimate the residual correction. Inthis analysis, the E T of the matched tower was adjustedby subtracting either p T c of the charged track or E T ,whichever was less. This procedure reduces the residualjet momentum corrections. It also reduces the sensitivityto fluctuations in the hadronic energy deposition, result-ing in an improved jet momentum resolution of (cid:39) (cid:39)
23% in previous analyses. The bottompanel of Fig. 1 demonstrates that this new “ p T subtrac-tion” scheme leads to an average for the neutral energyfraction (NEF) of the jet energy that is close to the valueof about 1/3 expected from isospin considerations.In this analysis, jets were required to have transverse Neutral Energy Fraction C oun t s · JP1+JP2JP1JP2Simulation > = 9.1 GeV/c T
= 28.1 GeV/c T
Jet+X fi p+p = 200 GeVs FIG. 1: (Color online.) Jet neutral energy fraction (NEF)comparing data (solid points) with simulations (histograms),where both are calculated with p T subtraction. Upper panelshows jets with 8 . < p T < . c , demonstrating the biasin NEF when jet p T is near the trigger threshold. Lower panelshows jets with 26 . < p T < . c , demonstrating anapparent bias persists well above threshold when using MIPsubtraction (open circles). The error bars show the simulationstatistics. Those for the data are smaller than the points. momentum p T > c and | η | < .
0. Non-collisionbackgrounds such as beam-gas interactions and cosmicrays, observed as neutral energy deposits in the BEMCand EEMC, were minimized by requiring the NEF to beless than 0.94. Only jets that pointed to a triggered jetpatch were considered. The top panel in Fig. 1 demon-strates the effect of the calorimeter trigger on the jetNEF. The trigger requirement skews the sample to largerneutral energies, especially for jets reconstructed near thetrigger threshold. The lower panel shows that this bias isminimized by the p T subtraction when the jet p T is wellabove threshold.Simulated events are used to calculate the jet momen-tum corrections and to estimate the systematic uncer-tainties. This analysis utilized simulated QCD eventsgenerated using the Perugia 0 tune [25] in PYTHIA 6.425[26]. The PYTHIA events were processed through theSTAR detector response package based on GEANT 3[27], and then embedded into randomly triggered events.As a result, the TPC tracks and calorimeter hits recon-structed in the simulation sample incorporate the samebeam background and pile-up contributions as the datasample, providing excellent agreement between the dataand simulation as shown in Fig. 1.The jet p T reconstructed at the detector level can becorrected to either the particle or parton level. Detectorjets, which are formed from charged tracks and calorime-ter towers, provide contact between the data and simula-tion. Particle jets are formed from the stable final-stateparticles produced in a collision. Parton jets are formedfrom the hard-scattered partons produced in the collision,including those from initial- and final-state radiation, butnot those from the underlying event or beam remnants.Previous STAR analyses [7–9] corrected the data back tothe particle level. Here, we correct the data to the partonjet level because parton jets provide a better representa-tion of the jets in an NLO pQCD calculation. The anti- k T algorithm with R = 0.6 was used to reconstruct partonjets for the simulated PYTHIA events described above.Simulated detector jets were matched to the parton jetclosest in η − φ space and within (cid:112) ∆ η + ∆ φ ≤ . p T to >
98% for p T > . c . Asymmetry valuesare given at the average parton jet p T for each detectorjet p T bin.The asymmetry A LL was evaluated according to A LL = (cid:80) ( P B P Y ) ( N ++ − rN + − ) (cid:80) ( P B P Y ) ( N ++ + rN + − ) , (2)in which P B,Y are the measured beam polarizations, N ++ and N + − denote the inclusive jet yields for equaland opposite proton beam helicity configurations, and r is the relative luminosity. Each sum is over individualruns that were 10 to 60 minutes long, a period muchshorter than typical time variations in critical quantitiessuch as P B,Y and r . Values of r were measured run-by-run, and range from 0.8 to 1.2.The STAR trigger biases the data sample by alteringthe subprocess fractional contributions ( gg vs. qg vs. qq ).At low p T , the JP efficiency for quark jets is approx-imately 25% larger than for gluon jets. For p T > c , the differences are negligible. Similarly, detectorand trigger resolutions may smear and distort the mea-sured A LL values. The size of these effects depends onthe value and shape of the polarized gluon distribution asa function of Bjorken- x . The A LL values for detector jetswere corrected for trigger and reconstruction bias effectsby using the simulation to compare the observed asym-metries at the detector and parton jet levels. PYTHIA isnot a polarized generator, but asymmetries can be con-structed by using the kinematics of the hard interactionto access polarized and unpolarized parton distributionfunctions (PDFs) and calculate the expected asymmetryon an event-by-event basis. In this way, the trigger andreconstruction biases were calculated