Phenomenology of quarkonia production in fixed target experiments and at the Tevatron and H

a r X i v :h e p -p h /9706374v 1 16 J u n 1997DESY 97-091

hep-ph/9706374

PHENOMENOLOGY OF QUARKONIA PRODUCTION IN FIXED TARGET EXPERIMENTS AND AT THE TEVATRON AND HERA COLLIDERS ?Matteo Cacciari Deutsches Elektronen-Synchrotron DESY,Hamburg,Germany cacciari@desy.de Abstract The phenomenology of heavy quarkonia production in ?xed target experiments and at the

Tevatron and HERA colliders is reviewed.The latest theoretical results are presented and compared with data,with emphasis on the predictions of the factorization approach by Bodwin,Braaten and Lepage.

1Introduction

The production of heavy quarkonia has been subjected to intense study in the last two or three years,with tens of papers having being produced on the problem of J/ψ’s,χ’s andΥ’s production in e+e?,γp,pˉp,pN,πN collisions and also B decays.

The reason for such a surge in interest was the appearance of a theoretical framework,the so called Factorization Approach(FA)by Bodwin,Braaten and Lepage[1],which seems able to solve the theoretical problems that quarkonia production models faced in the past,and also to reconcile theoretical predictions with experimental data,previously in disagreement up to factors of?fty in some instances.

In this talk I shall not review the Factorization approach in detail,leaving this theoretical introduction to other sources(see for instance[2,3,4]).I shall also not discuss in detail the Color Singlet Model(CSM)[5]and the Color Evaporation Model(CEM)[6](the latter has also been recently compared to data and found able to describe at least some of them[7,8]).

I shall just recall how the factorization approach writes the quarkonium state H production cross section in the following form:

σ(ij→QˉQ→H)= n?σ(ij→QˉQ[n]) O H(n) .(1) According to this equation,the cross section for producing the observable quarkonium state H is factorized into two steps.In the short distance part a QˉQ pair of heavy quarks is produced in the spin/color/angular momentum state2S+1L(c)J≡n by the scattering of the two light partons i and j.Successively this pair hadronizes into the quarkonium H,and O H(n) is formally a Non Relativistic QCD(NRQCD)matrix element describing this non perturbative transition.

An important feature of this equation is that also QˉQ pairs in a color octet state are allowed to contribute to the production of a color singlet quarkonium H:their color is neutralized via a non perturbative emission of soft gluons.While the corresponding matrix elements are suppressed by the need of such an emission,the short distance coe?cients can on the other hand be large,perhaps overcompensating the suppression of the non perturbative term.This explains why color octet contributions can play a very important role in predicting the total size of quarkonia production cross sections.

Many theoretical items would be worth discussing about the Factorization Approach.Ac-tually,they would probably be worth a seminar(or more)by themselves.As I said,I shall however skip such a detailed discussion and rather concentrate on some selected phenomeno-logical outcomes of the theoretical investigations which have been carried on so far.I shall restrict myself to analyses of experimental data coming from pˉp collisions at the Tevatron,γp collisions at HERA and?xed target experiment,reviewing the results of these investigations. References will be provided to the theoretical papers,leaving to them the task of properly citing the experimental ones.

The aim of the game will be to check whether the non perturbative matrix elements which can be extracted from these experimental data are mutually consistent with each other.In other words,we shall check whether the factorization approach can properly describe all the data with matrix elements truly universal and independent from the underlying short distance process,as they should.

2The Tevatron data in p ˉp collisions

Beginning with the Tevatron data looks appropriate as the explanation of its anomalously large ψ′production rate (a factor of ?fty above the Color Singlet Model prediction)was the ?rst phenomenological breakthrough of the FA.Braaten and Fleming [9]explained this large rate by assuming it was due to a color octet Q ˉQ pair originating via perturbative splitting from a large p T gluon.While the non perturbative matrix element for such a color octet pair to produce a ψ′is predicted by NRQCD to be about two order of magnitudes suppressed with respect to the one for a color singlet,the production rate of gluons (and hence of such pairs)is however so large that it can more than compensate for the suppression.Indeed,Braaten and Fleming could successfully describe the data ?tting a value for the matrix element in good agreement with the theoretically predicted two-orders-of-magnitude suppression.

