Hard production of a Z boson plus heavy flavor jets at LHC and the intrinsic charm content of a proton

The cross section of associated production of a Z boson with heavy flavor jets in $pp$ collisions is calculated using the SHERPA Monte Carlo generator and the analytical combined QCD approach based on kt-factorization at small x and conventional collinear QCD at large x. A satisfactory description of the ATLAS and CMS data on the $p_T$ spectra of Z bosons and c-jets in the whole rapidity, y, region is shown. Searching for the intrinsic charm (IC) contribution in these processes, which could be visible at large y>1.5, we study observables very sensitive to non-zero IC contributions and less affected by theoretical QCD scale uncertainties. One of such observables is the so-called double ratio: the ratio of the differential cross section of Z + c production in the central region of |y|<1.5 and in the forward region 1.5<|y|<2.5, divided by the same ratio for Z + b production. These observables could be more promising for the search of IC at LHC as compared to the observables considered earlier.


I. INTRODUCTION
Many hard processes within the Standard Model and beyond, such as the production of heavy flavor jets, of the Higgs boson, and other processes are quite sensitive to the heavy quark content of the nucleon. Studying the latter plays an increasingly significant role in the physics program of the Large Hadron Collider (LHC). Strange, charm and beauty parton distribution functions (PDFs) are essential inputs for the calculation of observables for these processes within the perturbative Quantum Chromodynamics (pQCD). Global QCD analysis allows one to extract the PDFs from comparison of hard-scattering data and pQCD calculations.
Hard production of vector bosons accompanied by heavy flavor 1 jets (V + HF) in pp collisions at LHC energies can be considered as an additional tool to study the quark and gluon PDFs compared to the deep inelastic scattering of electrons on protons. In these processes, in the rapidity region |y| < 2.5, which corresponds to the kinematics of ATLAS and CMS experiments, one can study these PDFs not only at low parton momentum fractions x < 0.1 but also at larger x values [1]. Therefore, such V + HF processes can give us new information on the PDFs at large x > 0.1, where the non-trivial proton structure (for example, the possible contribution of valence-like intrinsic heavy quark components) can be revealed [2][3][4][5].
Intense studies of an intrinsic charm (IC) signal in the production of vector (Z and W ) bosons or prompt photons γ accompanied by heavy-flavor jets in pp collisions at LHC energies were made in [1,[6][7][8][9]. It was shown that the contribution of IC to the proton PDFs can be visible in the transverse momentum spectra of γ/Z/W or c/b-jets in the forward rapidity region of the ATLAS and CMS kinematics, 1.5 < |y| < 2.5, at large p T > 100 GeV.
The shape of these p T spectra depends significantly on the IC probability in the proton w IC , while in the more central rapidity region |y| < 1.5 the IC signal may not be visible.
Up to now there is a long-standing debate about the w IC value [9][10][11][12] (see also [1] and references therein). A first estimate of the intrinsic charm probability in the proton was carried out in [13] utilizing recent ATLAS data on the production of prompt photons accompanied by c-jets at √ s = 8 TeV [14]. An upper limit w IC < 2.74% (3.77%) at 68% (95%) C.L. was set [13]. It is shown [13] that to extract the IC probability from these ATLAS data we have to eliminate a large theoretical uncertainty due to the QCD scale. In this paper we focus on looking for observables in Z + HF production processes, which are sensitive to the IC contribution in the proton PDF and are less dependent on the QCD scale. In [8] it is shown that such observables could be the ratio of γ/Z + c and γ/Z + b production cross sections in the forward rapidity region 1.5 < |y Z | < 2.5. Calculations [8] were performed applying the MCFM [15] Monte Carlo (MC) generator and k T -factorization of QCD.
In this paper we investigate Z + HF production processes at LHC energies within two approaches: the combined QCD approach, based on the k T -factorization formalism [16][17][18] in the small x domain and on conventional (collinear) QCD factorization at large x, and the Sherpa MC event generator [19]. Recently the combined QCD approach was successfully applied to describe LHC data on associated Z + b production at √ s = 7 TeV [20]. The Sherpa MC generator, which includes initial and final state parton showering, is supposed to provide a realistic description of multi-particle final states allowing for HF jets from higher perturbative orders, such as gluon splitting into heavy quark pairs. Sherpa can also model the full chain of hadronization and decays of unstable particles, that should allow us a more accurate comparison to experimental measurements of HF jets than achieved in previous studies [7,8]. Validation of these approaches is performed using ATLAS and CMS data [21,22] on Z boson production accompanied by charm and beauty jets for center-ofmass energies √ s = 7 and 8 TeV. One of the goals of this work is to study the influence of intrinsic charm on various kinematical distributions in these processes and to investigate the effects of initial and final state parton showers in the description of LHC data. We also focus on finding new observables which are sensitive to the IC content of a proton and which could help us to reduce the QCD scale uncertainties.
