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Meson cloud in the nucleon and d−u asymmetry from the Drell-Yan processes
NUCLEAR PHYSICS A
Nuclear Physics A570 (1994) 765-781 North-Holland
Meson cloud in the nucleon and d-U asymmetry from the Drell-Yan processes A. Szczurek a,b, J. Speth a, G.T. Garvey ’ a Institut fiir Kemphysik, Forschungszentrum Jiilich, W-51 70 Jiilich,
Gemzany
b Institute of Nuclear Physics, PL-31-342 Krakow, Poland ’ Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Received 14 May 1993 (Revised 29 October 1993)
Abstract Mesonic models predict violation of the SU(2) symmetry in the nucleon sea which seems to be necessary to explain the violation of the Gottfried sum rule. At the present time there is no generally accepted explanation of the effect. We find that careful analysis of the Drell-Yan processes in pp and pn collisions will provide complementary data to the Gottfried sum rule on the 6-p asymmetry. We also find that some combinations of experimental results are insensitive to details of the mesonic models, offering the possibility to demonstrate the existence of the mesonic cloud in the nucleon.
1. Introduction In the following article we present a discussion of the observed violation [l] of the Gottfried sum rule (GSR), the use of a meson-baryon model of the nucleon to account for the observed violation and a test of this model using the Drell-Yan (DY) process. It has been customarily assumed that the nucleon sea is flavor symmetric (&,(x) = E&x>>. Th ere is no general principle that forces one to this hypothesis other than the fact that it appears as a natural consequence of a perturbative approach to the nucleon’s parton distributions. There is of course no justification for such a restricted point of view to hadron structure and there is strong indication that nonperturbative physics is crucial. Specifically the observed violation of the GSR provides experimental evidence that the nucleon sea is not flavor symmetric. Several papers have recently been written on this subject but there remains no quantitatively compelling explanation for the effect. 0375-9474/94/$07.00
0 1994 - Elsevier Science B.V. All rights reserved
sSDI0375-9474(93)E0684-Z
A. Szczurek et al. / Meson cloud
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2. Gottfried sum rule
The Gottfried sum rule [2] addresses the value of the integral over x of the difference of the F,(x) structure function of the proton (p) and neutron (n). It is written as l
=
+jo’([u;(x) -d;(x)] ++,(x) -d,(x)]) dx,
(1)
where u;(x) = u,(x) - U,(x), etc., and charge symmetry has been assumed, i.e., u,(x) = d,(x), etc.. If one further makes the customary but ad hoc assumption that U,(x) = z&x), then
p;(x)
-F:(x)]:=;.
(2)
Eq. (2) is referred to as the GSR. However, the most recent measurement [ll of the relevant structure functions, over the interval 0.004
c[F;(x)-F;(n)]G=0.24&0.016
(3)
at Q* = 5 GeV*. Taken at face value, comparing Eqs. (11, (2) and (3) requires
jo’[&,(x)
-U,(x)]
dx=0.135*0.024
(4)
in marked disagreement with the customary assumption. It appears impossible [3] to generate such a large difference in the d- and i&distributions from perturbative processes; hence, the answer likely lies with more complicated nonperturbative physics. For example, there have been a few [4-121 attempts to calculate the difference due to virtual-meson emission, as is the case with the present paper. Without such a dynamical calculations, all that can be done is to reparameterize l
The structure functions F,(x) are, of course, functions of Q2, as are the quark distribution functions q(x). However, the Q2-dependence is suppressed to keep the expressions from being too cumbersome.
A. Szczurek et al. / Meson cloud
the U,(x)- and &(x)-distributions the GSR. Typically one defines
767
so that they agree with the observed violation of
CT+) =4(x)
+ id(x)
(5)
ii&x) =q(x)
-id(x),
(6)
and
where ‘A(x) /0
dx = 0.135 k 0.024.
(7)
flavor content of the sea in the nucleons can be tested in the Drell-Yan experiments, which is the subject of the present paper. Different assumptions on A(x) lead to different predictions for the target dependence of the Drell-Yan production rate. For instance, the initial reparameterization 1131used A(x) =A(1 - x)~, which placed the d - U difference at large x(x > 0.05) and led to very large values for ~&x)/U,(x) for x > 0.1. These large ratios have been ruled out by a recent reanalysis of earlier Drell-Yan data. More recent [14] parameterizations have a form A(x) =B(l -x)‘/x’/*, which places the bulk of the difference at smaller x. This creates two experimental difficulties-first, small x(x < 0.01) is inaccessible in fixed-target Drell-Yan experiments, and second, the ratio &,(x)/U,(x) + 1 at small x because the difference is fixed while the sea is much The
5.0
I’ I’
$s / / ,/
.= .....::. .. .... meson cloud model
0.02 0.0
0.1
0.2
0.3
0.4
0
X Fig. 1. The ratio z/ii as a function of the Bjorken variable. We phenomenological parameterizations with asymmetry: Field-Feynman Hinchliffe-Quigg [8] (dashed curve), Ellis-Stirling [13] (dash-dotted predictions of the meson-cloud model of ref.
present results obtained with [30] (dotted curve), Eichtencurve). In addition we present [lo].
768
A. Szczurek et al. / Meson cloud
larger at small x. Fig. 1 shows the ratio d,(x)/U,(x) for representative parameterizations. Thus, the task for theory is to calculate in a reliable fashion the difference zP(x) - L(P(x) and employ values for d,(x) + U,(x) that are consistent with the known properties of the nucleon sea. When QCD lattice gauge calculations are capable of generating the quark structure of the nucleon, they should reflect the measured d,(x) and U,(x) distributions.
3. Hybrid meson-baryon
model of the nucleon
In this section we briefly review a recent hybrid meson-baryon model of the nucleon [lo] and present its prediction for the asymmetry of the light sea antiquarks. In this model the nucleon is viewed as a quark-core, termed a bare nucleon, surrounded by the mesonic cloud. The nucleon wave function can be schematically (for simplicity we suppress the isospin decomposition of the ITN and ITA states) written as a superposition of a few principle Fock components,
IN)dressed
=
z1’2[
IWme
+alNn)
+/~~AIT) + (...)I.
(8)
The factor Z= 1/(1+(u2+p2+ . ..> measures the probability that the physical nucleon contains a bare nucleon. Different from other models available in the literature, the model of ref. [lo] includes all the mesons required in the description of the low-energy nucleon-nucleon and hyperon-nucleon scattering. Furthermore it ensures charge conservation, baryon number and momentum sum rules. The main ingredients of the model are the vertex coupling constants, the parton distribution functions for the virtual mesons and baryons and the vertex form factors which account for the extended nature of the hadrons. The coupling constants are assumed to be related via SU(3) symmetry. The measured free-hadron parton distributions are used. The only free parameter in the model [lo] is the cutoff parameter for the vertex form factor. It has been fixed [lo] by adjusting to the data of the E615 Collaboration [151 on the x-dependence of the SU(3) violation in the nucleon sea [16]. The data restrict the cutoff parameter of the form factor in a dipole parameterization to about 1.2 GeV. For this value of the cutoff parameter the largest violation of the Gottfried sum rule has been obtained, greater than half of that observed by NMC 111.Our form factor can be contrasted with softer form factors used by other authors [17,16] and harder form factors applied usually in nuclear physics. For the cutoff parameter of 1.2 GeV, only the components explicitly shown in the expansion (8) play an important role in the global description of the nucleon. This is especially true for the Gottfried sum rule where there is in addition a
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A. Szczurek et al. / Meson cloud
cancellation between different contributions [lo]. For the range of cutoffs allowed by experimental data, vector mesons play rather a marginal role [lo]. The x-dependence of the structure functions in the meson-cloud model can be written as a sum of components corresponding to the expansion given by Eq. (8): (x) +
[G’“‘F2(x)+GB)F2(x)]).
