A major part of the future COMPASS program is dedicated to

the study of Deeply Virtual Compton Scattering (DVCS) and Meson Production (DVMP) to investigate nucleon structure through Generalised Parton Distributions (GPD). The high energy of the muon beam allows us to measure the 

xB-dependence of the t-slope of the pure DVCS cross section and to study nucleon tomography. In a first phase the use of positive and negative polarised muon beams and of an unpolarised proton target allow measurements of the Beam Charge and Spin Difference of the DVCS cross sections to access the Compton form factor related to the dominant GPD H. In a second phase we consider to use a transversely polarized proton target to constrain the GPD E

d'Hose, N.

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DOI 10.1393/ncc/i2012-11206-9Colloquia: Transversity 2011IL NUOVO CIMENTO Vol. 35 C, N. 2 Marzo-Aprile 2012Hard Exclusive Processes at COMPASS and COMPASS-IIN. d’Hose for the COMPASS CollaborationCEA-Saclay - Gif-sur-Yvette, Francericevuto il 6 Dicembre 2011; approvato il 21 Dicembre 2011pubblicato online il 26 Marzo 2012Summary. — A major part of the future COMPASS program is dedicated tothe study of Deeply Virtual Compton Scattering (DVCS) and Meson Production(DVMP) to investigate nucleon structure through Generalised Parton Distributions(GPD). The high energy of the muon beam allows us to measure the xB-dependenceof the t-slope of the pure DVCS cross section and to study nucleon tomography. Ina first phase the use of positive and negative polarised muon beams and of an unpo-larised proton target allow measurements of the Beam Charge and Spin Difference ofthe DVCS cross sections to access the Compton form factor related to the dominantGPD H. In a second phase we consider to use a transversely polarized proton targetto constrain the GPD E.PACS 13.60.Fz – Elastic and Compton scattering.PACS 13.60.Le – Meson production.PACS 14.20.Dh – Protons and neutrons.1. – Introduction for GPD studies at COMPASSGeneralised Parton Distributions provide [1] a comprehensive description of the par-tonic structure of the nucleon and contain a wealth of new information. They embodyboth, form factors observed in elastic scattering and parton distribution functions mea-sured in deep inelastic scattering. A GPD can be considered as a momentum-dissectedform factor providing information on the transverse localisation of a parton as a functionof the fraction it carries of the nucleon’s longitudinal momentum. Thus one obtains a“3D picture” of the nucleon which is often referred to as “nucleon tomography” (one maingoal of COMPASS-II phase 1 [2]). GPDs also allow access to such a fundamental prop-erty of the nucleon as the orbital angular momentum of partons (goal of COMPASS-IIphase 2 in a future addendum to the present proposal).The COMPASS experiment is situated at the CERN SPS M2 beam line. It provideshigh-energy (50–280GeV) muon beams of either charges. The muons are produced inpion and kaon decays. Hence they are naturally longitudinally polarized and the helicityis charge dependent. As will be discussed later this is an important and unique feature ofc© Societa` Italiana di Fisica 305306 N. D’HOSE for the COMPASS COLLABORATIONFig. 