PACS Properties of specific particles 14.40.Lb Charmed mesons 12.39.-x Phenomenological quark models (12.39.Hg Heavy quark effective theory)

= Abstract

This article addresses the production of charmed D mesons. We start by pointing inconsistencies in the present simulations when describing the different meson yield measurements. We then describe the interplay of charmed mesons contributing to the measured yields, and show that there is a hadronization-related parameter, Pv, which can drastically change the proportion of those yields. We then proceed to review a wide range of measurements that can yield a determination of this parameter. We discard measurements that have doubtful theoretical foundations and which for the most part lead to the widespread belief that Pv=0.75 for D mesons. From the data gathered we conclude that Pv for charmed D mesons is universal across production systems, does not show any appreciable dependence on the center-of-mass energy above production threshold, its value being Pv=0.591+-0.007. We proceed to show how changing this parameter in the PYTHIA Monte Carlo event generator provides adequate description of p+p and pi+p data for the D+/D0 ratio. We then point out that the situation for beauty mesons is not the same as for charm. There, Pv~0.75, in accordance with naïve expectations from HQET. Finally we remark a few theoretical models from which values of Pv around 0.6 naturally stem out.

= Introduction

Charm is a very important probe of hard processes in high energy nuclear and elementary collisions. Ever since the discovery of the J/psi meson, the cq states (where q={u,d}) have been under intense study.

Starting from the first experiments looking for displaced decay vertices, through the first experiments using silicon detectors, many e^+e^- collider experiments and most recently the RHIC program at BNL, charm production has always been a topic of central importance.

Its production is the subject of close scrutiny because it is the lightest flavor whose production can be perturbatively calculated in QCD.

Charm production measurements usually rely on the measurement of charged and neutral D mesons, which account for ~80% of the total production cross section of charm.

Existing leading-order Monte Carlo simulations like PYTHIA properly describe the measured total charm cross section for a large range of sqrt{s}.

But despite PYTHIA's success at describing total cross sections, it has been noted (more than once) that the scaling (K) factors needed to bridge the gap to experimental data for different types of D mesons can differ by up to a factor 2, namely K_D^+ ~ 2 K_D^0.

When running PYTHIA with default settings we get for D+/D0 = 0.32, consistent with the assumption that Pv=0.75, as will be seen. This is in striking disagreement of this ratio for p+p and pi+p data, which clearly points at a larger D+/D0 ratio around 0.42, or, correspondingly, a lower Pv.

We believe that this fact is very easy to explain, given that the D+/D0 ratio depends on the hadronization properties of the charm quark when combining with the light quark.

Thoroughout this article summation over anti-particles will be implied unless otherwise stated.

= Understanding the D meson hierarchy

In order to understand how the final D meson yields are related to the primary charm quark production, we need to understand the D meson hierarchy.

The family of D mesons includes the D, D*, D1 and D2 mesons. The heavier states all finish in the lighter D mesons. This means that heavy D*, D1 and D2 mesons eventually contribute to the measured D meson yields. Furthermore, there is experimental evidence that supports the idea that decay hierarchy is fully symmetric with respect to the light flavor contents, except for the D*0 -> D+ X decay. This is forbidden since mD*0-mD+ = 137.30+-0.05 MeV < mpi+ (139.57018+-0.00035).

Hence, the measured D0 yield has contributions from both neutral and charged D* mesons that were directly produced, whereas the D+ yield only has a contribution from charged D* mesons.

We will focus on the D* and D mesons. Since these have the lowest angular momentum (L=0) they are the most abundantly produced states. They are angular momentum degenerate, the only difference residing in the their quarks spin alignment: D* mesons are vector states (thus an isospin triplet), while D mesons are a pseudoscalar singlet.

In trying to populate these states when a c and a d or u bind in a L=0 meson, we can argue that the mass of the c quark is much larger than that of the light quark. This effectively leads to the result that all states are equivalent, and to the expectation that D* vector mesons are 3 times as more abundant as D pseudoscalar mesons. This picture, called naïve spin counting, emerges naturally in the framework of heavy-quark effective theory.