c
(9)
MB
The contributions from the virtual mesons and baryons can be written as a convolution of the meson (baryon) structure functions and its longitudinal momentum distribution in the nucleon,
~Y’~‘F,(x) =
/IdyfM( y>Fz”
(10)
x
Eq. (10) can be written in an equivalent form in terms of the quark distribution functions
(11) The longitudinal momentum distributions of virtual mesons (or baryons) can be calculated assuming a model of the vertex, and depend on the coupling constants and form factors. For the dominant contributions (TN, rh) they are given by simple formulas:
(12)
waTTA
fV(d)(Y) = myjf,‘dt
x
(mk-mm,-t)2 i
4rni
2
(‘” t )I)2 [(mN +m,) t m2, _t I
-
tl (13)
We assume that the intrinsic sea in the bare baryons is symmetric, and that the d=U asymmetry is entirely due to the admittance of the aN, TA Fock states in the physical nucleon. In ref. [lo] an overall cutoff parameter has been used for simplicity. This led to the value of 0.28 for GSR, about $ times the original NMC effect. In principle the cutoff parameter can be slightly different for different components. In our model
A. Szczurek
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et al. / Meson cloud
the Gottfried sum rule is a delicate interplay between aN and rrA components and depends on their probabilities in the nucleon wave function. Lowering the probability of the nA component one lowers the value of GSR and could achieve a better agreement with the NMC result [ll. This is a crucial point in order to understand the NMC result and requires a more detailed analysis. Here we would like to point out that there is a direct experimental evidence for the softer NnA vertex than what is used in ref. [lo]. Phenomenologically the NrA vertex can be determined [181 by comparison of the one-pion exchange model (OPEM) with high-energy data, P(P, A++)X,
( 14a)
P(P, A++)X,
( 14b)
A++)X,
( 14c)
p( n-, A++)X.
( 14d)
P(n+,
The underlying mechanism of these reactions is identical to that of the deep-inelastic lepton scattering off virtual mesons or baryons. Furthermore, the spectrum of baryons (A’s) which carry the y = y, fraction of the proton momentum, directly probes the flux of pions f,(y,) at yM = 1 -y,, and the kinematics of the emission of pions is identical in both cases. For the discussion of the applicability of the OPEM we refer the reader to ref. [18]. In the Regge limit of yW K 1 for the p + A fragmentation process and for yn < 1 in the p -+ 7~ fragmentation process (which we do not consider here) one must rather consider the reggeized meson (baryon) exchange. In the p + A fragmentation process, however, the cross section is dominated by rather large values of y,, where the mesons can be treated as not reggeized. The cross section for the p(h, B)X reaction in the OPEM can be expressed as da dy,
dp,
=f( Y,, P,ht%
(15)
where f( y p I> is a function which involves the N-ITB from factor and a;: is a total cross section for the hr collision. For the A++ production, assuming the one-pion-exchange mechanism n,
F;,
(Y,
P,)
y;l_y)
f(Y,Pl)=*
X
[(Ym,+m,)2+P:]2[(Y~,-m,)2+P:]
6y3m:[ 4
-K&(Y7
P:)]
’
(16)
A. Szcnuek et al.
0
.l
p:C
.2 GeVZ/&
.3
/ Meson cloud
771
.4
p:[
GeV~c’l
Fig. 2. Differential cross section do/dp$ as a function of pp for A++ production in (a) pp collision [19] measured at Fermilab and (b) Bp collision [20] measured at Serpukhov. The solid line is for a cutoff of 1.0 GeV, whereas the dotted lines for 0.8 GeV and 1.2 GeV.
where M&(y, pt> is the invariant mass of the AT system [ll]. Reactions (14~) and (14d) require knowledge of the CT:: cross section which is not directly accessible experimentally. While reaction (14a) involves u?~ which is well known experimentally, reaction (14b) involves aFp which can be easily related to uTt,, also well known. Experimentally these cross sections approximately scale in a broad range of energies, making application of OPEM very simple. In the p + A fragmentation process the OPE mechanism dominates the region of intermediate y = 0.6-0.8. Because this is the region where the maximum of the cross section occurs, the comparison of the OPEM result with the y-integrated cross section seems to be justified. In Fig. 2 we show predictions of the OPEM with the y-integrated experimental data for p(p, A”)X [19] and p(p, A”>X [20] for different values of the cutoff parameter. The data for both reactions prefer a cutoff of about 1.0 GeV in a dipole parameterization. We note that a slight energy dependence of cross sections has been disregarded here and we have taken 24 mb for the a,$ cross section. We would like to point out here that in principle the cross section for the scattering of a virtual pion may deviate slightly from that for the real pion. Because, except of the OPE mechanism, other mechanisms may contribute to the cross section, extraction of the parameters of the NnA vertex from the y-integrated cross section may lead to a slight overestimation of the ~FA component. In the following we will use a cutoff parameter of 1.2 GeV for the components with octet baryons [lo] and of 1.0 GeV for the components with decuplet n
772
\, n/:-_ A. Szczurek et al. / Meson cloud 0.2
X
-0.1
13 X
,
:+
‘i> \t
0.0 0.0
0.1
0.2
0.3
0.4
0
Fig. 3. The sea-quark distributions for (a) ii and (b) d quarks. The solid line represents predictions of our model. In addition we present for comparison predictions of two sets of symmetric parton distributions: EHLQ [22] (dashed curve) and Owens [23] (dash-dotted curve).
baryons.The softer form factor for the NrA vertex than for NTN or NKA vertices seems to be an universal feature of high-energy scattering [11,211. The value obtained for the GSR with these cutoff parameters is 0.255 which is within experimental error of the NMC experiment. In Fig. 3 we present distributions of antiquarks calculated within the meson-cloud model for Q* = (5 GeV)* compared with different parameterizations [22,23] of the world experimental data. We get reasonable agreement with the parameterizations in the small-x region. At larger x we predict a slightly higher amount of sea, especially for the &distribution. One should, however, remember that the extraction of the sea distributions from the experiment is difficult at large x (sea contribution to the structure function is here very small in comparison to the valence one) and depends on the form of parameterization assumed in the fit of experimental data. Furthermore the result of the calculation at larger x is slightly dependent on the valence-quark distributions in mesons (taken here from ref. [24]) which is not accurately known at present. In Fig. 4 we present the difference x(d- U) for various parameterizations with asymmetric sea-quark distributions. It is interesting to notice that the mesonic model is qualitatively similar both in shape and in magnitude to the result of a recent global fit of Martin, Stirling and Roberts to the world deep-inelastic and Drell-Yan data [141. For instance the Gottfried sum rule obtained from our model
A. Szczurek et al. / Meson cloud
773
Fig. 4. The difference x&(x)- Z(x) magnified by the factor 10. The result of the meson-cloud model is shown by the solid line. We present also the difference for asymmetric phenomenological parameterizations: Eichten-Hinchliffe-Quigg [8] (dashed curve) and Martin-Stirling-Roberts [14] (dotted curve).
