We perform a NLO numerical study of the double transverse-spin asymmetries in
the $J/\psi$ resonance region for proton--antiproton collisions. We analyze the
large $x$ kinematic region, relevant for the proposed PAX experiment at GSI,
and discuss the implication of the results for the extraction of the
transversity densities.Comment: 8 pages, 6 figures, Talk given at "Transversity 2005" Como, Italy
  7-10 Sep. 2005; eds. World Scientific in pres

A. CAFARELLA

C. CORIAN

M. GUZZI

RATCLIFFE P.G.

V. BARONE

English

arXiv

Edited by V. Barone, P.G. Ratcliffe. Hackensack, World Scientific, 2006. 338p

CORIANO', Claudio

P. RATCLIFFE

Archivio Istituzionale della Ricerca- Università del Salento

arXiv:hep-ph/0604176v1  20 Apr 2006February 2, 2008 5:48 Proceedings Trim Size: 9in x 6in GuzziDOUBLE TRANSVERSE-SPIN ASYMMETRIES INDRELL–YAN AND J/ψ PRODUCTION FROMPROTON–ANTIPROTON COLLISIONSM. GUZZI1,2,3, V. BARONE4,5, A. CAFARELLA6,C. CORIANÒ1,2 and P.G. RATCLIFFE3,71Dip. di Fisica, Università di Lecce, 73100 Lecce, Italy2INFN, Sezione di Lecce, 73100 Lecce, Italy3Dip. di Fisica e Matematica, Università dell’Insubria, 22100 Como, Italy4Di.S.T.A., Università del Piemonte Orientale “A. Avogadro”15100 Alessandria, Italy5INFN, Gruppo Collegato di Alessandria, 15100 Alessandria, Italy6Dept. of Physics, University of Crete, 71003 Heraklion, Greece7INFN, Sezione di Milano, 20133 Milano, ItalyWe perform a NLO numerical study of the double transverse-spin asymmetries inthe J/ψ resonance region for proton–antiproton collisions. We analyze the large xkinematic region, relevant for the proposed PAX experiment at GSI, and discussthe implication of the results for the extraction of the transversity densities.1. IntroductionThe purpose of this talk is to illustrate a numerical analysis of the doubletransverse-spin asymmetries in Drell–Yan processes in the J/ψ resonanceregion and to discuss the results with regard to the proposed PAX experi-ment and the possibility of accessing the transversity densities in proton–antiproton collisions.2. Access to transversity densitiesThe missing leading-twist piece in the QCD perturbative description of thenucleon is the transversity density,1 which is defined as the difference ofprobabilities for finding a parton of flavour q at energy scale Q2 and light-cone momentum fraction x with its spin aligned (↑↑) or anti-aligned (↑↓)with that of transversely polarized parent nucleon∆T q(x,Q2) = q↑↑(x,Q2)− q↑↓(x,Q2) . (1)1February 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi2Given its chirally odd nature, transversity may be accessed in collisions oftwo transversely polarized nucleons (Drell–Yan) via the double transverse-spin asymmetries which are defined as the ratioATT =σ↑↑ − σ↑↓σ↑↑ + σ↑↓=∆Tσσunp(2)between the transversely polarized and unpolarized cross-sections.Doubly polarized Drell–Yan production (illustrated in Fig. 1) is thecleanest process for probing transversity distributions. It has recently beensuggested that collisions of transversely polarized protons and antiprotonsshould provide a very good opportunity to determine the nucleon transver-sity via measurement of ATT .Double transverse-spin asymmetries depend may only on quark andantiquark transversity distributionsATT =σ↑↑ − σ↑↓σ↑↑ + σ↑↓= âTT (ϕ)∑q e2q ∆T q(x1,M2)∆T q̄(x2,M2) + (1↔ 2)∑q e2q q(x1,M2) q̄(x2,M2) + (1↔ 2),(3)where âTT (ϕ) contains the azimuthal angular dependenceâTT (ϕ) =12 cos 2ϕ (4)and M is the dilepton invariant mass.Measurement of AppTT in the case of proton–proton collisions is plannedat