for a range of po-larized PDFs that bracket the measured A LL values. Theaverage of the minimum and maximum A partonLL − A detectorLL values for each jet p T bin was used to correct the mea-sured A LL by amounts ranging from 0.0002 at low p T to0.0011 at high p T , and half the difference was assignedas a (correlated) systematic uncertainty.Figure 2 shows the inclusive jet A LL plotted as a func-tion of parton jet p T for two η bins. The vertical size ofthe shaded uncertainty bands on the A LL points in Fig.2 reflects the quadrature sum of the systematic uncer-tainties due to corrections for the trigger and reconstruc-tion bias (2 − × − ) and asymmetries associatedwith the residual transverse polarizations of the beams(3 − × − ). The trigger and reconstruction biascontributions are dominated by the statistics of the sim-ulation sample. The residual transverse polarization con-tributions are dominated by the statistical uncertaintiesin the measurement of the relevant transverse double-spin asymmetry ( A Σ ) [9]. Both of these uncertaintiesare primarily point-to-point. Contributions to A LL fromnon-collision backgrounds were estimated to be less than2% of the statistical uncertainty on A LL for all jet p T bins and deemed negligible. The relative luminosity un-certainty ( ± × − ), which is common to all the points,is shown by the gray bands on the horizontal axes. It wasestimated by comparing the relative luminosities calcu-lated with the BBCs and Zero-Degree Calorimeters [17],and from inspection of a number of asymmetries expectedto yield null results. The horizontal size of the shadederror bands reflects the systematic uncertainty on thecorrected jet p T . This includes calorimeter tower gainand efficiency and TPC tracking efficiency and momen-tum resolution effects. An additional uncertainty hasbeen added in quadrature to account for the differencebetween the PYTHIA parton jet and NLO pQCD jetcross sections. The PYTHIA vs. NLO pQCD difference dominates for most bins, making the parton jet p T un-certainties highly correlatedLongitudinal single-spin asymmetries, A L , measureparity-violating effects arising from weak interactions,and hence are expected to be very small compared to A LL . A L was measured and found to be consistent withzero for each beam, as expected for the present datastatistics.The theoretical curves in Fig. 2 illustrate the A LL ex-pected for the polarized PDFs associated with the corre-sponding global analyses. These predictions were madeby inserting the polarized PDFs from BB [4], DSSV [2, 3],LSS [5] and NNPDF [6] into the NLO jet productioncode of Mukherjee and Vogelsang [16]. Theoretical uncer-tainty bands for A LL were also calculated, but are omit-ted from the figure for clarity. The BB10 and NNPDFpolarized PDFs are based only on inclusive DIS data,while LSS includes both inclusive and semi-inclusive DIS(SIDIS) data sets. LSS provides two distinct solutionsfor the polarized gluon density of nearly equal quality.The LSS10 gluon density has a node at x (cid:39) .
2, andthe LSS10p gluon is positive definite at the input scale (GeV/c) T Parton Jet p LL A -0.0100.010.020.030.040.050.060.07 | < 0.5 h | STAR 2009
Jet+X fi p+p =200 GeVs (GeV/c) T Parton Jet p LL A -0.0100.010.020.030.040.050.060.07 STARBB10DSSVLSS10pLSS10NNPDF | < 1 h – from polarization not shown FIG. 2: (Color online.) Midrapidity ( | η | < .
5, upper panel)and forward rapidity (0 . < | η | <
1, lower panel) inclusive jet A LL vs. parton jet p T , compared to predictions from severalNLO global analyses. The error bars are statistical. The grayboxes show the size of the systematic uncertainties. Q = 2 . . DSSV is the only fit that incorporatesDIS, SIDIS, and previous RHIC pp data.LSS10p provides a good description of these STARjet data. The STAR results lie above the predictions ofDSSV and NNPDF and below the predictions of BB10.However, the measurements fall within the combineddata and model uncertainties for these three cases. Incontrast, the STAR jet asymmetries are systematicallyabove the predictions of LSS10 and fall outside the LSS10uncertainty band for p T <
15 GeV/ c .The NNPDF group has developed a reweightingmethod [28, 29] to include new experimental data into anexisting PDF set without the need to repeat the entire fit-ting process. The method involves calculating weightedaverages over previously equivalent PDF sets, with theweight for each set derived from the χ probability forthe set to describe the new data. We have implementedthis method to produce a modified NNPDF fit that in-cludes the 2006 [9] and 2009 STAR jet data. When cal-culating the χ probabilities for the jet asymmetries, weincluded both the statistical and systematic uncertain-ties and their correlations. We find that the jet datahave a negligible impact on the polarized quark and anti-quark distributions, but a significant impact on the po-larized gluon distribution. Figure 3 shows the originalNNPDF polarized gluon distribution as a function of x at Q = 10 GeV , as well as the modified fit that in-cludes the 2006 and 2009 STAR data. The integral of∆ g ( x, Q = 10 GeV ) over the range 0 . < x < . . ± .
