We study Drell-Yan plus jet events where the gauge boson is produced in the
forward direction of one of the colliding protons and a jet is produced in the
forward direction of the second proton. The resulting large rapidity difference
between the final states then opens up the phase space for BFKL evolution.
First numerical results on partonic level are provided.Comment: 4 pages, 2 figures, proceedings of the XX Workshop on Deep-Inelastic
  Scattering and Related Subjects, 26-30 March, University of Bonn (2012

Hentschinski, M.

Salas, C.

English

arXiv

We study Drell-Yan plus jet events where the gauge boson is produced in the forward direction of one of the colliding protons and a jet is produced in the forward direction of the second proton. The resulting large rapidity difference between the final states then opens up the phase space for BFKL evolution. First numerical results on partonic level are provided

Hentschinski, Martin

Salas, Clara

DESY Publication Database

Forward Drell-Yan plus backward jet as a test of BFKL evolution

M., Hentschinski

UNT Digital Library

   BNL-99645-2013-CP     Forward Drell-Yan plus backward jet as a test of BFKL evolution  M. Hentschinski1 and C. Salas2 1Physics Department, Brookhaven National Laboratory, Upton, NY, USA 11973 2Instituto de Física Teórica UAM/CSIC, C/Nicolás Cabrera 13-15, Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, Spain  Presented at the XX Workshop on Deep-Inelastic Scattering and Related Subjects Bonn, Germany March 26 to 30, 2012   January 2013    Physics Department/Nuclear Theory Group/Office of Science  Brookhaven National Laboratory    U.S. Department of Energy [DOE Program Office of Science, Nuclear Physics]   Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.  This preprint is intended for publication in a journal or proceedings.  Since changes may be made before publication, it may not be cited or reproduced without the author’s permission.    DISCLAIMER  This report was prepared as an account of work sponsored by an agency of the United States Government.  Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors.  The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.   Forward Drell-Yan plus backward jet as a test ofBFKL evolutionMartin Hentschinski1, Clara Salas21Physics Department, Brookhaven National Laboratory, Upton, 11973, USA2Instituto de F́ısica Teórica UAM/CSIC, C/ Nicolás Cabrera 13-15,Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, SpainDOI: will be assignedWe study Drell-Yan plus jet events where the gauge boson is produced in the forwarddirection of one of the colliding protons and a jet is produced in the forward direction ofthe second proton. The resulting large rapidity difference between the final states thenopens up the phase space for BFKL evolution. First numerical results on partonic levelare provided.1 IntroductionDue to its large center of mass energy the LHC allows for the study of forward physics usingmethods of perturbative QCD. Among them we find forward production of different systemssuch as high pT jets [1], heavy quark pairs [2] and Drell-Yan (DY) processes where a virtualphoton or Z boson decays into a pair of leptons [3, 4]. The study of these type of processes isinteresting as they allow to probe parton distribution functions at very small values of x whichhave not been reached in so-far collider experiments. They therefore provide a possibility totest formalisms which have been especially developed for the description of small x processesand which go beyond the standard formulation in terms of collinear factorization by includingadditional small x enhanced contributions. The starting point of such studies is given by BFKLevolution which resums small x logarithms on the level of partonic scattering amplitudes atleading logarithmic (LL) [5] and next-to-leading-logarithmic (NLL) [6] accuracy. In addition,since small x evolution ultimatively leads to high parton densities, such processes may furtherallow for the observation of saturation effects which require an extension of the BFKL formalism,see e.g. [7].While studies of inclusive observables provide strong hints for the presence