NI^EF NATIONAAL INSTITUUT VOOR KERNFYSICA EN HOGE ENERGIEFYSICA
NIKHEF-H/86-3
Inclusive $ meson production, the parton fusion model and strange quark structure functions
H. Dijkstra0. R. Bailey b\ E. Belau5). T. BöhringerJ), M. Bosman}). V. Chabaud5). C. Dameree, C. Dauml). C. de Rijkl). 5. Gill*0. A. Cillman6). R. Gilmore2*. 2. Hajduks\ C. Hardwickl), W. Hoogland1'. B.D. Hyams55, R. Klanner5). S. Kwan2). U. kotz5). G. Lütjens^, G. Lutz5'. J. Malos2). W. Marmer5*. E. Neugeoauer5), H. Palka*\ M. Pepé6), J. Richardson6'. K. Rybicki4). H.J. Seebrunner5). U. Stierlin5'. R.J. Tapper2). H.G. Tiecke1'. M. Turala4). G. Waltermann '. S. Watts6). P. Weilhammer3). F. Wickens6'. L.W. Wiqgers". A. Wylie5). and T. Zeludziewicz5)
The ACCMOR Collaboration
ABSTRACT
The parton fusion model is used to describe the longitudinal differential cross section (do/dx..) of hadronic
particles. A comparison between the model and high
statistics data in the Feynman * range 0.
To be submitted to Zeitschrift für Physik C
1) NIKHEF-H. Amsterdam. The Netherlands 2) University of Bristol, Bristol, UK 3) CERN. Geneva. Switzerland 4) Institute of Nuclear Physics, Cracow, Poland 5) Max Planck Institut für Physik, Munich, Fed. Rep. Germany 6) Rutherford Appleton Laboratory, Chilton, Didcot, UK
NIKHEF SECTIE H POSTBUS 41882,1009 DB AMSTERDAM 1. Introduction
In 196$ Cell-Mann [I] and ?!weig [2 J introduced the idea of quark structure of hadrons. This model has now developed into a theory of strong interactions called Quantum CJhromo Dynamics (QCD). In practice QCD predictions are restricted to processes where the parameter that determines the scale of the process (CJ* or M*) is larje. thus allowing a perturbative approach. However the success of the quark part on model in describing the hadronic interactions at low momentum transfer has led to phenomenoloqical models based on the quark parton concept to describe such processes as welt. A review of such models is given in reference (J),
In previous experiments (WA5 and NAtl) the ACJCMOR collaboration had already made a systematic study of the inclusive production of $> mesons [4.5.6]. Ihe data were successfully interpreted in terms of the parton fusion model in which in particular the fusion of strange quarks plays an important role. In order to test the parton fusion model in more detail and possibly extract the momentum distribution functions for strange quarks in the interacting hadrons, a significant increase in statistics as well as a larger x range than previously accessible (O.LXx <(J.2) was called for. lhe experimental results discussed in this paper are based on a sample of &O0.ÜQO
In this paper inclusive 2. The parton fusion mode) Ihe parton fusion model [10] is an extension of the model first discussed by Orel I and Yan [ilj to describe the production of lept on pairs in hadronic inter actions, lhe model has been developed to explain t|» me»on production. In the Orell-Yan model a quark from one of the interacting hadrons fuses witn jn antiquark from the other hadron to form a virtual photon which couples to a lepton pair. F he inclusive cross section da/dx of the lepton pair is thought not to be altered by additional interactions between the initial state or final state particles. The differentia! cross section is related to the distributions of partons in the initial hadrons by: d o 4TKX Q - - q Here m and x> are the fractional momenta of the partons in the initial hadrons and M is the mass of the produced lepton pair- The sum is over the quark flavours q u.d.s.c.etc, Q is the charge of quark q and I- (x) are the momentum distributions for quarks of flavour q in the initial hadrons. lhe quark distribution