Defining Pv=V/(V+P), the probability of directly producing a vector meson, we have for naïve spin counting that Pv = 3/(3+1) = 0.75.

= The role of Pv in hadronization

We will make three assumptions in our attempt at understanding how Pv influences charm hadronization.

Firstly, we shall neglect the feed-down from beauty decays. This can be achieved experimentally by selecting on the offset of the decay. It has been demonstrated by CDF that it is possible to differentiate between directly produced charm, and charm coming from beauty decays.

Secondly, we will ignore any feed-down from the L=1 (D1, D2) states. It has been shown by several ee experiments that these states provide a small (5% level) effect on the D meson yield. Not only they are negligible, they have also been seen to decay symmetrically to cu and cd states.

Finally, we shall assume isospin symmetry throughout, thus assuming that the direct production of D0 and D+ (as well as D*0 and D*+) are identical. This is supported by experimental data from LEPII, CDF and ZEUS.

A fact that might not be common knowledge is that the family of D mesons only has known feed down from three sources: - B mesons (into D and D* mesons) - D_s(1,2) mesons (into D*) - decays of the psi(3770) meson (into D)

As we already mentioned, the first one is easy to separate experimentally, while the last two can be safely neglected.

Given the present accuracy of the measurements of the branching fraction of D*+ into D0 (B*=(67.7+-0.5)%), we are left with only one factor that can affect the relative balance of measured D0 and D+ mesons: the proportion of directly produced vector states (Pv).

This is better seen in the following expressions:

sig_D0 = sig_D0_dir + sig_D0_feeddown = sig_D0_dir + sig_D0_D*0->D0 + sig_D0_D*+->D0 = sig_cc K [ (1-Pv) + Pv*100% + Pv*(B*) ]

and, mutatis mutandi for the other particles:

sig_D+ = sig_D+_dir + sig_D+_feeddown = sig_D+_dir + sig_D+_D*0->D+ + sig_D+_D*+->D+ = sig_cc K [ (1-Pv) + Pv*0% + Pv*(1-B*) ]

sig_D* = sig_cc K Pv

= Experimental handles on Pv

Assuming the hypotheses laid out in the previous section, Pv can be deduced from any experiment that simultaneously measures the yields of at least two types of L=0 charmed mesons.

The most commonly measured cross-sections are: D0, D+, and D*+, through the channels Kpi, Kpipi and D0pi->kpipi. Measurements of the D*0 are not so common, since its decays include a gamma or a pi0.

The first Pv measurement was due to CLEO. In 1988 they published a value of Pv=0.85+-0.11+-0.17 from combining all their measured yields. This result, consistent with 0.75, led the community into validating the naïve spin counting for charm, as expected from HQET.

But the large errors urged for a different analysis.

This came in the 90's from several experiments that extracted Pv from "D* polarization analysis". All D* polarization analysis provided Pv values in the 0.75 ballpark, now with much smaller error bars.

But the method used to extract Pv from D* polarization analysis has, in itself, a statistical hypothesis on the distribution of the helicities of the charm quark.

In truth, all polarization measurements are only probing the relative population of the three helicity states of the D* mesons. The argument used to infer the population of D states is that that jet quarks are likely to have either helicity [old paper donoghue]. Then the population of J=0 states (D* and D) should be identical. This way, many experiments, measuring equal populations of D* mesons in the J=-1,0,1 states, concluded that Pv=0.75.

This method was actually abandoned by CLEOII and OPAL did not even use it, understanding the problems with the underlying hypothesis.

We would now like to point out that the 1988 CLEO Pv=0.85+-0.11+-0.17 is not really in the 0.75 ballpark.

As we already showed, the measured yields also depend on B*, the branching fraction for D*+ into D0. Unfortunately, this quantity suffered major revisions with time, to the extent that it was 25% lower than the present value for ten years (from 1984 to 1994).

Fortunately, CLEO mentions in its publication the intermediate result for Pv B* = 0.44+-0.04+-0.05.

Using present knowledge on B*, we can review CLEO's measurement to be Pv=0.65+-0.09.

While this value does not present conclusive evidence that Pv is not 0.75, it fits much better the systematics of the experimental picture for D+/D0 hadro-production data, since Pv~0.65 entails D+/D0~0.39 within our hypotheses.

