Transverse momentum dependent gluon distributions encode fundamental
information on the structure of the proton. Here we show how they can be
accessed in heavy quarkonium production in proton-proton collisions at the LHC.
In particular, their first determination could come from the study of an
isolated J/psi or Upsilon particle, produced back to back with a photon.Comment: 4 pages, 2 figures, to appear in the proceedings of the 49th
  Rencontres de Moriond, QCD and High Energy Interactions, La Thuile (Italy),
  22 - 29 March 201

Pisano, Cristian

English

arXiv

Transverse momentum dependent gluon distributions encode fundamental information on the structure of the proton. Here we show how they can be accessed in heavy quarkonium production in proton-proton collisions at the LHC. In particular, their first determination could come from the study of an isolated J/? or ? particle, produced back to back with a photon

Pisano C.

Archivio istituzionale della ricerca - Università di Cagliari

PROBING THE TRANSVERSE DYNAMICS AND POLARIZATION OF GLUONS INSIDE THE PROTON AT THE LHC CRJSTIAN PISANO Nikhef and Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, NL-1081 HV Amsterdam, The Netherlands Transverse momentum dependent gluon distributions encode fundamental information on the structure of the proton. Here we show how they can be accessed in heavy quarkonium pro­duction in proton-proton collisions at the LHC. In particular, their first determination could come from the study of an isolated J / 1f; or Y particle, produced back to back with a photon. 1 Formalism Transverse momentum dependent (TMD) gluon distributions inside an unpolarized proton are defined by the hadron matrix element of a correlator of the gluon field strengths FJLP(O) and F"O" (O. Expanding the gluon four-momentum as p =  x P + Pr +  p- n , with n being a lightlike vector conjugate to the momentum of the proton P, such correlator can be written as 1 (1) where gauge links have been omitted. The transverse projector gl"' is defined as g�" = gl'" -PJLn" /P·n - nl'P" /P·n. Moreover, p� = -p� and Mp is the proton mass. The gluon correlator of an unpolarized proton can therefore be expressed in terms of two independent TMD distribution functions: jf (x, Pi·l is the unpolarized one, while hfg(x, p�) denotes the T-even, helicity-flip distribution of linearly polarized gluons, which satisfies the model-independent positivity bound 1 2 21;,;.2 lhfg(x, p�) I  :S: fi(x, p�) · p (2) Like any TMD distribution, hf g might receive contributions from initial and final state interac­tions that can render it nonuniversal and even hamper its extraction in processes for which TMD factorization does not apply. 2 Phenomenology Several processes have been suggested to measure the experimentally unkown distributions .ff and hfg. Although it has been discussed how to isolate the contribution from hfg by means of an azimuthal angular dependent weighting of the cross section for dijet production in hadronic collisions 2 , TMD factorization is expected to be broken in this case due to the presence of both initial and final state interactions 3 . A theoretically cleaner and safer way would be to study dijet or heavy quark pair production in electron-proton collisions, for instance at a future Electron-Ion Collider 4•5. Another process where the problem of factorization breaking is absent is pp ---+ // X 6 , which however suffers from a huge background from 7ro decays and contaminations from quark­induced channels. In the following we show how TMD gluon distributions can be probed in heavy quarkonium production at the LHC. TMD factorization should hold in this case, provided that the two quarks that form the bound state are produced in a colorless state already at short distances. 