Possible indication to the QCD evolution of double parton distributions? A.M. Snigirev M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear Physics, 119991, Moscow, Russia (Dated: October 25, 2018) For the first time the process-independent parameter of double parton scattering, σ exp eff , has been measured newly in the D0 experiment at the three different resolution scales. If we interpret the measurement as a decrease of the effective cross section with a growth of the resolution scale it can indicate the QCD evolution of double parton distributions. PACS numbers: 12.38.-t The presence of multiple parton interactions in high energy hadron collisions has been convincingly demon- strated by the AFS [1], UA2 [2] and CDF [3] Collab- orations using events with the four-jet final state and later by the CDF Collaboration [4] using events with the γ + 3 jets final state. Recently the D0 Collaboration has measured the process-independent parameter of double parton scattering, σ exp eff , using the γ + 3 jets events at the three different resolution (energy) scales [5] provid- ing new and complementary information on the proton structure. The possibility of observing two separate hard collisions has been proposed since long [6], and from that has also developed in a number of works [7, 8, 10–13]. A brief review of the current situation and some progress in the modeling with account of correlated flavor, color, longitudinal and transverse momentum distributions can be found in Ref. [10]. In order to introduce the denotations and to be clear let us recall that, for instance, the inclusive differential cross section for the four-jet production due to the si- multaneous interaction of two parton pairs within one p ¯ p collision, σ$_{dp}$ , can be given by [7] where σ$_{ij}$ stands for the two-jet production cross section. The dimensional phenomenological parameter σ$_{eff}$ in the denominator is a factor characterizing a size of the ef- fective interaction region of the hadron (the factor 2 is introduced due to the identity of the two parton subpro- cesses). The relatively small value of ( σ$_{eff}$ )$_{CDF}$ measured by the CDF Collaboration [4] with respect to the naive expectation was, in fact, considered [8, 9] as evidence of nontrivial correlation effects between partons in the transverse space. But, apart from these correlations, the longitudinal momentum correlations can also exist and they were investigated in Ref. [14]. The factorization ansatz is just applied to the two-parton distributions en- tering Eq. (1): Multiple interactions require an ansatz for the struc- ture of the interacting hadrons, i.e. correlations between the constituent partons. As a simple ansatz, usually, the two-parton distributions (of the parton momentum frac- tion) are supposed to be the product of two single-parton distributions times a momentum conserving phase space factor. In recent papers [14] it has been shown that this hypothesis is in some contradiction with the leading loga- rithm approximation of perturbative QCD (in the frame- work of which a parton model, as a matter of fact, was es- tablished in the quantum field theories [15]). Namely, the two-parton distribution functions being the product of two single distributions at some reference resolution scale become dynamically correlated at any different scale of a hard process. where D$_{p}$ ( x$_{i}$, Q $^{2}$) are the single quark/gluon momentum distributions at the scale Q 2 (determined by a hard pro- cess). However multi-parton distribution functions sat- isfy the generalized Gribov-Lipatov-Altarelli-Parisi- Dokshitzer (GLAPD) evolution equations derived for the first time in Refs [16, 17] as well as single parton dis- tributions satisfy more known and cited GLAPD equa- tions [15, 18]. Under certain initial conditions these gen- eralized equations lead to the solutions, which are iden- tical with the jet calculus rules proposed originally for multiparton fragmentation functions by Konishi-Ukawa- Veneziano [19] and are in some contradiction with the factorization hypothesis (2). Here one should note that at the parton level this is a strict assertion within the leading logarithm approximation. The main purpose of the present letter is to show that these QCD dynamical correlations result effectively in a dependence of the experimentally measured effective cross section σ exp eff on the resolution scale unlike naive accepted expectations. The paper is organized as follows. Section II is de- voted to what is known from perturbative QCD theory on the two-parton distribution functions. The possible manifestation of correlations induced by QCD evolution is discussed in Sec. III. We summarize and conclude in Sec. IV. D$_{p}$ ( x$_{i}$, x$_{j}$, Q $^{2}$) = D$_{p}$ ( x$_{i}$, Q $^{2}$) D$_{p}$ ( x$_{j}$, Q $^{$^{2}$)(1}$− $^{x$_{i}$}$−x$_{j}$ ) , (2) σ$_{dp}$ = ∑ q/g ∫ σ$_{12}$σ$_{34}$ 2 σ$_{eff}$ D$_{p}$ ( x$_{1}$, x$_{3}$ ) D$_{¯}$ $_{p}$( x$_{2}$, x$_{4}$ ) dx$_{1}$dx$_{2}$dx$_{3}$dx$_{4}$, (1) II. DOUBLE PARTON DISTRIBUTIONS IN THE LEADING LOGARITHM APPROXIMATION I. INTRODUCTION arXiv:1001.0104v3 [hep-ph] 5 Feb 2010