of BFKL evo-lution in small x data, see e.g. [9], a proper identification of relevant effects at small x is hardto achieve. Cancellations between different final states minimize the sensitivity to the partic-ular feature of the employed method and deviations from inclusive evolution equations due tosmall x effects may be partly hidden into the chosen initial conditions. It is therefore necessaryto turn to the study of more exclusive observables to distinguish different effects at small x.Among these exclusive observables there is a class of events where the entire dependence of theprocess on the non-perturbative dynamics is treated within conventional collinear factorization.DIS 2012 1arXiv:1301.1227v1  [hep-ph]  7 Jan 2013These observables typically involve hard events in the forward region of both scattering protons,while the large difference in rapidity between the hard final states opens up the phase spacefor BFKL evolution. Among the best explored processes of this type are ‘Mueller-Navelet’ jetswhich consist of a high pT -jets in the forward regions of each proton. Currently this process isone of the few examples where a complete NLL BFKL description exists [8]. In contrast to näıveexpectations, the result reveals a strong dependence on the next-to-leading order corrections tothe jet impact factors. At the same time, the numerical differences between the NLL resummedresult and a pure collinear NLO result remain rather small for a large class of observables.This observation motivates the study of a new type of forward-backward observable, wherea DY pair is produced in the forward direction of one of the particles instead of a jet. Thehope is that this observable is able to better distinguish between standard NLO results and NLLBFKL resummed predictions and allows to identify universal features of BFKL evolution. Eventhough the large virtuality of the photon and/or the mass of the Z diminishes at first the valueof the strong coupling constant αs, the rapidity difference between lepton pair and backward jetremains large at the Large Hadron Collider, ∆Y < 7 and a study of BFKL evolution appearsmeaningful. In addition, study of new final states may also trigger new theoretical efforts for animproved definition of impact factors and lead to the identification of new BFKL observables.In the following we present some partial results of our study, which are currently restricted tothe partonic level. For details we refer to our paper in preparation [10].2 The leading-order DY impact factor= +(a) (b)Figure 1: a) A large difference in rapidity between the forward gauge boson (γ∗, Z) and thebackward jet opens up the phase space for BFKL evolution. b) The leading order DY impactfactor is obtained as the sum of two effective diagrams where the t-channel gluon carries eikonalpolarizations.In the current study we restrict to the LO impact factor, where relevant diagrams can befound in Fig. 1.b. A complete NLO study seems possible using Lipatov’s effective action [11]2 DIS 2012which is currently explored at NLO [12]. The leading order impact factor readsΦZq =cfαs√N2c − 1πk2Nc[zk2((1− z)2 + 1)+ 2M2(1− z)zD1D2− M2z(1− z)D21− M2(1− z)zD22]D1 = (q − zk)2 + (1− z)M2 D2 = q2 + (1− z)M2 (1)Here M denotes the mass of the Z boson and the virtuality of the photon respectively, whilecf yields the coupling of the gauge boson to the quark. q and k are the transverse momentaof the final state gauge boson and initial gluon, while z is the momentum fraction of the initialquark momentum carried on by the gauge boson.3 Preliminary numerical results at partonic levelThe above impact factor carries a logarithmic singularity if the final state quark turns to be soft.After convolution of the impact factor with the BFKL Green’s function, this corresponds tothe limit z → 1. To avoid this singularity we study ratios of angular coefficients Cn = 〈cosnφ〉,where φ denotes the azimuthal angle between the jet and the gauge boson.In a preliminary study, see Fig. 2, which restricts to the partonic level and conformal part ofthe NLO BFKL kernel, we use a fixed value z = 0.9 while the QCD coupling is taken at the Z-scale. As in the jet-jet case