Charmed hadron asymmetries from intrinsic charm

ELSEVIER

| I l I I I I W-,1 ,',!1 ",,i| L'k'! [ I k l

Nuclear Physics B (Proc. Suppl.) 55A (1997) 135-142

P R O C E E D I N G S SUPPLEMENTS

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. I n t r o d u c t i o n

Much progress has been made in the theory of heavy quark production at NLO [1]. 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 threshold at leading [2,3] and next-to-leading logarithm [4]. The leading log resummation technique of Ref. [2] has recently been applied to charm production [5], 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 z F . Typical charm fragmentation functions based on e+e - measurements [6] underpredict hadroproduction at high XF [7]. Conversely, string models tend to harden the x F

distributions too much [8,9], particularly for the charmed baryons [10]. 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 asymmetry [8,11,12]. Measurements of the charm structure function, F~(x) , by the EMC collaboration [13] at Q2 ~ 75 GeV 2 and XBj ~-~ 0.42 also suggest that the charm distribution is harder than

*This work was supported in par t by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U. S. Depar tment 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 charmonium production, particularly the nuclear target dependence as a function of xF [14]. Addition- ally, ¢¢ pair production has been measured only at large laboratory momentum [15].

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 asymmetry between leading and nonleading charmed hadrons.

2. C h a r m p r o d u c t i o n in p e r t u r b a t i v e Q C D

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 substantial. Although a complete calculation of still higher order terms is not possible for all values 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 [2], analogous to resummation of the Drell-Yan process. The method, first applied to top production [2] and

I36 R. Vogt/Nuclear Physics B (Proc. Suppl.) 55A (1997) 135 142

recently extended to charm and bo t t om [5], relies on the propor t ional i ty of the higher order terms to the Born cross section. A cutoff parameter , /z0, is in t roduced to keep the running coupling constant finite and moni tor the sensitivity of the cross section to nonper turba t ive higher-twist effects. If the resummed cross section is s trongly dependent on #0, a precise de terminat ion of the cross section requires full knowledge of the nonper turbat ive contributions.

Because mc is relatively small, 1.2 _< me _< 1.8 G e V / c 2, charm product ion must be t reated with some care. The da ta 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 product ion, a bet ter unders tanding of c~ product ion at the lower fixed-target energies may be reached. The results are compared to da ta with bo th pion and proton beams. The only consistent NLO evaluat ion of the pion and proton par ton densities is GRV HO [16], in the MS scheme. This set has the addit ional advantage of a ra ther small initial scale so tha t we use # = mc = 1.5 G e V / c 2. Note tha t any set tha t provides a consistent description of the pion and proton par ton densities and has an initial scale such tha t the scale can be t reated on the same level for all heavy quarks, p =- mQ, should produce similar results. We find tha t resummed cross section in the q~ channel in the MS scheme converges 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 agreement with the convergence ratios for b o t t o m and top product ion.

In Fig. 1 we plot the resummed cross section, ~r res, with our chosen values of #0 as a funct ion of x/S. Since the exact NLO results are known, we also show the per tu rba t ion theory improved c r o s s sections, 0 "imp : o'res-'~ O "(1) ]exact --O'(1) lapp

to exploit the fact tha t 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~ approximat ion of O'(1)[exact is bet ter 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 difference is large for c~ product ion, o "res is &fac-

I00

50--

I0--

5--

IO0

50

i0

5

1 1 0

f

2 0 3 0 - ~ - (GeV)

Figure 1. We show ~r res (solid), 0 "imp (dashed), and the NLO (dot-dashed) c~ cross sections as a funct ion of x /~ in (a) 7r-p and (b) pp interactions. Both cr re~ and O "imp a r e calculated with

P0 = 0.15me in the q~ channel and #0 = 0.35mc in the gg channel. Ext reme values of ~r res obtained when varying me, # and the par ton densities are shown in the dot ted 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? results up to ~ = 30 GeV even though the per- turbat ive expansion no longer converges and re- s u m m a t i o n 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 dot ted curves indicate the bounds of convergence of crreS when me, p and the par ton densities are varied. Note tha t the upper dotted curves, with # = mc = 1.3 GeV/c 2, increase faster than crreS, implying tha t the resummat ion breaks down at even lower energies for the lighter quark mass. The lower dot ted curves are calculated with # /2 = rn~ = 1.8 G e V / 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 -~ [20] proton and SMRS P2 [21] 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 ratios, 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 [3] 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 production processes [4]. The corrections to top production are not large.