is 0.255, with 0.235 in the experimentally measured region. This can be compared with the value of 0.26 obtained from the recent MSR fit. The Eichten-HinchliffeQuigg [8] and Ellis-Stirling [13] parameterizations give larger differences; however, they have been adjusted to reproduce the NMC value [l] of the Gottfried sum rule. The antiquark distribution functions presented in Fig. 3 arise from two sources. One is a symmetric intrinsic sea that occurs in both the bare nucleons and mesons while the other are the antiquarks that are generated from valence quarks in the virtual mesons. It is this latter contribution that gives rise to the asymmetry in the &, I&distributions. As an estimate for the symmetric intrinsic sea we take the Owens parameterization [23] of the overall sea distribution scaled by the factor 0.7. When this intrinsic sea is supplemented by the “sea” from valence quarks in mesons as obtained from our mesonic model, we find the total sea distribution which is consistent with the experiment. In Table 1 we present the contributions of each of the components in Eq. (8). One notes that only the processes involving virtual T and p mesons contribute to the asymmetry. The antiquarks due to those mesons are shown as the shadowed areas in Fig. 5 as a function of X. Numerically, this contribution makes a large piece of both Z(X) and Z(X), and for this reason the ratio [Z(X) - S(x)]/[d(x) + U(X)] turns out to be rather insensitive to the detailed shape of the intrinsic parton distributions in mesons and the bare baryons.
4. Drell-Yan
processes
The Drell-Yan process with incident nucleons can be made extremely sensitive to the zP(x)/Zr,(x)-distribution in the target. This point has already been made in
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A. Szczurek et al. / Meson cloud
Table 1 A list of the processes contributing to the violation of the ii-a symmetry in the nucleon sea. In addition we show also probabilities (in %) of the individual Fock components in the expansion of the nucleon wave function given by Eq. (8) and numbers of antiquarks contained in the proton wave function Component bare N x+N P+N
P+A P+A
symm. cont. sum
n
d
59.38 21.15 1.73 10.69 0.30 6.75
_ 0.0353 0.0029 0.0712 0.0020 0.0256
_ 0.1763 0.0144 0.0356 0.0010 0.0256
_ 0.1410 0.0115 - 0.0356 - 0.0010
100.00
0.1370
0.2529
0.1159
Probability (%)
J-ii
the literature [13] but is developed in a bit more detail, as the approach used here is somewhat different. The Drell-Yan process [25] involves the electromagnetic annihilation of a quark (antiquark) from the incident hadron A with an antiquark (quark) in the target hadron B. The resultant virtual photon materializes as a dilepton pair (IL+[l-) with muons being the pair most readily detected in experiments.
X
Fig. 5. The x-distribution of the component of the valence quarks in mesons in comparison to the total distribution.
A. Szczurek et aL / Meson cloud
775
The cross section for the DY process can be written
l
as
daAB dx, dx, where s is the square of the center-of-mass energy and xi and x2 are the longitudinal momentum fractions carried by the quarks of flavor f. The qi(x,) and q&x2) are the quark distribution functions of the beam and target, respectively. The factor K(x,, x2) accounts for the higher-order QCD corrections that enter the process. Its value over the kinematic range where experiments are typically carried out is 152.0. The value of x1 and x2 is extracted from experiment via
M2 = sxlX2
P,+P,-
=
(18)
cos &+k-,
where M is the mass of the dilepton pair, P,+ and PL- are the laboratory momenta of the leptons, and 0r+t- is the angle between their momenta vectors. The longitudinal momentum of the lepton (P,++ Ph-jL fixes xi -x2 via
x,
2cpiL++ p,-)I_ _ 1
-x2=xF=
(19)
s
In order to avoid spurious contributions to the DY yield from vector-meson decay, all measurements are made for A4 > 4 GeV, and the region 9 GeV < A4 < 11 GeV is excluded to avoid the T-resonances. The valence-quark distribution in the nucleon falls off as a much smaller power of 1 -x than does its sea-quark distribution, so that as x + 1, there are only valence quarks and no sea quarks. Indeed, if xi is selected such that xi =x2 + 0.3, the first term in Eq. (17) dominates the second term by a factor of more than 10. Fig. 6 shows the ratio of the second to first term for two choices of xi -x2. Thus, forming the ratio of the Drell-Yan yields for p + p to p + n, we have da;; da&
2.
4~,wq~2)
+~,(4d,(x,)
4~P(~l)dp(~2)
+$44q4x2)
(20) x+0.3
where it is assumed that K&x,, x2) = KJx,, the ratio h&x,) = d,(xl)/u,(x,) yields da& dagy l
= l+ x+0.3
See previous footnote.
’
x2> and u,(x) = d,(x), etc.. Defining
~~,(Xl)4(X,)/~,(X,)
~PGZ)/qdXZ)
+ $$(x,)
*
(21)
776
A. Szczurek et al. / Meson cloud
Owens parametrization
0.1
0.0
I
I
0.2
0.3
/
4
0.4
0.5
X tup* Fig. 6. The ratio of the second to the first term in the Drell-Yan line) and proton-neutron (dashed line) scattering as a function
In the limit x1 + 1, h,(x,)
formula (23) for proton-proton of the target x2 for hvo choices
(solid of xF.
+ 0, and in that limit one has
(22) As neutron hence,
targets are not available, real experiments
must use deuterium
CD);
(23) which is a special case of 2 da;+ -A da%
N-Z XF>O.3
x,+l
=
1 +
d,(n,)
-Up(x2)
d,G,)
+
(24)
A
qdx2)
.
The ideas contained in this last expression have been used [26] to examine the ratio of the DY yield from W as compared to an isoscalar target (such as deuterium). Even though the (N - Z)/A factor in this case is only 0.196, the results are sufficiently sensitive to rule out the reparameterizations of zP(x) and U,(x) that account for the violation of the GSR by placing the difference in d,(x) - U,(x) at large x [13,81. It is clear from Eqs. (23) and (24) that the most sensitive measurement of d,(x)/U,(x) comes from comparing the yield from hydrogen to that from deuterium. Using the FNAL external proton beam, this comparison [27] can be made
A. Szczurek et al. / Meson cloud
:i_::r::
~~~1 0.0
0.1
0.2
0.3
0.4
777
0.5
0.0
0.1
0.2
&la
0.3
0.4
0.5
Lml
Fig. 7. (a) The ratio uPn/aPP as a function of the target x2 for selected values of the beam x1. Predictions of the meson-cloud model are shown on the left hand side, while the result of a phenomenological parameterization [23] with symmetric antiquark distributions is presented on the right hand side.