functions r^(x) can be determined by measuring the differential cross section do/dx of the lepton pair. Such experiments yield quark distributions of the nucleons which are similar to the distributions measured in DIS experiments. Up to now the Drell-Yan mechanism is the only source of information for the quark distributions in the tr and K mesons. In formula (1) it is assumed that the structure functions f- (x) are only a function of *. In practice however, there is a small Q* dependence, the exact form of which is given by fJfJL). I hese scaling violations are neglected in our further discussion, f-.xpression (l) leads to a good description of the observed differential cro^i section in Drell-Yan processes, however it underestimates the absolute normalisation by a factor of about 2, generally referred to as the K factor. The determination of the quark distribution in a hadron by using a quark (Drell Yan) or a lepton (UIS) as a probe is assumed to be valid only when the momentum transfer is sufficiently large. However as shown in the next section, it is found for neutrino data that the DIS formulism is already applicable at small v 'ues of the momentum transfer, i.e. Q7~l GeVa. 1 his led us to the assumption that the parton fusion model may be applied to a tow Q process such as inclusive $ meson production, furthermore, we assume that within the x-range (0.0 V iqure 1 shows the parton fusion diagrams to be considered for do /s Uv q~ _ F 2r. (J> q Av a u.d 3 ATI W Here x, is the f- cynman x of the tf meson, f is the energy uf the 4> meson in the overall centre of mass system and xi and XJ are the fractional momenta of the partons m the beam and target hadrons respectively, lhe three couplinq constants q /4n, q./An and q,/4>i do not only determine the relative contributions of the A l L» (VI allowed fusion. f)/| irhibited fusion and qluon fusion respectively, but also insure the overall normalization, i.e. the equivalent of the K factor in Urell-Yan processes. The fractional longitudinal momenta xi and xj are related to the x, of the $ meson by the following expressions: X, :»l - X» XIXJS - M* 2M * where s is the total centre of mass energy squared and M is the mass of the d> meson. The parton mass M is taken to be O.b CieV/c for the s quark and zero for the other partons. Figure 2 shows the relation between x and xi and x:, The fractional longitudinal momentum xi is almost equal to the f eynrnan x of the Apiirt from the three unknown coupling constants we are left with the parton distribution functions F. .{x) and L Jx). I he choice made for these functions is described in the next section. 3. The parton distribution in hadrons As input for the parton fusion model we need the parton distributions in v , K , P and p. In the quark model the hidrons contain valence quarks which qive the hadron its quantum numbers, virtual quark anti quark pairs continuously created out of the vacuum called sua quarks, and gluons. For our purpose we need the part on distributions at (J -1 CeV in the x range Ü.O In the following the structure functions of valence quark a and sea quark b in hadron h are denoted by V (x) and S. (x) respectively. The gluon structure function in hadron h is denoted by (J (X), 1 he structure functions are normalized as follows: ƒ* \JV* (x)/x dx ; ƒ* V- (x)/x dx .- I (5 a; J-1 vV (x)/y dx - j l V* (x)/x dx ^ I (5 -b> O O o O 1 l J Vt^*(x)y* dx = J V* (x)/x dx : I (3 c) X1 V*+(x)/xdx ; J"1 V* (x)/x dx : I (3d) os o s JlVP{x)/xdx= /l v£(x)/x dx =2 (5-e) o U o U J1 v£ (x)/x dx - Jl v5(x)/x dx - l (3 f) o d o o The above valence quark distributions are the only ones to be considered in if . K , p and p. The normalization of the sea quarks and gluons are obtained from momentum conservat ion. i.e. ƒ* (Vh • Sh • Gh) dx = t (4) o where V and S represent the summations over all valence quarks and all sea quarks respectively. 