Measurements of the polarization of $\jp$ produced in pion-nucleus collisions
are in disagreement with leading twist QCD prediction where $\jp$ is observed
to have negligible polarization whereas theory predicts substantial
polarization. We argue that this discrepancy cannot be due to poorly known
structure functions nor the relative production rates of $\jp$ and $\chi_J$.
The disagreement between theory and experiment suggests important higher twist
corrections, as has earlier been surmised from the anomalous non-factorized
nuclear $A$-dependence of the $\jp$ cross section.Comment: 8 page

Brodsky, S. J.

Hoyer, P.

Tang, W. -K.

Vänttinen, M.

English

arXiv

Measurements of the polarization of J/{psi} produced in pion-nucleus collisions are in disagreement with leading twist QCD prediction where J/{psi} is observed to have negligible polarization whereas theory predicts substantial polarization. The authors argue that this discrepancy cannot be due to poorly known structure functions nor the relative production rates of J/{psi} and {chi}{sub j}. The disagreement between theory and experiment suggests important higher twist corrections, as has earlier been surmised from the anomalous non-factorized nuclear A-dependence of the J/{psi} cross section

Tang, W.K.

Brodsky, S.J.

Vaenttinen, M.

UNT Digital Library

* SLAC-PUB-6576 July 1994 (WE) Polarization as a Probe to the Production Mechanisms of Charmonium in TN Collisions’ W.-K. Tang2 and S. J. Brodsky2 Stanford Linear Accelerator Center Stanford University, Stanford, CA 94309 M. Vanttinen and P. Hoyer Department of Physics University of Helsinki, Finland Abstract Measurements of t,.e polarization of J / $  produced in pion-nuc,ms collisions are in disagreement with leading twist QCD prediction where J / $  is observed to have negli- gible polarization whereas theory predicts substantial polarization. We argue that this discrepancy cannot be due to poorly known structure functions nor the relative produc- tion rates of J/$ and X J .  The disagreement between theory and experiment suggests important higher twist corrections, as has earlier been surmised from the anomalous non-factorized nuclear A-dependence of the J / $  cross section. 1 Introduction One of the most sensitive tests of the QCD mechanisms for the production of heavy quarko- nium is the polarization of the J / $  in hadron collisions. In fact, there are serious disagree- ments between leading twist QCD prediction [2] and experimental data [3, 4, 5, 6, 71 on the production cross section of ‘direct’ J / $  and xl. We would like to advocate that polariza- tion of J / $  provides strong constraints on the production mechanisms of J / $  and thus can pinpoint the origin of these disagreements. In this paper we will present some preliminary results on the theoretical calculation of the polarization of J / $  in T N  collisions. The completed analysis will be published in a later paper[l]. We found that the polarization of J / $  provides important constraints on the nature of the production mechanisms and urge that polarization measurement of J / $  should be included in the design of future charm production experiment. The paper is organized as follow. In section 2, we show that from the experimental data on the production cross sections and leptonic decay widths of direct J / $  and $’, the long distance physics of formation of bound states of cc can be separated from the short distance physics of production of the ci? pair. Thus, the perturbative analysis is under control in ‘Presented by W.-K. Tang at  QCD Tests Working Group, Workshop on the Future of High Sensitivity Charm Experiments: Charm2000, Fermilab, Batavia,-Il., June 7-9, 1994 ’Work supported by the Department of Energy, contract DE-AC03-76SF00515 calculating J / $  production even though the mass of charm quark is not much larger than A Q ~ D .  Once the validity of perturbative method is established, we calculate the production cross sections of direct J / $ ,  x1 and x2 in 7rN collisions in PQCD. These results are presented in section 3 and discrepancies are observed. We show that, in comparison with the recent E705 and E672 data [8, lo], the predicted ratio of direct J / $  production compared to the x2 production is too low by a factor of about 3. In addition the production ratio of production cross sections of x1 to x 2  is too low by a factor of 10 compared to data. A similar conclusion has been reached in [ll]. The polarization data of J / $  [12, 13, 141 allows us to make further conclusion of the origin of the disagreements. In section 4, we find that even if the relative production rates of the J /+ ,  x1 and x 2  are adjusted (using I(-factors) to agree with the data, the J/I+!I polarization data is still not reproduced. Therefore, the discrepancies do not arise from an incorrect relative normalization of the various channels and new production mechanisms are needed. We will present our conclusion in the last section. 