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Nuclear Physics B (Proc. Suppl.) 55A (1997) 135-142
Charmed Hadron Asymmetries From Intrinsic Charm R. Vogt a*
aNuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA and Physics Department, University of California at Davis, Davis, CA, USA
We discuss charm production anomalies at large xF in the context of the intrinsic charm model. In particular, we focus on recent data on charm meson and baryon asymmetries.
1. In t roduct ion
Much progress has been made in the theory of heavy quark production at NLO . However, uncertainties still remain in the charmed quark mass, the renormalization and factorization scale parameters, and the gluon distribution. P~esum- mation techniques have been developed for the soft and virtual gluon contributions near thresh- old at leading [2,3] and next-to-leading logarithm . The leading log resummation technique of Ref.  has recently been applied to charm pro- duction , showing some improvement in the agreement with data at fixed-target energies.
Despite this progress, perturbative QCD still fails to explain some aspects of charm production, particularly at large zF . Typical charm fragmen- tation functions based on e+e - measurements  underpredict hadroproduction at high XF . Conversely, string models tend to harden the xF distributions too much [8,9], particularly for the charmed baryons . The asymmetry between leading and nonleading charmed mesons [8,11,12] cannot be explained in pQCD since no flavor correlations are predicted. On the other hand, string models tend to overpredict this asymme- try [8,11,12]. Measurements of the charm struc- ture function, F~(x), by the EMC collaboration  at Q2 ~ 75 GeV 2 and XBj ~-~ 0.42 also sug- gest that the charm distribution is harder than
*This work was supported in part by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U. S. Department of Energy under Contract Number DF.,-AC03- 76SF0098
0920-5632/97/S17.00 ~' I997 Elsevier Science B.V All rights reserved. PII: S0920-5632(97)00165-5
expected from photon-gluon fusion or QCD evo- lution. Anomalies are also observed in charmo- nium production, particularly the nuclear target dependence as a function of xF . Addition- ally, pair production has been measured only at large laboratory momentum .
We first briefly review the status of higher- order charm production. We then introduce the intrinsic charm model and point out how this higher-twist process can dominate production at large XF. We describe the model predictions for one specific case mentioned above-the asym- metry between leading and nonleading charmed hadrons.
2. Charm product ion in per turbat ive QCD
Next-to-leading order calculations of charm production show a large correction to the Born cross section, a factor of two or more, suggest- ing that further higher order corrections are sub- stantial. Although a complete calculation of still higher order terms is not possible for all val- ues of center of mass energy, v~, and mr, im- provements may be made in specific kinemati- cal regions. Near threshold there can be large logarithms in the perturbative expansion, arising from an imperfect cancellation of the soft-plus- virtual (S+V) terms, which must be resummed to make more reliable theoretical predictions. An approximation of the S+V gluon contributions was used to resnm the leading logarithmic terms to all orders in perturbation theory , analogous to resummation of the Drell-Yan process. The method, first applied to top production  and
I36 R. Vogt/Nuclear Physics B (Proc. Suppl.) 55A (1997) 135 142
recently extended to charm and bottom , relies on the proportionality of the higher order terms to the Born cross section. A cutoff parameter, /z0, is introduced to keep the running coupling constant finite and monitor the sensitivity of the cross section to nonperturbative higher-twist ef- fects. If the resummed cross section is strongly dependent on #0, a precise determination of the cross section requires full knowledge of the non- perturbative contributions.
Because mc is relatively small, 1.2 _< me _< 1.8 GeV/c 2, charm production must be treated with some care. The data is available in a region where the expansion parameter, c~s(m2)ln(x/S/m), is not small. However, if the model is reliable for charm production, a better understanding of c~ production at the lower fixed-target energies may be reached. The results are compared to data with both pion and proton beams. The only consistent NLO evaluation of the pion and pro- ton parton densities is GRV HO , in the MS scheme. This set has the additional advantage of a rather small initial scale so that we use # = mc = 1.5 GeV/c 2. Note that any set that provides a consistent description of the pion and proton parton densities and has an initial scale such that the scale can be treated on the same level for all heavy quarks, p =- mQ, should pro- duce similar results. We find that resummed cross section in the q~ channel in the MS scheme con- verges for #0 ~ 0.15me while the g9 channel, with its larger color factor, converges for #0 -,~ 0.35mc. The ratios po/m in both channels are in agree- ment with the convergence ratios for bottom and top production.
