Diffractive production of heavy mesons at the LHC within k t - factorization approach
aa r X i v : . [ h e p - ph ] J un Diffractive production of heavy mesons at the LHCwithin k t - factorization approach Marta Luszczak ∗ † University of Rzeszów, PL-35-959 Rzeszów, PolandE-mail: [email protected]
Antoni Szczurek
Institute of Nuclear Physics PAN, PL-31-342 Cracow, PolandE-mail: [email protected]
We discuss diffractive production of heavy mesons at the LHC [1, 2]. The differentialcross sections for single- and central-diffractive mechanisms for c ¯ c pair production arecalculated in the framework of the Ingelman-Schlein model corrected for absorption ef-fects. Here, leading-order gluon-gluon fusion and quark-antiquark anihilation partonicsubprocesses are taken into consideration. Both pomeron flux factors as well as partondistributions in the pomeron are taken from the H1 Collaboration analysis of diffrac-tive structure function and diffractive dijets at HERA. The extra corrections from sub-leading reggeon exchanges are also taken into consideration. In addition to standardcollinear approach, for the first time the differential cross sections for the diffractive c ¯ c pair production are calculated in the framework of the k t -factorization approach, i.e. ef-fectively including higher-order corrections. The unintegrated (transverse momentumdependent) diffractive parton distributions in proton are calculated with the help of theKimber-Martin-Ryskin prescription where collinear diffractive PDFs are used as input.Some correlation observables, like azimuthal angle correlation between c and ¯ c , and c ¯ c pair transverse momentum were obtained for the first time. The hadronization of charmquarks is taken into account by means of fragmentation function technique. XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects11-15 April, 2016DESY Hamburg, Germany ∗ Speaker. † This work was partially supported by the Polish National Science Centre grant DEC-2013/09/D/ST2/03724. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ iffractive production of heavy mesons
Marta Luszczak
1. Introduction
Diffractive hadronic processes were studied theoretically in the so-called resolvedpomeron model [3]. During the studies performed at Tevatron, it was realized that themodel, previously used to describe deep-inelastic diffractive processes must be correctedto take into account absorption effects related to hadron-hadron interactions. Such in-teractions, unavoidably present in hadronic collisions at high energies are not present inelectron/positron induced processes. In theoretical models this effect is taken into accountby multiplying the diffractive cross section calculated using HERA diffractive PDFs by akinematics independent factor called the gap survival probability – S G . Two theoreticalgroups specialize in calculating such probabilities [4, 5]. At high energies such factors,interpreted as probabilities, are very small (of the order of few %). This causes that thepredictions of the diffractive cross sections are not as precise as those for the standard in-clusive non-diffractive cases. This may become a challenge when a precise data from theLHC will become available.In this study we consider diffractive production of charm for which rather large crosssection at the LHC are expected, even within the leading-order (LO) collinear approach[1]. On the other hand, it was shown that for the inclusive non-diffractive charm pro-duction the LO collinear approach is a rather poor approximation and higher-order cor-rections are crucial. Contrary, the k t -factorization approach, which effectively includeshigher-order effects, gives a good description of the LHC data for inclusive charm pro-duction at √ s = 7 TeV (see e.g . Ref. [6]). This strongly suggests that application of k t -factorization approach to diffractive charm production is useful. This presentation isbased on our recent study in [2].
2. Formalism x IP p a p b p a Y XQ ¯ Qβ x F g ( x , k t , µ ) F Dg ( x , k t , µ ) k t = 0 k t = 0 t p a p b p b Y XQ ¯ Qβ x x IP F Dg ( x , k t , µ ) k t = 0 k t = 0 t F g ( x , k t , µ ) Figure 1:
A diagrammatic representation for single-diffractive production of heavy quark pairswithin the k t -factorization approach. A sketch of the theoretical formalism is shown in Fig. 1. Here, extension of the stan-dard resolved pomeron model based on the LO collinear approach by adopting a frame-work of the k t -factorization is proposed as an effective way to include higher-order cor-rections. According to this model the cross section for a single-diffractive production2 iffractive production of heavy mesons Marta Luszczak of charm quark-antiquark pair, for both considered diagrams (left and right diagram ofFig. 1), can be written as: d σ SD ( a ) ( p a p b → p a c ¯ c XY ) = Z dx d k t π dx d k t π d ˆ σ ( g ∗ g ∗ → c ¯ c ) × F Dg ( x , k t , µ ) · F g ( x , k t , µ ) , (2.1) d σ SD ( b ) ( p a p b → c ¯ cp b XY ) = Z dx d k t π dx d k t π d ˆ σ ( g ∗ g ∗ → c ¯ c ) × F g ( x , k t , µ ) · F Dg ( x , k t , µ ) , (2.2)where F g ( x , k t , µ ) are the unintegrated ( k t -dependent) gluon distributions (UGDFs) inthe proton and F Dg ( x , k t , µ ) are their diffractive counterparts – diffractive UGDFs (dUGDFs).Details of our new calculations can be found in Ref. [2].
