From deep-inelastic structure functions to two-photon dilepton production in proton-proton collisions
aa r X i v : . [ h e p - ph ] J un From deep-inelastic structure functionsto two-photon dilepton productionin proton-proton collisions
Antoni Szczurek ∗ † Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152,PL-31-342 Kraków, PolandE-mail: [email protected]
Marta Łuszczak
Department of Theoretical Physics, University of Rzeszów, PL-35-959 Rzeszów, PolandE-mail: [email protected]
Wolfgang Schäfer
Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152,PL-31-342 Kraków, PolandE-mail: [email protected]
We compare two different approaches used for calculating cross sections for the two-photon pp → l + l − X process. In one of the approaches photon is treated as a collinear parton in theproton. In the second approach a recently proposed k T -factorization method is used. In this pre-sentation we discuss sensitivity of the results to the choice of structure function parametrizationand experimental cuts in the k T -factorization approach. We compare results of our calculationswith recent experimental data for dilepton production and find that in most cases the contributionof the photon-photon mechanism is rather small. We discuss how to enhance the photon-photoncontribution. We also compare our results to those of recent measurements of exclusive and semi-exclusive e + e − pair production with certain experimental data by the CMS collaboration. XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects11-15 April, 2016DESY Hamburg, Germany ∗ Speaker. † The work has been supported by the Polish National Science Center grant DEC-2014/15/B/ST2/02528. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ rom deep-inelastic structure functions
Antoni Szczurek
1. Introduction
In this presentation we show our recent results published in [1] where we have considered pp → ppl + l − (exclusive) and pp → l + l − (semiexclusive, with proton dissociation) double photonfusion processes in the proposed somewhat earlier k t -factorization approach [2]. In our presenta-tion at DIS2016 we have focussed on the relation of the cross section for the charged lepton pairproduction with the dependence of the deep-inelastic structure functions F , that are the input forour approach, on x and Q .The main mechanisms of the dilepton production considered in [1] are shown in Fig.1. Theconsidered mechanism has the same final state as the dominant Drell-Yan mechanism. For k t -factorization approach to the Drell-Yan see [3, 4, 5, 6]. In our recent paper [1] we discussed indetail the photon-photon mechanism. p p f elel f p p +−ll p p X X f ine +−llf ine p p f el f p +X ine
2l −l p p f el f +−X1 ine p ll Figure 1:
Different mechanisms of two-photon production of dileptons included in [1].
2. Basic formulae
In collinear approximation the cross sections are calculated as: d s g in g in dy dy d p t = p ˆ s x g i ( x , m ) x g j ( x , m ) | M gg → l + l − | , (2.1)where i,j=el,in and f i are photon PDFs. The elastic photon fluxes are calculated using the Drees-Zeppenfeld parametrization, where a simple parametrization of nucleon electromagnetic form fac-tors was used.In the k t -factorization approach the differential cross section can be written as: d s ( i , j ) dy dy d p d p = Z d q p q d q p q F ( i ) g ∗ / A ( x , q ) F ( j ) g ∗ / B ( x , q ) d s ∗ ( p , p ; q , q ) dy dy d p d p , (2.2) where i,j=el,ine and F k are unintegrated fluxes of photons. As shown in [1] the unintegrated fluxescan be expressed in terms of the (deep-inelastic) structure functions F ( x , Q ) .1 rom deep-inelastic structure functions Antoni Szczurek
3. Numerical results
