We explore the feasibility to study exclusive meson production (EMP) in hard
muon-proton scattering at the COMPASS experiment. These measurements constrain
the off-forward parton distributions (OFPD's) of the proton, which are related
to the quark orbital contribution to the proton spin.Comment: Workshop on Exclusive and Semi-Exclusive Processes at High Momentum
  Transfer, Jefferson Lab, 20-22 Mai 199

Mankiewicz, Lech

Moinester, Murray

Piller, Gunther

Pochodzalla, Josef

Sandacz, Andrzej

Vanderhaeghen, Marc

English

arXiv

We explore the feasibility to study exclusive meson production (EMP) in hard muon-proton scattering at the COMPASS experiment. These measurements constrain the off-forward parton distributions (OFPD's) of the proton, which are related to the quark orbital contribution to the proton spin.We explore the feasibility to study exclusive meson production (EMP) in hard muon-proton scattering at the COMPASS experiment. These measurements constrain the off-forward parton distributions (OFPD's) of the proton, which are related to the quark orbital contribution to the proton spin.We explore the feasibility to study exclusive meson production (EMP) in hard muon-proton scattering at the COMPASS experiment. These measurements constrain the off-forward parton distributions (OFPD's) of the proton, which are related to the quark orbital contribution to the proton spin

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arXiv:hep-ph/9909534v1  28 Sep 1999EXCLUSIVE MESON PRODUCTION AT COMPASSJosef Pochodzallaa, Lech Mankiewiczb, Murray Moinesterc, Gunther Piller b,Andrzej Sandaczd, Marc VanderhaegheneaMax-Planck-Institut fu¨r Kernphysik, 69029 Heidelberg, GermanybPhysics Department, Technical University Munich, D-85747 Garching, GermanycSchool of Physics and Astronomy, R. and B. Sackler Faculty of Exact Sciences,Tel Aviv University, 69978 Ramat Aviv, IsraeldSoltan Institute for Nuclear Studies, 00681 Warsaw, PolandeUniversity Mainz, D-55099 Mainz, GermanyWe explore the feasibility to study exclusive meson production (EMP) in hardmuon-proton scattering µ p → µ p M at the COMPASS experiment. These mea-surements constrain the off-forward parton distributions (OFPD’s) of the proton,which are related to the quark orbital contribution to the proton spin.1 IntroductionThe internal structure of the proton has been a subject of high interest formany decades. In general, the spin of the proton resides in its quark and gluonconstituents and in their orbital angular momenta:12〈∆qv〉+12〈∆S〉+ 〈∆G〉+ Lq + Lg =12(1)Here, 12 〈∆qv〉 denotes the spin in the valance quarks,12 〈∆S〉 is the total spincarried by the sea quarks and antiquarks, 〈∆G〉 represents the spin residing inthe gluonic field, Lq and Lg represent the orbital momenta of the quarks andgluons, respectively. A main goal of the COMPASS experiment at CERN isthe determination of the gluon contribution ∆G. In COMPASS, ∆G will bestudied via the photon-gluon fusion process, tagged either by charm-anticharmproduction, or by high-pT hadron pair production1.A factorization theorem for deeply-virtual Compton scattering (DVCS)was provided by Ji 2 and Radyushkin 3,4. For exclusive meson production bylongitudinally polarized photons, a factorization theorem was proven recentlyby Collins, Frankfurt, and Strikman 5. The theorem allows one to separatethe meson production amplitudes into a perturbatively calculable component,describing the interaction of the virtual photon with quarks and gluons ofthe target, and a matrix element component which contains all informationabout the long-distance non-perturbative strong interaction dynamics in theproduced meson and the nucleon target. The latter component can be param-eterized, at leading order PQCD, in terms of 4 generalized structure functions,1p p′x′ x′-xqVFigure 