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Z-Scaling and Prompt Photon Production in Hadron-Hadron Collisions at High Energies

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Z-Scaling and Prompt Photon Production in Hadron-Hadron Collisions at High Energies E2-98-92 M.V. Tokarev Z-SCALING AND PROMPT PHOTON PRODUCTION IN HADRON-HADRON COLLISIONS AT HIGH ENERGIES Submitted to «Physical Review D» / 30 - 07 1 Introduction A search for general properties of quark and gluon interactions beyond Quantum Chromodynamics (QCD) in hadron-hadron, hadron-nucleus and nucleus-nucleus colli­ sions is one of the main goals of high energy particle and relativistic nuclear physics. A high colliding energy allows us to study hadron-hadron collisions in the framework of perturbative QCD [1], At present systematic investigations of prompt photon production at a colliding energy up to -Js = 1800 GeV are performed at Tevatron by the CDF [2] and DO [3] Collaborations. A high energy of colliding hadrons and a high transverse momentum of produced photons guarantee that QCD can be used to describe the interaction of hadron constituents. Prompt photon production is one among very few signals which can provide direct information on the partonic phase of interaction. ’Penetrating probes ’, photons and dilepton pairs are traditionally considered to be one of the best probes for quark- gluon plasma (QGP) [4], Direct photons do not feel strong forces, they provide both an undisturbed picture of the collision at very short times and a comparison sample for understanding the interaction between quarks and gluons and the surrounding nuclear matter. It is considered that the fragmentation of partons into hadrons might be one of the least understandable features of QCD [5], Even though the primary scattering process is described in term of perturbative QCD, the hadronization chain contains very low g_L-hadrons, respective to the parent parton. Therefore, the whole process is clearly a non-perturbative phenomenon involving final state interactions which have to conserve colour and baryon number. In contrast to the foregoing, it is often assumed that the direct photon production probes the parton-parton interaction without the ambiguities associated with jet identification, fragmentation and energy measurement. It is considered that there is a possibility to identify the process which is well understood from the theoretical point of view and in which the gluon contribution can be determined. In pp collisions at high energies, the dominant mode of direct photon production is through the process of Compton scattering (gq —* yq). The cross section is thus sensitive to the gluon distribution at low momentum fraction x. A search for general properties of prompt photon production in hadron-hadron collisions is of great interest, especially in connection with commissioning such large accelerators of nuclei as RHIC [6, 7] at Brookhaven and LHC [8] at CERN. The main physical goal of investigations on these colliders is to search for quark-gluon plasma, the hot and superdense phase of nuclear matter. Therefore, the features of direct photon production observed in hadron-hadron interactions allow us to extract nuclear effects and to study the influence of nuclear matter on the mechanism of photon formation in pA and AA collisions. A comparison of the cross sections of direct photons produced in hadron-hadron, hadron-nucleus and nucleus-nucleus interactions both in central and non-central rapidity regions allows us to understand in detail underlying physical phenomena due to the presence of nuclear matter. It is considered that nuclear matter can transit from a usual hadronic phase to an exotic state, named partonic phase or QGP. However, the direct photon production in the partonic phase of hadron-hadron in ­ teractions can differ from that in the hadronic phase. The process is connected with 1 the space-time evolution of a primary (point-like) photon. During the evolution, the primary photon interacts with vacuum and nuclear fields through gg-pair fluctuations and forms a ’’coat”. The process of bare photon ’’dressing ” is photon hadronization. Photon hadronization is the process forming the hadronic (non-perturbative) compo ­ nent of the photon structure function. The existence of the hadronic component of the photon is established in the investigations of deep-inelastic electron-proton scat­ tering with jet production at HERA [9]. It is possible that the photon hadronization has features which differ from the particle hadronization but they might have general features, too. We consider the direct photon production based on the concept of z-scaling. The hypothesis of the z-scaling of prompt photon production in pp collisions has been suggested in [10] and studied in [11]. Based on the physics sense of the scaling function H(z) and the variable z, we can study a fundamental process - photon hadronization and hadron content of the photon in different processes, for example, in pp and pp collisions. The function H(z) describes the probability to form the hadronic component