3.1 1 he parton distribution in protons Several authors have given a parameterization for the parton distribution function in terms of x and fja in nucleons. They are Buras Caemers (BLi) [lb], Gluck-Hoffmann-Heya (GHR) [16]. Duke Owens (17], who give two parameten nations (DOl) and (Dull), Lichten et al. [18]. who also give two parameterization* (KHl CJ1) and (E.HKCJ2), and Mahapatra (19]. lhe parameter* are determined by comparing the distributions to experimental results. Most authors only give distributions for U1 above some tower limit Qa. lhe parametenzations make use of different data sets o and use different lower limits on fj' (=Qa). o lo compare the various parameterizations we show the parton distribution functions of the models at their lowest QJ : Q3 value in figure 5. F-or the model of O Mahapatra we have taken Q* = l CieVa. Figure 3 shows Vp. V^. S^SJjvS^sC., 2SP and Gp for the various models. In the low (Ja region (Q*<5 GeV*) the contribution of the quarks which are heavier than the s quark is negligible, and these distributions are assumed to bo /era. The s quark distribution cannot be determined unambiguously by D1S experiments and consequently the various quark distribution parameterizations differ mainly in the s quark distribution. In addition the shape of the gluon distribution cannot be measured directly by DIS experiments. The method explored to extract the gluon distribution is the use of the Q evolution of the sea quark distributions, to which that of the gluon distribution is related. We assume that we may extend these distributions down to Q3 = l GeV*. I o check this assumption we have compared the prediction of the models, in the x range of our experiment Q,0 3.2 1 he parton distribution in n1 and K1 The distribution of the valence quarks in n mesons is taken from Badier et al. [22], who have determined V**d at Q%2S GeV*. assuming that the distribution o\ u and d valence quarks in the ir meson is equal. The distribution is parameterized with 1 he Q dependence of the structure function as measured by Badier at al. is small and we will assume the distribution to be valid at Q'~1 GeV*. The sea structure function of the n mesons as measured by Badier et al. will not be adopted by us to evaluate the differential cross section of • Ihe * region covered by Badier at al., i.e. x, >0.2. is dominated by valence- valence annihilation, introducing large errors in the sea quark distribution evaluation. • According to the parton fusion model the We will leave the shape of the sea quark distribution in the tt meson as a free parameter, to be determined by the inclusive 4> meson data, ^o limit the number of free parameters, the sea in the n meson is assumed to be symmetric in u,d and s quarks and will be parameterized with Cs.ü.d.;W-<'">1' (6. As has been shown in section 3.1 the present data on the parton distributions in nucleons do not allow an unambiguous determination of the gluon distribution functions. For this reason the choice for the gluon distribution in the « meson is somewhat arbitrary. Moreover in our experiment the transition of the £J-*1 gg system into the C^-l $ meson will further obscure the picture. The gluon distribution in n mesons has been measured (23.26J using hadronic ^ meson production in n p interactions, and folding in the known branching ratios of x+tyy. lhe two experiments aqrec within errors on the shape of the gluon distribution and we will use the distribution obtained by Badier et al (23J if) GMf (x) : 1.69 (I-*)2** [4] in which bQ% of the « meson momentum is carried by the qluons. The normalization of the sea quark distribution in the r. meson (expression (6)) is thus constrained by the momentum sum rule given in expression (4). lhe valence u quark distribution in the K meson is obtained from the K n measurement of the ratio V_ (*Vvn ^ l^' using Drell-Yan data with incident n >.ndK, I his gives v£ (xWj (x)a(l-„)UJb {8) leadinq to the following distribution for the valence up quark *n the K meson, usinq expression {!