1: Illustration of the fac-torization theorem for exclusivemeson production 5.0.2 0.4 0.6 0.8 112345Carlitz - KauerBartelski - TaturGehrmann-StirlingxFdσ/dx B(t=t min,Q2=4GeV2 )    (nb/GeV2 )Figure 2: Differential cross section for pi0 produc-tion at t = tmin, Q2 = 4 GeV 2, as a function ofxB , in units of nb/GeV2, for the three differentvalence quark parametrizations 15,16,17,18.the so called skewed or off-forward parton distributions (OFPD’s). Ji showed2 that the second moment of these OFPD’s determines the total quark angu-lar momentum, the sum of the intrinsic quark spins and their orbital angularmomentum. The OFPD’s differ from the usual parton distributions probedin inclusive reactions by having a non-zero momentum transfer between theproton in the initial and final state. Therefore, the OFPD’s are not acces-sible in standard inclusive measurements. They can, however, be measuredin deeply-virtual Compton scattering or in hard exclusive lepto-production ofmesons (EMP). Thus, exclusive meson production provides a unique tool toexplore the contribution of orbital angular momentum and the valance quarkpolarization to the nucleon spin.EMP are important not only because they relate to the quark orbital mo-mentum contribution to the proton spin. They should test our understandingof QCD generally, and of OFPD’s in particular. COMPASS may lead in thestudy of these new processes, that are only now calculable in QCD.In principle, Deeply Virtual Compton Scattering represents the most el-ementary process to access the OFPD’s. This reaction has been consideredfor COMPASS 6. It was, however, realized that this channel may suffer frompotentially large backgrounds. Detailed understanding of (exclusive) mesonproduction is therefore a precondition for studying DVCS. In turn, DVCS mayrepresent an important complement for the Exclusive Meson Production study,which we discuss below.With the high muon beam energy and high luminosity in COMPASS 7experiment, large Q2 values can be reached with reasonable rates. For ρ0 for2example, a Q2 range between 2 and 20 (80) GeV2 is accessible for incident 100GeV/c (200 GeV/c) muon beam. Thus, this COMPASS program extends theapproved activity of the CLAS collaboration at JLAB8, which will explore theOFPD in a limited Q2 range up to about 4 GeV2. We distinguish between EMPchannels in which the final state meson (ρ0, π+ 9, φ, etc.) can be detected viamagnetic spectrometers, and those which require electromagnetic calorimetry.The charged cases can be detected with higher resolution and more easilywithout EM calorimetry.As another important aspect of this study, we also consider EMP of a ”di-pion” (both resonant and non-resonant), such as π+π−, K¯K, πK, as studiedrecently by Polyakov 10. These works demonstrated that the shape (not ab-solute cross sections!) of these ”di-pion” mass distributions carry importantinformation about quark distribution in the pion (kaon), and also about thestructure of resonances (ρ, f2,K∗, etc.).2 The Proposed Experiment2.1 Experimental methodology and triggerWe base our considerations on the scattered muon trigger that is forseen inthe COMPASS experiment to study spin dependent DIS. The trigger fires ifthe muon is scattered at large angle θµ. In our simulations we assumed a goodangular acceptance for the range 10(5) < θµ < 50 mrad for 100 (200) GeVbeam energy. The trigger is based on the X-Y correlations between hodoscopeelements at about 31 and 50 meters downstream of the target.Average recoil proton energies for EMP are quite low (∼30-40 MeV). Thus,the recoil proton kinematics for COMPASS do not allow installing an efficientproton recoil detector to isolate ”elastic” reactions. In order to be able to makeoptimal use of the experimental setup employed by the main muon program,or even to run