we find that the best convergence of the BFKL prediction is achievedfor ratios which do not contain the angular coefficient C0. A complete study at hadronic levelfaces additional complications. Even though formally finite, the limit z → 1, which is naturallyencountered once the convolution with parton distribution functions is included, leads to largecontributions which can even cause negative results for some of the angular coefficients. Thestudy of these effects and their appropiate treatment as well as the inclusion of the runningcoupling corrections of the NLO BFKL Green’s function is currently in progress.AcknowledgmentsWe are grateful for financial support from the MICINN under grant FPA2010-17747, the Re-search Executive Agency (REA) of the European Union under the Grant Agreement numberPITN-GA-2010-264564 (LHCPhenoNet) and Comunidad de Madrid (HEPHACOS ESP-1473).M.H. further acknowledges support from the German Academic Exchange Service (DAAD)and the U.S. Department of Energy under contract number DE-AC02-98CH10886 and a BNL“Laboratory Directed Research and Development” grant (LDRD 12-034).References[1] M. Deak, F. Hautmann, H. Jung and K. Kutak, Eur. Phys. J. C 72 (2012) 1982 [arXiv:1112.6354[hep-ph]].[2] C. Salas, J. Stirling, in preparation.[3] S. Marzani and R. D. Ball, Nucl. Phys. B 814 (2009) 246 [arXiv:0812.3602 [hep-ph]].[4] F. Hautmann, M. Hentschinski and H. Jung, Nucl. Phys. B 865 (2012) 54 [arXiv:1205.1759 [hep-ph]],arXiv:1205.6358 [hep-ph].[5] V. S. Fadin, E. A. Kuraev and L. N. Lipatov, Phys. Lett. B 60 (1975) 50, I. I. Balitsky and L. N. Lipatov,Sov. J. Nucl. Phys. 28 (1978) 822 [Yad. Fiz. 28 (1978) 1597].DIS 2012 31 2 3 4 5 6 7D y0.10.20.30.40.50.60.7C1C01 2 3 4 5 6 7D y0.0010.0020.0030.0040.0050.006C2C0(a) (b)1 2 3 4 5 6 7D y0.0040.0050.0060.0070.0080.009C2C1(c)Figure 2: Ratios of angular coefficients C1/C0, C2/C0 and C2/C1 versus ∆y = |yZ − yjet| onpartonic level with αs(M2Z) and z = 0.9. The transverse momentum of the Z-boson is taken tobe q = 2 GeV while jets with transverse momenta p > 20 GeV are considered. The dependenceon ∆y is described by the LL (purple), NLL (blue) and NLL RG improved (see [13] for details)(red) BFKL Green’s function[6] V. S. Fadin and L. N. Lipatov, Phys. Lett. B 429 (1998) 127 [hep-ph/9802290], M. Ciafaloni andG. Camici, Phys. Lett. B 430 (1998) 349 [hep-ph/9803389].[7] M. A. Betemps, M. B. Gay Ducati and M. V. T. Machado, Phys. Rev. D 66 (2002) 014018[hep-ph/0111473], F. Gelis and J. Jalilian-Marian, Phys. Rev. D 66 (2002) 094014 [hep-ph/0208141],F. Gelis and J. Jalilian-Marian, Phys. Rev. D 76 (2007) 074015 [hep-ph/0609066], K. Golec-Biernat,E. Lewandowska and A. M. Stasto, Phys. Rev. D 82, 094010 (2010) [arXiv:1008.2652 [hep-ph]].[8] D. Colferai, F. Schwennsen, L. Szymanowski and S. Wallon, JHEP 1012 (2010) 026 [arXiv:1002.1365[hep-ph]], F. Caporale, D. Y. .Ivanov, B. Murdaca and A. Papa, arXiv:1211.7225 [hep-ph].[9] M. Hentschinski, A. Sabio Vera and C. Salas, arXiv:1209.1353 [hep-ph].[10] M. Hentschinski, C. Salas, in preparation.[11] L. N. Lipatov, Nucl. Phys. B 452 (1995) 369 [hep-ph/9502308].[12] M. Hentschinski and A. S. Vera, Phys. Rev. D 85 (2012) 056006 [arXiv:1110.6741 [hep-ph]M. Hentschinski, Nucl. Phys. B 859 (2012) 129 [arXiv:1112.4509 [hep-ph]], G. Chachamis,M. Hentschinski, J. D. Madrigal Martinez and A. Sabio Vera, Nucl. Phys. B 861 (2012) 133[arXiv:1202.0649 [hep-ph]], arXiv:1211.2050 [hep-ph], arXiv:1212.4992 [hep-ph].[13] A. Sabio Vera, Nucl. Phys. B 722 (2005) 65 [hep-ph/0505128], A. Sabio Vera and F. Schwennsen, Nucl.Phys. B 776 (2007) 170 [hep-ph/0702158 [HEP-PH]].4 DIS 2012

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DOI: will be assigned We study Drell-Yan plus jet events where the gauge boson is produced in the forward direction of one of the colliding protons and a jet is produced in the forward direction of the second proton. The resulting large rapidity difference between the final states then opens up the phase space for BFKL evolution. First numerical results on partonic level are provided. 

Forward Drell-Yan plus backward jet as a test of BFKL evolution

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