In Fig. 1 we plot the resummed cross section, ~r res, with our chosen values of #0 as a function of x/S. Since the exact NLO results are known, we also show the perturbation theory improved cross sections, 0 "imp : o'res-'~ O "(1) ]exact --O'(1) lapp to exploit the fact that cr (1) ]exact is known and ~(1) lapp is included in a res . The difference between ~r res and O "imp is larger in pp produc- tion, presumably because the q~ approximation of O'(1)[exact is better than the g9. We also show the NLO cross section calculated with the same mass and scale factors as cr res and c rimp. The dif- ference is large for c~ production, o "res is &fac-
I0 - -
5 - -
20 30 -~- (GeV)
Figure 1. We show ~r res (solid), 0 "imp (dashed), and the NLO (dot-dashed) c~ cross sections as a function of x/~ in (a) 7r-p and (b) pp inter- actions. Both cr re~ and O "imp are calculated with P0 = 0.15me in the q~ channel and #0 = 0.35mc in the gg channel. Extreme values of ~r res ob- tained when varying me, # and the parton densi- ties are shown in the dotted lines.
tor of five or more larger than the NLO result, improving the agreement with the 7r-p [17,18] and pp [17,19] data. We have shown the c? re- sults up to ~ = 30 GeV even though the per- turbative expansion no longer converges and re- summation fails in the gg channel. This can be clearly seen in the faster increase of cr res and O "imp with energy compared to 0 "NLO for v/S ~> 20 GeV. The dotted curves indicate the bounds of convergence of crreS when me, p and the parton densities are varied. Note that the upper dot- ted curves, with # = mc = 1.3 GeV/c 2, increase faster than crreS, implying that the resummation breaks down at even lower energies for the lighter quark mass. The lower dotted curves are calcu- lated with #/2 = rn~ = 1.8 GeV/c 2. The scale
R. Vogt/Nuclear Physics B (Proc. Suppl.) 55A (1997) 13~142 137
has been increased so that parton densities with a larger initial scale, the MRS D -~  proton and SMRS P2  pion distributions, can be used. The larger quark mass improves convergence at higher energies although the larger scales needs a larger #0 for convergence. We remark that nei- ther of these extremes produce convergence ra- tios, I~o/mc that agree with those found for heav- ier quarks.
Finally, we note that other leading logarithm resummation techniques that avoid the cutoff have appeared  but have not been applied to charm production. The resummation has recently been taken to next-to-leading logarithm, paying close attention to the color structure of the pro- duction processes . The corrections to top pro- duction are not large.
3. In t r ins ic Charm Product ion
In leading-twist charm production, there is no connection between the spectator and participant partons. However, in higher-twist processes, the interaction between spectators and participants can be strong. These higher-twist processes are
O2 2 usually suppressed by s(Md~)/Mg, z relative to leading-twist production. However, if the trans- verse distance between the partons is small, they may interact during the time they are near each other, allowing the higher-twist processes to be- come dominant . Components of the projec- tile wavefunction can have a small transverse size if they carry a large fraction of the momentum. Heavy-quark pairs in the projectile can be gen- erated by gluon exchanges between the projec- tile valence quarks. These c~ fluctuations carry a large fraction of the projectile momentum and have a small transverse size. They can be liber- ated by a relatively soft interaction if the scat- tering occurs during the time, At ---- 2plab/M~, that the fluctuations exist. These intrinsic charm components can dominate the wavefunction if the invariant mass of the Fock configuration, M S = Zi (m~ + (k~,,i))/xi, is minimal.
The probability distribution, independent of the Lorentz frame, for n-particle intrinsic c~ Fock
states as a function of x is 
dPic - Nn (~(Mc7)6(1 - ~i~a xi) (1) dXl " "din (rn2h -- ~n=i(~'12,i/Xi))2 '
where Nn normalizes the Fock state probability. The vertex function irL the Fock state wavefunc- tion is assumed to be slowly varying so that the distributions are control