This apparent success of the factorization approach on the ψ′anomaly problem made imme-diately clear the potential importance of color octet mediated channels and stimulated similar research in other reactions:by the time of this Conference,the Braaten and Fleming’s paper has received more than 120citations.

Cross sections for large p T J/ψ’s and χ’s production at the Tevatron have been analyzed,and a more detailed study of ψ′has also been performed.It was found the theoretical curves could describe the shape of the data pretty well.The following matrix elements values were returned by the ?ts,performed either within the fragmentation approximation [10,11]or evaluating the full leading order matrix elements [12,13]:

O J/ψ8(3S 1) ?(1.5[11],1.1[14],1.06[13])×10?2GeV 3(2)

O J/ψ

8(1S 0) +3m 2

O J/ψ8(3P 0) ?4.38×10?2GeV 3[13](4)

O ψ′8(3S 1) ?(4.3[11],3.8[14],4.4[13])×10?3GeV 3(5)

O ψ′

8(1S 0) +3m 2 O ψ′8(3P 0) ?1.8×10?2GeV 3

[13]

(7) O χJ 8(3S 1) ?(2J +1)m 2×3.6×10?3GeV 5

[11](8)m is the charm mass,usually taken equal to 1.5GeV.Figure 1shows the CDF data from the Tevatron and the curves which ?t them with these parameters.

The uncertainties on these ?ts are certainly not smaller than a factor of two,due to the many systematics entering their determination:parton distribution functions (responsible for the di?erence between [14]and [13]),charm quark mass,αs value,higher order QCD corrections,etc.They could,however,even be larger.Indications in this direction come from a ?t [15]which makes use of PYTHIA for simulating the e?ect of initial state radiations from the partons before they collide to produce the Q ˉQ

pair:this changes the slope of the theoretical predictions and

Figure 1:

Fits to J/ψplot also

shows by how much the is the J/ψpolarization pattern predicted [13]by the factorization approach.hence the result of the ?t:

O J/ψ8(3S 1) ?3×10?3GeV 3

[15](9)

O J/ψ8(1S 0) +3d cos θ∝1+α(ψ)cos 2θ

(11)

Figure2:Total cross section(left)and inelasticity distribution(right)in photoproduction at HERA [18].Color octet curves with parameters?tted to Tevatron data in[12].

J/ψ’s produced at the Tevatron at large p T are predicted to be almost fully transversely po-larized,i.e.α(J/ψ)?1[16],as a result of the production via gluon fragmentation into3S(8)1 states being largely dominant.At smaller p T,on the other hand,non-fragmentation channels involving1S(8)0and3P(8)J become important:the J/ψ’s are then predicted to be produced es-sentially unpolarized in the low transverse momentum region,around p T?5GeV[13].The observation of such a polarization pattern,shown in?gure1,would provide great support for the factorization approach to quarkonia production.

3The HERA data inγp collisions

Withinγp collisions J/ψ’s can be produced in leading order at non-zero p T via the color singlet channelγp→3S(1)1g→J/ψX([5],?rst reference).Next-to-leading order QCD corrections to this channel have been recently computed[17],and the results have been found in fairly good agreement with the experimental results from the ZEUS and H1experiments:the absolute normalization of the total cross section agrees within the theoretical uncertainties,and the shape of the inelasticity distribution of the J/ψ(usually denoted by z,with z=E J/ψ/Eγin the proton rest frame)is well described by the calculation.

Color octet contributions to J/ψphotoproduction have been investigated in leading order [18,19].In the non-zero p T region the?veγp→(1S0(8),3S1(8),3P J(8))g channels contribute. Figure2shows the results for the total cross section and the inelasticity distribution with the inclusion of these channels:matrix elements of the order of the ones?tted to the Tevatron data without using PYTHIA have been employed in these plots,taking O J/ψ8(3S1) = O J/ψ8(1S0) = O J/ψ8(3P J) /(2J+1)m2=1×10?2GeV3.