RHIC but the asymmetry is expected to be small (2–3%).2,3 In fact, AppTTcontains antiquark distributions and the RHIC kinematics (√s = 200GeV,M < 10GeV, x1x2 = M2/s < 3 × 10−3) probes the low-x region where,compared to q(x), ∆T q(x) is suppressed by QCD evolution. Such problemsmay be avoided by measuring App̄TT in proton–antiproton collisions at lowercentre-of-mass energies;2,4 this is the program of the PAX experiment atGSI.5 For the GSI kinematics we have s = 30 or 45GeV2 in fixed-target, ands = 200GeV2 in collider mode, M > 2GeV and τ = x1x2 = M2/s > 0.1.The GSI kinematics is such that the asymmetries for double transverseDrell–Yan proton–antiproton processes are dominated by valence distribu-tions and thus probe the product ∆T q ×∆T q. At LO we can writeApp̄TT = âTT∑qe2q[∆T q(x1,M2)∆T q(x2,M2) + ∆T q̄(x1,M2)∆T q̄(x2,M2)]∑qe2q[q(x1,M2)q(x2,M2) + q̄(x1,M2)q̄(x2,M2)](5)and App̄TT /âTT is found to be of order of 30%.4,6February 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi3Figure 1. Drell–Yan processAt NLO the factorization formula of the cross-section for dilepton pro-duction in transversely polarized proton–antiproton scattering is 7,8d∆TσdM dy dϕ=∑qe2q∫ 1ξ1dx1∫ 1ξ2dx2[∆T q(x1, µ2)∆T q(x2, µ2)+ ∆T q̄(x1, µ2)∆T q̄(x2, µ2)] d∆T σ̂dM dy dϕ, (6)where µ2 is the factorization scale, y is the rapidity of the dilepton pair andthe momentum fractions ξ1 and ξ2 are defined asξ1 =√τ ey, ξ2 =√τ e−y, y =12lnξ1ξ2. (7)February 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi4The NLO hard-scattering cross-section isd∆T σ̂(1),MSdM dy dϕ=2α29sMCFαs(µ2)2π4τ(x1x2 + τ)x1x2(x1 + ξ1)(x2 + ξ2)cos(2ϕ)×{δ(x1 − ξ1)δ(x2 − ξ2)[14ln2(1− ξ1)(1− ξ2)τ+π24− 2]+ δ(x1 − ξ1)[1(x2 − ξ2)+ln2x2(1− ξ1)τ(x2 + ξ2)+(ln(x2 − ξ2)x2 − ξ2)++ln(ξ2/x2)x2 − ξ2]+12[(x1 − ξ1)(x2 − ξ2)]++(x1 + ξ1)(x2 + ξ2)(x1ξ2 + x2ξ1)2−3 ln(x1x2+τx1ξ2+x2ξ1)(x1 − ξ1)(x2 − ξ2)+ lnM2µ2[δ(x1 − ξ1)δ(x2 − ξ2)(34+12ln(1− ξ1)(1− ξ2)τ)+ δ(x1 − ξ1)1(x2 − ξ2)+]}+[1←→ 2]. (8)In order to predict asymmetries, some assumption for the transversity dis-tributions is needed. For instance, we may take transversity equal to helicityat some low scale (as suggested by certain models)∆T f(x, µ) = ∆f(x, µ) (minimal bound) (9)or, alternatively, saturation of the Soffer inequality 92 |∆T f(x, µ)| = f(x, µ) + ∆f(x, µ) . (10)We use NLO GRV input densities,10 with starting scale µ = 0.63GeV.The relation between transversity and the GRV distributions is set atthis scale. QCD evolution is performed via the appropriate NLO DGLAPequations.11,12 In Fig. 2 we see that in the energy range relevant for thePAX experiment the asymmetries are around 35%. From Fig. 3 we seethat in the case of the Soffer bound the asymmetries are systematicallylarger than the asymmetries obtained in the case of the minimal bound. InFig. 4 we display the asymmetry at larger M , where it grows up to 45%(but one should recall that the cross-section falls rapidly as M increases).Applying the constraint ∆T f(x, µ) = ∆f(x, µ) at, say, 1GeV instead of0.63GeV would produce slightly larger asymmetries; this is due to QCDevolution effects since ∆T f(x, µ) is less suppressed by evolving from 1 GeVthan from 0.63GeV. The comparison between LO and NLO results is shownin Fig. 5, where one sees that NLO corrections have very little affect on theasymmetries.February 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi500.050.10.150.20.250.30.350.40 0.5 1 1.5 2ATT     (y)/aTT    (ϕ)yNLO s=30 GeV2NLO s=45 GeV2NLO s=80 GeV2NLO s=200 GeV2Figure 2. ATT (y)/âTT (ϕ) at NLO, with M integrated from 2 to 3GeV using GRVinput