1. – Kinematic domains for measurements of hard exclusive processes.COMPASS-II to access GPDs via DVCS and DVMP. The existing COMPASS set-up [3]equipped with a 2.5m long liquid-hydrogen target will be used. In order to accomplishthe detection of exclusive events a 4m long recoil proton detector (CAMERA) will beinstalled around the target. For the DVCS channel the photon detection assured atsmall angle by the two existing electromagnetic calorimeter (ECAL1 and ECAL2) willbe completed at larger angle by a new electromagnetic calorimeter (ECAL0) placedjust downstream of the target. This will increase significantly the acceptance of theDVCS photon detection. Hence COMPASS-II will become a facility measuring exclusivereactions within a kinematic Bjorken variable ranging from xB ∼ 0.01 to about 0.1and a photon virtuality Q2 from 1 to 10GeV2, which cannot be explored by any otherexisting or planned facility in the near future (fig. 1). COMPASS-II will thus explore theuncharted xB domain between the HERA collider experiments H1 and ZEUS and thefixed-target experiments as HERMES and the planned 12GeV extension of the JLab [4].2. – Study of the GPD H through DVCS with high-energy polarised μ+ and μ−beams and an unpolarized proton target and with recoil proton detectionin COMPASS-II phase 1DVCS which is the golden channel to study GPDs, has the same final state as the com-peting Bethe-Heitler (BH) process, which is elastic lepton-nucleon scattering with a hardphoton emitted by either the incoming or outgoing lepton. The two processes interfereat the amplitude level and the differential cross section for hard exclusive muoproductionof a single real photon off an unpolarised proton target can be written as(1)d4σ(μp → μpγ)dxBdQ2d|t|dφ = dσBH +(dσDV CSunpol + Pμ dσDV CSpol)+ eμ (Re I + Pμ Im I) ,(1) For simplicity dσ is used in the following instead of d4σ(μp→μpγ)dxBdQ2d|t|dφ .HARD EXCLUSIVE PROCESSES AT COMPASS AND COMPASS-II 307Fig. 2. – Top: Monte Carlo simulation of the exclusive muoproduction of a single real photonat COMPASS-II without ECAL0 showing the φ angle distributions of reconstructed events forthree bins in xB for Q2 > 1GeV2. Bottom: φ angle distributions measured in the DVCS 2009test run at COMPASS and the solid lines represent the expected BH yield.where Pμ and eμ are the polarisation and the charge of the muon beam respectively and Iis the interference term between DVCS and BH. t is the four-momentum transfer squaredbetween the initial and final nucleon state and φ is the angle between the scattering planeand the photon production plane. Due to the high energy beam, COMPASS offers theadvantage to provide various kinematic domains where either BH or DVCS dominates.This is illustrated in fig. 2 on the upper part showing a Monte Carlo simulation forQ2 > 1GeV2 based on the acceptance of the presently existing COMPASS set-up, i.e.,using the calorimeters ECAL1 and ECAL2. For xB < 0.01 the BH process dominateswhich provides an excellent reference yield to monitor the detector acceptance and theluminosity measurement. For x > 0.03 DVCS dominates. The distribution for DVCS isnot flat in φ due to the present limited acceptance at large photon angles. This will beimproved by the addition of the new calorimeter ECAL0. The size of the interferenceterm increases with rising xB and offers via its characteristic φ variation additionalpossibilities to access real or imaginary part of the complex DVCS amplitude.In 2008 and 2009 tests measurements were performed using the COMPASS detec-tor in the configuration dedicated to the hadron spectroscopy program. A 40 cm long308 N. D’HOSE for the COMPASS COLLABORATIONFig. 3. – Projected statistical (error bars) and systematic (grey band) accuracy for the measure-ment of the φ dependence of DCS,U for 0.03 ≤ x ≤ 0.07 and 1 ≤ Q2 ≤ 4GeV2 and for 280 daysof running time with a 2.5m LH2 target, an intensity of 4.6 × 108μ in a 48 s SPS spill periodand an overall global efficiency global = 0.1.liquid-hydrogen target surrounded by a 1m long recoil was used. The short run in2008 proved the capability of the detection and reconstruction of exclusive single photonevents. In 2009 approximatively 10 times more statistics was collected giving access tothe φ distributions in three bins in xB (see fig. 2 lower part). The solid lines represent theexpected BH event yield while the