In Section II we present two theoretical approaches adopted in our calculations. The results and discussion are presented in Section III, and Section IV is the Conclusion.

II. THEORETICAL APPROACHES TO ASSOCIATED Z + HF PRODUCTION
To calculate the total and differential cross sections of associated Z + HF production within the combined QCD approach, we strictly follow the scheme described earlier [20]. In this scheme, the leading contribution comes from the O(αα 2 s ) off-shell gluon-gluon fusion subprocess g * + g * → Z + Q +Q (where Q denotes the heavy quark), calculated in the k T -factorization approach. The latter has certain technical advantages in the ease of including higher-order radiative corrections in the form of transverse momentum dependent (TMD) parton distributions (see [23][24][25] for more information). To extend the consideration to the whole kinematic range, several subprocesses involving initial state quarks, namely flavor excitation q + Q → Z + Q + q, quark-antiquark annihilation q +q → Z + Q +Q and quark-gluon scattering q + g → Z + q + QQ, are taken into account using the collinear QCD factorization (in the tree-level approximation). The IC contribution is estimated using the O(αα s ) QCD Compton scattering c + g * → Z + c, where the gluons are kept off-shell but the incoming non-perturbative intrinsic charm quarks are treated as on-shell ones 2 . Thus we rely on a combination of two techniques, with each of them being used for the kinematics where it is more suitable 3 (off-shell gluon-gluon fusion subprocesses at small x and quark-induced subprocesses at large x values). More details of the above calculations can be found in [20].
In contrast to earlier studies [7,8] of Z + HF production within the MCFM routine (that performs calculation in the fixed order of pQCD), in the present paper the Sherpa 2.2.1 [19] MC generator is applied. It uses matrix elements that are provided by the builtin generators Amegic++ [30] and COMIX [31]; OPENLOOPS [32] is used to introduce addtional loop contributions into the NLO calculations. We use matrix elements calculated at the next-to-leading order (NLO) for up to 2 final partons and at the leading-order (LO) for up to 4 partons. They are merged with the Sherpa parton showering [33] following the ME+PS@NLO prescription [34]. This is different from the study of Z + c production carried out in [12] where the matrix element was calculated in the LO and merged following the ME+PS@LO method [35]. The latter approach was also used in this study as a cross-check, with the LO matrix element allowing for up to 4 final partons. In both approaches, the five-flavor scheme (5FS) is used where c and b quarks are considered as massless particles in the matrix element and massive in both the initial and final state parton showers. Sherpa can also model the full chain of hadronization and unstable particle decays for an accurate comparison with experimental measurements of HF jets. 2 The perturbative charm contribution is already taken into account in the off-shell gluon-gluon fusion subprocess. 3 An essential point of consideration [20] is using a numerical solution of the CCFM evolution equation [26][27][28] to derive the TMD gluon density in a proton. The latter smoothly interpolates between the small-x BFKL gluon dynamics and high-x DGLAP dynamics. Following [20], below we adopt the latest JH'2013 parametrization [29], adopting the JH2013 set 2 gluon as the default choice.

III. RESULTS AND DISCUSSION
A. Comparison with the LHC data at √ s = 7 and 8 TeV In this section we present comparisons of our calculations for Z + HF production made with the Sherpa generator and within the combined QCD approach to the LHC Run 1 data, in order to verify the applicability of these approaches for further predictions. Following [1,[6][7][8][9], we mainly concentrate on the transverse momentum distributions of Z bosons and/or HF jets, where the IC effects are expected to appear 4 .
The first comparison is performed for associated Z+b production measured by the ATLAS Collaboration [21] at √ s = 7 TeV. According to [21], the following selection criteria were applied to generated events. Two leptons originating from the Z boson decay are required to have an invariant mass 76 GeV < m < 106 GeV with a minimum transverse momentum of each lepton p T > 20 GeV and rapidity |y | < 2.5. In Sherpa generated events, jets are built using all stable particles excluding the lepton pair from the Z boson decay with the anti-k T algorithm with a size parameter R = 0.4. They are required to have a rapidity |y jet | < 2.4 and minimum transverse momentum p jet T > 20 GeV. Each jet is also required to be separated from any of the two leptons by ∆R jet, > 0.5. Jets are identified as b-jets, if there is a weakly decaying b hadron with a transverse momentum p b T > 5 GeV within a cone ∆R = 0.3 around the jet direction. The same kinematic requirements are applied to final state b quarks (treated as b-jets at a parton level) when using the combined QCD approach.
