New single- and double-parton scattering mechanisms for double charmed meson production
Antoni Szczurek, Rafal Maciula, Vladimir A. Saleev, Alexandra V. Shipilova
aa r X i v : . [ h e p - ph ] J un New single- and double-parton scatteringmechanisms for double charmed meson production
Antoni Szczurek ∗ † Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152,PL-31-342 Kraków, PolandE-mail: [email protected]
Rafał Maciuła
Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152,PL-31-342 Kraków, PolandE-mail: [email protected]
Vladimir A. Saleev
Samara National Research University, Moscow Highway, 34, 443086, Samara, RussiaE-mail: [email protected]
Alexandra V. Shipilova
Samara National Research University, Moscow Highway, 34, 443086, Samara, RussiaE-mail: [email protected]
We discuss charm meson-meson pair production recently observed by the LHCb Collaborationat √ s = 7 TeV in proton-proton scattering. We examine double-parton scattering (DPS) mecha-nisms of double c ¯ c production and following cc → D D hadronization as well as double g andmixed gc ¯ c production with gg → D D and gc → D D hadronization calculated with the helpof the scale-dependent KKKS08 fragmentation functions. A new single-parton scattering (SPS)mechanism of gg production is also taken into consideration. Calculated differential distributionsas a function of transverse momentum p T of one of the D mesons, pair invariant mass M D D andazimuthal angle j D D distributions are confronted with the measured ones. The manifestation ofthe new SPS mechanisms with g → D fragmentation within the scale-dependent fragmentationscheme change the overall picture suitable for standard scale-independent fragmentation whereonly DPS cc → D D mechanism is present. Some consequences of the new mechanisms arediscussed. 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/ ouble charm meson production at the LHC
Antoni Szczurek
1. Introduction
At present, double charm production is expected to be one of the most promising channels forstudies of double-parton scattering (DPS) effects at the LHC. This was predicted [1] and furthersupported by the experimental observations reported by the LHCb Collaboration [2]. Next, the phe-nomenology of DD meson-meson pair production was carefully examined in the k t -factorizationapproach and a relatively good description of the LHCb experimental data was achieved for boththe total yield and the dimeson correlation observables [3]. In the theoretical analyses, both,single- and double-parton scattering mechanisms were taken into consideration. The contribu-tion of single-parton scattering (SPS) mechanism gg → c ¯ cc ¯ c , discussed in detail in the collinear [4]and k t -factorization [5] approaches, was found to be rather small and definitely not able to describerelatively large DD cross sections measured by the LHCb.The phenomenological studies of the DD pair production were based on the rather standardfragmentation scheme with scale-independent Peterson fragmentation function (FF) [6], whereonly c → D transition is included. However, an alternative approach is to apply scale-dependentFFs that undergo DGLAP evolution equations, e.g. KKKS08 model [7], where each parton (gluon, u , d , s , ¯ u , ¯ d , ¯ s , c , ¯ c ) can contribute to D meson production. In the latter scenario, the c → D con-tribution is reduced by the evolution of the FF but a very important contribution from g → D fragmentation appears (see e.g. Ref. [8]).In this presentation we report on first investigation how important is the gluon fragmentationmechanism for the double D -meson production.
2. A sketch of the theoretical formalism
RR c ¯ cRR c ¯ c RR gRR g
RR gc ¯ cRR RR gg
Figure 1:
A diagrammatic illustration of the considered mechanisms.