histogram shows the measured single photon yieldswhich include pure DVCS events and also misidentified π0 events.1. Building the Beam Charge (C) and Spin (S) Difference of the cross section forUnpolarized (U) proton target, BH contribution cancels out:DCS,U ≡ dσ+← − dσ−→ = 2 [PμdσDV CSpol + eμRe I] ∝ (cI0 + cI1 cosφ).In the last step the DVCS amplitude is expanded in 1/Q keeping only leadingtwist-2 terms [5]. The coefficients cI0 and cI1 are for COMPASS kinematics relatedto the dominant real part of the Compton Form Factors (CFF) H which is inleading order a weighted sum over flavors f of convolutions of the GPDs Hf with akernel describing the hard interaction of virtual photon and quark. The projectedstatistical accuracy of the measurement of DCS,U is shown in fig. 3. It correspondsto a luminosity of L = 1222 pb−1, which is equal to 280 days of data taken over twocalendar years. Two of the curves are calculated using the VGG GPD model [6]which is based on a “reggeized” parameterisation of the correlated x, t dependenceof the GPDs. It uses a shrinkage parameter α′ to describe the decrease in nucleonsize with increasing x. As this model is meant to be applied mostly in the valenceregion, typically a large value α′ = 0.8 is used. For comparison, also the modelfor the “factorised” x, t dependence is shown, which corresponds to α′ ≈ 0.1 inthe “reggeized” ansatz. The other two curves are predictions based on first fitsto world data [7]. These fits which include next-to-next-to leading order (NNLO)corrections were successfully applied to describe DVCS observables from very smallHARD EXCLUSIVE PROCESSES AT COMPASS AND COMPASS-II 309Fig. 4. – Left: Projections for measuring the xB dependence of the t-slope parameter B(xB) ofthe DVCS cross section, calculated for 1 < Q2 < 8GeV2. A comparison to HERA results withsimilar 〈Q2〉 is shown [8, 9]. The left vertical bar on each data point indicates the statisticalerror only while the right one includes also the systematic uncertainty, using only ECAL1 andECAL2 (first row) and also ECAL0 (second row). Two different parameterisations are shownusing α′ = 0.125GeV−2 and 0.26GeV−2. Right: Transverse proton radius as a function of xB .New and significant information will be obtained in the uncharted xB region, further elucidatingthe issue of “nucleon tomography”.values of xB , for the HERA collider to large xB for HERMES and JLab. It hasto be noted that the real part of the Compton form factor H was found positiveat H1 and ZEUS and negative at HERMES and JLab. The COMPASS kinematicdomain is expected to provide the node of the real part of this amplitude, which isan essential input for any global fit analysis.2. At leading twist the cross section of the Beam Charge (C) and Spin (S) Sum forUnpolarized (U) proton target can be written as:SCS,U ≡ dσ+←+dσ−→ = 2[dσBH+dσDV CSunpol +eμPμIm I] ∝ 2dσBH+cDV CS0 +sI1 sinφ,in which the BH contribution does not cancel out.– The analysis of the φ-dependence of SCS,U will provide via the term Im Ithe leading twist-2 quantity sI1. Its dominant contribution is related to theimaginary part of the Compton form factor H, which is proportional to theGPD H.– A parallel analysis can be performed subtracting the BH contribution andintegrating over φ to get rid of the complete interference term. Thus theDVCS leading twist-2 quantity cDV CS0 can be isolated and its character-istic t-slope as a function of xB can be determined, from which conclu-sions can be drawn on the evolution of transverse size of the nucleon overthe xB-range accessible to COMPASS. Such a mapping in xB is referredto as “Nucleon Tomography”. Figure 4 shows the projected statistical ac-curacy for a measurement at COMPASS of the xB-dependence of the t-slope parameter B(xB) of the DVCS cross section. In the simple ansatz310 N. D’HOSE for the COMPASS COLLABORATIONFig. 