of the photon with formation length z and, consequently, the space-time evolution of the process. In this paper, we use the formalism of z-scaling [12] for the description of direct photon production in pp and pp collisions at high energies. The paper is organized as follows. The scaling is based on such fundamental principles of nature as self­ similarity, locality, scale-relativity, fractality, and scale-relativity. First, one reflects the dropping of certain dimensional quantities or parameters out of the physical pic ­ ture of interactions. Second, one concludes that the momentum-energy conservation law is locally valid for interacting constituents. Third, the fractality principle says that both the structure of interacting particle and its formation mechanism are self- similar in a kinematic range. Fourth, the scale relativity principle states that the structures of interactions and interacting objects reveal self-similarity and fractality on any scale [13, 14]. It has been found [12] that the scaling function H(z) is expressed via two exper ­ imental observables, inclusive cross section Etfo/dq3 and the multiplicity density of charged particles dN/drj\ n^0 = p(s). The function H(z) is found to be independent of center-of-mass energy x/i and the angle of produced particle 8. The symmetry properties of H(z) allow us to connect the scaling functions for different particles (Tt±,K±). The transformation parameter ah/ ’r+ is interpreted as a relative formation length. The scaling function H(z) describes the probability to form the hadron with formation length z. The universality of H(z) means that the hadronization mecha ­ nism of particle production is of universal nature. So, the function is well defined in hadron-hadron collisions, and therefore it can be used to study the feature of prompt photon production as well as hadrons. The z-scaling of direct photon production in pp and pp collisions at high energies is studied in this paper. The general concept of z-scaling is described in Section 2. Such fundamental principles as self-similarity, locality, scale-relativity and fractality are used to construct the scaling function H{z). The properties of the function H(z), as well as energy and angular independence, are verified. The results of our analysis of the available experimental data and their comparison with usual data presentation of the data are given in Section 3. The available experimental data for direct photon production are shown to confirm both the energy and angular scaling of H(z) over a 2 wide range of Vs and 07. The obtained results and their interpretation are discussed in Section 4. Based on the physical meaning of the function H(z) as a probability to form the photon with formation length, the conclusion is drawn that H(z) describes the space-time evolution of the photon hadronic component. The universality of the scaling function H(z) is used to predict the cross sections of photon production at RHIC, LHC and VLHC energies. Some conclusions are summarized in Section 5. 2 General concept of z-scaling Let. us consider the inclusive process M,+M2 — m1+X. (1) where Mi and M2 are the masses of colliding hadrons and rn, is the mass of produced inclusive particle. In accordance with Stavinsky's ideas [15], the gross features of the inclusive particle distributions for reaction (1) at high energies can be described in terms of the corresponding kinematic characteristics of the exclusive parton subprocess (.'£]Mi) 4- (x2M2) —» it'll 4- (:CjMj 4- x2M2 4- ni2). (2) The parameter m2 is a minimum mass introduced in connection with internal con ­ servation laws (for isospin, baryon number and strangeness). The X\ and x2 are the scale-invariant fractions of the incoming 4-momenta Pi and P> of colliding objects = (P2g) + M2m2 = (Pt(j) + M in i2 1 (P,P2)-M,M2’ '2 (P,P2)-M,M2 M The secondary particle carries away momentum q. The centre-of-mass energy of subprocess (1) is defined as s = xi ■ M’f + x2 ■ Ml + 2x, • x2 ■ {P\P2) (4) and represents the energy of colliding constituents necessary for the production of the inclusive particle. The cross section of the inclusive particle production in hadron- hadron interactions in the framework of the parton model is governed by the mini ­ mum energy of colliding constituents o ~ lAsmi„(xi,:c2). (5) The fractions :ti and x2 which correspond to the minimum value of (2) were found in [12] under an additional constraint 9Aq(X],X 2) 9A,( xi,x2) = 0, (d) 9x, dx 2 where A,(xi,x2) is given by the equation (x,P, + x2P2 — q)2 — (xiMj + x2M2 4- m-2)*' 4- A(/(xi,x2) (7) 3 So, the fractions xL and x2 minimize the value of A,, simultaneously fulfilling the symmetry requirement of the problem, i.e. z2 = x2 for the inclusive particle detected at 90° in the corresponding NN centre-of-mass system. In accordance with the self-semilarity principle, we search for the solution where has to be a scaling function, and we choose the variable z as a physically meaningful variable which could reflect self-similarity as a general pattern of hadron production.
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