We will compare numerical results for double D -meson production obtained with the twodifferent fragmentation schemes. In the (new) scenario with scale-dependent KKKS08 FFs and g → D fragmentation the number of contributing processes grows compared to the standard (old)scenario with c → D fragmentation only. According to the new scenario one has to consider moreprocesses for single D meson production ( c and g → D components). This also causes an extensionof the standard DPS DD pair production by new mechanisms. In addition to the coventional DPS cc → DD (left diagram in Fig.1) considered in Refs. [3, 4, 5] there is a double g → D (or double g → ¯ D ) fragmentation mechanism, called here DPS gg → DD (middle-left diagram in Fig.1) aswell as the mixed DPS gc → DD contribution (middle-right diagram in Fig.1).1 ouble charm meson production at the LHC Antoni Szczurek
As a consequence of the new approach a new SPS gg → DD mechanism shows up (right dia-gram in Fig.1). In this case the two produced gluons are correlated in azimuth and the mechanismwill naturally lead to an azimuthal correlation between the two D mesons. Such a correlation wasactually observed in the LHCb experimental data [2] and could not be explained by the SPS 2 → gg → c ¯ cc ¯ c contribution (see e.g. Ref. [5]) which is very small.DPS cross section for production of cc , gg or gc system, assuming factorization of the DPSmodel, can be written as: d s DPS ( pp → ccX ) dy dy d p , t d p , t = s e f f · d s SPS ( pp → c ¯ cX ) dy d p , t · d s SPS ( pp → c ¯ cX ) dy d p , t , (2.1) d s DPS ( pp → ggX ) dy dy d p , t d p , t = s e f f · d s SPS ( pp → gX ) dy d p , t · d s SPS ( pp → gX ) dy d p , t . (2.2) d s DPS ( pp → gcX ) dy dy d p , t d p , t = s e f f · d s SPS ( pp → gX ) dy d p , t · d s SPS ( pp → c ¯ cX ) dy d p , t . (2.3)The often called pocket-formula is a priori a severe approximation. The flavour, spin and colorcorrelations lead, in principle, to interference effects that result in its violation as discussed e.g.in Ref. [9]. Even for unpolarized proton beams, the spin polarization of the two partons from onehadron can be mutually correlated, especially when the partons are relatively close in phase space(having comparable x ’s). Moreover, in contrast to the standard single PDFs, the two-parton distribu-tions have a nontrivial color structure which also may lead to a non-negligible correlations effects.Such effects are usually not included in phenomenological analyses. They were exceptionally dis-cussed in the context of double charm production [10]. However, the effect on e.g. azimuthalcorrelations between charmed quarks was found there to be very small, much smaller than effectsof the SPS contribution associated with double gluon fragmentation discussed here. In addition,including perturbative parton splitting mechanism also leads to a breaking of the pocket-formula[11]. This formalism was so far formulated for the collinear leading-order approach which forcharm (double charm) may be a bit academic as this leads to underestimation of the cross section.Imposing sum rules also leads to a breaking of the factorized Ansatz but the effect almost vanishesfor small longitudinal momentum fractions [12]. Taken the above we will use the pocket-formulain the following.All the considered mechanisms (see Fig. 1) are calculated in the k t -factorization approach withoff-shell initial state partons and unintegrated ( k t -dependent) PDFs (unPDFs). Fully gauge invari-ant treatment of the initial-state off-shell gluons and quarks can be achieved in the k t -factorizationapproach only when they are considered as Reggeized gluons or Reggeons. The relevant Reggeizedamplitudes can be presented using Fadin-Kuraev-Lipatov effective vertices. The useful analyticalformulae for | M RR → g | , | M RR → gg | and | M RR → c ¯ c | squared amplitudes used in the calculationshere can be found in Refs. [8, 13]. We use the LO Kimber-Martin-Ryskin (KMR) unPDFs, gener-ated from the LO set of a up-to-date MMHT2014 collinear PDFs fitted also to the LHC data. In theperturbative part of the calculations we use a running LO a S provided with the MMHT2014 PDFs.The charm quark mass is set to m c = . ouble charm meson production at the LHC Antoni Szczurek equal to m = p t for RR → g subprocess, to the averaged transverse momentum m = ( p t + p t ) / RR → gg , and to the averaged transverse mass m = ( m t + m t ) / RR → c ¯ c case, where m t = p p t + m c (for more details see Ref.[14]).In order to calculate correlation observables for two mesons we follow here, similar as in thesingle meson case, the fragmentation function technique for hadronization process: d s DPS ( pp → DDX ) dy dy d p D t d p D t = Z D c → D ( z , m ) z · D c → D ( z , m ) z · d s DPS ( pp → ccX ) dy dy d p c t d p c t dz dz + Z D g → D ( z , m ) z · D g → D ( z , m ) z · d s DPS ( pp → ggX ) dy dy d p g t d p g t dz dz + Z D g → D ( z , m ) z · D c → D ( z , m ) z · d s DPS ( pp → gcX ) dy dy d p g t d p c t dz dz , (2.4)where: p g , c t = p D , t z , p g , c , t = p D t z and meson momentum fractions z , z ∈ ( , ) .The same formula for SPS DD -production via fragmentation of each of the gluon reads d s SPSgg ( pp → DDX ) dy dy d p D t d p D t ≈ Z D g → D ( z , m ) z · D g → D ( z , m ) z · d s SPS ( pp → ggX ) dy dy d p g t d p g t dz dz , (2.5)where: p g t = p D , t z , p g , t = p D t z and meson momentum fractions z , z ∈ ( , ) .
