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An Analysis on Single and Central Diffractive Heavy Flavour Production at Hadron Colliders

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An Analysis on Single and Central Diffractive Heavy Flavour Production at Hadron Colliders 416 Brazilian Journal of Physics, vol. 38, no. 3B, September, 2008 An Analysis on Single and Central Diffractive Heavy Flavour Production at Hadron Colliders M. V. T. Machado Universidade Federal do Pampa, Centro de Cienciasˆ Exatas e Tecnologicas´ Campus de Bage,´ Rua Carlos Barbosa, CEP 96400-970, Bage,´ RS, Brazil (Received on 20 March, 2008) In this contribution results from a phenomenological analysis for the diffractive hadroproduction of heavy flavors at high energies are reported. Diffractive production of charm, bottom and top are calculated using the Regge factorization, taking into account recent experimental determination of the diffractive parton density functions in Pomeron by the H1 Collaboration at DESY-HERA. In addition, multiple-Pomeron corrections are considered through the rapidity gap survival probability factor. We give numerical predictions for single diffrac- tive as well as double Pomeron exchange (DPE) cross sections, which agree with the available data for diffractive production of charm and beauty. We make estimates which could be compared to future measurements at the LHC. Keywords: Heavy flavour production; Pomeron physics; Single diffraction; Quantum Chromodynamics 1. INTRODUCTION the diffractive quarkonium production, which is now sensitive to the gluon content of the Pomeron at small-x and may be For a long time, diffractive processes in hadron collisions particularly useful in studying the different mechanisms for have been described by Regge theory in terms of the exchange quarkonium production. of a Pomeron with vacuum quantum numbers [1]. However, the nature of the Pomeron and its reaction mechanisms are In order to do so, we will use the hard diffractive factoriza- not completely known. Currently, a promising way to clar- tion, where the diffractive cross section is the convolution of ify these questions is using the hard scattering to resolve the diffractive parton distribution functions and the corresponding quark and gluon content in the Pomeron [2], regarding that a diffractive coefficient functions. At high energies there are im- parton structure is natural in a modern QCD approach to the portant contributions from unitarization effects to the single- strongly interacting Pomeron. Form the experimental point Pomeron exchange cross section. These absorptive correc- of view, observations of diffractive deep inelastic scattering tions cause the suppression of any large rapidity gap process, (DDIS) at HERA have increased the knowledge about the except elastic scattering. In the black disk limit the absorp- QCD Pomeron, where its diffractive distributions of singlet tive corrections may completely terminate those processes. quarks and gluons have been phenomenologically determined This partially occurs in (anti)proton–proton collisions, where [3]. unitarity is nearly saturated at small impact parameters [6]. In hadronic collisions, a single diffractive event is charac- These multiple-Pomeron contributions depends on the partic- terized by one of the colliding hadrons emitting a Pomeron ular hard process and it is called survival probability factor, that scatters off the other hadron. Hard diffractive events with which are important for the reliability of theory predictions. a large momentum transfer are also set by the absence of hadronic energy in certain angular regions of the final state The present contribution is organized as follows. In next phase space (large rapidity gaps). For events in which both section, we present the main formulas to compute the in- colliding hadrons remain intact as they each emit a Pomeron clusive and diffractive cross sections for heavy quarkonium we have the so-called central diffractive events. In the latter hadroproduction. We also present the parameterization for case, also known as double Pomeron exchange (DPE) pro- the diffractive partons distribution in the Pomeron, extracted cesses, both incoming hadrons are quasi-elastically scattered recently in DESY-HERA, and theoretical estimations for the and the final states system in the center region is produced by gap survival probability factor. In the last section we present Pomeron-Pomeron interaction. the numerical results for Tevatron and perform predictions to Here, we concentrate on the single diffractive processes future measurements at the LHC experiment. The compat- p + p(p¯) ! p + J=Y[¡] + X and the central diffractive re- ibility with data is analyzed and the comparison with other actions, p + p(p¯) ! p + J=Y[¡] + p(p¯). The diffractive approaches is considered. As an anticipation of the main re- heavy quarkonium production has drawn attention because sults, at the Tevatron the single