Production of charmed meson-meson pairs at the LHC: Single- versus double-parton scattering mechanisms
aa r X i v : . [ h e p - ph ] O c t Proceedings of the Second Annual LHCPJuly 24, 2018
PRODUCTION OF CHARMED MESON-MESON PAIRS AT THE LHC:SINGLE- VERSUS DOUBLE-PARTON SCATTERING MECHANISMS
RAFAL MACIULA and ANTONI SZCZUREK Institute of Nuclear Physics PAN, PL-31-342 Cracow, Polandand University of Rzesz´ow, PL-35-959 Rzesz´ow, Poland
ABSTRACTWe discuss hadroproduction of open charmed mesons ( D , D ± , D ± S ) at the LHCenergy √ s = 7 TeV. The cross section for inclusive production of cc pairs iscalculated within the k ⊥ -factorization (or high-energy factorization) approachwhich effectively includes higher-order corrections. Results of the k ⊥ -factorizationapproach are compared to NLO parton model predictions. The hadronization ofcharm quarks is included with the help of the Peterson fragmentation functions.Inclusive differential distributions in (pseudo)rapidity and transverse momentumfor several charmed mesons are calculated and compared to recent results of theALICE, ATLAS and LHCb experiments. We also take into consideration amechanism of double charm (two pairs of cc ) production within a simpleformalism of double-parton scattering (DPS). Surprisingly for LHC energies theDPS cross sections are found to be larger than those from the standard SPSmechanism. We compare our predictions for DD meson-meson pair productionwith recent measurements of the LHCb collaboration, including correlationobservables. Our calculations clearly confirm the dominance of DPS in theproduction of double charm, however some strength seems to be still lacking.Possible missing contribution from the so-called single-ladder-splitting DPSmechanism is also discussed.PRESENTED ATThe Second Annual Conferenceon Large Hadron Collider PhysicsColumbia University, New York, U.S.AJune 2-7, 2014 This work was supported in part by the Polish grants DEC-2011/01/B/ST2/04535 and DEC-2013/09/D/ST2/03724 aswell as by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzesz´ow.
Introduction
Inclusive distributions for different species of pseudoscalar D and vector D ∗ open charm meson have beenmeasured recently by ATLAS [1], ALICE [2] and LHCb [3] experiments. The LHCb group has also performedmore exclusive studies of correlation observables for DD pairs in the forward rapidity region 2 < y < k t -factorization approach is commonly used as a very efficient tool for more exclusive studiesof kinematical correlations between produced particles (see e.g. [5] and references therein). In this approachthe transverse momenta of incident partons are taken into account and their emission is described by theso-called unintegrated gluon distribution functions (UGDFs). This allows to construct different correlationdistributions which are strictly related to the transverse momenta of incident particles.It was concluded recently that the cross section for cccc production at the LHC may be very large due tomechanism of double-parton scattering (DPS) [6]. Meanwhile, the LHCb collaboration measured unexpect-edly large cross section for the production of DD meson-meson pairs at √ s = 7 TeV [4]. Those data sets fordouble open charm production have been studied differentially only within the k ⊥ -factorization approach,where several correlation observables useful to identify the DPS effects have been carefully discussed. In or-der to draw definite conclusions about the DPS effects in double charm production it is necessary to estimateprecisely contribution to cccc final state from the standard mechanism of single-parton scattering [8]. The cross section for the production of a pair of charm quark – charm antiquark within the k t -factorizationapproach can be written as: dσ ( pp → ccX ) dy dy d p t d p t = 116 π ˆ s Z d k t π d k t π |M offshell | × δ (cid:16) ~k t + ~k t − ~p t − ~p t (cid:17) F g ( x , k t , µ ) F g ( x , k t , µ ) . (1)The essential components in the formula above are off-shell matrix elements for g ∗ g ∗ → c c subprocess andunintegrated (transverse momentum dependent) gluon distributions (UGDF). The relevent matrix elementsare known and can be found, e.g in Ref. [9]. The unintegrated gluon distributions are functions of longitudinalmomentum fraction x or x of gluon with respect to its parent nucleon and of gluon transverse momenta k t . Some of them depend in addition on the factorization scale µ . In contrast to the collinear gluondistributions (PDFs) they differ considerably among themselves. One may expect that they will lead todifferent production rates of cc pairs at the LHC. Since the production of charm quarks is known to bedominated by the gluon-gluon fusion, the charm production in hadronic reactions at the LHC can be usedto verify the quite different models of UGDFs.The hadronization of heavy quarks is done with the help of fragmentation functions technique, using thestandard Peterson model [10], normalized to the proper branching fractions from Ref. [11].In Fig. 1 we show transverse momentum distribution of D mesons. In the left panel we present resultsfor different UGDFs known from the literature. Most of the UGDFs applied here fail to describe the ALICEdata. The KMR UGDF [12] provides the best description of the measured distributions. Therefore in thefollowing we shall concentrate only on the calculations based on the KMR UGDF. In the right panel weshow the uncertainties of our predictions due to the charm quark mass m c = 1 . ± . µ = ζm t , where ζ ∈ (0 .