3. Comparison to the LHCb data
Before we start a comparison of the theoretical results with the LHCb double charm datawe wish to stress that the both fragmentation schemes considered here lead to a very good (andvery similar) description of the LHCb data for inclusive single D meson production [14]. So bothprescriptions together with the k t -factorization approach seem to be a good and legitimate startingpoints for double charm production studies. (GeV)p ( nb / G e V ) / dp s d -1 ) X D (D fi p p = 7 TeVs < 4.0 D = 0.05 c e Peterson FF:
KMR MMHT2014lo = 15 mb eff s D D fi DPS cc
LHCb (GeV)p ( nb / G e V ) / dp s d -1 ) X D (D fi p p = 7 TeVs < 4.0 D SUM = 30 mb eff s D D fi DPS gc + cg D D fi DPS cc D D fi SPS gg D D fi DPS gg
LHCb
KKKS08 FF with DGLAP evolution
Figure 2: D meson transverse momentum distribution within the LHCb acceptance region. The left panelis for the first scenario and for Peterson c → D fragmentation function while the right panel is for the secondscenario and for the fragmentation function that undergo DGLAP evolution equation. ouble charm meson production at the LHC Antoni Szczurek
Now we wish to compare results of our theoretical approach for double charm production de-scribed briefly in the previous section with the LHCb experimental data for D D pair production.In Fig. 2 we compare results of our calculation with experimental distribution in transverse momen-tum of one of the meson from the D D pair. We show results for the first scenario when standardPeterson FF is used for the c → D fragmentation (left panel) as well as the result for the secondscenario when the KKKS08 FFs with DGLAP evolution for c → D and g → D are used. Onecan observe that the DPS cc → D D contribution in the new scenario is much smaller than in theold scenario. In addition, the slope of the distribution in transverse momentum changes. Both theeffects are due to evolution of corresponding FF in the second scenario, compared to lack of suchan effect in the first scenario. The different new mechanisms shown in Fig. 1 give contributionsof similar size. We can obtain a better agreement in the second case provided s e f f parameter isincreased from 15 mb to 30 mb. Even then we overestimate the LHCb data for 3 < p T < (GeV) D D M ( nb / G e V ) D D / d M s d -1 ) X D (D fi p p = 7 TeVs < 4.0 D D D fi DPS cc = 0.05 c e Peterson FF:
KMR MMHT2014lo = 15 mb eff s LHCb (GeV) D D M ( nb / G e V ) D D / d M s d -1 ) X D (D fi p p = 7 TeVs < 4.0 D SUM = 30 mb eff s D D fi DPS gc + cg D D fi DPS cc D D fi SPS gg D D fi DPS gg
KKKS08 FF with DGLAP evolution
LHCb
Figure 3:
The same as in the previous figure but for M D D dimeson invariant mass distribution. p |/ jD | | ( nb ) jD / d | s d p LHCb ) X D (D fi p p = 7 TeVs < 4.0 D = 0.05 c e Peterson FF:
KMR MMHT2014lo = 15 mb eff s D D fi DPS cc < 12 GeV3 < p p |/ jD | | ( nb ) jD / d | s d p LHCb ) X D (D fi p p = 7 TeVs < 4.0 D SUM = 30 mb eff s D D fi DPS gc + cg D D fi DPS cc D D fi SPS gg D D fi DPS gg
KKKS08 FF with DGLAP evolution < 12 GeV3 < p
Figure 4:
The same as in the previous figure but for the distribution in azimuthal angle j D D . In Fig. 3 we show dimeson invariant mass distribution M D D again for the two cases con-sidered. In the first scenario we get a good agreement only for small invariant masses while inthe second scenario we get a good agreement only for large invariant masses. The large invari-ant masses are strongly correlated with large transverse momenta, so the situation here (for theinvariant mass distribution) is quite similar as in Fig. 2 for the transverse momentum distribution.In Fig. 4 we show azimuthal angle correlation j D D between D and D . While the correlationfunction in the first scenario is completely flat, the correlation function in the second scenario shows4 ouble charm meson production at the LHC Antoni Szczurek some tendency similar as in the experimental data. The observed overestimation comes from theregion of small transverse momenta.