initially in parallel with the main program, we will evaluate theinelasticity I ∝ (M2x −M2p ) using measured momenta of the incident and finalmuons and produced meson 11. The resolution will, however, not be sufficientto cleanly resolve events with a recoil proton or a recoil ∆+ or N∗ in thefinal state. However, the OFPD’s for these processes are related 12. Thus, acomparison of the data should be made to model calculations which combineboth, proton, ∆+ and N∗ production.The main goal of the proposed program is to obtain high statistics EMPdata on a pure unpolarized proton target during dedicated data runs. Thiswould also help to avoid ”dilution” by the presence of different target nucleiin the polarized proton target. Also, with the liquid hydrogen target, thedetection efficiency of produced π0 decay γ’s would increase due to the bigger3total radiation length of the LH. However, in order to explore the feasibility ofthis program already during the initial data taking period of COMPASS, weassumed the standard polarized target for our present simulations and countrate estimates.2.2 Cross section for exclusive meson production (EMP)We estimate the dependence of the cross section for the reaction µ p→ µ p π0on the kinematic variables Q2, xB, and t, using models for off-forward partondistributions. Following 3,4, we constructed the relevant off-forward partondistributions starting from polarized valence quark distributions.The exact QCD calculation involves time-consuming numerical integra-tion, which is inconvenient for Monte Carlo purposes. However, neglectingQCD logarithmic evolution of off-forward parton distributions, one can obtaina simple parametrization based on a fit to the results of the exact formulae:dσdt(γL p→ π0 p) =dσdt(x,Q2)∣∣∣∣t=tmin× eB(t−tmin), (2)where:d σd t(x,Q2)∣∣∣∣t=tmin=αS2(Q2) · PF(x,Q2) ·UF(x)Q2(Q2 +M2)2. (3)Here, αS(Q2) is the one-loop QCD coupling constant, which – as usual for LOcalculations – was evaluated with ΛQCD = 0.2 GeV and with NF = 4 for thenumber of active flavors. In this equation, PF(x,Q2) is given by:PF(x,Q2) =Q4 (1− x)(−Q2 − 0.881721 x+Q2 x)2 . (4)UF(x) is the part of the cross-section which is independent of Q2. It wouldacquire a logarithmic Q2 dependence when QCD evolution effects are included.The shape of UF(x) depends on the model of the off-forward parton distribu-tions used in the actual calculation.Figure 2 shows the differential cross section for π0 production at t = tmin,Q2 = 4 GeV 2, as a function of Bjorken xB, in units of nb/GeV2, for thethree different valence quark parametrizations. The solid line refers to theGehrmann-Stirling polarized valence parametrization 15, the short-dashed lineis based on the Carlitz-Kaur model 13,16,17 and the long-dashed line resultsfrom the Bartelski-Tatur polarized valence distribution 18. We do not includetwist-2 contributions to the OFPD, which according to recent calculations20,21may change the absolute cross sections for EMP.42.3 Monte Carlo resultsThe events of exclusive π0 production, µ+p→ µ+p+π0 with the subsequentdecay π0 → γγ, were generated with rates proportional to the estimates ofdifferential cross sections from Ref. 18. The directly measured cross sectioncould be expressed in terms of the virtual photoproduction cross section:dσµN→µNpi0 (ν,Q2, t)dνdQ2dt= Γ(Q2, ν)dσγ∗N→Npi0(x = Q2/(2Mpν), Q2, t)dt, (5)where Γ is the flux of virtual photons:Γ =α(ν − Q22Mp)2πQ2E2µ(1− ǫ). (6)Here, α is the fine structure constant, and ǫ is the virtual photon polarization.The cross sections were estimated for proton and carbon targets. The latterone is more representative for the complex material of the COMPASS polarizedtarget. For the proton target, dσγ∗N→Npi0(x,Q2, t)/dt is given by the Eqs. (2-4) and B = 4.5 GeV−2. For x = 0.1, Q2 = 4 GeV2 and t = tmin,dσdtis equalto 