in the interval 0.03 4 GeV, while the upper limit arises from the vanishing sea-quark distribution for x > 0.3. In Fig. 7 we present the prediction of the meson-cloud model sketched in the previous section for the ratio aP%r, _r2>/aPP(x1, x2) as a function of x2 for the expected experimental range of x1. We also present the results obtained from the symmetric phenomenological sea-quark distributions of ref. [23]. As is clearly seen from the figure, the experimental ratio, larger or smaller than unity in the experimentally meaningful region x2 < 0.3, should definitely discriminate between a symmetric/ asymmetric nucleon sea. It would also give a quantitative measure of the effect, putting further constraints on the mesonic models. As Eq. (24) shows, the ratio of the DY yield from a nucleus with N - Z # 0 to that from an isoscalar target such as deuterium is sensitive to the d,(x) - U,(x) difference. These ratios have been measured by the E772 Collaboration at FNAL [28] for carbon, calcium, iron and tungsten targets. In practice, Eq. (24) should be replaced by a more exact expression which takes into account all terms in Eq. (17). Elementary algebra leads to the following result: 2 a;‘$ --=
A CT&
22
N-Z
A+
A
2@“( xi, x2) upp(xl,
x2) +aPn(xl,
x2) ’
(25)
where Z, N, A are the number of protons, neutrons and the atomic number, respectively. In the case of natural targets an additional averaging over isotopes is required. In Fig. 8 we present the ratios for iron and natural tungsten targets as a function of x2 (target) for fixed value xi = 0.3, which correspond roughly to the experimental situation. For comparison we present also the experimental data of the E772 Collaboration. In addition we show the results with flavor-symmetric sea distributions of ref. [23]. No big difference between the result of the mesonic
778
A. Szczurek et al. / Meson cloud
Fe
Fig. 8. The ratio 2~7g~~/Aug$* as a function of the target xz for iron and natural tungsten. The experimental data are taken from refs. [26,28]. Predictions of the meson-cloud model is presented by the solid line and the result with the symmetric sea-quark distribution by the long dashed line. Results obtained from the phenomenological parameterization with the asymmetry built in are shown for comparison: Field-Feynman [30] (dotted curve), Eichten-Hin~hliffe-Quip [8] (dashed curve), EllisStirhng 1131(dash-dotted curve). Please note that no nuclear effects have been included.
model and the symmetric parameterization can be seen. In our opinion the data do not select in a convincing way the s~metric/antisymmetric distributions *. We present also in Fig. 8 similar results with the flavor-asymmetric sea-quark distributions of refs. [8,13,30]. As can be seen from the figure the data exclude such asymmetric parameterizations. In this context it is necessary to mention that in obtaining Eq. (25) we have omitted compIetely all nuclear effects like shadowing [17,31-351 and excess pions [36,37]. The nuclear-shadowing effects are significant only at x < 0.03 and should not contribute to the flavor asymmetry of the sea distributions. Because of (N - Z)/A .=+K 1, th e nuclear excess pions [36-381 contribute predominatly to the flavor-symmetric sea. Furthe~ore, the realistic calculation [393 shows that the contributions from the excess pions and from the nuclear shadowing tend to cancel each other at x > 0.03, so that the approximation (24) is accurate enough in the * In the course of preparatjon of this paper we have learned about a similar analysis within the chiral quark model f.291. The conclusions in ref. 1291 are identical to ours, despite a slightly different dynamics [8].
A. Szczurek et al. / Meson cloud
719
kinematical region of interest. Large z-ii asymmetry is expected at values of x at which neither the shadowing nor excess pions are important. The weak nuclear shadowing in the deuteron is somewhat more important, as it affects the determination of the neutron deep-inelastic structure function from the deuteron data. If this correction is taken into account, the value of GSR is lowered from the NMC value [35,40,41]. As a matter of fact, comparison of the Drell-Yan production in the proton-proton and in the proton-deuteron reactions could facilitate accurate extraction of the neutron structure functions from the deuteron data, which is a strong argument in favor of such experiments.
5. Discussion In the light of recent experiments on the deep-inelastic muon scattering off nucleons, the understanding of the nucleon structure has become one of the intriguing problems of particle and nuclear physics. The recent observation of the Gottfried-sum-rule violation suggests a flavor asymmetry of the light sea quarks in the nucleon. Although the asymmetry does not contradict any fundamental rules, the flavor symmetry of the nucleon sea had become a part of the folklore in the particle-physics community. An asymmetry occurs in a natural way within certain nonperturbative models of the nucleon, built with valence quarks surrounded by a meson cloud. There exist two classes of models of this type. In the chiral quark model [S] the mesons are directly coupled to quarks. In the model discussed in the present paper, the nucleon is regarded as quark-core which couples to the meson cloud. This picture of the nucleon provides a good description of nucleon electric polarizabilities [42]. It also has a close connection to models of low-energy hadron-hadron scattering [43,44] and high-energy fragmentation processes [11,18,21] and leads to the parameter-free predictions for the d=U asymmetry. In contrast to phenomenological parameterizations of the z-ii asymmetry, the meson-cloud model discussed here predicts asymmetry concentrated at small X, quite similar to a recent fit [14] to the world data for DIS and Drell-Yan processes. As a consequence our model predicts only a lo-20% deviation to be observed in a Fermilab experiment [27] measuring the relative dilepton yield in proton-proton and proton-deuteron Drell-Yan processes. Another aspect of the Drell-Yan experiment to emphasize is the x-dependence of the difference J(X) - E(X). It is much more difficult to extract from deep-inelastic lepton scattering. In that case, the integrand of the GSR involves not only J(X) - U(x), but also U,(X) - d,(x) which introduces large uncertainties in the extraction of the interesting asymmetry. The knowledge of the x-dependence of z - U will be a very useful constraint for all theoretical models of the nucleon. This
A. Szczurek et al. / Meson cloud
780
supplementary character of the Drell-Yan experiment will prove essential to investigate the problem discussed in the present paper. Summarizing, measurement of the relative dilepton yield from a proton beam on hydrogen and deuterium targets (in order to reduce systematic errors) will give information on the SU(2),-symmetry breaking in the nucleon sea, supplemental of that obtained from the Gottfried sum rule. This work was supported in part by the Polish KBN grant 224099102. G.T.G. was partially supported by the US Department of Energy, Office of High Energy and Nuclear Physics, the A. von Humboldt Foundation and the Sherman Fairchild Distinguished Scholar Program at Caltech. We thank N.N. Nikolaev for many suggestions and useful discussions.
Note added (Au~st
1993)
After this paper was submitted for publication the NMC Collaboration has presented the new determination of the deuteron structure functions at small x [451. The new value for the GSR is 0.258 f 0.010.