One can see from the plots how the data do not need any octet contributions:the color singlet channel by itself can describe them well.More than this,the octet terms evaluated

with the Tevatron parameters look at variance with the data,suggesting a non-universality of these NRQCD matrix elements.We have however seen how indications exist[15]that the?ts to the Tevatron data may be a signi?cant overestimate:if we reduce the value of the matrix elements used in the photoproduction calculation by a factor of three,to bring them in line with the smaller Tevatron?ts returned by using PYTHIA,the discrepancy in the inelasticity distribution is greately reduced.Further unaccounted for contributions,like higher orders near the phase space end point,could easily provide large corrections and bring the prediction in agreement with the data.See refs.[4,20]for a more detailed discussion about this point.

An analysis of photoproduction data within the factorization approach has also been at-tempted in the elastic region,by?tting experimental results with the leading order prediction given by the octet channelsγg→1S(8)0,3P(8)0,3P(8)2.This gives the result[21]

7

O J/ψ8(1S0) +

O J/ψ8(3P0) ?3×10?2GeV3[23](13)

m2

7

Oψ′8(1S0) +

1020

3040

50

100

200

300

400

500

Figure 3:

J/ψ(left)and ψ′(right)production in pN ?xed target experiments,compared with

theoretical ?ts with the color octet contributions [23].A few more observables can o?er a good handle on the validity of a given quarkonium production framework,namely χ’s production,relative fraction of ψ’s and χ’s,and polarization of the produced quarkonium.Let us consider them in turn.

The ratio σ(χ1)/σ(χ2)has been measured in many experiments,both in pN and in πN collisions.An average value for πN is about 0.6,while two pN experiments give smaller values (0.34±0.16for E771,0.24±0.3for E673)but with large errors.A new preliminary result,0.45±0.2,has been presented by E771at this Conference [25].

These experimental results have to be compared with a theoretical prediction,within the FA,of about 0.08[23].The reason for such a small prediction is that at leading order the

gg →3P (1)1→χ1process vanishes in the FA,and the color octet channel q ˉq →3S (8)1→χJ only

contributes a small fraction.One should however consider that more color octet channels can contribute to both χ1and χ2production.These processes go through the octet states 1S (8)0,3P (8)J and 3D (8)J ,and an accurate assessment of their relevance is prevented by our ignorance of the values of the NRQCD matrix elements weighing their transition to the observable χstates.A very crude estimate of their e?ect [23,4]returns a value around 0.3,in good agreement with the pN data but smaller that the πN ones 1.

One more interesting observable is the fraction of J/ψcoming from χ’s decays,σ(J/ψ←χ)/σ(J/ψ),which is of course also a part of the ratio of J/ψand χ’s cross sections.The experimental data,both in ?xed target experiments in pN and πN collisions and also in p ˉp collisions at the Tevatron,gather around a central value of 0.3–0.4.The FA,making use of ?ts to Tevatron data for the χ’s matrix elements and to ?xed target data for J/ψones predicts a value of about 0.3[23],thus in good agreement with the experiment.

What’s special about this observable is that its value is strikingly di?erent in γp collisions.

This is because the leading order reactionγg→χJ g is forbidden due to charge conjugation invariance.Indeed,no experimental data exist forσ(J/ψ←χ)/σ(J/ψ)in photoproduction,due to the vanishingly smallχ’s yield,but only an upper limit by NA14[26]:σ(J/ψ←χ)/σ(J/ψ)< 0.08.The reason why this is important is that the Color Evaporation Model,in that it is not concerned with the details of the particles initiating the reaction,would predict the same ratio for hadro-and photoproduction.Hence,one could say that the CEM is ruled out by this result,though more independent con?rmations of the photoproduction experimental result would actually be welcome.

One further key observable is the polarization of the quarkonium,measured according to eq.(11).One?nds,experimentally,

α(J/ψ)=0.02±0.14(15)

α(ψ′)=0.028±0.004(16)

That is,the quarkonia are found to be produced essentially unpolarized.