>): V- (x) - VKf (x) . O.Vl xÜAl (lx)115 u u The attribution of strange valence quarks in the K meson will be parameterized with: v£ (x) = v£ * The shape of the sea quarks distribution in the K meson is assumed to be the same as in the n meson (6): su.d.s.ü.a.?t'<>^AK(,->Y <,0> I he qluon distribution in the K meson has been determined by badier at al. [?3] in the same way as in the n meson. A good fit to the data was obtained if it was assumed K r that G is identical to G , i.e. Gkl (x) : Gr* 00 = 1.69(1 -x)2-58 (II) Then, the gluons and the valence up quark carry iOX and li.6% respectively of the momentum of the K meson. The way in which the residual 54.4% of the momentum is distributed over the valence s quark and the sea quarks is left as a free parameter to be determined by the inclusive 4.1 T he decay angular distribution In a parton fusion model the mass of the fusing partons (M J can be related to the decay angular distribution jt pT=0.0 CieV/c by [26] I 3pu I -4M*/M' ...... _„_g.—s_ tI2. p" |*4MVM' q $ where M is the mass of the The mass value obtained is an average over the masses of the partons in the three diagrams (see figure I) which contribute to lhe evaluation of the longitudinal momentum distribution in our model is given by expression (2). Ihe structure functions of the interacting hadrons discussed in section J are used with the following free parameters: • the coupling constants for O/l allowed (gt/4u), O/l inhibited (g'/4n) and gluon fusion (Q?V4TT), • the shape of the sea quark distribution in n and K mesons, y in expressions (6) and (10). • the fraction of the K n oson momentum carried by the K meson sea quarks, which is determined by A in expression (10) and • the shape of the valence s quark in the K meson, a in expression (9). 1 he value of [Ï in expression (9) is determined using the momentum sum rule, i.e. f5 :a(t/K-I )-l where H-l- ƒ * (VK*6Sk *fJk)dx. o u Introducing a larger number of free parameters, for instance by allowing the strange component in the n meson sea to be determined separately by our data, would mean that some parameter: *ire no longer determined independently by the fit to our longitudinal momentum distributions. The motivation for our choice of free parametor*; is the following. The parameters which influence the O/l allowed ss fusion and which are difficult to probe by Drell-Yan experiments are left free. i.e. the strange quark components in TT and K mesons. Distributions which are not well known, but only contribute to the O/A inhibited light quark fusion, as for instance the tight quark sea in it and K mesons, are not allowed to vary independently. We wil! use the inclusive the free parameters are determined by a x' minimah^ation. where x * is given by: t h, . h. .. i (m .{*) c .