References ]l] P. Amaudruz et al., Phys. Rev. Lett. 66 (1991) 2712 [2] K. Gottfried, Phys. Rev. L&t. 18 (1967) 1174 [3] D.A. Ross and C.T. Sachrajda, Nucl. Phys. B149 (1979) 497 [4] E.M. Henley and G.A. Miller, Phys. Lett. B251 (1990) 453 [5] A. Signal, A.W. Schreiber and A.W. Thomas, Mod. Phys. Lett. A6 (1991) 271 [6J W. Melnitchouk, A.W. Thomas and A.I. Signal, Z. Phys. A340 (1991) 8.5 [7] S. Kumano and J.T. Londergan, Phys. Rev. D44 (1991) 717 [8] E. Eichten, I. Hinchliffe and C. Quigg, Phys. Rev. D45 (1992) 2269 [9] W-Y.P. Hwang, J. Speth and G.E. Brown, Z. Phys. Rev. A339 (1991) 383 [lOI A. Szczurek and J. Speth, Nucl. Phys. A555 (1993) 249 [ll] V.R. Zoller, Z. Phys. C53 (1992) 443 1121J.T. Londergan and S. Kumano, Phys. Rev. D46 (1992) 457 [13] S.D. Ellis and W.J. Stirling, Phys. Lett. B256 (1991) 258 1141 A.D. Martin, W.J. Stirling and R.G. Roberts, Phys. Rev. D47 (1993) 867 [15] J.G. Heinrich et al., Phys. Rev. Lett. 63 (1992) 356 [16] S. Kumano, Phys. Rev. D43 (1991) 59 1171 L. Frankfurt and M. Strikman, Nucl. Phys. B316 (1989) 340 1181 G.G. Arakelyan and A.A. Grigoryan, Sov. J. Nucl. Phys. 34 (1981) 745 [19] D. Brick et al., Phys. Rev. D21 (1980) 632 [20] E.G. Boos et al., Nucl. Phys. B151 (1979) 193 [21] H. Holtmann, A. Szczurek and J. Speth, in preparation [22] E. Eichten, I. Hinchliffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56 (1984) 579 1231J.F. Owens, Phys. I&t B266 (1990 126 [24] J. Badier et al., Z. Phys. Cl8 (1983) 281 1251 S.D. Drell and T.M. Yan, Ann. Phys. 66 (1971) 578
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[26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45]
781
P.L. McGaughey et al., Phys. Rev. Lett. 69 (1992) 1726 G.T. Garvey et al., FNAL proposal P866 (1992) D.M. Alde et al., Phys. Rev. Lett. 64 (1990) 2479 E. Eichten, I. Hinchliffe and C. Quigg., Phys. Rev. D47 (1993) R747 R.D. Field and R.P. Feynman, Phys. Rev. D15 (1977) 2590 L.V. Gribov, E.M. Levin and M.G. Ryskin, Nucl. Phys. B188 (1981) 555 S.J. Brodsky and H.J. Lu, Phys. Rev. Lett. 64 (1990) 1342 G. Piller and W. Weise, Phys. Rev. C42 (1990) 1834 N.N. Nikolaev and B.G. Zakharov, Z. Phys. C49 (1991) 607 V. Barone, M. Genovese, N.N. Nikolaev, E. Predazzi and B.G. Zakharov, Z. Phys. C58 (1993) 541 C.H. Llewellyn Smith, Phys. Lett. B128 (1983) 107 E.L. Berger, F. Coester and R.B. Wiringa, Phys. Rev. D29 (1984) 398 G.E. Brown, Z.B. Li and K.F. Liu, Nucl. Phys. A555 (1993) 225 W-Y.P. Hwang, J. Speth and J. Wambach, unpublished V.R. Zoller, Z. Phys. C54 (1992) 425 W. Melnitchouk and A.W. Thomas, Phys. Rev. D47 (1993) 3783 V. Bernard, N. Kaiser and U.G. Meissner, Nucl. Phys. B373 (1992) 346 R. Machleidt, K. Holinde and Ch. Elster, Phys. Reports 149 (1987) 1 B. Holzenkamp, K. Holinde and J. Speth, Nucl. Phys. A500 (1989) 485 A. Briill, Talk at the PANIC Conf., Perugia, June 1993
Nuclear Physics A570 (1994) 765-781 North-Holland
Meson cloud in the nucleon and d-U asymmetry from the Drell-Yan processes A. Szczurek a,b, J. Speth a, G.T. Garvey ’ a Institut fiir Kemphysik, Forschungszentrum Jiilich, W-51 70 Jiilich,
Gemzany
b Institute of Nuclear Physics, PL-31-342 Krakow, Poland ’ Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Received 14 May 1993 (Revised 29 October 1993)
Abstract Mesonic models predict violation of the SU(2) symmetry in the nucleon sea which seems to be necessary to explain the violation of the Gottfried sum rule. At the present time there is no generally accepted explanation of the effect. We find that careful analysis of the Drell-Yan processes in pp and pn collisions will provide complementary data to the Gottfried sum rule on the 6-p asymmetry. We also find that some combinations of experimental results are insensitive to details of the mesonic models, offering the possibility to demonstrate the existence of the mesonic cloud in the nucleon.
1. Introduction In the following article we present a discussion of the observed violation [l] of the Gottfried sum rule (GSR), the use of a meson-baryon model of the nucleon to account for the observed violation and a test of this model using the Drell-Yan (DY) process. It has been customarily assumed that the nucleon sea is flavor symmetric (&,(x) = E&x>>. Th ere is no general principle that forces one to this hypothesis other than the fact that it appears as a natural consequence of a perturbative approach to the nucleon’s parton distributions. There is of course no justification for such a restricted point of view to hadron structure and there is strong indication that nonperturbative physics is crucial. Specifically the observed violation of the GSR provides experimental evidence that the nucleon sea is not flavor symmetric. Several papers have recently been written on this subject but there remains no quantitatively compelling explanation for the effect. 0375-9474/94/$07.00
0 1994 - Elsevier Science B.V. All rights reserved
sSDI0375-9474(93)E0684-Z
A. Szczurek et al. / Meson cloud
766
2. Gottfried sum rule
The Gottfried sum rule [2] addresses the value of the integral over x of the difference of the F,(x) structure function of the proton (p) and neutron (n). It is written as l
=
+jo’([u;(x) -d;(x)] ++,(x) -d,(x)]) dx,
(1)
where u;(x) = u,(x) - U,(x), etc., and charge symmetry has been assumed, i.e., u,(x) = d,(x), etc.. If one further makes the customary but ad hoc assumption that U,(x) = z&x), then
p;(x)
-F:(x)]:=;.
(2)
Eq. (2) is referred to as the GSR. However, the most recent measurement [ll of the relevant structure functions, over the interval 0.004
c[F;(x)-F;(n)]G=0.24&0.016
(3)
at Q* = 5 GeV*. Taken at face value, comparing Eqs. (11, (2) and (3) requires
jo’[&,(x)
-U,(x)]
dx=0.135*0.024
(4)
in marked disagreement with the customary assumption. It appears impossible [3] to generate such a large difference in the d- and i&distributions from perturbative processes; hence, the answer likely lies with more complicated nonperturbative physics. For example, there have been a few [4-121 attempts to calculate the difference due to virtual-meson emission, as is the case with the present paper. Without such a dynamical calculations, all that can be done is to reparameterize l
The structure functions F,(x) are, of course, functions of Q2, as are the quark distribution functions q(x). However, the Q2-dependence is suppressed to keep the expressions from being too cumbersome.
A. Szczurek et al. / Meson cloud
the U,(x)- and &(x)-distributions the GSR. Typically one defines
767
so that they agree with the observed violation of
CT+) =4(x)
+ id(x)
(5)
ii&x) =q(x)
-id(x),
(6)
and
where ‘A(x) /0
dx = 0.135 k 0.024.
(7)
flavor content of the sea in the nucleons can be tested in the Drell-Yan experiments, which is the subject of the present paper. Different assumptions on A(x) lead to different predictions for the target dependence of the Drell-Yan production rate. For instance, the initial reparameterization 1131used A(x) =A(1 - x)~, which placed the d - U difference at large x(x > 0.05) and led to very large values for ~&x)/U,(x) for x > 0.1. These large ratios have been ruled out by a recent reanalysis of earlier Drell-Yan data. More recent [14] parameterizations have a form A(x) =B(l -x)‘/x’/*, which places the bulk of the difference at smaller x. This creates two experimental difficulties-first, small x(x < 0.01) is inaccessible in fixed-target Drell-Yan experiments, and second, the ratio &,(x)/U,(x) + 1 at small x because the difference is fixed while the sea is much The
5.0
I’ I’
$s / / ,/
.= .....::. .. .... meson cloud model
0.02 0.0
0.1
0.2
0.3
0.4
0
X Fig. 1. The ratio z/ii as a function of the Bjorken variable. We phenomenological parameterizations with asymmetry: Field-Feynman Hinchliffe-Quigg [8] (dashed curve), Ellis-Stirling [13] (dash-dotted predictions of the meson-cloud model of ref.
present results obtained with [30] (dotted curve), Eichtencurve). In addition we present [lo].