3. I n t r i n s i c C h a r m P r o d u c t i o n

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

O¢2 2 usually suppressed by s(Md~)/Mg, z relative to leading-twist production. However, if the transverse 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 [22]. Components of the projectile 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 projectile 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 = Z i ( 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 [23]

dPic - Nn (~(Mc7)6(1 - ~ i~a xi) (1) d X l " "d in (rn2h -- ~n=i(~'12,i /Xi))2 '

where Nn normalizes the Fock state probability. The vertex function irL the Fock state wavefunction is assumed to be slowly varying so that the distributions are controlled by the energy denom- inator and phase space. Equation (1) general- izes for an arbitrary number of light and heavy constituents. The distribution of the final-state charm hadrons reflects the underlying shape of the Fock state wavefunction.

The intrinsic c~ production cross section from an Invc-5) configuration (nv = ~d for ~r- and uud for protons) is

p2 c~ic(hN) -=- Piccrk~ 4 ~ ' (2)

This cross section was extracted from 200 GeV proton- and pion-inducded interactions and found to be cric(Tr-N ) ,~ 0.5 /zb and aie(pN) ~ 0.7 #b [9]. The soft interaction scale parameter, #2 ~ 0.2 GeV 2, was fixed by the assumption that the diffractive fraction of the total production cross section is the same for charmonium and charmed hadrons. The probability of finding a c~ pair in the proton wavefunction, Pie ~ 0.31%, was determined from a fit to the EMC charm structure function [13]. A recent study at NLO of the leading-twist and intrinsic charm contributions to the charm structure function has con- firmed these results at the 95% confidence level [24]. In our calculations, the total charm production cross section is the sum of the leading-twist fusion described in the previous section and the higher-twist intrinsic charm,

d(r(hN) do'it do-ic - - - - - + - - ( 3 )

dxF dxF d i e

We now discuss one specific aspect of charm production in the context of this model. A crit- ical test of flavor correlations in charm production is the asymmetry between leading and nonleading charm. For example, in ~r-(Kd) interactions, the D-(~d) is leading since it has a valence quark in common with the projectile while

138 R. Vogt/Nuclear Physics B (Proc. Suppl.) 55A (1997) 135-142

the D + (cd) with no valence quark in common, is nonleading. This observed leading behavior sug- gests that hadronization at large x r involves the coalescence of the charmed quarks with projectile spectator quarks. Indeed, when the charm quarks coalesce with sea quarks, there is no leading charm hadron. Quantitative measurements of the asymmetry,

,4 = ~(leading) - c~(nonleading) (4) it(leading) + a(nonleading) '

as a function of XF and p2 T have been reported [8,11,12]. The pT-integrated asymmetry, A(xF) , increases from ~ 0 for xF near zero to ~ 0.5 around x/ = 0.65 while the xr- in tegrated asymmetry, .A(p~), is ~ 0 [11] or ~ 0.1 [12] for 0 < p~ < 10 GeV 2. These facts are consistent if the leading charm asymmetry is localized at large xF, involving only a small fraction of the total cross section. The PYTHIA generator [25] predicts a significantly larger D - excess than the measurements suggest [8,11,12].

In this model the asymmetry depends on the hadronization of the intrinsic c~ pair. There are two ways of producing D mesons from intrinsic c~ pairs. The first is through standard fragmentation processes. We assume that the momentum of the quark lost through fragmentation is small so that the meson and quark z r distributions are identical. The hadron distribution, dP~f/dxF, is then obtained by integrating over all particles in the Fock state other than the charm quark. This assumption describes nonleading D hadroproduction [7,9]. If a fragmentation function is taken from e+e - annihilation [6], the nonleading D distribution is much softer than the measurement. Thus factorization of the initial and final states does not seem to apply to low PT charm production, even when the charm ha&on is nonleading. The c quarks can also coalesce with projectile valence spectators to produce leading charmed mesons. Coalescence introduces flavor correlations between the projectile and the final-state hadrons. Coalescence is modeled by the combi- nation of the charm quark with other quarks in the state so that for D - production, dPiCc/dXD-, is obtained by convolution of eq. (1) with the delta function 6(XD- -- x ~ - Xd). In ~r-N inter-

. . . . , Zff

0 . 5

O0 L , , , , ] , , , , • (a) x, > 0

0 .5 - / /

o ,o , , , , i ( b , ) - , , , , < , 0

0.0 0.5 1.0 X 1

Figure 2. Our calculated asymmetry, .A(xF), is compared with the PYTHIA predictions (crosses) for D - / D + (a) and At /At (b) production. The D - / D + data from WA82 [8] (circles), E769 [11] (stars), and E791 [12] (squares) is also shown in (a). In (b) the asymmetry is given for x r < 0 but the absolute value, [xrl, is shown. The curves here are for the parameter r = 1 (solid), 10 (dashed) and 100 (dot-dashed).