2. 1 Transverse momentum distributions of C = + quarkonia We consider first the process p(PA) + p(PB) ---+ Q(q) + X, where Q is a heavy quark-antiquark bound state with C = +, and the four-momenta of the particles are given between brackets. Assuming TMD factorization, the corresponding cross section can be written as d<T = 1 d3q J 2 2 4 4 - ( ) 'l 0 dxa dxb d Par d Pbr (27r) /j (Pa+Pb-q) 2s 27r · 2q X if>�v(xa, Par) if>�,, (xb, Pbr) L Aµp A�,, (pa ,Pb; q) , colors (3) with s = (PA + PB)2 being the total energy squared in the hadronic center-of-mass frame and A denoting the hard scattering amplitude of the dominant subprocess g(pa) + g(pb) ---+ Q(q) . The amplitude A is evaluated at order a; within the framework of the color-singlet model. Color octet contributions should be negligible, according to nonrelativistic QCD arguments 7. For small transverse momentum, q,7. « JM�, with JI.IQ being the quarkonium mass, the resulting transverse momentum distributions for 1)Q and XQ0,2 ( Q = c, b) are given by 1 d<T(1)Q) <T(1JQ) dy dq� 1 <l<T(XQo) dXQ) dy dq� 1 d<T(XQ2) <T(XQ) dy dq?. C[jf if] J dq� c [.ff .ff] C [jfffl f dq� C[Jf if] C [ffjf] I dq� C[Jf if] , [1 - R(q�)] [1 + R(q�)] , (4) where <T = J dq� d<T and y is the rapidity of the quarkonium along the direction of the incoming protons. Furthermore, Xa,b = Jl.ilQ/ Vs e±Y , 2 C [w hf9 hf 9] R(qr) = C [ff .ff] W = 2�[4 [(Par · Pbr)2 - � P�rP�r] , (5) and we have used the following definition of convolution of two TMD distributions f and g, C[w j g] = j d2Par j d2Pbr 62 (Par + Pbr - qr) W(Par, Pbr) J(xa, P�r) g(xb, P�r) · (6) Our numerical estimates are shown in Fig. 1 ,  where we have assumed that the gluon distribu­tions have a simple Gaussian dependence on transverse momentum. Namely, g 2 - if ( x) ( p� ) f1 (x, Pr) - 7r\p�) exp - \p�) , (7) where ff (x) is the collinear gluon distribution and the width (p�) is taken to be independent of x and the energy scale, set by Jl.:IQ. The bound in Eq. (2) is satisfied, although not everywhere saturated, by the form h_1_g( . 2 ) _ Jl.:IiJf(x) 2(1 - r) . (l _ � P� ) 1 x , pr - /�2 )2 exp / 2 ) ' 7r \I'r r r \Pr (8) 0.8 0.7 0.6 0.5 0.4 0.3 0 .2 0.1 " ·. ' ·. ' (p�)  = 1 GeV2 · .. \ ... ' · .. ' "· \ "·· ... ', ·· .. :-.. ··-.. � 0 L,._�������������=-oo 0 0.5 1 1 .5 2 qT (GeV) 2.5 3 0.8 0.6 0 .5 0.4 0.3 0.2 0 .1 0 0 Xo · · · · · · · · · · · (hy 8 = 0) X2 -­llQ - - - -' / .  ' I ·.. \ I \ I \ I \ I \ (p�)  = 1 GeV2 / '·. \ 0.5 ·. \ 1 1 .5 2 qT (GeV) 2.5 3 Figure 1 - Transverse momentum distributions for C = + quarkonia evaluated at y = 0, obtained using the input distributions in Eqs. (7)-(8), with (p�) = 1 GeV2 and two different values of r: r = 2/3 (left) and r = 1/3 (right). with 0 < r < 1 .  The distributions for '/)c,b and Xc,bO are similar to the ones for a pseudoscalar and a scalar Higgs boson s,9, and can be used to extract h� 9, while ff can be accessed by looking at Xc,b2 .  A comparison among the different spectra could help to cancel out uncertainties. This experiment requires forward detectors like the LHCb, which hopefully will be able to provide such data in the near future. 2.2 C = - quarkonium production in association with a photon Along the lines of the previous section, we study the process p(PA) +p(PB) -+ Q(PQ)+1(P1) +X, where now Q is a C = - quarkonium (J/'l/J or Y) produced almost back to back with the photon. Hence the imbalance qT = P QT + P1T will be small, but not the individual transverse momenta of the two particles. No forward detector is therefore needed in this case. The cross section has the following structure, where Q and Y are the invariant mass and the rapidity of the pair, to be measured, like qT, in the hadronic center-of-mass frame. On the other hand, the