content_image/417555.jpg content_image/417554.jpg
# 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. 

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]. 

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. 

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. 

PACS numbers: 12.38.-t 

## I. INTRODUCTION 

## II. DOUBLE PARTON DISTRIBUTIONS IN THE LEADING LOGARITHM APPROXIMATION 

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] 

<img src='content_image/417555.jpg'>

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): 

<img src='content_image/417554.jpg'>

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. 