5; 2). The gray shaded bands representthese both sources of uncertainties summed in quadrature. In addition, the results of relevant calculationswithin the LO and NLO collinear approach are presented for comparison. The k t -factorization approachwith the KMR UGDF is consistent with the NLO collinear calculations.The left panels of Fig. 2 shows transverse momentum (top) and pseudorapidity (bottom) distributionsof charged pseudoscalar D ± mesons measured by the ATLAS experiment. Overall situation is very similaras for the ALICE case except of the agreement with the experimental data points, which is somewhat worsehere. Only the very upper limit of the KMR result is consistent with the ATLAS data. This is also truefor the other standard collinear NLO pQCD approaches. The worse description of the ATLAS data may be1 (GeV)p b / G e V ) µ ( / dp σ d -1 X D → p p = 7 TeVs | < 0.5 D |y = m µ = 0.05 c ε Peterson FF ALICE
KMRJung setA+Jung setA0Jung setA-Jung setB+KMSKutak-Stasto (GeV)p b / G e V ) µ ( / dp σ d -1 ALICE X D → p p = 7 TeVs | < 0.5 D |y MSTW08 = 0.02 c ε Peterson FF -fact. t KMR kFONLLNLO PMLO PM
Figure 1:
Transverse momentum distribution of D meson for different UGDFs (left) and for the KMR UGDFcompared to the pQCD collinear calculations (right) together with the ALICE data. (GeV)p b / G e V ) µ ( / dp σ d -1 ATLAS
Preliminary ) X - + D + (D → p p = 7 TeVs | < 2.1 D η | = m µ MSTW08 = 0.02 c ε Peterson FF -fact. t KMR kFONLLNLO PMLO PM (GeV)p b / G e V ) µ ( / dp σ d LHCb Preliminary ) X S- + D S+ (D → p p = 7 TeVs < 4.5 D = m µ MSTW08 = 0.05 c ε Peterson FF -fact. t KMR kFONLLNLO PMLO PM D η b ) µ | ( D η / d | σ d ATLAS
Preliminary ) X - + D + (D → p p = 7 TeVs ≥ p = m µ = 0.02 c ε Peterson FF -fact. t KMR kFONLLNLO PM y b ) µ / d y ( σ d LHCb Preliminary ) X S- + D S+ (D → p p = 7 TeVs < 8 GeV0 < p = m µ = 0.05 c ε Peterson FF -fact. t KMR kFONLLPythiaJung setA+
Figure 2:
Transverse momentum (top) and (pseudo)rapidity (bottom) distribution of D ± meson for the ATLASexperiment (left) and of D ± S meson for the LHCb experiment (right). Together with our predictions for the KMRUGDF (solid line with shaded band). Results of pQCD collinear approaches are also shown. caused by much broader range of pseudorapidities than in the case of the ALICE detector. Potentially, thiscan be related to double-parton scattering (DPS) effects [7].Recently the LHCb collaboration presented first results for the production of different D mesons in inthe forward rapidity region 2 < y < .