Sherpa results were obtained within the ME+PS@NLO model. In both approaches the CTEQ66 PDF set [36] was used.
In Fig. 1 the associated Z+b-jet production cross section (for events with at least one b-jet) calculated as a function of the Z boson transverse momentum p Z T is presented in comparison with the ATLAS data [21]. Here and below central values, marked by horizontal lines,   One can see that the Sherpa results are in perfect agreement with the ATLAS data within the scale uncertainties in the whole p Z T range. In the combined QCD approach, we observe some underestimation of the data at high p Z T and a slight overestimation at low transverse momenta. The latter can be attributed to the TMD gluon density used in the calculations, because the region p Z T < 100 GeV is fully dominated by the off-shell gluongluon fusion subprocess [20]. However, the results obtained within both approaches under consideration in this region are rather close to each other. A noticeable deviation of the combined QCD calculations from the data at large p Z T is explained by the absence of the effects of parton showers, hadronization and additional contributions of NLO diagrams, including loop ones, in these calculations. Such contributions, which are taken into account by Sherpa, considerably improve the description of data. The influence of the parton showers and of higher-order pQCD corrections is investigated in detail in the next Section.
It is important to note that our results obtained with Sherpa are in good agreement with the results obtained within a similar approach [37]. Now, we turn to the associated Z + c-jet production measured by the CMS Collaboration at √ s = 8 TeV [22]. The following selection criteria are applied to generated events for this comparison. Two leptons originating from a Z boson decay must have an invariant mass 71 GeV < m < 111 GeV, a minimum transverse momentum of p T > 20 GeV and rapidity |y | < 2.1. Jets built with the anti-k T algorithm with a size parameter R = 0.5 are required to have p jet T > 25 GeV and |y jet | < 2.5 and to be separated from the leptons by ∆R jet, > 0.5. Similar b and c flavor identification criteria to those described above are used.
In Fig. 2 our results for the differential cross sections of associated Z + c-jet production calculated as functions of the Z boson and c-jet transverse momenta are shown in comparison with the CMS data [22]. A comparison with the measured ratio of the cross sections σ(Z + c)/σ(Z + b) is also presented. We find that the particle-level Sherpa calculations agree well with the data. The parton-level combined QCD calculations also describe the CMS data within the theoretical and experimental uncertainties (except at low p c T < 40 GeV), although they tend to underestimate the Sherpa results. As in the case of associated Z + b-jet production, we attribute the latter to the parton showering effects and additional NLO contributions, missing in the combined QCD calculations (to be precise, mainly in the tree-level quark-induced subprocesses, since the off-shell gluon-gluon fusion only gives a negligible contribution at large transverse momenta). Note that the scale uncertainties of our calculations partially cancel out when considering the σ(Z + c)/σ(Z + b) ratio 5 (see Fig. 2, right plots).
One can see that a better description of the CMS data is achieved with the Sherpa tool and, therefore, we consider Sherpa calculations as the most reliable ones. Thus, we mainly concentrate on them when investigating the possible effects from IC in the LHC experiments below.
B. Z+HF spectra for √ s = 13 TeV and prediction for the IC contribution The purpose of the calculation of Z + HF differential cross sections in this paper is to investigate the effect of an IC signal on the observables, which can be measured at the LHC by general purpose detectors at √ s = 13 TeV. As it was mentioned above, a sensitivity to the IC at ATLAS and CMS experiments on Z + c-jet production can be achieved in the forward rapidity region 1.5 < |y Z | < 2.5 and p Z T > 50 GeV [7,8]. In this kinematical region the shape of the σ(Z + c)/σ(Z + b) ratio is sensitive to effects of IC and is less affected by scale uncertainties than those of the transverse momentum spectra. This fact provides an opportunity to measure the IC contribution.
In Sherpa, predictions for Z + HF production are calculated within the ME+PS@NLO model using the CT14nnlo PDF set [12] containing PDFs with IC probabilities w IC = 0, 1 and 2% [12]. The following selection criteria are used in this analysis. Two leptons from the Z boson decay are required to have a mass 76 GeV < m < 106 GeV, transverse momentum p T > 28 GeV and rapidity |y | momenta the results of the combined QCD approach are consistently close to parton-level Sherpa predictions obtained at the NLO level, that demonstrates it is effective to take into account higher-order pQCD corrections in the off-shell gluon-gluon fusion subprocess supplemented with the CCFM gluon dynamics. Therefore, we can conclude that there are no large contradictions between our two theoretical approaches at the parton level.