0.88 nb/GeV2. For similar conditions, Vanderhaeghen et al. 13 give about4 times larger cross section. We will therefore give counting rate estimatesin this report with an uncertainty, which reflects the difference between thesetwo theoretical estimates. The present theoretical uncertainties are mainly dueto different assumptions on the shapes/magnitudes of the valence quark spindistributions. For the carbon target, the cross section was assumed to be theproduct of the proton cross section and a function:f(t) = 8.12 e−47.7(t−tmin) + 0.3 . (7)This function was obtained from the parametrization of the NMC data forexclusive ρ0 production on a carbon target 19.In our simulations, we considered the kinematic range of 1 GeV2 < Q2 <Q2maxGeV2 , and 10(15)GeV < ν < 85(180)GeV. Here, Q2max = 4Eµ(Eµ− ν) ·sin2(θmaxµ /2), θmaxµ = 50mrad , and Eµ is the incident muon energy. The valuesoutside (inside) the brackets correspond to the beam energy of 100 (200) GeV.The same convention will be used hereafter. The upper cut on ν was chosen toeliminate the kinematic region where the amount of radiative events is large,whereas the lower one to eliminate events with poor kinematic resolution. Thevalue of Q2max is about 20 (90) GeV2. The cross section integrated within thiskinematic regime5Q2   (GeV2)ν   (GeV)18m212m27m24m218m29m2efficiencyFigure 3: The total acceptance to observe exclusive pi0 events as a function of ν (top) andQ2 (bottom) at a beam energy of 100 GeV. The different histograms correspond to differentgeometrical acceptances of the electro-magnetic calorimeterThe total acceptance ǫpi0 to observe an exclusive π0 event, taking intoaccount the geometric acceptance, the absorption of the decay photons beforeentering the calorimeter, and the reconstruction of π0 from the calorimetricmeasurements, is shown in the top parts of Fig. 3 as function of ν by thesolid histograms. The main effect on ǫpi0 is due to a poor reconstruction of lowenergy π0 mesons from the calorimetric measurements, at small ν, and due tothe absorption of photons in the polarized target, most significantly at largeν. The average total efficiency ǫpi0 is 0.43 for both incident beam energies. Forthe kinematic range ν > 15 GeV, Q2 > 1 GeV2, 0.02 < x < 0.2, the efficiencyis quite large, varying between 0.3 and 0.5.Taking the above values of cross sections, and the expected luminosityfor the COMPASS experiment 7 of 43 pb−1day−1, we evaluate the number ofdeep inelastic exclusive π0 events per day, N totµpi0N/day(Q2 > 1 GeV2), to beabout 248-992 (53-212) for 100 (200) GeV. After taking into account effectsof acceptance, secondary interactions, and the efficiency of π0 reconstruction,the number of events, N cutsµpi0N/day(Q2 > 1 GeV2), is about 107-428 (23-92).The expected numbers of exclusive π0 events for a running period of 150 days6(corresponding to a 1 year period) assuming an overall (SPS and COMPASS)efficiency of 25% are 4013-16050 (855-3420). For Q2 > 4GeV 2, we expect only130 (42) counts. Adopting the Carlitz-Kauer valence quark parametrizationthe last numbers will increase by about a factor of 4. Thus, in 1 year ofCOMPASS operation we will collect at most 500 π0 events with Q2 > 4GeV 2.Up to this point we assumed full size electro-magnetic calorimeters (totalof 18 m2) at their default positions. The different curves in Fig. 3 show theresult if only limited coverage is assumed. While a reasonable efficiency maystill be obtained with about half the calorimeter size (9 m2), a further cut (e.g.down to 7 m2) significantly reduces the π0 efficiency. Furthermore, the countrates presented above were based on a polarized target. Assuming that theoverall length of a target is limited to typically 2 m, a dedicated LH targetwould lead to a reduced luminosity (about a factor of 4) unless the