18 for the original NNPDF fit and 0 . ± . x > .
05 and indicates a preference for the x -2 -1
10 1 g ( x ) D x -0.3-0.2-0.100.10.20.3 = 10 GeV Q NNPDFpol1.0+ 2006 and 2009 STAR Jets
FIG. 3: (Color online.) Gluon polarizations from NNPDF(blue dot-dashed curve, hatched uncertainty band) [6], andfrom a modified version of NNPDF that we obtain when in-cluding the 2006 and 2009 STAR inclusive jet A LL resultsthrough reweighting (red solid curve and uncertainty band). gluon helicity contribution to be positive in the RHICkinematic range.The DSSV group has performed a new global anal-ysis [30] including the STAR jet A LL results re-ported in this Letter. They find that the integral of∆ g ( x, Q = 10 GeV ) over the range x > .
05 is 0 . +0 . − . at 90% C.L., consistent with the value we find byreweighting the NNPDF fit. DSSV indicates that theSTAR jet data lead to the positive gluon polarizationin the RHIC kinematic range. The functional form ofthe polarized parton distribution functions assumed byDSSV is less flexible than that assumed by NNPDF, butDSSV also includes substantially more data in their fit.Both features may contribute to the smaller uncertaintyfor DSSV relative to NNPDF.In summary, we report a new high-precision measure-ment of the inclusive jet longitudinal double-spin asym-metry A LL in polarized pp collisions at √ s = 200 GeV.The results are consistent with predictions from severalrecent NLO polarized parton distribution fits. When in-cluded in updated global analyses, they provide evidencefor positive gluon polarization in the region x > . [1] C. A. Aidala, S. D. Bass, D. Hasch, and G. K. Mallot,Rev. Mod. Phys. , 655 (2013); and references therein.[2] D. de Florian, R. Sassot, M. Stratmann, and W. Vogel-sang, Phys. Rev. Lett. , 072001 (2008).[3] D. de Florian, R. Sassot, M. Stratmann, and W. Vogel-sang, Phys. Rev. D , 034030 (2009).[4] J. Bl¨umlein and H. B¨ottcher, Nucl. Phys. B841 , 205(2010).[5] E. Leader, A. V. Sidorov, and D. B. Stamenov, Phys.Rev. D , 114018 (2010).[6] R. D. Ball et al. [NNPDF Collaboration], Nucl. Phys. B874 , 36 (2013).[7] B. I. Abelev et al. [STAR Collaboration], Phys. Rev. Lett. , 252001 (2006). [8] B. I. Abelev et al. [STAR Collaboration], Phys. Rev. Lett. , 232003 (2008).[9] L. Adamczyk et al. [STAR Collaboration], Phys. Rev. D , 032006 (2012).[10] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. D , 091102 (2006).[11] A. Adare et al. [PHENIX Collaboration], Phys. Rev. D , 051106 (2007).[12] A. Adare et al. [PHENIX Collaboration], Phys. Rev.Lett. , 012003 (2009).[13] A. Adare et al. [PHENIX Collaboration], Phys. Rev. D , 012003 (2009).[14] A. Adare et al. [PHENIX Collaboration],arXiv:1402.6296.[15] B. J¨ager, M. Stratmann, and W. Vogelsang, Phys. Rev.D , 034010 (2004).[16] A. Mukherjee and W. Vogelsang, Phys. Rev. D ,094009 (2012).[17] K. H. Ackermann et al. [STAR Collaboration], Nucl. In-strum. Meth. A , 624 (2003), and references therein.[18] O. Jinnouchi et al. , arXiv:nucl-ex/0412053.[19] H. Okada et al. , arXiv:hep-ex/0601001. [20] B. Schmidke et al. , BNL C-A Dept. Rep. C-A/AP/490,http://public.bnl.gov/docs/cad/Pages/Home.aspx(2013).[21] J. Kiryluk [for the STAR Collaboration], arXiv:hep-ex/0501072.[22] M. Cacciari, G. P. Salam, and G. Soyez, JHEP , 063(2008).[23] M. Cacciari, G. P. Salam, and G. Soyez, Eur. Phys. J. C , 1896 (2012).[24] G. C. Blazey et al. , arXiv:hep-ex/0005012.[25] P. Z. Skands, arXiv:0905.3418.[26] T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP ,026 (2006).[27] GEANT 3.21, CERN Program Library.[28] R. D. Ball et al. [NNPDF Collaboration], Nucl. Phys. B849 , 112 (2011) [
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