768
A. Szczurek et al. / Meson cloud
larger at small x. Fig. 1 shows the ratio d,(x)/U,(x) for representative parameterizations. Thus, the task for theory is to calculate in a reliable fashion the difference zP(x) - L(P(x) and employ values for d,(x) + U,(x) that are consistent with the known properties of the nucleon sea. When QCD lattice gauge calculations are capable of generating the quark structure of the nucleon, they should reflect the measured d,(x) and U,(x) distributions.
3. Hybrid meson-baryon
model of the nucleon
In this section we briefly review a recent hybrid meson-baryon model of the nucleon [lo] and present its prediction for the asymmetry of the light sea antiquarks. In this model the nucleon is viewed as a quark-core, termed a bare nucleon, surrounded by the mesonic cloud. The nucleon wave function can be schematically (for simplicity we suppress the isospin decomposition of the ITN and ITA states) written as a superposition of a few principle Fock components,
IN)dressed
=
z1’2[
IWme
+alNn)
+/~~AIT) + (...)I.
(8)
The factor Z= 1/(1+(u2+p2+ . ..> measures the probability that the physical nucleon contains a bare nucleon. Different from other models available in the literature, the model of ref. [lo] includes all the mesons required in the description of the low-energy nucleon-nucleon and hyperon-nucleon scattering. Furthermore it ensures charge conservation, baryon number and momentum sum rules. The main ingredients of the model are the vertex coupling constants, the parton distribution functions for the virtual mesons and baryons and the vertex form factors which account for the extended nature of the hadrons. The coupling constants are assumed to be related via SU(3) symmetry. The measured free-hadron parton distributions are used. The only free parameter in the model [lo] is the cutoff parameter for the vertex form factor. It has been fixed [lo] by adjusting to the data of the E615 Collaboration [151 on the x-dependence of the SU(3) violation in the nucleon sea [16]. The data restrict the cutoff parameter of the form factor in a dipole parameterization to about 1.2 GeV. For this value of the cutoff parameter the largest violation of the Gottfried sum rule has been obtained, greater than half of that observed by NMC 111.Our form factor can be contrasted with softer form factors used by other authors [17,16] and harder form factors applied usually in nuclear physics. For the cutoff parameter of 1.2 GeV, only the components explicitly shown in the expansion (8) play an important role in the global description of the nucleon. This is especially true for the Gottfried sum rule where there is in addition a
769
A. Szczurek et al. / Meson cloud
cancellation between different contributions [lo]. For the range of cutoffs allowed by experimental data, vector mesons play rather a marginal role [lo]. The x-dependence of the structure functions in the meson-cloud model can be written as a sum of components corresponding to the expansion given by Eq. (8): (x) +
[G’“‘F2(x)+GB)F2(x)]).
c
(9)
MB
The contributions from the virtual mesons and baryons can be written as a convolution of the meson (baryon) structure functions and its longitudinal momentum distribution in the nucleon,
~Y’~‘F,(x) =
/IdyfM( y>Fz”
(10)
x
Eq. (10) can be written in an equivalent form in terms of the quark distribution functions
(11) The longitudinal momentum distributions of virtual mesons (or baryons) can be calculated assuming a model of the vertex, and depend on the coupling constants and form factors. For the dominant contributions (TN, rh) they are given by simple formulas:
(12)
waTTA
fV(d)(Y) = myjf,‘dt
x
(mk-mm,-t)2 i
4rni
2
(‘” t )I)2 [(mN +m,) t m2, _t I
-
tl (13)
We assume that the intrinsic sea in the bare baryons is symmetric, and that the d=U asymmetry is entirely due to the admittance of the aN, TA Fock states in the physical nucleon. In ref. [lo] an overall cutoff parameter has been used for simplicity. This led to the value of 0.28 for GSR, about $ times the original NMC effect. In principle the cutoff parameter can be slightly different for different components. In our model
A. Szczurek
110
et al. / Meson cloud
the Gottfried sum rule is a delicate interplay between aN and rrA components and depends on their probabilities in the nucleon wave function. Lowering the probability of the nA component one lowers the value of GSR and could achieve a better agreement with the NMC result [ll. This is a crucial point in order to understand the NMC result and requires a more detailed analysis. Here we would like to point out that there is a direct experimental evidence for the softer NnA vertex than what is used in ref. [lo]. Phenomenologically the NrA vertex can be determined [181 by comparison of the one-pion exchange model (OPEM) with high-energy data, P(P, A++)X,
( 14a)
P(P, A++)X,
( 14b)
A++)X,
( 14c)
p( n-, A++)X.
( 14d)
P(n+,
The underlying mechanism of these reactions is identical to that of the deep-inelastic lepton scattering off virtual mesons or baryons. Furthermore, the spectrum of baryons (A’s) which carry the y = y, fraction of the proton momentum, directly probes the flux of pions f,(y,) at yM = 1 -y,, and the kinematics of the emission of pions is identical in both cases. For the discussion of the applicability of the OPEM we refer the reader to ref. [18]. In the Regge limit of yW K 1 for the p + A fragmentation process and for yn < 1 in the p -+ 7~ fragmentation process (which we do not consider here) one must rather consider the reggeized meson (baryon) exchange. In the p + A fragmentation process, however, the cross section is dominated by rather large values of y,, where the mesons can be treated as not reggeized. The cross section for the p(h, B)X reaction in the OPEM can be expressed as da dy,
dp,
=f( Y,, P,ht%
(15)
where f( y p I> is a function which involves the N-ITB from factor and a;: is a total cross section for the hr collision. For the A++ production, assuming the one-pion-exchange mechanism n,
F;,
(Y,
P,)
y;l_y)
f(Y,Pl)=*
X
[(Ym,+m,)2+P:]2[(Y~,-m,)2+P:]
6y3m:[ 4
-K&(Y7
P:)]
’
(16)
A. Szcnuek et al.
0
.l
p:C
.2 GeVZ/&
.3
/ Meson cloud
771
.4
p:[
GeV~c’l
Fig. 2. Differential cross section do/dp$ as a function of pp for A++ production in (a) pp collision [19] measured at Fermilab and (b) Bp collision [20] measured at Serpukhov. The solid line is for a cutoff of 1.0 GeV, whereas the dotted lines for 0.8 GeV and 1.2 GeV.