(*)) h^iT ,p,K i a (K)* {mA*)-r\|.clV)) 3 h = iT ,p.K i ox (x) where m. (x) and c (x) represent the measured and calculated do/dx , values respectively, o is the error on m and N is the parameter which allows for a different normalization of the 100 GeV/c and 120 GeV/c data samples. A simultaneous fit to the pp and pp data samples determines the coupling constants and the normalization N. These distributions do not depend on other free parameters. Table? lists the results obtained for this fit for the various structure function parameten/ations described in section J.I. Unly the Buras-C-lacmers parameterization is unable to describe the data satisfactorily. The gluon distribution proposed by BU is so steep that it excludes a possible contribution of gluon -gluon fusion to $> meson production, lo describe the data at higher x values Bf.. need a significant O/l inhibited contribution, which results in a difference in the pBe and pBe cross sections (N = l.?2), which is much larger than the expected systematic uncertainty. 15] Another extreme is the result of the Mahapatra parameterization, which explains the $ meson production process mainly by gluon -gluon fusion. The sea and gluon distributions of the proton proposed by Mahapatra are similar in shape and consequently the correlation coefficients for the coupling constants are close to one. Ihe coupling constant which governs the 0/1 allowed quark fusion of the fit to tJHR is large as a result of the very small s quark distribution in the proton. Ihc seven parameteri/ations alt differ in the relative contributions of the U/l allowed, 0/1 inhibited and gluon fusion diagrams despite the fact that they all give a satisfactory description of the DIS data, except perhaps for DO II. I his is a reflection of the fact that the distributions which are relevant for Table ? lists the results of the simultaneous fit to the 100 CieV/c and l?0 (jeV/c data over all incident particles. The BLi parameterization, having already a bad x for the incident p and p data, must allow some gluon-gluon fusion to describe the combined data, hence the description of the incident p and p data becomes even worse and the total x' is rather large. fJMN is penalized for the small strange quark component in the proton sea. 1 his parameterization must reduce q^/Arr to describe the incident n and K data. As a result the incident p and p data contribute ^>00 to the total x3 of 670. Both sets of DO give an acceptable x * for the simultaneous fit over all incident beam particles, hor both sets the 4> incaon is mainly produced by sS fusion, whereas the remaining cross section is due to a light quark anti quark fusion contribution of 10 l^>% for incident TI ,p and p and ~ bit for incident K . lhe strange sea distribution in the ti meson, i.e. (1 x) , is much flatter than the distribution of light sea quarks determined in a Drell-Van experiment [?2], where (I x) ' was found. Ihe KMl (J parameteri/ations give fits which attribute most of the $ meson production with incident n ,p and p to gluon-gluon fusion. With incident K mesons the 4> mesons are for 60-/0% produced with the valence s quark of the incident K mesons, lhe fJ/1 inhibited fusicn is responsible for less than 10% of the \ of the cross section is due to light quark fusion, lhe stranqe sea distribution in the n meson is consistent with the distribution as derived from the DU parameterization. Mahapatra ascribes most of the cross section to gluon gluon fusion, which makes the fit insensitive to the strange sea quark distributions in n mesons and kaons. 