4. Conclusions
In the present paper we have discussed production of D D pairs in proton-proton collisions atthe LHC. We have considered the DPS mechanism of double c ¯ c production and subsequent doublehadronization of two c quarks or two ¯ c antiquarks using c → D or c → ¯ D FFs that undergoDGLAP evolution. Furthermore, we have included also production of gg (both SPS and DPS) andDPS gc final states and their subsequent hadronization to the neutral pseudoscalar D mesons.When added together the new mechanisms with adjusted s e f f give similar result as in the firstscenario with one subprocess ( cc → DD ) and scale-independent FF. However, some correlationobservables, such as dimeson invariant mass or azimuthal correlations between D mesons, areslightly better described.In our calculation, within the second scenario a larger value of s e f f is needed to describethe LHCb data than found from the review of several experimental studies of different processes.This can be partially understood by a lower contribution of perturbative-parton splitting as foundin Ref. [11] and/or due to nonperturbative correlations in the nucleon which may lead to transversemomentum dependent s e f f . Clearly more involved studies are needed to understand the situationin detail. Some problem may be also related to the fact that the FFs used in the second scenariowere obtained in the DGLAP formalism with massless c quarks and ¯ c antiquarks which may bea too severe approximation, especially for low factorization scales (i.e. low transverse momenta).We expect that including mass effects in the evolution would lower the g → c fragmentation.The presence of the new SPS mechanism may mean that the extraction of s e f f directly fromthe LHCb experimental data [2] may be not correct.For more references and details of the calculations presented here we refer the reader to ourregular article [14]. References [1] M. Luszczak, R. Maciula and A. Szczurek, Phys. Rev. D , 094034 (2012).[2] R. Aaij et al. [LHCb Collaboration], JHEP , 141 (2012) Addendum: [JHEP , 108 (2014)].[3] R. Maciula and A. Szczurek, Phys. Rev. D , 074039 (2013) [arXiv:1301.4469 [hep-ph]].[4] A. van Hameren, R. Maciula and A. Szczurek, Phys. Rev. D , 094019 (2014).[5] A. van Hameren, R. Maciula and A. Szczurek, Phys. Lett. B , 167 (2015).[6] C. Peterson, D. Schlatter, I. Schmitt and P. M. Zerwas, Phys. Rev. D , 105 (1983).[7] T. Kneesch, B. A. Kniehl, G. Kramer and I. Schienbein, Nucl. Phys. B , 34 (2008).[8] A. V. Karpishkov, M. A. Nefedov, V. A. Saleev and A. V. Shipilova, Phys. Rev. D , 054009 (2015).[9] M. Diehl, D. Ostermeier and A. Schafer, JHEP , 089 (2012).[10] M. G. Echevarria, T. Kasemets, P. J. Mulders and C. Pisano, JHEP , 034 (2015).[11] J. R. Gaunt, R. Maciula and A. Szczurek, Phys. Rev. D , 054017 (2014).[12] K. Golec-Biernat, et al., Phys. Lett. B , 559 (2015).[13] M. A. Nefedov, V. A. Saleev and A. V. Shipilova, Phys. Rev. D , 094030 (2013).[14] R. Maciula, V. A. Saleev, A. V. Shipilova and A. Szczurek, Phys. Lett. B , 458 (2016)., 458 (2016).