where M&(y, pt> is the invariant mass of the AT system [ll]. Reactions (14~) and (14d) require knowledge of the CT:: cross section which is not directly accessible experimentally. While reaction (14a) involves u?~ which is well known experimentally, reaction (14b) involves aFp which can be easily related to uTt,, also well known. Experimentally these cross sections approximately scale in a broad range of energies, making application of OPEM very simple. In the p + A fragmentation process the OPE mechanism dominates the region of intermediate y = 0.6-0.8. Because this is the region where the maximum of the cross section occurs, the comparison of the OPEM result with the y-integrated cross section seems to be justified. In Fig. 2 we show predictions of the OPEM with the y-integrated experimental data for p(p, A”)X [19] and p(p, A”>X [20] for different values of the cutoff parameter. The data for both reactions prefer a cutoff of about 1.0 GeV in a dipole parameterization. We note that a slight energy dependence of cross sections has been disregarded here and we have taken 24 mb for the a,$ cross section. We would like to point out here that in principle the cross section for the scattering of a virtual pion may deviate slightly from that for the real pion. Because, except of the OPE mechanism, other mechanisms may contribute to the cross section, extraction of the parameters of the NnA vertex from the y-integrated cross section may lead to a slight overestimation of the ~FA component. In the following we will use a cutoff parameter of 1.2 GeV for the components with octet baryons [lo] and of 1.0 GeV for the components with decuplet n
772
\, n/:-_ A. Szczurek et al. / Meson cloud 0.2
X
-0.1
13 X
,
:+
‘i> \t
0.0 0.0
0.1
0.2
0.3
0.4
0
Fig. 3. The sea-quark distributions for (a) ii and (b) d quarks. The solid line represents predictions of our model. In addition we present for comparison predictions of two sets of symmetric parton distributions: EHLQ [22] (dashed curve) and Owens [23] (dash-dotted curve).
baryons.The softer form factor for the NrA vertex than for NTN or NKA vertices seems to be an universal feature of high-energy scattering [11,211. The value obtained for the GSR with these cutoff parameters is 0.255 which is within experimental error of the NMC experiment. In Fig. 3 we present distributions of antiquarks calculated within the meson-cloud model for Q* = (5 GeV)* compared with different parameterizations [22,23] of the world experimental data. We get reasonable agreement with the parameterizations in the small-x region. At larger x we predict a slightly higher amount of sea, especially for the &distribution. One should, however, remember that the extraction of the sea distributions from the experiment is difficult at large x (sea contribution to the structure function is here very small in comparison to the valence one) and depends on the form of parameterization assumed in the fit of experimental data. Furthermore the result of the calculation at larger x is slightly dependent on the valence-quark distributions in mesons (taken here from ref. [24]) which is not accurately known at present. In Fig. 4 we present the difference x(d- U) for various parameterizations with asymmetric sea-quark distributions. It is interesting to notice that the mesonic model is qualitatively similar both in shape and in magnitude to the result of a recent global fit of Martin, Stirling and Roberts to the world deep-inelastic and Drell-Yan data [141. For instance the Gottfried sum rule obtained from our model
A. Szczurek et al. / Meson cloud
773
Fig. 4. The difference x&(x)- Z(x) magnified by the factor 10. The result of the meson-cloud model is shown by the solid line. We present also the difference for asymmetric phenomenological parameterizations: Eichten-Hinchliffe-Quigg [8] (dashed curve) and Martin-Stirling-Roberts [14] (dotted curve).
is 0.255, with 0.235 in the experimentally measured region. This can be compared with the value of 0.26 obtained from the recent MSR fit. The Eichten-HinchliffeQuigg [8] and Ellis-Stirling [13] parameterizations give larger differences; however, they have been adjusted to reproduce the NMC value [l] of the Gottfried sum rule. The antiquark distribution functions presented in Fig. 3 arise from two sources. One is a symmetric intrinsic sea that occurs in both the bare nucleons and mesons while the other are the antiquarks that are generated from valence quarks in the virtual mesons. It is this latter contribution that gives rise to the asymmetry in the &, I&distributions. As an estimate for the symmetric intrinsic sea we take the Owens parameterization [23] of the overall sea distribution scaled by the factor 0.7. When this intrinsic sea is supplemented by the “sea” from valence quarks in mesons as obtained from our mesonic model, we find the total sea distribution which is consistent with the experiment. In Table 1 we present the contributions of each of the components in Eq. (8). One notes that only the processes involving virtual T and p mesons contribute to the asymmetry. The antiquarks due to those mesons are shown as the shadowed areas in Fig. 5 as a function of X. Numerically, this contribution makes a large piece of both Z(X) and Z(X), and for this reason the ratio [Z(X) - S(x)]/[d(x) + U(X)] turns out to be rather insensitive to the detailed shape of the intrinsic parton distributions in mesons and the bare baryons.
4. Drell-Yan
processes
The Drell-Yan process with incident nucleons can be made extremely sensitive to the zP(x)/Zr,(x)-distribution in the target. This point has already been made in
774
A. Szczurek et al. / Meson cloud
Table 1 A list of the processes contributing to the violation of the ii-a symmetry in the nucleon sea. In addition we show also probabilities (in %) of the individual Fock components in the expansion of the nucleon wave function given by Eq. (8) and numbers of antiquarks contained in the proton wave function Component bare N x+N P+N
P+A P+A
symm. cont. sum
n
d
59.38 21.15 1.73 10.69 0.30 6.75
_ 0.0353 0.0029 0.0712 0.0020 0.0256
_ 0.1763 0.0144 0.0356 0.0010 0.0256
_ 0.1410 0.0115 - 0.0356 - 0.0010
100.00
0.1370
0.2529
0.1159
Probability (%)
J-ii
the literature [13] but is developed in a bit more detail, as the approach used here is somewhat different. The Drell-Yan process [25] involves the electromagnetic annihilation of a quark (antiquark) from the incident hadron A with an antiquark (quark) in the target hadron B. The resultant virtual photon materializes as a dilepton pair (IL+[l-) with muons being the pair most readily detected in experiments.
X
Fig. 5. The x-distribution of the component of the valence quarks in mesons in comparison to the total distribution.
A. Szczurek et aL / Meson cloud
775
The cross section for the DY process can be written
l
as
daAB dx, dx, where s is the square of the center-of-mass energy and xi and x2 are the longitudinal momentum fractions carried by the quarks of flavor f. The qi(x,) and q&x2) are the quark distribution functions of the beam and target, respectively. The factor K(x,, x2) accounts for the higher-order QCD corrections that enter the process. Its value over the kinematic range where experiments are typically carried out is 152.0. The value of x1 and x2 is extracted from experiment via
M2 = sxlX2
P,+P,-
=
(18)
cos &+k-,
where M is the mass of the dilepton pair, P,+ and PL- are the laboratory momenta of the leptons, and 0r+t- is the angle between their momenta vectors. The longitudinal momentum of the lepton (P,++ Ph-jL fixes xi -x2 via
x,
2cpiL++ p,-)I_ _ 1
-x2=xF=
(19)
s
In order to avoid spurious contributions to the DY yield from vector-meson decay, all measurements are made for A4 > 4 GeV, and the region 9 GeV < A4 < 11 GeV is excluded to avoid the T-resonances. The valence-quark distribution in the nucleon falls off as a much smaller power of 1 -x than does its sea-quark distribution, so that as x + 1, there are only valence quarks and no sea quarks. Indeed, if xi is selected such that xi =x2 + 0.3, the first term in Eq. (17) dominates the second term by a factor of more than 10. Fig. 6 shows the ratio of the second to first term for two choices of xi -x2. Thus, forming the ratio of the Drell-Yan yields for p + p to p + n, we have da;; da&
2.
4~,wq~2)
+~,(4d,(x,)
4~P(~l)dp(~2)
+$44q4x2)
(20) x+0.3
where it is assumed that K&x,, x2) = KJx,, the ratio h&x,) = d,(xl)/u,(x,) yields da& dagy l
= l+ x+0.3
See previous footnote.