16] F igore 4 shows the inclusive $ meson cross section with the parton fusion mode) fit based on the DO set I parameterization of the proton constituents (full line). The dashed, dash-dotted and dotted curves indicate the contributions from the O/I allowed,. O/l inhibited and gluon fusion diagrams respectively. Fhe ratio of the strange valence quark over the up valence quark distribution in the K meson has been determined by Arestov et al, 121] by measuring the invariant cross section t- do/dxf for DO I : FHLQ 2: V^t-)-2.l-,-D*tl-»»°-S" In the fits with both DO I and r.Hl (J 2 the kaon momentum is carried for MJ% by the gluons and for 16% by the valence u quark, and tht; remainder is nearly all assigned to the valence s quark. The fits are insensitive to the sea of the kaon due to the relatively large errors for incident kaons at small x values, lhe parameteri/ations of DO I and fcHl ti ? result in distributions for the strange sea quarks in the n meson which is rather flat compared to the light quark sea distribution as determined by Badier et at. [?2| üül: 5*1 (*) -0A\ O-*)3*2 F.HLQ?: $**(*) ,0.10(1 x)2'' 5. Conclusions The average mass of the partons which fuse to form the meson, fjiven the uncertainties in the parton distributions in the interacting hadrons our fusion model is able to give a satisfactory description of the shape of the longitudinal momentum distributions of inclusive 6. Acknowledgements We acknowledge the assistance of S. de Jong for the comparison with neutrino data. (1] M. Getl-Menn, Phys, Lett. $( 19*4) 214. (2] G. Zweig. CtRN 1H 401. 1964. [3] K. F ialfcowski and H. Kit tel. Rep. Prog, Phys. 46 (1983) 1263. (4) C. Daum et el.. Nucl. Phys. 3186(1981)203. (51 C. Daum et al.. Phys. Lett. 9§g (1981) 313. (6) C. Daum et el.. Z. Phys. C - Particles and f ields 18 (1983) I. (?) H. Dijkstra et el.. NIKHtF -H/86 I. submitted to X. Phys. C - Particles and Fields. [8] H. Dijkstra. Ph. O. thesis. NlKHth -H. Amsterdam. 1983. [9] H. Dijkstra et al.. NIKHtF -H/86-2, submitted to ?.. Phys. CJ - Particles and Fields. (10) M.B. Green. H Jacob and P.V. Landshoff. Nuovo Cim. 29A (1973) 123 A. Donnachie and P.V. Landshoff. Nucl. Phys. BU2M9/6) 233. (I IJ S.D. Drell and T. Van. Annals of Physics 66 (1971) 378. (12] R.C. Arnold et al.. Phys. Rev. Lett. V£ (1984) 72/. (13] S. Okubo. Phys. Lett. 3 (1963) 163 G. Zwetg, CtRN-TH 412. 1964 3. hwka. Supp. Prog. Theor. Phys. U (1966) 37. [14] F. FZisete. Proc. of the 21st International Conference on High F.nergy Physics, edited by P. Pettan and M, Porneuf. Paris, J. de Phys. 43. suppl 12. (1982) C3-337 K. Rith, Proc. of the International Europhysics Conference on High tnergy Physics, edited by J. Cay and C. Costain. Brighton. 80, 1983. 17] C151 A.J, Buret and K.J.F. CMmtn. Nucl. Phyt. BI32 (1978) 249. (16] M. Cluck. E. Hoffmann and E. Reye, Z. Phyt. C - Particle* and Fieldt JfJ (19B2) 119, (17] Ü.W.CXike and J.F.Ghvent, Phyt. Rev. Q2Q( 1984) 49. (18) t. F. ichten ct at.. Rev. of Modern Phyt. *£ {1984) * 79. (19] B.P. Mahapatra. Phyt. Rev. Q& (1982) 5002. (20) H. Abramowicz ct at.. Z. Phyt. C - Particle» and Fieldt Ü (1983) 283. (21) Ü. A Mafia et al.. 7. Phyt, C - Particle* and Fieldt 29 (1985) 321. (72) J. Badier et al.. Z. Phys. C - Particle» and Fieldt Ifi (1983) 281. (23] J. Badier et al.. Z. Phy». C - Particle» and F ieldt 20 (1983) 101. [24] J.Ü. Mctwen et al.. Phyt. Lett. 12 IB (1983) 198, [2i] J. Badier et al., Phyt. Lett, 93_g (1980) 354, [26] K.V. Vatavada, Phyt. Rev. D16 (197/) 146. (27) Yu, Arettov et al.. Z. Phyt. C - Particle» and F ieldt 9 (1981) 283. m Table 1 : Th. values of the mass of the fusing partons (M ) obtained from the decay distribution of the + meson at 0.0 incident pi» GeV/c partiele GeV/c* 100 0.31110.003 CM I (HO, 00/ 100 0.510*0.00* 0.40*10.012 120 awitoooi 0.36510.013 120 P O.3OBtO.O06 o.5%to.on 200 w" o.ïi3iaooe 0.4i8iO.Oi« 200 P 0,28Si0,0l0 0.29 t0.03 TeWe 2: Th» coupling constants o^Mw, «,"/*• and g^4« determined in the fit to 4a Ate in pBe and PBe interaction». Tha normalization constant N is defined in expression (15). Tha parton distribution functions used are described in section 3.1. Ah, lh and Gh are the contributions (in %) to the inclusive + meson cross section for 0.0 BC CHR OOI DO II g;/«* .SI t.03 3.95 t.19 .25 1.04 .25 1.01 Q,*/«w .01381.0003 .004 1.002 .006 1.002 .0 1.002 9r>* .0 t.0001 .00151.0007 .00191.0005 .005 1.001 N 1.2210.0) 0.9710.05 1.0210.04 0.9110.04 A/!