beamintensity can be correspondingly increased.The detailed discussion of the possibility for COMPASS experiment tomeasure another exclusive vector meson production channel, µ + N → µ +N + ρ0, is presented in Ref. 11. Here we only briefly summarize the resultsof the Monte Carlo calculations for this reaction. The kinematic range issomewhat narrower than for the previous channel: 2GeV 2 < Q2 < Q2max and20(40) < ν < 90(180)GeV. The estimated value of the measured cross sectionσthρ0, is equal to 0.46 nb (0.5 nb) for 100 GeV (200 GeV). These values areobtained using a parametrization of the cross section measured in the NMCexperiment 19. For the given kinematic range, the average total acceptanceǫρ0 is 0.73 (0.68). Taking into account the expected luminosity for the COM-PASS experiment, and the effects of acceptance and secondary interactions,the number of events with the invariant mass of two pions in the central partof ρ0 peak, 0.62 < mpipi < 0.92 GeV,Ncutsµρ0N/day(Q2 > 2 GeV2), is about 104for both beam momenta. For a running period of 150 days assuming again anoverall (SPS and COMPASS) efficiency of 25% this will result in about 3.7·105events. For Q2 > 4GeV 2 we expect 75 k (107 k) events.3 ConclusionsWe explored the feasibility to study exclusive meson production in hard muon-proton scattering µ p → µ p M at the COMPASS experiment. For moderateQ2 > 1 GeV 2, a significant counting rate for exclusive π0 production can bereached. For the experimental conditions assumed in our calculations, stillup to 500 events beyond a Q2 of 4 GeV2 can be collected during 1 year ofoperation.On the other hand, COMPASS may provide already during the first main7µ runs, high statistics data on exclusive ρ0 production even at Q2 beyond val-ues presently accessible at JLAB. Furthermore, data taken with the polarizedtarget may also allow a first view at polarization phenomena.AcknowledgementsThis work was partially supported by the Polish State Committee for ScientificResearch (KBN), by the U.S.-Israel Binational Science Foundation (BSF) andthe Israel Science Foundation founded by the Israel Academy of Sciences andHumanities.————————————————————————References[1] A. Bravar, D. von Harrach, and A. Kotzinian, Phys. Lett. B421, 349(1998).[2] X. Ji, Phys. Rev. Lett.78, 610 (1997); Phys. Rev. D55, 7114 (1997).[3] A.V. Radyushkin, Phys. Lett. B 380, 417 (1996); Phys. Lett. B385,333 (1996); Phys. Rev. D56, 5524 (1997); hep-ph/9805342.[4] I. V. Musatov and A. V. Radyushkin, Phys. Rev. D56, 2713 (1997).[5] J. C. Collins, L. Frankfurt, and M. Strikman, Phys. Rev. D56, 2982(1997).[6] N. d’Hose, COMPASS collaboration meeting presentation (1998).[7] COMPASS collaboration, CERN/SPSLC 96-14, SPSC/P 297.[8] CLAS collaboration, JLab exp. E98-107/E99-105, spokespersons M.Guidal, C. Marchand and E.Smith (1998).[9] L. Mankiewicz, G. Piller, A. Radyushkin, hep-ph/9812467.[10] M.V. Polyakov, hep-ph/9809483, hep-ph/9901315, hep-ph/9906261.[11] A. Sandacz, Compass Note 1998-5.[12] L. Frankfurt, M.V. Polyakov and M. Strikman, hep-ph/9808449.[13] M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, Phys.Rev.Lett. 80(1998) 5064; P. A. M. Guichon, M. Vanderhaeghen, Prog. Part. Nucl.Phys. 41 125 (1998); hep-ph/9806305.[14] L. Mankiewicz, G. Piller, and T. Weigl, Eur. Phys. J. C5 119 (1998).[15] T. Gehrmann and W. J. Stirling, Phys. Rev. D53, 6100 (1996).[16] R. Carlitz and J. Kauer, Phys. Rev. Lett.38, 673 (1977).[17] M. Goshtasbpour and G.P. Ramsey, Phys. Rev. D55, 1244 (1997).[18] M. Kurzela, J. Bartelski, S. Tatur, hep-ph/9807355.[19] NMC collaboration, M. Arneodo et al., Nucl. Phys. B429, 503 (1994).[20] V. Yu. Petrov et al., Phys. Rev. D57, 4325 (1998).[21] M.V. Polyakov and C. Weiss, hep-ph/9902451.8

Exclusive meson production at COMPASS

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