with the minimal bound ∆T q(x, µ) = ∆q(x, µ).00.20.40.60.810 0.5 1 1.5 2ATT     (y)/aTT    (ϕ)yNLO s=30 GeV2NLO s=45 GeV2NLO s=80 GeV2NLO s=200 GeV2Figure 3. ATT (y)/âTT (ϕ) at NLO, with M integrated from 2 to 3GeV using GRVinput and saturating the Soffer bound.3. Dilepton production via the J/ψ resonance in the GSIregimeTo achieve a higher counting rate, one may exploit the J/ψ peak, wherethe cross-section is two orders of magnitude larger. If J/ψ production isdominated by qq̄ annihilation channel, the corresponding asymmetry hasthe same structure as in the continuum region, since the J/ψ is a vectorFebruary 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi600.10.20.30.40.50.60.70 0.2 0.4 0.6 0.8 1 1.2 1.4ATT     (y)/aTT    (ϕ)yNLO s=80 GeV2NLO s=200 GeV2Figure 4. ATT (y)/âTT (ϕ) at NLO with M integrated from 4 to 7GeV using GRVinput with the minimal bound.00.10.20.30.40.50.60 0.2 0.4 0.6 0.8 1 1.2 1.4ATT    (y)/aTT    (ϕ)yLO s=45 GeV2NLO s=45 GeV2LO s=200 GeV2NLO s=200 GeV2Figure 5. ATT (y)/âTT (ϕ) at LO (solid curve) vs. NLO (dashed curve) at M = 4GeVand s = 45GeV2 and ATT (y)/âTT (ϕ) at LO (dotted curve) vs. NLO (dot-dashed curve)at M = 4GeV and s = 200 GeV2 using GRV input with the minimal bound.particle and the qq̄ − J/ψ couplings are similar to qq̄ − γ∗.4 SPS data 13show the pp̄ cross-section for J/ψ production at s = 80GeV2 to be about 10times larger than the corresponding pp cross-section, indicating the domi-nance of the qq̄ annihilation mechanism. Thus, the helicity structure of theasymmetries is preserved and, replacing the couplings in Eq. (5), we canFebruary 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi700.10.20.30.40.50.60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8Au TT (y)/aTT    (ϕ)yNLO s=45 GeV2NLO s=80 GeV2NLO s=200 GeV2Figure 6. The double transverse-spin asymmetry in the J/ψ resonance region for variousc.m. energies. As usual, the minimal bound is used for the input distributions.writeAJ/ψTT = âTT (11)×∑q(gVq )2[∆T q(x1,M2)∆T q(x2,M2) + ∆T q̄(x1,M2)∆T q̄(x2,M2)]∑q(gVq )2 [q(x1,M2)q(x2,M2) + q̄(x1,M2)q̄(x2,M2)]In the large x1, x2 region the u and d valence quarks dominate and, since theqq̄− J/ψ coupling is the same for u and d quarks, the asymmetry becomesAJ/ψTT ≃ âTT∆Tu(x1,M2)∆Tu(x2,M2) + ∆Td(x1,M2)∆T d(x2,M2)u(x1,M2)u(x2,M2) + d(x1,M2)d(x2,M2).(12)The condition ∆Tu(x)≫ ∆Td(x), satisfied by all models at large x, permitsa further simplification and one obtainsAJ/ψTT ≃ âTT∆Tu(x1,M2)∆Tu(x2,M2)u(x1,M2)u(x2,M2). (13)The J/ψ asymmetry is then essentially the DY asymmetry evaluated atMJ/ψ and, for s = 80GeV2, lies in the range 0.25–0.45 (see Fig. 6). Inas-much as the gg fusion diagram may be neglected, as old pp̄ data suggest,this remains true at NLO (i.e. considering gluon radiation).4. Threshold resummationThe kinematic region corresponding to M ≈ 1 − 4GeV and with a centre-of-mass energy s ≈ 30GeV2 is not properly contained in the domain ofFebruary 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi8perturbative QCD, (i.e. factorization, parton model etc.). Thus, depend-ing on kinematics, higher-order corrections to the cross-sections may beimportant and must be well understood.For the sake of simplicity, we shall merely sketch what occurs, withlittle quantitative detail. The factorization theorem for the hadronic cross-section in terms of twist-2 parton densities is not exact, but holds only to theleading power of M , and the corrections generally increase as τ increases.In the region z = τ/(x1x2) ≃ 1 the kinematics is such that virtual