/Gp 66/34/0 72/11/17 4V13/42 54/0/46 A/1/GP 47/53/ 0 65/18/17 38/22/40 50/0/50 J x 66.3 34.5 35.0 35.3 tULOl U4.Q2 Mehapatre gj^w 1.2 1.4 1.8 1.3 .0 1.01 g,V4w .74 t.3 .9 i.) .45 1.09 .14 t.04 .09 t,05 .50 1.02 todo./d*F in pBe and pBe interactions. The normalization constant N is defined m expression (13). 7 is defined in (6) end (10), a in K (9) and A in (10). The parten distribution functions used are described in section 3. A . 1 and G are the contributions (in %) to the inclusive • meson cross section for 0.0 BG GHR DO I rMDU q;/«. ,17 1.02 .75 1.03 .30 1.02 .233 1.008 o*/4w .01491.0003 .00601.0009 .007 1.001 .00471.0007 .OOlOi.OOOl .00371.0003 .00151.0003 .00291.0003 N 1.1110.01 1.0710.02 1.0310.02 1.0210.01 T V* 10,4 3.0 10.2 3.2 1Ü.2 3.2 10.2 a i.s 10.2 0.8710.05 0.6210.06 0.6110.03 AK .02Ci0.006 a t0.0006 .OOU0.009 0. 10.008 A/l/G** 30/26/43 44/13/43 59/13/29 57/10/33 A/l/cP 21/36/43 19/23/58 52/15/33 5//13/30 A/|/CK* 66/5/29 70/2/28 80/2/19 /// 2/21 A/l/G* 27/32/42 42/15/43 56/15/29 55/12/33 A/l/G* ivm/3i IV32/53 44/25/31 49/20/30 K wvc 66/9/24 72/4/24 80/4/16 79/ 3/18 x" 283.6 619,9 132.4 135.3 LHLQI LHLQ2 Mehapetra g^Mw .4) 1.02 .53 1.02 .145 1.005 9,*/4e .46 1.08 .41 1.0B .59 1.05 q£/4w .2021.009 .25 i.OI .406 1.006 N 1.0210.02 1.0310-01 t.0310.01 V 3.2 10.2 2.7 10.2 41. 17. a 1.3010.09 1.0310.07 3.5 10.3 AK 0, 10.002 0. 10.0004 0. 10.008 AWi1* 3 V 8/59 39/ 7/54 2/6/92 A/VGP U/8/80 17/9/75 12/8780 A/1/GK* 61/ 1/38 65/ 1/34 40/ 1/59 A/l/U* 32/9/59 3// 8/54 2/7/91 A/|/GP 9/16/75 14/16/70 10/16/74 AMiK 65/ 2/32 68/2/30 46/3/51 I2 137.1 168.4 135.2 [9] Figure captions Figure I : Diagrams for • meson production in the parton fusion modal. The three diagrams which contribute to • meson production are: a) OZI allowed $1 fusion, b) OZI inhibited light quark fusion and c) gluon fusion. Figure 2 : F ractional longitudinal momenta xi and x» as a function of x.. Figure 3 ; Structure functions of the proton as parameterized by BG (I), CHR (2), DO set I (3). DO set II (4). EHLQ set 1 (J) and fcHLQ set 2 (6) for Q*-Q*. Mahapatra (7) is evaluated at Q*=l GeV*. The functions are indicated in each figure. F igure 4 : 1 he parton fusion model compared with do/dx _. of the 4 meson. The incident particles ere indicated in each figure. The full line is the fit of the parton fusion model to the data with the DO 1 parameterization for the proton. The dashed, dash-dotted and dotted curves indicate the contribution of OZI allowed, OZI inhibited and gluon fusion respectively. F igure b : 1 he ratio of invariant cross sections for 4 and p as measured by Arestov et al. [27] compared with the ratio of the valence quark distributions K K V /V_ in the kaon as determined from the inclusive • data. Ihe * ° K K proportionality constant between the data and V /V_ has been fitted for each parameterization. The parameterization which is used for the parton structure functions in nucleons is indicated in each figure. (Q) (b) (c) * Figure 1. m, • O G.V/cJ _.- m, .0»eeV/e2 Figiirt 2. Figure 3. it* 120 p 120 K* 120 1.41- 1.2 1. 0.8 0.6 f 0.4 u 0.2 X •D 0. 1 I I lTT-f- iii TTY^ —1—W-.I—J..1-J—1 I •o 1.4 n' 100 p 100 K" 100 1.2 1. 0.8 0.6 0.4 0.2 i i i i rf*TTii TTT-r-t-t-^HH ' 0. 0,1 02 0.3 0. 01 0.2 0.3 0. 0.1 02 0.3 *F Figure 4. M 1.5 1.0 05 2 O 10 - 00 I DO ïï 8 1.5 6 10 4 -0.5%, V 2 x 0 •o 10 - EHLQ 1 EHLQ 2 C 1.5W 8 6 4 2 *4 0 UI 10 " Mahopatro 0.4 0.8 X 8 6 1.5 4 1.0 2 0.5 Figure 5.