In our studies in [1] we have used a few different parametrizations of the proton structurefunction F taken from the literature: • ALLM [8, 9]. This parametrization gives a very good fit to F in most of the measured region. • FJLLM [10]. This parametrization explicitly includes the nucleon resonances and gives anexcellent fit of the CLAS data. • BDH [11]. This parametrization concentrates on the low- x , or high mass region. It featuresa Froissart-like behaviour at very small x . • SY [12]. This paramerization of Suri and Yennie from the early 1970’s does not includeQCD-DGLAP evolution. It is still today often used as one of the defaults in the LPAIR eventgenerator. • SU [13]. A parametrization which concentrates to give a good description at rather small andintermediate Q at not too small x .We also show F calculated from the CTEQ6L parametrization [14].In Fig.2 we show only two examples of the proton structure function F ( x , Q ) obtained fromthe various parametrizations at Q = . , . as a function of Bjorken- x .It is surprising that the old Suri-Yennie [12] fit, still gives a reasonable description of F exceptof very small x . For explicit account of resonances we recommend to use the Fiore et al. [10], butcare has to be taken to stay within the resonance region, as the quality of the fit beyond this regionquickly deteriorates. The overall best description appears to be given by the ALLM [8, 9] fit. Figure 2:
The proton structure function F ( x , Q ) as a function of x for Q = . (left), and Q = . (right). Shown are results for different parmetrizations available in the literature. In Ref.[1] we have compared our calculations with measured dilepton data [15, 16, 17, 18, 19].Here we show only a few examples.Most of the experiments for the dilepton production concentrate on determination of dileptoninvariant mass distributions. In Fig.3 we show invariant mass distributions of dilepton pairs pro-duced in the photon-photon inelastic-inelastic mechanism for kinematical conditions relevant for2 rom deep-inelastic structure functions
Antoni Szczurek different experiments. We show results obtained with the different parametrizations of the struc-ture functions known from the literature. Surprisingly the different structure functions give quitedifferent results. For completeness in some cases we also show the result obtained in the collinearapproach with the MRST2004(QED) photon distribution [7] with (solid black line) and similar onewhen ignoring the initial input (long-dashed black line). The result obtained within the collinearapproach with the MRST2004(QED) distribution is much above the results obtained within the k t -factorization approach. In our opinion this is mainly related to the large input photon distributionat the initial scale Q = 2 GeV . If the input is discarded (long-dashed black line) the collinearresult is similar to the results obtained within the k T -factorization. The inelastic-inelastic contri-bution gives only a small fraction of the measured cross section for most experimental conditions(ATLAS,LHCb). (GeV) - m + m M ( pb / G e V ) - m + m / d M s d - - - - - - - - - = 7 TeVs X - m + m fi p p £ – m y £ -2.5 15 GeV ‡ p ATLAS data SU BDHSYFFJLMALLM inelastic-inelastic collinear MRST04 QEDcollinear (without input) (GeV) - m + m M ( pb / G e V ) - m + m / d M s d - - - - = 7 TeVs X - m + m fi p p £ – m y £ ‡ p LHCb data SU BDHSYFFJLMALLM inelastic-inelastic collinear MRST04 QEDcollinear (without input)
Figure 3:
The inelastic-inelastic contribution to dilepton invariant mass distributions for ATLAS (left) andLHCb (right) experiments for different structure functions.
In Fig.4 we show dilepton invariant mass distributions for elastic-inelastic and inelastic-elastic(added together) contributions. As for inelastic-inelastic contribution the results strongly dependon the parametrization of the structure functions used. The spread of results for different F fromthe literature is now somewhat smaller than in the case of inelastic-inelastic contributions wherethe structure functions enter twice. As for the double inelastic case we also show a result for thecollinear approach. The mixed components give similar contribution to the dilepton invariant massdistributions as the inelastic-inelastic one.In most of the cases considered so far Drell-Yan processes dominate [4, 5, 6]. The two-photon processes are interesting by themselves. Can they be measured? In order to reduce theDrell-Yan contribution and relatively enhance the two-photon contribution one can impose an extracondition on lepton isolation. First trials have been done by the CMS collaboration [20]. In theiranalysis an extra lepton isolation cuts were imposed in order to eliminate the dominating Drell-Yancomponent. In Figs. 5,6,7 we show our results for two different (SY and ALLM) parametrizationsof the structure functions for distributions in dimuon invariant mass, in transverse momentum ofthe pair and in relative azimuthal angle between m + m − . SY and ALLM parametrizations givealmost the same contributions to all the distributions considered. In the first evaluation we havetaken into account integrated luminosity of the experiment ( L = 63.2 pb − ) as well as experimentalacceptances given in Ref.