2 Can direct J / $  production be calculated in PQCD? In leading twist QCD, the production of the J / $  at low transverse momentum occurs both ‘directly’ from the gluon fusion subprocess gg + J / $  + g [Fig. la] and indirectly via the production and decay of x1 and x 2  states. These states have sizable decay branching fractions x1,2 -+ J / $  + y of 27% and 13%, respectively. In this model, we assume that the non-perturbative physics, which is described by the wave function at the origin in cases of production of J / +  and $’, is separable from the perturbative hard subprocess, i.e., factorization holds. As the wave function at the origin can be related to the leptonic decay amplitude [Fig. lb], the ratio of +’ to direct J / $  production can be expressed in terms of the ratio of their leptonic decay width. More precisely, taking into account of the phase space factor, where adzr (J /$ )  is the cross section for direct production of the J/+. The ratio (1) should hold for all beams and targets, independently of the size of the higher twist corrections in producing the point-like CE state. The energy should be large enough for the bound state to form outside the target. The available data is indeed compatible with (1). In particular, the E705 value [8] is 0.24. In Table 1, the ratio of $‘ to direct J / $  production with different projectiles is presented. They are all consistent with the value 0.24. The anomalous nuclear target A-dependence observed for the J / $  is also seen for the $’ [15], so that the ratio (1) is indeed independent of A. Therefore, at high energies, the quarkonium bound state forms long after the production of the CC pair and the formation process is well described by the non-relativistic wavefunction at the origin. 3 Production rates of $ and X J  states at leading twist In leading twist and to leading order in a,, J / $  production can be computed from the convolution of hard subprocess cross section gg + J / $ g ,  gg -+ xj, etc., with the parton L DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. 7-94 7748A1 Figure 1: Fig. l a  shows direct J / $  production through gg scattering. The formation of bound state is described by the wavefunction S;,,(O) at the origin. Fig. l b  shows leptonic decay of J / $  into e+e- pair. The probability of finding the cc pair is given by the wavefunction @ J/* (0 1. distribution functions in the beam and target. Higher order corrections in cy,, and rela- tivistic corrections to the charmonium bound states, are unlikely to change our qualitative conclusions at moderate XF. Contributions from direct J / $  production, as well as from indirect production via x1 and x2 decays, will be included. Due to the small branching fraction xo + J / $  + y of 0.7%, the contribution from x o  to J / $  production is expected (and observed) to be negligible. Decays from the radially excited a3S1 state, 4’ -+ J / $  + X ,  contribute to the total J / $  rate at the few per cent level and will be ignored here. a($/> Enbl Odir(J/$) 4 V ) / Q i r ( J / $ )  n+ 2 2 f 5  97 f 14 0.23 f 0.07 n- 2 5 f 4  102% 14 0.25 f 0.05 p 2 0 5 3  89 f 12 0.23 f 0.05 Table 1: Production cross sections for $’, direct J / $  and their ratio in 7r+N, 7r-N and p N  collisions. The data is from Ref. [8]. The T N  + x 2  + X production cross section to  lowest order is Experiment Theory where T = Mz,/s and the quantity ao(gg + x2) = ~ ~ T ~ N ~ I B > ( O ) ~ ~ / M ~ ~  [18]. We restrict the x2 momentum range to the forward CM hemisphere (XF > 0) in accordance with the available data, and use the structure functions of Ref. [16, 171 evaluated at Q2 = M;2. We also take the renormalization scale to be Q2 = M&. The direct T N  + J / $  + X cross section is similarly given by 4 x 2 )  [nbl odir ( J / $ )  /O(Xa) 4x1 )ldx2) 188 f 30 f 21 0.54 f 0.11 f 0.10 0.70 f. 0.15 f 0.12 72 0.19 0.069 where t^ is the invariant momentum transfer in the subprocess, and Eq. (3) also applies to the 7rN -+ x1 + X reaction, in which case a sum over the relevant subprocesses gg -+ xlg, gq -+ xlq, gq + x1Q and qq -+ x1g is