5. – Asin(φ−φS)UT using the transversely polarized NH3 (proton) COMPASS 2007 data andcompared to the predictions of the GPD model [12] at 〈Q2〉 = 2GeV2 and 〈W 〉 = 8GeV.dσdt ∝ exp(−B(xB) |t|) with B(xB) = B0 + 2α′ log(x0x ). At small xB, whereamplitudes are predominantly imaginary, the overall transverse size of thenucleon 〈r2⊥(xB)〉 ≈ 2 · B(xB). Data on B exist only for the HERA colliderxB-range from 10−4 to 0.01 [8,9], below the COMPASS range 0.01 < xB < 0.1.No evolution with xB was observed and a first transverse proton radius hasbeen determined 〈r2⊥〉 = 0.65 ± 0.02 fm using H1 data [8]. In the valenceregion, where no experimental determinations of B exist, some informationcomes from fits adjusted to form factor data which give α′  1GeV2 [10, 11].For the simulation two values α′ = 0.125 and α′ = 0.26 are shown whichcorrespond to the half and the total of the value for Pomeron exchange in softscattering processes. The largest value can be determined with an accuracybetter than 2.5σ by using the two existing calorimeters ECAL1 and ECAL2while the smallest value requires the new calorimeter ECAL0 to get a betterprecision at large xB.3. – Study of the GPD E using transversely polarized protons (NH3 target)A sensitivity to the GPD E requires either the use of a neutron target or a transverselypolarized proton target. This second way is investigated at COMPASS for exclusivemeson production. It will be still further investigated both for DVCS and DVMP, usinga transversely polarized proton target and a recoil detector. This will be the goal of afuture addendum to the COMPASS-II proposal for a second phase of GPD measurements.1. Exclusive rho production from transversely polarized protons has already beenstudied using the 2007 COMPASS data obtained with a polarized NH3 target.The ρ0 mesons are selected by the detection of two charged pions of invariant massmππ between 0.5 and 1.1GeV2. Because of this early stage, recoil protons arenot detected, a cut is applied on the missing energy Emiss = (M2X − M2p )/2Mpwhere MX is the mass of the undetected particle and Mp the proton mass. Thetransverse target spin dependent cross section is accessed experimentally by themodulation of the cross section asymmetry Asin(φ−φS)UT as a function of sin(φ− φS)(φS is the azimuthal angle of the transverse target spin vector relative to the leptonscattering plane). This asymmetry is presented in fig. 5 as a function of p2T thetransverse momentum of ρ0 with respect to the direction of the virtual photon. ThisHARD EXCLUSIVE PROCESSES AT COMPASS AND COMPASS-II 311Fig. 6. – Projections for the statistical accuracy of the transverse target asymmetry comparedto measurements done at HERMES [13].asymmetry is proportional to pT and to a weighted sum of convolutions of the GPDEq,g with the distribution amplitude of the produced meson and a hard scatteringkernel. The weights depend on the contributions of quarks of various flavours andgluons to the production of a given vector meson. The model [12] explains thesmall value of the asymmetry as due to an approximate cancellation of two sizablecontributions of opposite signs for the GPDs Eu and Ed for the valence u and dquarks, respectively. In contrast the model predicts larger asymmetry for exclusiveproduction of ω meson or ρ+ meson.2. DVCS using high-energy polarised μ+ and μ− beams with a transverse polarizedNH3 target and recoil proton detection will be proposed at a further stage ofCOMPASS-II. The modulation of the cross section asymmetry as a function ofsin(φ−φS) will provide Asin(φ−φS)UT which involves the quark GPD Ef unsuppressedrelatively to the GPD Hf . Predictions are given in fig. 6 as a function of t, xBand Q2 for a measurement in 280 days using a 160GeV beam and ECAL1 andECAL2. The