[20]. Rather good agreement with the low statistics CMS experimentaldata is achieved without including any extra corrections due to absorption effects. It may mean that3 rom deep-inelastic structure functions Antoni Szczurek (GeV) - m + m M ( pb / G e V ) - m + m / d M s d - - - - - - - - - = 7 TeVs X - m + m fi p p £ – m y £ -2.5 15 GeV ‡ p ATLAS data SU BDHSUFFJLMALLMelastic-inelastic + inelastic-elastic collinear MRST04 QEDcollinear (without input) (GeV) - m + m M ( pb / G e V ) - m + m / d M s d - - - - = 7 TeVs X - m + m fi p p £ – m y £ ‡ p LHCb data SU BDHSYFFJLMALLM elastic-inelastic + inelastic-elastic collinear MRST04 QEDcollinear (without input)
Figure 4:
The (elastic-inelastic)+(inelastic-elastic) contribution to dilepton invariant mass distributions forATLAS (left) and LHCb (right) experiments for different structure functions. the absorption effects are small or alternatively that a contamination of the Drell-Yan contributionis still not completely removed. Both effects should be therefore studied in detail in a future. (GeV) - e + e M E v en t s / G e V - - = 7 TeVs X - e + e fi p p £ – e y £ -2.5 5.5 GeV ‡ p CMS dataSY F2 inelastic-inelastic elastic-inelastic + inelastic-elastic elastic-elasticsum (GeV) - e + e M E v en t s / G e V - - = 7 TeVs X - e + e fi p p £ – e y £ -2.5 5.5 GeV ‡ p CMS dataALLM F2 inelastic-inelastic elastic-inelastic + inelastic-elastic elastic-elasticsum
Figure 5:
Number of events per invariant mass interval for the CMS experimental cuts for SY (left) andALLM (right) structure functions. The experimental data points are from Ref.[20]. (GeV) ) - e + T(e p E v en t s / G e V - - = 7 TeVs X - e + e fi p p £ – e y £ -2.5 5.5 GeV ‡ p CMS dataSY F2 inelastic-inelastic elastic-inelastic + inelastic-elastic elastic-elasticsum (GeV) ) - e + T(e p E v en t s / G e V - - = 7 TeVs X - e + e fi p p £ – e y £ -2.5 5.5 GeV ‡ p CMS dataALLM F2 inelastic-inelastic elastic-inelastic + inelastic-elastic elastic-elasticsum
Figure 6:
Number of events per pair transverse momentum interval for the CMS experimental cuts for SY(left) and ALLM (right) structure functions. The experimental data points are from Ref.[20]. rom deep-inelastic structure functions Antoni Szczurek (rad) - e + e f E v en t s / . r ad - - = 7 TeVs X - e + e fi p p £ – e y £ -2.5 5.5 GeV ‡ p CMS dataSY F2 inelastic-inelastic elastic-inelastic + inelastic-elastic elastic-elasticsum (rad) - e + e f E v en t s / . r ad - - = 7 TeVs X - e + e fi p p £ – e y £ -2.5 5.5 GeV ‡ p CMS dataALLM F2 inelastic-inelastic elastic-inelastic + inelastic-elastic elastic-elasticsum
Figure 7:
Number of events per pair relative azimuthal angle interval for the CMS experimental cut for SY(left) and ALLM (right) structure functions. The experimental data points are from Ref.[20].
4. Conclusions
We summarize our studies in [1] as follows: • Two different approaches (collinear and k t -factorization) for gg → l + l − processes were dis-cussed and compared. • Strong dependence on the structure function input in the k t -factorization approach werefound. • Semi-exclusive contributions with proton dissociation is large (this may be interesting lessonfor other processes such as e.g. the pp → ppJ / y reaction). • Photon-photon contribution is rather small compared to Drell-Yan contribution but is impor-tant in precision calculations. • Reasonable description of the CMS data with isolated electrons was achieved (recently alsoATLAS obtained similar result). • The regions of the arguments of the structure function F important for the discussed gg → l + l − process was identified. • So far only collinear approach was applied to pp → ( gg ) → W + W − XY processes which isimportant in searches for Beyond Standard Model effects. References [1] M. Luszczak, W. Schäfer and A. Szczurek, “Two-photon dilepton production in proton-protoncollisions: Two alternative approaches”, Phys. Rev.
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