= Pv measurements

We will now turn to the several measurements of charm production that may lead to the extraction of a value of Pv, under the assumptions laid out in section XXXX.

We have corrected all measured cross-sections for the most recently available branching fractions. We have furthermore assumed that all quoted errors (statistical, systematical and theory-driven) can be summed in quadrature when propagating uncertainties. This is an incorrect procedure in itself, but since the sources of data are so plentiful, its effect should not be considerable.

[...]

Averaging over all values above the D*D* production threshold, we obtain Pv=0.591+-0.007.

The many collected measurements in this article can be broadly grouped along two dimensions: center-of-mass energy and production system. It is seen that there are no strong pulls with respect to either.

= PYTHIA and Pv

From the PYTHIA manual one finds that there are three parameters that are Pv values. The PARJ array, indices 11 through 13, are the Pv for light mesons, strange mesons, and charm and heavier mesons respectively.

The default value for the latter, PARJ(13), is 0.75, the naïve spin counting default. For light mesons PARJ(11)=0.5, whereas for strange mesons PARJ(12)=0.6.

Running PYTHIA with PARJ(13)=0.591 and generating only charm events, we can extract a D+/D0 ratio of 0.44, in good agreement with the average of p+p and pi+p data: 0.42+-0.03.

We have also compared pair production abundances as measured by E791 with the output of PYTHIA using PARJ(13)=0.75 or 0.6.

= Beauty and Pv

The few existing measurements of Pv for B mesons with L=0 all come from LEP II and give an average of 0.75+-0.04. This is in line with the fact that the b quark mass is some 3 times heavier than charm and that consequently the approximations used in HQET do apply in the production of bq (q=u,d) mesons.

= Theoretical understanding

A very simple model by Rapp and Shuryak that takes into account for the mass differences between the vector and pseudoscalar states with a Boltzmann-like factor way, gives a Pv=0.595.

Also statistical hadronization models predict values well below 0.75.

For instance, Becattini fits light and strange meson and baryon data. The resulting data is used to predict D meson production. From those predictions, an effective Pv = 0.64 can be derived.

Similarly, Andronic et al., using only the number of directly produced ccbar pairs and the number of charged particles produced at mid-rapidity, also predict yields of D mesons in agreement with a Pv of 0.56.

= Consequences

Presently a big effort on the understanding of charm production at RHIC is under way.

The total charm cross section measurements from STAR and PHENIX disagree by a factor of two. Though only 1.6 sigma away from each other, the D0 data from d+Au collisions from STAR does not agree with the single-electron data from Au+Au collisions from PHENIX.

It can be easily seen that the simulated electron yield from charged and neutral D mesons depends on the proportions of the two in the simulation.

What happens if we change Pv from 0.75 to 0.60? The measured yield of charged D mesons increases by 20%, while that of neutral D mesons decreases by 7%.

Using the inclusive single-electron branching fractions:

D+->e+X = 17.2+-1.9% D0->e+X = 6.87+-0.28%

We can easily see that for Pv=0.60 we expect 13% more electron yield from D meson decays than if Pv=0.75.

= Conclusions

We have shown that charm physics has reached a precision level that needs more accurate results from simulations.

To that end we have collected as many as possible measurements from which a Pv value for charmed D mesons can be derived, using assumptions based in experimental evidence.

This exercise leads to a value of Pv=0.591+-0.007 for the ratio of directly produced D* mesons over directly produced D mesons.

We then showed how using this value in PYTHIA provides a much better description of charm hadro-production data in p+p and pi+p.

We pointed out that beauty seems to follow naïve spin counting, an argument stemming from heavy quark effective theory, that predicts Pv=0.75.

We have also shown how early measurements of Pv were either affected by the scarce knowledge on B* or of doubtful theoretical correctness.

Finally, we pointed out some reasons why Pv for charm could be lower than 0.75 as is the case for strange and light mesons.

= Acknowledgements

It is a pleasure to acknowledge intense discussions with C. Lourenço and H. Woehri. Their interest in charm production triggered this work. This work has been funded by the FCT under grant SFRH/BD/4761/2001