necessary. The differential cross sections do/dt^  for all subprocesses are given in [18, 191. In Table 2 we compare the x2 production cross section, and the relative rates of direct J / $  and x1 production, with the data of E705 and WAll on T-N collisions at Elab = 300 GeV and 185 GeV [8]. Table 2: Production cross sections for xl, x2 and directly produced J / $  in T-N collisions. The data from Ref. [8, 91 include measurements at 185 and 300 GeV. The theoretical calculation is at 300 GeV. The x2 production rate in QCD agrees with the data within a ‘K-factor’ of order 2 to 3. This is within the theoretical uncertainties arising from the J / $  and x wavefunctions, higher order corrections, structure functions, and the renormalization scale. A similar factor is found between the lowest-order QCD calculation and the data on lepton pair production [20,21]. On the other hand, Table 2 shows a considerable discrepancy between the calculated and measured relative production rates of direct J / $  and x1, compared to x2 production. A priori we would expect the K-factors to be roughly similar for all three processes. We conclude that leading twist QCD appears to be in conflict with the data on direct J / $  and x1 production. Although in Table 2 we have only compared our calculation with the E705 and WA11 T - N  data, this comparison is representative of the overall situation (for a recent comprehensive review see [ll]). . I 4 4 Polarization of the J / $  The polarization of the J / $  is determined by the angular distribution of its decay muons in the J / $  rest frame. By rotational symmetry and parity, the angular distribution of massless muons, integrated over the azimuthal angle, has the form da d cos 0 oc 1 + Xcos26, ( 5 )  where we take 0 to be the angle between the pf and the projectile direction ( L e . ,  we use the Gottfried-Jackson frame). The parameter X can be calculated from the c.? production amplitude and the electric dipole approximation of radiative x decays. The electric dipole approximation of the radiative decay x J ---$ $7 is exact in the heavy quark limit; i .e.,  when terms of O(E,/rn,) are neglected. As a consequence, the heavy quark spins are conserved in the decay, while the orbital angular momentum changes. The lowest order subprocess g ( p I j g ( p 2 )  + CC --$ x,(J,) only produces x2 with J,  = f2 states assuming that the transverse momenta of the incoming gluons are neglected. In the J ,  = f2 polarization state the spin and orbital angular momenta of its constituent charm quarks are aligned, S, = L,  = fl. Since S, is conserved in the radiative decay xz -+ J / $  + y, it follows that J z ( J / $ )  = S, = fl ( L  = 0 for the J / $ ) .  Thus the J/$’s produced via x2  decay are transversely polarized, ie., X = 1 in ( 5 ) .  This result is exact if both the photon recoil and the intrinsic transverse momenta of the incoming partons are neglected. Smearing of the beam parton’s transverse momentum distribution by a Gaussian function exp [-(k1/500 MeV)’] would bring X down to X cx 0.85. From the gg --$ J / $  + g amplitude we find for direct J / $  production, T N  + J / $  + X + P+P- + x, where B,, is the J / $  + p+p- branching fraction, XF = 2p$/& is the longitudinal- momentum fraction of the J / $ ,  and 0 is the muon decay angle of Eq. (5). The e l l , e o o  are the density matrix elements and can be found in [l]. For the T N  --$ x1 + X t J / $  + y + X + p fp -  + y + X production process we get similarly x [eYo + 3eY1 + - cos2 O ]  , (7)  where the density matrix elements for ij = gg, gq gq and qq scattering are again given in In Fig. 2a we show the predicted value of the parameter X of Eq. ( 5 )  in the GJ-frame as a function of XF, separately for the direct J / $  and the xl,2 + J / $  + y processes. Direct J / +  production gives X N 0.25, whereas the production via x1 results in X 2~ -0.15. [11- 5 shows the effect of multiplying the partial J / $  cross sections with the required IC-factors. The X parameter is still predicted incorrectly over most of the XF range. A similar conclusion is reached (within somewhat larger experimental errors) if we com- pare our calculated value for the polarization of direct J / $  production, shown in Fig. 2a, with the measured value of X for $‘ production. In analogy to Eq. (l), the $‘ polarization data should agree with the polarization of directly produced J/+’s, regardless of the produc- tion mechanism. Based on the angular distribution of the muons from $’ -+ p+p- decays in 253 GeV T-W