5. In this case one can test asymmetric configuration of gluonlongitudinal momentum fractions: x ∼ − and x > − . Standard collinear gluon distributions as wellas unintegrated ones were never tested at such small values of x . In the right panels of Fig. 2 we presentdistributions corresponding to the ATLAS case but for D ± s meson. The main conclusions are the same asfor ALICE and ATLAS conditions. Our results with the KMR UGDF within uncertainties are consistent(with respect to the upper limits) with the experimental data and with the NLO collinear predictions.2 Single- and double-parton scattering effects in DD meson-mesonpair production at the LHC c ¯ cc ¯ cp p x x x ′ x ′ c ¯ cc ¯ cp p x x x ′ x ′ c ¯ cc ¯ cp p x x x ′ x ′ Figure 3:
The standard (left) and single-ladder-splitting (middle and right) diagrams for DPS production of cccc . Production of cccc (4-parton) final state is particularly interesting especially in the context of experimentsbeing carried out at the LHC and has been recently carefully discussed [6, 7]. The double-parton scatteringformalism in the simplest form assumes two independent standard single-parton scatterings (see left diagramof Fig. 3). Then in a simple probabilistic picture, in the so-called factorized Ansatz, the differential crosssection for DPS production of cccc system in the k ⊥ -factorization approach can be written as: dσ DP S ( pp → ccccX ) dy dy d p ,t d p ,t dy dy d p ,t d p ,t = 12 σ eff · dσ SP S ( pp → ccX ) dy dy d p ,t d p ,t · dσ SP S ( pp → ccX ) dy dy d p ,t d p ,t . (2)This formula assumes that the two subprocesses are not correlated and do not interfere. The parameter σ eff in the denominator of the above formula from a phenomenological point of view is a non-perturbativequantity related to the transverse size of the hadrons and has the dimension of a cross section. The depen-dence of σ eff on the total energy at fixed scales is rather small and one expect, that the value should beequal to the total non-diffractive cross section, if the hard-scatterings are really uncorrelated. More detailsof the theoretical framework for DPS mechanism applied here can be found in Ref. [7]. (GeV)p ( nb / G e V ) / dp σ d -1 LHCb ) X D (D → p p = 7 TeVs < 4.0 D = 0.02 c ε Peterson FF
DPS + SPSDPSSPS (GeV) D D M ( nb / G e V ) D D / d M σ d -1 LHCb ) X D (D → p p = 7 TeVs < 4.0 D = 0.02 c ε Peterson FF
DPS + SPSDPSSPS
Figure 4:
Distributions in meson transverse momentum when both mesons are measured within the LHCb acceptanceand corresponding distribution in meson-meson invariant mass for DPS and SPS contributions.