solid angle n = (B, r/>) is measured in the Collins-Soper frame, where the final pair is at rest and the ±z-plane is spanned by PA and PB, with the ±-axis set by their bisector. The transverse weights are given by ( 10) and the light-cone momentum fractions are Xa,b = exp[±Y] Q/ ,,/S. Explicit expressions for Fi,3,4 can be found elsewhere 10 . We propose the measurement of the following three observables, 5(n) = J dr/> cos(n r/>) dQdY��qTdO qT - f d 2 f d,I, da ' qT � dQdYd2qTdfl ( 1 1) with n = 0, 2, 4, and where the q� integration in the denominator is up to (Q/2)2 . In this way we are able to single out the three terms in Eq. 9: 8co) _ C[/fjf] 8(2) _ F3 C [w3Jfhf9 + Xa B Xb] qr - f dq� C [Jf!f] ' qr - 2F1 f dq� C [/fjf] ' ( 12) Our model predictions are presented in Fig. 2 for Y + '"Y production, in a kinematic region where color octect contributions are suppressed 10 . The size of 8J� should be sufficient to allow for a determination of the shape of If as a function of qr. Since 5J� and 5J;f are considerably smaller, one would need to integrate them over q� [up to (Q/2)2] to get at least an experimental evidence of a nonzero hf 9 .  - SetB 0.10or--.... � ·--- KMR 0.0501 '',.,, --· CGC sl�(GeV-2) �:=�:::G•� -0.00061 \ ,/ --·- KMR + max s,.;cGeY-2) 0.00041 0.0003 0.0002 -Set B + max •••• KMR + max --· CGC Gaussian + max �:� ,,;., io qdGeV) -0.0000 1 \_/, --· �:cssian + max -0.00101 0.0001 � ' Qr(GeV) 2 4 6 8 10 Figure 2 - Model predictions for S�':') , S�;J and S�� for the process p(PA) + p(PB) -; Q(PQ) + 1(P7) + X at y8 = 14 TeV in the kinematic region defined by Q = 20 GeV, Y = 0, 0 = n:/2, and Xa = Xb "' 1.4 x 10-3 . 3 Conclusions The distribution of linearly polarized gluons inside an unpolarized proton hf 9 leads to a mo­dulation of the transverse momentum distribution of scalar (xc0, XbO) and pseudoscalar (rye, "lb) quarkonia that depends on their parity. It does not contribute to the transverse spectra of Xc2 and Xb2 , which can be used to probe the unpolarized gluon distribution ff. No angular analysis is needed for such measurements and experimental opportunities are offered by LHCb and the proposed fixed-target experiment AFTER at LHC 11 • Furthermore, a first determination of hf 9 and Ji could come from J/'lfJ(Y) + '"Y production at the running experiments at the LHC, where yields are large enough to perform these analyses with existing data at y's = 7 and 8 TeV. We have shown that, together with similar studies in the Higgs sector, quarkonium production can be used to extract gluon TMDs and investigate their process and energy scale dependences. Acknowledgments This work was supported by the European Community under the Ideas program QWORK (con­tract 320389). References 1. P.J. Mulders and J. Rodrigues, Phys. Rev. D 63, 094021 (2001) .  2. D.  Boer, P .  J .  Mulders, and C.  Pisano, Phys. Rev. D 80,  094017 (2009). 3. T.C. Rogers and P.J. Mulders, Phys. Rev. D 81, 094006 (2010). 4. D. Boer, S.J. Brodsky, P.J. Mulders, C. Pisano, Phys. Rev. Lett. 106, 132001 (2011) .  5. C .  Pisano et  al, JHEP 1310, 024 (2013). 6. J.W. Qiu, M. Schlegel, and W. Vogelsang, Phys. Rev. Lett. 107, 062001 (2011) .  7. D.  Boer and C.  Pisano, Phys. Rev. D 86, 094007 (2012). 8. D.  Boer et al, Phys. Rev. Lett. 108, 032002 (2012). 9. D.  Boer, W.J. den Dunnen, C.  Pisano, and M. Schlegel, Phys. Rev. Lett. 111, 032002 (2013) . 10. J.P. Lansberg, W.J. den Dunnen, C. Pisano, and M. Schlegel, arXiv:1401.7611 .  11 .  S.J. Brodsky, F. Fleuret, C .  Hadjidakis, and J.P. Lansberg, Phys. Rept. 522, 239 (2013). 

Probing the transverse dynamics and polarization of gluons inside the proton at the LHC

Abstract

Similar works

Full text

Available Versions

Archivio istituzionale della ricerca - Università di Cagliari