’
x2> and u,(x) = d,(x), etc.. Defining
~~,(Xl)4(X,)/~,(X,)
~PGZ)/qdXZ)
+ $$(x,)
*
(21)
776
A. Szczurek et al. / Meson cloud
Owens parametrization
0.1
0.0
I
I
0.2
0.3
/
4
0.4
0.5
X tup* Fig. 6. The ratio of the second to the first term in the Drell-Yan line) and proton-neutron (dashed line) scattering as a function
In the limit x1 + 1, h,(x,)
formula (23) for proton-proton of the target x2 for hvo choices
(solid of xF.
+ 0, and in that limit one has
(22) As neutron hence,
targets are not available, real experiments
must use deuterium
CD);
(23) which is a special case of 2 da;+ -A da%
N-Z XF>O.3
x,+l
=
1 +
d,(n,)
-Up(x2)
d,G,)
+
(24)
A
qdx2)
.
The ideas contained in this last expression have been used [26] to examine the ratio of the DY yield from W as compared to an isoscalar target (such as deuterium). Even though the (N - Z)/A factor in this case is only 0.196, the results are sufficiently sensitive to rule out the reparameterizations of zP(x) and U,(x) that account for the violation of the GSR by placing the difference in d,(x) - U,(x) at large x [13,81. It is clear from Eqs. (23) and (24) that the most sensitive measurement of d,(x)/U,(x) comes from comparing the yield from hydrogen to that from deuterium. Using the FNAL external proton beam, this comparison [27] can be made
A. Szczurek et al. / Meson cloud
:i_::r::
~~~1 0.0
0.1
0.2
0.3
0.4
777
0.5
0.0
0.1
0.2
&la
0.3
0.4
0.5
Lml
Fig. 7. (a) The ratio uPn/aPP as a function of the target x2 for selected values of the beam x1. Predictions of the meson-cloud model are shown on the left hand side, while the result of a phenomenological parameterization [23] with symmetric antiquark distributions is presented on the right hand side.
in the interval 0.03
A CT&
22
N-Z
A+
A
2@“( xi, x2) upp(xl,
x2) +aPn(xl,
x2) ’
(25)
where Z, N, A are the number of protons, neutrons and the atomic number, respectively. In the case of natural targets an additional averaging over isotopes is required. In Fig. 8 we present the ratios for iron and natural tungsten targets as a function of x2 (target) for fixed value xi = 0.3, which correspond roughly to the experimental situation. For comparison we present also the experimental data of the E772 Collaboration. In addition we show the results with flavor-symmetric sea distributions of ref. [23]. No big difference between the result of the mesonic
778
A. Szczurek et al. / Meson cloud
Fe
Fig. 8. The ratio 2~7g~~/Aug$* as a function of the target xz for iron and natural tungsten. The experimental data are taken from refs. [26,28]. Predictions of the meson-cloud model is presented by the solid line and the result with the symmetric sea-quark distribution by the long dashed line. Results obtained from the phenomenological parameterization with the asymmetry built in are shown for comparison: Field-Feynman [30] (dotted curve), Eichten-Hin~hliffe-Quip [8] (dashed curve), EllisStirhng 1131(dash-dotted curve). Please note that no nuclear effects have been included.
model and the symmetric parameterization can be seen. In our opinion the data do not select in a convincing way the s~metric/antisymmetric distributions *. We present also in Fig. 8 similar results with the flavor-asymmetric sea-quark distributions of refs. [8,13,30]. As can be seen from the figure the data exclude such asymmetric parameterizations. In this context it is necessary to mention that in obtaining Eq. (25) we have omitted compIetely all nuclear effects like shadowing [17,31-351 and excess pions [36,37]. The nuclear-shadowing effects are significant only at x < 0.03 and should not contribute to the flavor asymmetry of the sea distributions. Because of (N - Z)/A .=+K 1, th e nuclear excess pions [36-381 contribute predominatly to the flavor-symmetric sea. Furthe~ore, the realistic calculation [393 shows that the contributions from the excess pions and from the nuclear shadowing tend to cancel each other at x > 0.03, so that the approximation (24) is accurate enough in the * In the course of preparatjon of this paper we have learned about a similar analysis within the chiral quark model f.291. The conclusions in ref. 1291 are identical to ours, despite a slightly different dynamics [8].
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kinematical region of interest. Large z-ii asymmetry is expected at values of x at which neither the shadowing nor excess pions are important. The weak nuclear shadowing in the deuteron is somewhat more important, as it affects the determination of the neutron deep-inelastic structure function from the deuteron data. If this correction is taken into account, the value of GSR is lowered from the NMC value [35,40,41]. As a matter of fact, comparison of the Drell-Yan production in the proton-proton and in the proton-deuteron reactions could facilitate accurate extraction of the neutron structure functions from the deuteron data, which is a strong argument in favor of such experiments.
5. Discussion In the light of recent experiments on the deep-inelastic muon scattering off nucleons, the understanding of the nucleon structure has become one of the intriguing problems of particle and nuclear physics. The recent observation of the Gottfried-sum-rule violation suggests a flavor asymmetry of the light sea quarks in the nucleon. Although the asymmetry does not contradict any fundamental rules, the flavor symmetry of the nucleon sea had become a part of the folklore in the particle-physics community. An asymmetry occurs in a natural way within certain nonperturbative models of the nucleon, built with valence quarks surrounded by a meson cloud. There exist two classes of models of this type. In the chiral quark model [S] the mesons are directly coupled to quarks. In the model discussed in the present paper, the nucleon is regarded as quark-core which couples to the meson cloud. This picture of the nucleon provides a good description of nucleon electric polarizabilities [42]. It also has a close connection to models of low-energy hadron-hadron scattering [43,44] and high-energy fragmentation processes [11,18,21] and leads to the parameter-free predictions for the d=U asymmetry. In contrast to phenomenological parameterizations of the z-ii asymmetry, the meson-cloud model discussed here predicts asymmetry concentrated at small X, quite similar to a recent fit [14] to the world data for DIS and Drell-Yan processes. As a consequence our model predicts only a lo-20% deviation to be observed in a Fermilab experiment [27] measuring the relative dilepton yield in proton-proton and proton-deuteron Drell-Yan processes. Another aspect of the Drell-Yan experiment to emphasize is the x-dependence of the difference J(X) - E(X). It is much more difficult to extract from deep-inelastic lepton scattering. In that case, the integrand of the GSR involves not only J(X) - U(x), but also U,(X) - d,(x) which introduces large uncertainties in the extraction of the interesting asymmetry. The knowledge of the x-dependence of z - U will be a very useful constraint for all theoretical models of the nucleon. This
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supplementary character of the Drell-Yan experiment will prove essential to investigate the problem discussed in the present paper. Summarizing, measurement of the relative dilepton yield from a proton beam on hydrogen and deuterium targets (in order to reduce systematic errors) will give information on the SU(2),-symmetry breaking in the nucleon sea, supplemental of that obtained from the Gottfried sum rule. This work was supported in part by the Polish KBN grant 224099102. G.T.G. was partially supported by the US Department of Energy, Office of High Energy and Nuclear Physics, the A. von Humboldt Foundation and the Sherman Fairchild Distinguished Scholar Program at Caltech. We thank N.N. Nikolaev for many suggestions and useful discussions.
Note added (Au~st
1993)
After this paper was submitted for publication the NMC Collaboration has presented the new determination of the deuteron structure functions at small x [451. The new value for the GSR is 0.258 f 0.010.
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