This is in contrast with theoretical calculations within the FA,which predict instead a sizeable degree of polarization,returning0.31<α(J/ψ)<0.62and0.15<α(ψ′)<0.44[23], the large band taking into account the very approximate knowledge we have of the NRQCD matrix elements’values.

Such a discrepancy is certainly disturbing,and if con?rmed would be a serious problem for the factorization approach.At the present stage of our understanding we must however be aware that many unaccounted for contributions may still play an important role here.For instance,a proper inclusion of e?ects which would lead to o?-shell rather than on-shell colliding gluons could signi?cantly change the picture presented above.I therefore think it would not be wise to bury the factorization approach at this stage and because of this discrepancy.

5Conclusions

With this brief survey of a few of the phenomenological consequences of the factorization approach to quarkonia production(which I should urge you not to call“Color Octet Model”!) we have seen how it looks able to describe in a satisfactory way experimental results previously at great variance with the Color Singlet Model,both in?xed target experiments and at the Tevatron.

Problems appear in photoproduction at HERA,where the color singlet contribution alone appears on the other hand to well describe the data.But the uncertainties are still large and can accomodate for the discrepancy.

Polarization data are also troublesome for the factorization approach(as they are for the CSM,while the CEM cannot give a prediction at all).But I feel,once again,the uncertainties to be still too large for an assessment of the validity of this approach based on these data.

Surely enough,the factorization approach appears superior to both the CSM(of which it is an extension)and the CEM.One could say the CSM approximation still appears to work fairly well when few gluons are involved(in photoproduction),whereas the CEM can work when very many gluons are around(in hadron-hadron collisions).But neither of them can even attempt

to describe the whole yield of data:for instance,the CSM can be ruled out by the Tevatron data alone,and the CEM could possibly be ruled out byχJ photoproduction.

It is quite a widespread belief(though by no means universal!)that the factorization approach is the right theory for heavy quarkonia production and decay.As a matter of fact, the NRQCD lagrangian on which it is based is nothing but a limit of the QCD lagrangian itself, and not an ad hoc model.

If anything,a problem of the FA is not of being inadequate,but rather of being perhaps even too general.Many di?erent NRQCD matrix elements enter the phenomenological predictions (because the corresponding operators enter the nonrelativistic limit of the QCD lagrangian), and it is di?cult to produce accurate numerical results with so many unknown parameters. These matrix elements are on the other hand rigorously de?ned and in principle calculable by lattice QCD,so it is possible they will be more precisely determined in the future either this way or by global analyses of experimental data.

Given the reasonable correctness of the underlying lagrangian,discrepancies of the theoret-ical predictions with experimental data may still be originated by the approximations included in the calculations.

Higher twist corrections to the factorization approximation can be large,especially for charmonium(one should never forget thatΛ/m c?0.3,not really a negligibly small number). Higher order corrections,both in the strong coupling(αs(m c)?0.3)and in the velocity of the heavy quarks(again,v2?0.3for charm),can also be large.The value of v2(and higher powers)determines–via scaling rules[27]–which matrix elements are dominant,and also how accurately–via spin symmetry–di?erent matrix elements can be equated to each other.These approximations are widely used in the phenomenological predictions,to truncate the series and to decrease the number of independent parameters.How reliable they are is therefore extremely important for the accuracy of the theoretical result:the fairly large value of v2for charmonium systems may help explaining discrepancies between nowadays predictions and experimental data.

The situation should be much better for bottomonium systems,for which all the expansion parameters I mentioned take signi?cantly smaller values,around0.1.All the approximations should therefore be much better justi?ed,and one should expect a better agreement between theory and data.A detailed study of such systems,both theoretically and experimentally,will therefore greatly help?nally confronting the factorization approach to quarkonia production and decay with the real world.

Acknowledgements.I wish to thank the Organizers of this Conference,Patrick Aurenche for inviting me to give this talk,and all the participants for the pleasant atmosphere I enjoyed during my stay.

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