actions, the intrinsic charm model assumes that nonleading D +'s are produced by fragmentation only while leading D - ' s can be produced by ei- ther fragmentation or coalescence. The asymmetry depends on the ratio of coalescence production to the total intrinsic D - production since the asymmetry produced by leading-twist processes is negligible. Figure 2(a) shows the D - / D + asymmetry predicted by our model, assuming 90% of the D - mesons from intrinsic charm are produced by coalescence, and the default PYTHIA prediction compared to the data [8,11,12]. Note that the intrinsic charm model has zero asymmetry at xF ~ 0 since equal D + and D - production was assumed. The slightly negative asymmetry

R. Vogt/Nuclear Physics B (Proc, Suppl.) 55A (1997) 135-142 139

at Xr ~ 0.2 is also due to this assumption. In a recent work, we extended this model to

other charmed hadrons [26]. As expected, the asymmetries predicted by the intrinsic charm coalescence model are a strong function of XF. We find that A~ production in the proton fragmentation region (x r < 0 in ~r-p collisions) is dominated by the coalescence of the intrinsic charm quark with the ud valence quarks of the proton. The production of D~/Ds and, at xF > O, Ac/A~ by coalescence must occur within still higher Fock states such as Invc-dd-d) and [nvc-dsg}. These states are normalized from a calculation of ¢~ production from Invc-dc-d) con- figurations [27]. The probability of the double intrinsic charm state, Picc -,~ 4.4% P~c, allows us to obtain the probability of additional light quark pairs in the Fock states by mass scaling, /~cq ~-, (~-nc/Fnq)2Picc, leading to Picu = Picd ~ 70.4% Pic

and Pies ~ 28.5% /~¢. We note that as more partons are included in the Fock state, the coalescence distributions soften and approach the fragmentation distributions, eventually producing charmed hadrons with less momentum than uncorrelated fragmentation from the Inve-d) state if a sufficient number of qg pairs are included. Thus we do not consider A~ production by coalescence at xF < 0 since a minimal nine-parton Fock state is required.

In the proton fragmentation region, coalescence is only important for the A¢, leading naturally to an asymmetry between h~ and h~. We will assume that the same number of A~ and Ac are produced by fragmentation and that any excess of A~ production is solely due to coalescence. Then, at XF < O,

- ( 5 ) dxx~ dx-£~

c d ,f - + , - - ( 6 )

dxA~ dxA¢ dxA¢ "

The parameter r is related to the integrated ratio of A~ to A~ production. We use three values of r: 1, 10, and, as an extreme, 100. Intrinsic charm fragmentation produces a slight broadening of the A~ distribution fragmentation over leading-twist fusion. The Ac distribution, strongly dependent

on r, is considerably broadened in this region. The results for the three values of r are given in Fig. 3(a).

10 3

102 101

~'~b 100 10- -1

lO-~ 10-8

10-3

10-4

lO-5

~10-6 10--7 10--8

--1

l I I I i I I I I

- : ; - : " S

(b) PYTttlA - - + A o

I I ' i i , i i i

0 1 Ic F

Figure 3. The Ac/A~ x r distributions predicted by the two-component model in (a), normalized to our calculated cross section. The solid curve is the A~ distribution (identical to he for x r > 0) while the dashed, dot-dashed, and dotted curves show he distributions with r = 1, i0, and 100. The results from the PYTttIA Monte Carlo [25] for he and A~ production are shown in (b), normalized to the number per event.

The value r = 1 is compatible with early low statistics measurements of charmed baryon production [28]. The data is often parameterized as (1 - l a y ] ) nAc, where

1 - IXF, mi.I - - 2 . ( 7 )

For XF < 0, we predict nAc = 4.6. We find rather large values of nAt since the average Xr is dominated by the leading-twist fusion corn-

140 R. Vogt/Nuclear Physics B (Proc. Suppl.) 55A (1997) 135-142

ponent at low XF. If we restrict the integra- tion to xp < -0 .5 , then nA, decreases to 1.42. The shape of the Ac distribution measured at the ISR is consistent with this prediction. For z r > 0.5, nn, = 2.1 -4- 0.3 was found [29] while for z p > 0.35, nAo = 2.4-4-1.3 [30]. Hard charmed baryon distributions have also been observed at large xF in n N interactions at the Serpukhov spectrometer with an average neutron energy of 70 GeV, finding nn, = 1.5 -4- 0.5 for XF > 0.5 [31]. Charmed hyperons E,(usc) produced by a 640 GeV neutron beam [33] do not exhibit a strong leading behavior, nz¢ = 4.7 -4- 2.3. This is similar to the prediction for nA~ when XF < O. On the other hand, charmed hyperons produced with a E - ( d d s ) beam [32,10] are leading with n~.¢ = 1.7 =t= 0.7 for XF > 0.6 [32]. Thus in the proton fragmentation region r = 1 is compatible with the shape of the previously measured A¢ xF distributions. When we compare the A¢ cross section in the proton fragmentation region with that of leading-twist fusion, the coalescence mechanism increases the cross section by a factor of 1.4-1.7 over the fusion cross section and by 30% over the A¢ cross section.