In Fig. 4 we show distributions in meson transverse momentum (left panel) and meson-meson invariantmass (right panel). The shape in the transverse momentum is almost correct but some cross section is lacking.In the case of the DD invariant mass distribution one can also see some lacking strength at large invariantmasses. In both cases, the SPS contribution (dash-dotted line) is compared to the DPS one (dashed line).The dominance of the DPS mechanism in description of the LHCb double charm data is clearly confirmed.The DPS mechanism gives a sensible explanation of the measured distribution, however some strength isstill missing. This can be due to the single-ladder-splitting mechanisms discussed recently in Ref. [13].3 |/ ϕ∆ | | ( nb ) ϕ ∆ / d | σ d π LHCb data ) X D (D → p p ) X D (D → p p = 7 TeVs < 4.0 D X)cccDPS + SPS (c X)c-fact. (c t KMR k y| ∆ | y | ( nb ) ∆ / d | σ d LHCb data ) X D (D → p p ) X D (D → p p = 7 TeVs < 4.0 D X ) ccc D PS + SPS ( c X ) c - f a c t. ( c t K M R k Figure 5:
Azimuthal angle correlation between D D and D D (left) and distribution in rapidity distance betweentwo D mesons and between D D . In Fig. 5 we compare correlations for D D and D D in azimuthal angle (left panel) and in rapiditydistance (right panel). In the case of the azimuthal angle distribution the experimental data suggest somesmall correlations at small and large angles in contrast to the flat result of the standard DPS calculation. Inaddition, the azimuthal angle distribution for identical mesons is somewhat flatter than that for D D whichis consistent with the claim of the dominance of the DPS contribution. The rapidity distance distributionfor D D falls down somewhat faster than in the case of identical D mesons.Recently, it has been found that there are (at least) two different types of contribution to the DPS crosssection, which are accompanied by different geometrical prefactors ( σ eff, v and σ eff, v ) (see e.g. [15]).One of these is the standard conventional contribution (2v2) in which two separate ladders emerge fromboth protons and interact in two separate hard interactions (see the left panel of Fig. 3). This is the onethat is often considered in phenomenological analyses and has been applied in the studies presented above.The other type of process is the perturbative single-ladder-splitting (2v1) which is similar to the con-ventional mechanism except that one proton initially provides one ladder, which perturbatively splits intotwo (see the middle and right diagrams in Fig. 3). Recently, the relative importance of the conventional andsingle-ladder-splitting DPS processes has been studied in Ref. [14]. (GeV) t p ( m b / G e V ) t / dp σ d -6 -5 -4 -3 -2 -1 Xc c c c → DPS: p p = 7 TeVs ≤ | c |y = m µ , = m µ = 1.5 GeV c m y -8 -6 -4 -2 0 2 4 6 8 / d y ( m b / G e V ) σ d -5 -4 -3 -2 -1 Xc c c c → DPS: p p = 7 TeVs
20 GeV ≤ t p = m µ = m µ = 1.5 GeV c m Figure 6:
Transverse momentum (left panel) and rapidity (right panel) distribution of charm quark/antiquark for √ s = 7 TeV for conventional and single-ladder-splitting DPS mechanisms. In Fig. 6 we show transverse momentum (left panel) and rapidity (right panel) distribution of the charmquark/antiquark for the DPS mechanisms calculated within LO collinear approach at √ s = 7 TeV. Theconventional and splitting terms are shown separately. The splitting contribution (lowest curve, red online)is smaller, but has almost the same shape as the conventional DPS contribution. The ratio of the DPSsingle-ladder splitting contribution to the conventional one in the case of double-charm production has beenroughly estimated to be at the level of 30 − σ eff that depends only rather weakly on energy, scale and momentum fractions.In Fig. 7 we show how the empirical (experimentally accessible) σ eff value depends on centre-of-massenergy when both 2v2 and 2v1 components are taken into account (assuming that the value of σ eff, v is independent of energy). We see a clear dependence of σ eff on energy in the plot, and also on therenormalization/factorization scales. Assuming that there is no other mechanism for an energy dependence, σ eff is therefore expected to increase with centre-of-mass energy. Note also that the empirical σ eff valueobtained here is in the ballpark of the values extracted in experimental measurements of DPS (15 −
20 mb). (GeV) s ) ( m b ) s ( e ff σ Xc c c c → DPS: p p ≤ | c |y 20 GeV ≤ t p t = m µ t = m µ , cc = M µ , cc = M µ /2 eff,2v2 σ = eff,2v1 σ Figure 7:
Energy and factorization scale dependence of σ eff for cccc production as a consequence of existence of the2v2 and 2v1 components. In this calculation we have taken σ eff, v = 30 mb and σ eff, v = 15 mb. It is not clear in the moment how to combine the higher-order effects with the perturbative splittingmechanism. An interesting question is whether the ratio between the conventional and splitting contributionschanges when higher-order corrections are included. Further studies in this context are clearly needed tofully include the splitting DPS contributions for the LHCb double charm experimental data.
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