3. Results
In Fig. 2 we show rapidity (left panel) and transverse momentum (right panel) dis-tribution of c quarks (antiquarks) for single diffractive production at √ s =
13 TeV. Dis-tributions calculated within the LO collinear factorization (black long-dashed lines) andfor the k t -factorization approach (red solid lines) are shown separately. We see signifi-cant differences between the both approaches, which are consistent with the conclusionsfrom similar studies of standard non-diffractive charm production (see e.g . Ref. [6]). Herewe confirm that the higher-order corrections are very important also for the diffractiveproduction of charm quarks. c y -8 -6 -4 -2 0 2 4 6 8 ( nb ) c / d y σ d Xc p c → p p = 13 TeVs (single-diffractive) = m F2 µ = R2 µ = 0.05 G SIP+IR < 30 GeV T p -factorization (solid) t kLO collinear (dashed) (GeV) cT p ( nb / G e V ) c T / dp σ d Xc p c → p p = 13 TeVs (single-diffractive) = m F2 µ = R2 µ = 0.05 G SIP+IR| < 8 c |y -factorization (solid) t kLO collinear (dashed) Figure 2:
Rapidity (left panel) and transverse momentum (right panel) distributions of c quarks(antiquarks) for a single-diffractive production at √ s =
13 TeV. Components of the g ( IP ) - g ( p ) , g ( p ) - g ( IP ) , g ( IR ) - g ( p ) , g ( p ) - g ( IR ) mechanisms are shown. The correlation observables can not be calculated within the LO collinear factoriza-tion but can be directly obtained in the k t -factorization approach. The distribution ofazimuthal angle ϕ c ¯ c between c quarks and ¯ c antiquarks is shown in the left panel of Fig. 3.3 iffractive production of heavy mesons Marta Luszczak (deg) cc ϕ ( nb / r ad ) cc ϕ / d σ d Xc p c → p p = 13 TeVs (single-diffractive) = m F2 µ = R2 µ = 0.05 G S KMR UGDFIP+IRIPIR| < 8 c |y -factorization t k (GeV) ccT p ( nb / G e V ) cc T / dp σ d Xc p c → p p = 13 TeVs (single-diffractive) = m F2 µ = R2 µ = 0.05 G S KMR UGDFIP+IRIPIR| < 8 c |y -factorization t k Figure 3:
The distribution in φ c ¯ c (left panel) and distribution in p c ¯ cT (right panel) for k t -factorizationapproach at √ s = 13 TeV. The c ¯ c pair transverse momentum distribution p c ¯ cT = | ~ p ct + ~ p ct | is shown on the right panel.Results of the full phase-space calculations illustrate that the quarks and antiquarks inthe c ¯ c pair are almost uncorrelated in the azimuthal angle between them and are oftenproduced in the configuration with quite large pair transverse momenta. Figures 4 and Figure 4:
Double differential cross sections as a function of initial gluons transverse momenta k T and k T for single-diffractive production of charm at √ s =
13 TeV. The left and right panelscorrespond to the pomeron and reggeon exchange mechanisms, respectively. k T and k T ) and transverse momenta of outgoing c and ¯ c quarks ( p T and p T ), respectively. We observe quite large incident gluon transverse momenta. The majorpart of the cross section is concentrated in the region of small k t ’s of both gluons but longtails are present. Transverse momenta of the outgoing particles are not balanced as theywere in the case of the LO collinear approximation.
4. Conclusions
Charm production is a good example where the higher-order effects are very impor-4 iffractive production of heavy mesons
Marta Luszczak
Figure 5:
Double differential cross sections as a function of transverse momenta of outgoing c quark p T and outgoing ¯ c antiquark p T for single-diffractive production of charm at √ s = tant. For the inclusive charm production we have shown that these effects can be ef-fectively included in the k t -factorization approach [6]. In our approach we decided touse the so-called KMR method to calculate unintegrated diffractive gluon distribution.As usually in the KMR approach, we have calculated diffractive gluon UGDFs based oncollinear distribution, which in the present case is diffractive collinear gluon distribu-tion. In our calculations we have used the H1 Collaboration parametrization fitted tothe HERA data on diffractive structure function and di-jet production. Having obtainedunintegrated diffractive gluon distributions we have performed calculations of severalsingle-particle and correlation distributions. In some cases the results have been com-pared with the results obtained in the leading-order collinear approximation. In gen-eral, the k t -factorization approach leads to larger cross section. However, the K -factor isstrongly dependent on phase space point. Some correlation observables, like azimuthalangle correlation between c and ¯ c , and c ¯ c pair transverse momentum were obtained in [2]for the first time. References [1] M. Luszczak, R. Maciula and A. Szczurek, Phys. Rev. D (2015) no.5, 054024[arXiv:1412.3132 [hep-ph]].[2] M. Luszczak, R. Maciula, A. Szczurek and M. Trzebinski, arXiv:1606.06528 [hep-ph].[3] G. Ingelman, P.E. Schlein, Phys. Lett. B , 256 (1985).[4] V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C , 167 (2000) [hep-ph/0007359].[5] U. Maor, AIP Conf. Proc. , 248 (2009).[6] R. Maciula and A. Szczurek, Phys. Rev. D , 094022 (2013) [arXiv:1301.3033 [hep-ph]]., 094022 (2013) [arXiv:1301.3033 [hep-ph]].