collisions, Ref. [23] quotes X G ~  = 0.02 f 0.14 for ZF > 0.25, appreciably smaller than our QCD values for direct J/$’s in Fig. 2a. 5 Discussion We have seen that the J / $  and x1 hadroproduction cross sections in leading twist QCD are at  considerable variance with the data, whereas the x2  cross section agrees with measurements within a reasonable IC-factor of 2 to 3. On the other hand, the inclusive decays of the charmonium states based on the minimal perturbative final states (gg and qqg) have been studied in detail using perturbation theory [24, 25, 111, and appear to work fairly well. It is therefore improbable that the treatment of the CC binding should require large corrections. This conclusion is supported by the fact that the relative rate of +‘ and direct J / $  production (Eq. l),  which at high energies should be independent of the production mechanism, is in agreement with experiment. In a leading twist description, an incorrect normalization of the charmonium production cross sections can arise from large higher order corrections or uncertainties in the parton distributions[ll]. Taking into account that the normalization may be wrong by as much as a factor of 10 and that even such a IC-factor does not explain the polarization data of J / $ ,  a more likely explanation may be that there are important higher-twist contributions to the production of the J / $  and x1 as suggested in large XF case [26, 271. Further theoretical work is needed to establish that the data on direct J / +  and x1 production indeed can be described from higher twist mechanisms. Experimentally, it is important to check whether the J/$’s produced indirectly via x2 decay are transversely polarized. This would show that x 2  production is dominantly leading twist, as we have argued. Thus, the polarization of J / $  production from different channels provides a very sensitive discriminant of different production mechanisms. References [l] M. Vanttinen, P. Hoyer, S. J. Brodsky and W.-K. Tang, in preparation. [2] V. Barger and A. D. Martin, Phys. Rev. D31, 1051 (1985). [3] A. G. Clark, et al., Nucl. Phys. B142, 29 (1978). [4] R806: C. Kourkoumelis et ad., Phys. Lett. B81, 405 (1979) [5] WA11: Y. Lemoigne, e t  a/., Phys. Lett. B113, 509 (1982). 7 ~ 16) E673: S. R. Hahn, et ai., Phys. Rev. D30, 671 (1984); D. A. Bauer, et al., Phys. Rev. Lett. 54, 753 (1985). [7] F. Binon, et al., Nucl. Phys. B239, 311 (1984). [8] E705: L. Antoniazzi, et al., Phys. Rev. Lett. 70, 383 (1993) [9] E705: L. Antoniazzi, e t  al., Phys. Rev. D46, 4828 (1992) [lo] E672: A. Zieminski, et al., Proc. XXVI Int. Conf. on High Energy Physics, Dallas, Texas, 1992, AIP Conf. Proc. No. 272, Ed. by J. R. Sanford, p. 1062. [ll] G. A. Schuler, preprint CERN-TH.7170/94. [la] NA3: J. Badier, et al., Z. Phys. C20, 101 (1983). [13] C. Biino, et a]., Phys. Rev. Lett. 58, 2523 (1987). [14] E537: C. Akerlof, et al., Phys. Rev. D48, 5067 (1993). I151 E772: D. M. Alde, et d., Phys. Rev. Lett. 66, 133 (1991). [16] J. F. Owens, Phys. Rev. D30, 943 (1984). [17] J. F. Owens, Phys. Lett. B266, 126 (1991). El81 R. Baier and R. Riickl, 2. Phys. C19, 251 (1983). 119) R. Gastmans and T. T. Wu, The Ubiquitous Photon: Helicity Method fo r  QED and QCD, Clarendon Press, Oxford, 1990 [20] J. Badier, et al., Z. Phys. C18, 281 (1983). [all J. S. Conway, et al., Phys. Rev. D39, 92 (1989). [22] P. Chiappetta and M. Le Bellac, 2. Phys. C32, 521 (1986) E231 J. G. Heinrich, et ai., Phys. Rev. D44, 1909 (1991). I241 W. Kwong, J. L. Rosner and C. Quigg, Ann. Rev. Nucl. Part. Sci. 3'7, 325 (1987). [25] L. Kopke and N. Wermes, Phys. Rep. 174, 67 (1989). [26] S. J. Brodsky, P. Hoyer, A. H. Mueller and W.-K. Tang, Nucl. Phys. B369, 519 (1992). 1271 P. Hoyer, M. Vsnttinen and U. Sukhatme, Phys. Lett. B246,217 (1990). ---- - ~  DISCLAIMER^---- - - This report was prepared as an a m u n t  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, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracj, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 

Polarization as a probe to the production mechanisms of charmonium in {pi}N collisions

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Polarization as a Probe to the Production Mechanisms of Charmonium in $\pi N$ Collisions

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Polarization as a Probe to the Production Mechanisms of Charmonium in πN\pi NπN Collisions

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Polarization as a Probe to the Production Mechanisms of Charmonium in $\pi N$ Collisions