and central diffractive J=Y their large masses provide a natural scale to guarantee the ap- and ¡ production are observable with a single diffractive ra- SD plication of perturbative QCD. There are several mechanisms tio R (Tevatron) that is between 1 % (charmonium) and 0.5 proposed for the quarkonium production in hadron colliders % (bottomonium), with lower values at the LHC. Also, it is J=Y [4, 5], as the color singlet model, the color octet model and predicted that Rtheory = 1:12 § 0:19 %. The central diffractive the color evaporation model. An important feature of these cross sections are still feasible to be measured, despite the perturbative QCD models is that the cross section for quarko- very small diffractive ratios. Therefore, we stress that the the- nium production is expressed in terms of the product of two oretical model dependence is either large and more detailed gluon densities at large energies. This feature is transferred to studies are timely. M. V. T. Machado 417 2. DIFFRACTIVE HADROPRODUCTION OF HEAVY the three ¡ states (¡ + ¡0 + ¡00) in the dilepton decay channel QUARKONIUM are shown [4]. The agreement of the CEM model with accel- erator data is very good and an extrapolation to the LHC is For our purpose we will use the Color Evaporation Model presented. The results give us considerable confidence in the (CEM) [7]. The main reasons for this choice are its sim- extrapolation to the LHC energy. plicity and fast phenomenological implementation, which are the base for its relative success in describing high energy data[4, 5]. In such an approach, the cross section for a pro- 2.1. Diffractive cross section - single–Pomeron exchange cess in which partons of two hadrons, h1 and h2, interact to CP produce a heavy quarkonium state, h1 + h2 ! H(nJ ) + X, For the hard diffractive processes we will consider the is given by the cross section of open heavy-quark pair produc- Ingelman-Schlein (IS) picture [2], where the Pomeron struc- tion that is summed over all spin and color states. All infor- ture (quark and gluon content) is probed. In the case of sin- mation on the non-perturbative transition of the QQ¯ pair to the gle diffraction, a Pomeron is emitted by one of the colliding heavy quarkonium H of quantum numbers JPC is contained in hadrons. That hadron is detected, at least in principle, in the the factor FnJPC that a priori depends on all quantum numbers final state and the remaining hadron scatters off the emitted [7], Pomeron. The diffractive cross section of a hadron–hadron collision is assumed to factorise into the total Pomeron– CP ¯ s(h1 h2 ! H[nJ ]X) = FnJPC s¯ (h1 h2 ! QQX); (1) hadron cross section and the Pomeron flux factor [2]. The CP where s¯ (QQ¯) is the total hidden cross section of open heavy- single diffractive event, h1 + h2 ! h1;2 + H[nJ ] + X, may quark production calculated by integrating over the QQ¯ pair then be written as mass from 2mQ to 2mO, with mO is the mass of the associated dsSD (h + h ! h + H[nJCP] + X) i j i = open meson. The hidden cross section can be obtained from (i) the usual expression for the total cross section to NLO. These dxIP djtij ¡ ¢ hadronic cross sections in pp collisions can be written as (i) ¯ FnJPC £ fIP=h (xIP ;jtij)s¯ IP + h j ! QQ + X ; (3) Z i p 2 p 2 p 2 spp( s;mQ) = ∑ dx1 dx2 fi (x1;µF ) f j (x2;µF ) where the Pomeron kinematicalq variable xIP is defined as i; j=q;q;g p x(i) = s( j)=s , where s( j) is the center-of-mass energy in 2 2 2 IP IP i j IP p £ sbi j( s;mQ;µF ;µR); (2) p the Pomeron–hadron j system and si j = s the center- of-mass energy in the hadron i–hadron j system. The mo- where x1 and x2 are the fractional momenta carried by the col- p mentum transfer in the hadron i vertex is denoted by ti.A liding partons and fi are the proton parton densities. The par- tonic cross sections are known up to NLO accuracy [8]. Here, similar factorization can also be applied to central diffrac- tion, where both colliding hadrons can in principle be de- we assume that the factorization scale, µF , and the renormal- tected in the final state. The central quarkonium production, ization scale, µR, are equal. We also take µ = 2mQ, using the h + h ! h + H[nJCP] + h , is characterized by two quasi– quark masses mc = 1:2 GeV and mb = 4:75 GeV, which pro- 1 2 1 2 vide an adequate description of open heavy-flavour produc- elastic hadrons with rapidity gaps between them and the cen- 2 2 tral heavy quarkonium products. The central diffractive cross tion [8]. The invariant mass is integrated over 4mc · sˆ · 4mD 2 2 section may then be written as, in the charmonium case and 4mb · sˆ · 4mB for ¡ produc- tion. The factors FnJPC are experimentally determined [9] to CD CP ¡2 ¡2 ds (h + h ! h + H[nJ ] + h ) ¡¡ ¡¡ i j i j be F11 ¼ 2:5£10 for J=Y and F11 ¼ 4:6£10 for ¡. = F PC £ (i) ( j) nJ These coefficients are obtained with NLO cross sections for dxIP dxIP djtijdjt jj heavy quark production [9].
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