andreal-emission diagrams become strongly unbalanced (real-gluon emission issuppressed) and in these conditions there are large higher-order logarithmiccorrections to the partonic cross-section of the formαks[ln(1 − z)]2k−1(1− z) (14)The region z ≈ 1 is dominant in the kinematic regime relevant for GSI,hence the large logarithmic contributions need to be resummed to all ordersin αs. NLL-resummed perturbation theory has been extensively studied14and resummation corrections for ATT are found to be less than 10% andrather dependent on the infrared cut-off for the soft gluon emission.5. ConclusionsIn the GSI regime Drell–Yan double transverse-spin asymmetries are siz-able, of the order of 30%, and are not spoiled by NLO (and resummation)effects. Transverse asymmetries for J/ψ production at moderate energiesare expected to be similar (with the advantage of much higher countingrates). Transversely polarized antiproton experiments at GSI will thus pro-vide an excellent window onto nucleon transversity.AcknowledgmentsWe would like to thank M. Anselmino, N.N. Nikolaev and our colleaguesof the PAX collaboration for prompting the study reported here and forvarious useful discussions. This work is supported in part by the ItalianMinistry of Education, University and Research (PRIN 2003).References1. V. Barone, A. Drago and P.G. Ratcliffe, Phys. Rep. 359 (2002) 1.2. V. Barone, T. Calarco and A. Drago, Phys. Rev. D56 (1997) 527.February 2, 2008 5:48 Proceedings Trim Size: 9in x 6in Guzzi93. O. Martin, A. Schäfer, M. Stratmann and W. Vogelsang, Phys. Rev. D57(1998) 3084.4. M. Anselmino, V. Barone, A. Drago and N.N. Nikolaev Phys. Lett. B5(2004) 97.5. PAX Collaboration, V. Barone et al., “Antiproton–Proton Scattering Exper-iments with Polarization”, Technical Proposal, hep-ex/0505054 (2005).6. A. Efremov, K. Goeke and P. Schweitzer, Eur. Phys. J. C35 (2004) 207.7. O. Martin, A. Schäfer, M. Stratmann and W. Vogelsang, Phys. Rev. D60(1999) 117502.8. A. Mukherjee, M. Stratmann and W. Vogelsang, Phys. Rev. D67 (2003)114006.9. J. Soffer, Phys. Rev. Lett. 74 (1995) 1292.10. M. Glück, E. Reya and A. Vogt, Eur. Phys. J. C5 (1998) 461; M. Glück,E. Reya, M. Stratmann and W. Vogelsang, Phys. Rev. D63 (2001) 094005.11. A. Cafarella and C. Corianò, Comput. Phys. Commun. 160 (2004) 213.12. A. Cafarella, C. Corianò and M. Guzzi, JHEP 0311 (2003) 059.13. M.J. Corden, Phys. Lett. B98 (1981) 220.14. H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, Phys. Rev. D71(2005) 11407.

Double transverse-spin asymmetries in Drell-Yan and J / psi production from proton-antiproton collisions.

We perform a NLO numerical study of the double transverse-spin asymmetries in the J/psi resonance region for proton–antiproton collisions. We analyze the large x kinematic region, relevant for the proposed PAX experiment at GSI, and discuss the implication of the results for the extraction of the transversity densities

Double transverse-spin asymmetries in Drell--Yan and $J/\psi$ production from proton--antiproton collisions

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Archivio istituzionale della ricerca - Università dell'Insubria

Double transverse-spin asymmetries in Drell--Yan and J/ψJ/\psiJ/ψ production from proton--antiproton collisions

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Archivio Istituzionale della Ricerca- Università del Salento

Archivio istituzionale della ricerca - Università dell'Insubria

Double transverse-spin asymmetries in Drell--Yan and $J/\psi$ production from proton--antiproton collisions