We note that the more extreme value of the parameter, r = 100, agrees with the forward A¢ production cross section measured at the ISR [29]. In this case, there is a secondary peak in the r - p distributions at ZF "~ --0.6, the average Ae momentum from coalescence. This is similar to but not as strong as the diquark coalescence mechanism in PYTHIA which produces a second, larger peak at xF ~ -0 .9 , implying that O-ic >> O'tt- While a measurement of the h~ cross section over the full phase space in the proton fragmentation region is lacking, especially for pp interactions at x r > 0, no previous measurement shows an increase in the A¢ XF distributions as implied by these results. However, the reported Ac production cross sections are relatively large [29-31,33], between 40

2The p a r a m e t e r i z a t i o n (1 - x F ) n is only good if t he dis- t r i bu t i on is mono ton i c . However, ou r t w o - c o m p o n e n t Ac d i s t r i bu t ion does no t fit th i s p a r a m e t e r i z a t i o n over all x F . At low XF, t h e lead ing- twis t c o m p o n e n t d o m i n a t e s . If only the h igh xF par t is inc luded , t he value of ([xF[) is a more accu ra t e reflection of the s h a p e of t he in t r ins ic c h a r m c o m p o n e n t .

pb and 1 mb for 10 _< v/~ < 63 GeV. In particular, the low energy cross sections are much larger than those reported for the c~ total cross section at the same energy. Thus, a few remarks con- cerning the data are in order here. Some of these analyses [30,31] extract the total cross section by extrapolating fiat forward zv distributions back to z e ='0 and also assume associated production, requiring a model of D production. On the other hand, the reported c~ total cross sections are usually extracted from D measurements at low to moderate xF and would therefore hide any important coalescence contribution to charmed baryon production at large z r . High statistics measurements of charmed mesons and baryons over the full forward phase space ( x f > 0) in pp interactions would help resolve both the importance of coalescence and the magnitude of the total c~ production cross section.

At XF > 0 there is no asymmetry in 7r-p interactions since both the baryon and antibaryon can be produced by fragmentation from a [~dc'~) state and by coalescence from a [~dc-~q'q) state (q = u,d). Then

Pieq dPg dXAc -- dzx¢ = d x h ¢ -4- Pic d X h c "

(s)

The coalescence contribution produces a small shoulder in the distributions at xF > 0, as can be seen in Fig. 3(a). We extract nA¢ = 4.1 for ZF.min = 0, in good agreement with the NA32 measurement, nAc = 3.5 5= 0.5 [35]. The same mechanism can account for both Ac and Ae production in the 7r- fragmentation region since no asymmetry is observed [34], which is also in ac- cord with the NA32 result, O-(h¢)/o-(Ac) ~ 1 [35]. To look for these subtle coalescence effects it is important to measure the full momentum distributions. The PYTHIA xF distributions for the Ac and Ac are shown in Fig. 3(b) to compare with our model results in Fig. 3(a).

We note that no significant enhancement from coalescence occurs in D, production since Pi¢~ < PiCu. The average momentum gain over uncorrelated fragmentation is small. We find A D . / - ~ , ( z r ) = 0 for all z r since the production mechanisms are identical everywhere.

R. Vogt/Nuclear Physics B (Proc. SuppL) 55A (1997) 135-142 141

Our calculated asymmetries for the three r values are compared with the results from PYTHIA in Fig. 2(b). Note that the XF < 0 part of the distribution is shown as a function of IxFI. The behavior of the two models is most similar for r = 100 although the PYTHIA asymmetry does not increase as abruptly. Preliminary data on 7r-A interactions at 500 GeV from E791 [34] indicate a significant asymmetry for x r as small as -0.1, albeit with large uncertainty. The naive intrinsic charm model can only produce such asymmetries if r > 100, against intuition. However, a softer Ac distribution from coalescence would make a larger asymmetry at lower ]XFI, thus requiring a smaller r. Such a softening could arise from e.g. a different assumption about the ]nvc5) wavefunction [36] or a stronger dependence on the initial and final-state wavefunction overlap. We are studying leading particle production by coalescence on the amplitude level, combining leading-twist c~ production with the final-state charmed hadron wavefunction [37]. We find similar D - / D + asymmetries in this model.

4. S u m m a r y

Much progress has been made toward an un- derstanding of charm production, particularly at x r ~ 0 in the center of mass. However, it ap- pears that factorization breaks down at large x r and higher-twist processes can dominate the cross section. While the circumstantial evidence for intrinsic charm production is substantial, more ex- periments are needed to confirm this hypothesis.

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Charmed hadron asymmetries from intrinsic charm