solid and open circles correspond to the simulations for two hypo-thetic configurations of the polarized target and the recoil proton detector design.The predictions are compared to HERMES results [13] with its statistical errors.In the next future before new facilities are built, only COMPASS-II using a 160GeVmuon beam and JLab using a 12GeV electron beam will perform DVCS measurementsto access GPDs. JLab has an excellent luminosity to study in details the valence regionthrough the interference between DVCS and BH while COMPASS-II with its high energyμ+ and μ− beams will study a complementary domain at smaller xB ranging from 0.01to about 0.1 which has never been investigated so far. COMPASS-II will consider GPDstudies both through the BH and DVCS interference and the almost pure DVCS crosssection. A first DVCS test using the new recoil detector CAMERA around the long LH2target and a new ECAL0 partially equipped will be performed in autumn 2012. The fulltwo years DVCS experiment is foreseen in 2015-16 according a tentative schedule for thefull COMPASS-II program comprising also Drell-Yan experiments. Then COMPASS-IIwill investigate in a complementary approach subtle effects of either intrinsic transverseparton momenta or transverse parton localisation.312 N. D’HOSE for the COMPASS COLLABORATIONREFERENCES[1] Mu¨ller D. et al., Fortschr. Phys., 42 (1964) 101; Ji X.-D., Phys. Rev. Lett., 78 (1997)610; Phys. Rev. D, 55 (1997) 7114; Radyushkin A. V., Phys. Lett. B, 385 (1996) 333;Phys. Rev. D, 56 (1997) 5524; Burkardt M., Int. J. Mod. Phys. A, 18 (2003) 173, Phys.Lett. B, 595 (2004) 245.[2] COMPASS-II proposal, CERN/SPSC-2010-014, SPSC-P-340,http://cdsweb.cern.ch/record/1265628/files/SPSC-P-340.pdf, May 17, 2010.[3] Abbon P. et al. (COMPASS Collaboration), Nucl. Instrum. Methods A, 577 (2007)455.[4] Proposals on DVCS at JLab 12GeV: PR12-06-114, PR12-06-119, E12-11-003.[5] Belitsky A. V., Mu¨ller D. and Kirchner A., Nucl. Phys. B, 629 (2002) 323.[6] Vanderhaeghen M., Guichon P. A. M. and Guidal M., Phys. Rev. Lett., 80 (1998)5064; Phys. Rev. D, 60 (1999) 094017; Goeke K., Polyakov M. V. and VanderhaeghenM., Prog. Part. Nucl. Phys., 47 (2001) 401.[7] Kumericki K., Mueller D. and Passek-Kumericki K., Nucl. Phys. B, 794 (2008) 244,Kumericki K. and Mueller D., arXiv:0904.0458 [hep-ph].[8] Aktas A. et al. (H1 Collaboration), Eur. Phys. J. C, 44 (2005) 1, Aaron F. D. etal. (H1 Collaboration), Phys. Lett. B, 659 (2008) 796.[9] Chekanov S. et al. (ZEUS Collaboration), DESY-08-178, arXiv:0812.2517v3 [hep-exp].[10] Diehl M., Feldmann Th., Jakob R. and Kroll P., Eur. Phys. J. C, 39 (2005) 1.[11] Guidal M., Polyakov M. V., Radyushkin A. V. and Vanderhaeghen M., Phys. Rev.D, 72 (2005) 054013.[12] Goloskokov S. V. and Kroll P., Eur. Phys. J. C, 59 (2009) 809.[13] Airapetian A. et al. (HERMES Collaboration), JHEP, 06 (2008) 066.

Hard Exclusive Processes at COMPASS and COMPASS-II

A major part of the future COMPASS program [1] is dedicated to the study of Deeply Virtual Compton Scattering (DVCS) and Meson Production (DVMP) to investigate nucleon structure through Generalised Parton Distributions (GPD). The high energy of the muon beam allows us to measure the xB-dependence of the t-slope of the pure DVCS cross section and to study nucleon tomography. In a first phase the use of positive and negative polarised muon beams and of an unpolarised proton target allow measurements of the Beam Charge and Spin Difference of the DVCS cross sections to access the Compton form factor related to the dominant GPD H. In a second phase we consider to use a transversely polarized proton target to constrain the GPD E

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Hard Exclusive Processes at COMPASS and COMPASS-II

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