Quark degrees of freedom in the production of soft pion jets
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EMENTARY PARTICLES AND FIELDS Theory
Quark Degrees of Freedom in the Production of Soft Pion Jets V. A. Okorokov* National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409 Russia Received July 30, 2014
Abstract—Experimental results obtained by studying the properties of soft jets in the 4-velocity space at √ s ∼ 2 to 20 GeV are presented. The changes in the mean distance from the jet axis to the jet particles, the mean kinetic energy of these particles, and the cluster dimension in response to the growth of the collision energy are consistent with the assumption that quark degrees of freedom manifest themselves in processes of pion-jet production at intermediate energies. The energy at which quark degrees of freedom begin to manifest themselves experimentally in the production of soft pion jets is estimated for the first time. The estimated value of this energy is 2.8 ± 0.6 GeV. DOI: 10.1134/S1063778815020246
Investigation of the properties of soft pion jets at intermediate energies may furnish new important information about the behavior of quantum systems in the nonperturbative region. A relativistic-invariant method was proposed in [1] for studying collective effects in the case where particle-beam interaction with a target leads to the formation of a multiparticle final state in the reaction b + t → 1 + 2 + . . . . Special features of this method in the case of the production of two jets were considered in detail in [2–5]. In that case, secondary particles refer to the regionof target (beam) fragmentation if Xtk ≥ (≤)Xbnd Xbk ≤ (≥)Xbnd , where Xpk = [mk (Uk Ur )][mp (Up Ur )]−1 , p, r = t, b; p = r; mk is the mass of the kth secondary particle; mt/b is the mass of the target/beam particles; Uk = Pk /mk is the 4-velocity; k = t, b, 1, 2, . . . ; and Xbnd = 0.1−0.2. The square of the distance from the kth particle to the beam axis V in the space of Uk is defined as bk = − (V − Uk )2 (k = t, b, 1, 2, . . . ), where V = UJ /|UJ | and UJ = N i=1 Ui [1, 6]. A relation between bk and αS , which is the renormalized strong-coupling constant, was obtained in [5]. From this relation, it follows that, within the approach in question, the interval of 10−2 ≤ bk ∼ 1 corresponds to the transition from the dominance of baryon– meson degrees of freedom to the manifestation of the internal structure of primary particles and, accordingly, quark–gluon degrees of freedom in processes involving the production of jets of secondary particles. This complies with the conclusion drawn in [6]. The temperature defined as the mean kinetic energy of particles in the jet rest frame, Tk , is estimated *
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on the basis of the functions F (bk ) that, for pion jets, have the form [3] F (bk ) = (ε/N )dN/dbk , where ε ≡ 4/[m2π bk 1 + 4/bk ], and which characterize the invariant cross section [6]. In [7], it was proposed to study the geometric properties of jets in the Uk space with the aid of the cluster dimension D defined on the basis of the relation between the number of particle
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