The combined QCD approach can be used to predict Z + HF production cross sections at the parton level at moderate transverse momenta, but such approximation becomes worse towards high transverse momenta where the effects described above are quite large.
Next, the effects of adding parton showers and NLO corrections to the parton level Sherpa LO predictions for differential cross section ratios σ(Z + c)/σ(Z + b) are illustrated in Fig. 6. These ratios are calculated using CTEQ66(c) PDF sets with w IC = 0% and 3.5%. One can see that including parton showers does significantly decrease the excess in the spectrum caused by the non-zero IC component, while adopting the ME+PS@NLO instead of the ME+PS@LO approach makes little difference. Thus, both Sherpa predictions made at a particle level give the IC effect in the forward region at 200 < p T < 500 GeV (irrespectively of whether p T of the jet or of the Z boson is considered) of the order of 10 -20%, compared to the much larger effect predicted by the parton-level calculations (Sherpa at LO or the combined QCD approach) to be at the level of a factor of about 2. This observation is in qualitative agreement with that made in [12] when comparing the predictions for integral cross sections of Z + c-jet production from fixed order MCFM calculations and those from Sherpa within the ME+PS@LO approach.
Now we turn to the discussion of our theoretical uncertainties and uncertainties of the LHC measurements. These uncertainties have been shown [13] to impose a strong restriction on the precision of the IC probability estimation from the experimental data. So new observables which may be less affected by such uncertainties are of high interest. A new variable satisfying this criterion can be defined as follows. The ATLAS and CMS rapidity range is divided into a central region |y Z | < 1.5 and a forward region 1.5 < |y Z | < 2.5. Then, the ratio of the Z + c production cross sections in the forward region and in the central region is divided by the same ratio for Z + b production. This so-called double ratio σ(Zc f wd /Zc ctr )/σ(Zb f wd /Zb ctr ) is shown in Fig. 7 as a function of the transverse momentum of the Z boson p Z T at the left and of the leading jet p jet T at the right. One can see that in those ratios the IC effect is already visible at the transverse momentum p T 50 GeV. This value is much less than if one studies the differential cross sections of Z +c production. Moreover, the uncertainties related to the QCD scale in theoretical calculations are significantly suppressed in this double ratio (see Fig. 7). Therefore, the latter could be a more promising variable in the search for intrinsic charm at LHC as compared to other observables considered previously.
Moreover, to obtain more reliable information on the probability of IC being present in the proton from future LHC data at √ s = 13 TeV one can perform a better estimation of theoretical scale uncertainties and reduce systematic uncertainties. This problem can be addressed by employing the "principle of maximum conformality" (PMC) [38] which sets renormalization scales by shifting the β terms in the pQCD series into the running coupling.
The PMC predictions are independent of the choice of renormalization scheme -a key requirement of the renormalization group. However, up to now there is no direct application of the PMC to the hard processes discussed in this paper. One can expect forthcoming ATLAS and CMS experimental results on associated Z + HF production to be sensitive to the effect of IC in a proton. [GeV/c]

IV. CONCLUSION
Associated production of the Z boson and heavy flavor jets in pp collisions at LHC energies has been considered applying the Sherpa Monte Carlo generator and the combined QCD factorization approach using PDF sets with different intrinsic charm components.
The combined QCD approach employs both the k T -factorization and the collinear QCD factorization with each of them used in the kinematical conditions of its reliability. The best description of the ATLAS and CMS data on the Z + b and Z + c production at √ s = 7 and 8 TeV was obtained within the Sherpa 5FS ME+PS@NLO model. Effects arising from parton showers and higher-order pQCD corrections have been investigated. We found these effects to strongly suppress the sensitivity of our predictions to the intrinsic charm content of a proton. However, despite this suppression, one can expect forthcoming ATLAS and CMS measurements of Z + HF production at √ s = 13 TeV to be very important to search for the IC contribution in the proton. We suggest to measure a new observable, namely, the double ratio of cross sections σ(Zc f wd /Zc ctr )/σ(Zb f wd /Zb ctr ), which is extremely sensitive to the IC signal. This observable can be very promising for precision estimation of the IC probability, since it is less affected by QCD scale uncertainties, as compared to the observables considered previously.