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Inclusive $ Meson Production, the Parton Fusion Model and Strange Quark Structure Functions

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Inclusive $ Meson Production, the Parton Fusion Model and Strange Quark Structure Functions 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 <p production. The doVdx,- for $ production in ^p.^pp and K p interactions is evaluated in the model by using structure functions for the constituents of the interacting particles. A comparison between the model and high statistics data in the Feynman * range 0.<xF(*)<0.4 allows the determination of the strange valence quark distribution in K mesons and the strange sea quark distribution in ii mesons, which appears to be harder than the light sea quark distribution. The comparison also shows that a significant part of inclusive $ production is due to the OZ1 allowed fusion of strange quarks, while the OZt inhibited fusion diagrams are strongly suppressed. 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 <t» mesons in the kinematic range U.U<x, (0.4 and have been presented elsewhere l'/.8]. Ihis model also explains naturally the observed enhanced production of strange particles jointly with the <(> meson [4,9) as well as the different shapes of the differential cross sections do/dx for incident -n mesons, protons and K mesons. In this paper inclusive <t> data will be interpreted in terms of the parton fusion model [10J. which relates the differential cross section do/dx of inclusive <J> meson production to the parton distributions in the interacting hadrons. lhe distribution of the momentum of a nucleon over its partons has been parameterized by several authors (section 3). lhe parameters are adjusted to give agreement with the parton distributions measured in deep inelastic lepton scattering (DIS), Drell Yan processes and ty production experiments. In section 5 the validity of the parameteri/ations at low momentum transfer is checked. Those parameteri/ations which also qive an acceptable description of D1S data at low momentum transfer will be used as an input to the parton fusion model. In section 4 the prediction of the parton fusion model *s compared with our inclusive <fc meson data. Ihe conclusions which can be drawn from this comparison are presented in section ü. [I] 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<x<0.i) of our experiment, the structure functions obtained with a Be target instead of with nucleons arc not influenced by the fc.MU effect, which follows from measurement (Ji!j. [2] V iqure 1 shows the parton fusion diagrams to be considered for <J> meson production. In figure 1 -a two s quarks combine to produce the hidden strangeness <fc($s") meson, lhe coupling constant (q.Au) of this process is expected to be larqe compared to that for the non strange quark fusion process (figure ! b) {qf/Av) reflecting the empirical rule invented by Okubo. /weig and U/uku [15] (U/l) that disconnected quark diagrams, like the one in figure lb. are inhibited. I he IJ--1 $> meson cannot be directly produced by the fusion of two qluons. Only L H ss states are allowed by this process. However such a L' ;*•! state may radiate off a photon or qluon to produce the $> meson. Indeed in inclusive iir meson production it has been observed that a large fraction of the cross section can be accounted fur by the production of U - * I x states and their subsequent decay into ij»>. In order to take such an admixture uf qluon diaqrams into account the diagram of tiqure 1 c has been included m our expression for the 4* meson cross section. In (?) the differential cross section do/dx, for inclusive <$> meson production is therefore expressed in terms of the quark distribution functions V . .(x). where q u.d.s for the three quark flavours considered and b and t denote the beam and target hadron, and qluon distributions 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.
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