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Antoni Szczurek

Publications and source records attributed to Antoni Szczurek.

At least 19 recordsLinked to original sources
arXiv2026

Mechanisms of $D \bar{D}$ pair production in $e^{+} e^{-} \to e^{+} e^{-} D \bar{D}$ and $AA \to AA D \bar{D}$ reactions and production of exotic charmonia

We discuss mechanisms of $D \bar{D}$ pair production in $e^+ e^-$ collisions. We consider the $D^0 {\bar D}^0$-continuum mechanism with the $t/u$-channel $D^*$ vector-meson exchanges, where the $D^* D γ$ coupling constants are derived from the $D^* \to D γ$ decays. For the $D^+ D^-$ channel, we consider mainly the $D^{\pm}$ exchanges. We find a relatively large continuum contribution for the $D^0 {\bar D}^0$ channel and a significantly smaller one for $D^+ D^-$, concluding that the broad bump at $M_{D^0 {\bar D}^0} = 3.8$ GeV observed by the Belle and BaBar Collaborations has a continuum origin rather than corresponding to the broad $χ_{c0}(3860)$ resonance. We also investigate the resonant production of $D \bar{D}$ pairs, including $χ_{c0}(3860)$ and $χ_{c2}(3930)$. The $χ_{c2}(3930)$ meson is a good candidate for the first excited $P$-wave charmonium $χ_{c2}(2P)$ state. This resonance can decay into both $D \bar{D}$ channels; however, its branching fractions are not well known at present. Comparing our model result with $Γ(χ_{c2}(2P) \to γγ) = 0.544$ keV (corresponding to the Buchmüller-Tye potential) to the BaBar data, we find $B(χ_{c2}(3930) \to D \bar{D}) = 0.58 \pm 0.13$. We present results for differential distributions in several variables for Belle II kinematics. Finally, we shortly mention predictions for the ultraperipheral heavy-ion reaction $Pb Pb \to Pb Pb D \bar{D}$ for low invariant mass ($M_{D \bar{D}} < 4.3$ GeV) at the LHC.

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arXiv2026

Production of $π^{+}π^{-}$ pairs in diffractive photon-proton and in proton-proton collisions revisited, in particular concerning the Drell-Söding contribution

We discuss the exclusive photoproduction of $π^{+}π^{-}$ pairs in photon-proton and in proton-proton collisions at high energies. The $ρ^{0}$, $ω$, $f_{2}(1270)$, and non-resonant (Drell-Söding) contributions are considered. The calculation is based on the tensor-pomeron model. In the Drell-Söding contribution we have different subenergies for the $π^{+}p$ and $π^{-}p$ systems. In the method which we propose now we take this into account. Respecting the gauge-invariance constraints is then a nontrivial problem for which, however, we present a solution here. In the present paper we give in this way a substantial improvement of the calculations for real photoproduction of $π^{+}π^{-}$ from JHEP 01, 151 (2015), and we extend the calculations to low $Q^{2}$ electroproduction, $0 \leqslant Q^{2} \leqslant 0.5$ GeV$^{2}$. The photo- and electroproduction amplitudes are then the basis for the calculation of central exclusive production (CEP) of $π^{+}π^{-}$ pairs in $pp$ collisions, where at least one proton participates in the CEP via a virtual-photon emission. The revised model leads to enhanced cross sections and gives an increased skewing of the $ρ^{0}$ spectral shape. For the $pp \to pp π^{+}π^{-}$ reaction, we calculate differential cross sections as function of the two-pion invariant mass, pion transverse momentum and pion pseudorapidity. This research is relevant in the context of ALICE, ATLAS, CMS, and LHCb measurements in $pp$ collisions. Our results can also serve as basis for the description of coherent $π^{+}π^{-}$ production in ultra-peripheral $p$A and AA collisions at the LHC. The formulas given in our paper can be used for the analysis of photoproduction and small-$Q^{2}$ electroproduction in $ep$ collisions at high energies. Such data exist from the HERA experiments and will be obtained in the future at the electron-ion colliders.

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arXiv2026

Central exclusive production of $η$ and $η'$ mesons in diffractive proton-proton collisions at the LHC

We discuss central exclusive production (CEP) of $η$ and $η'(958)$ mesons in high-energy proton-proton collisions using the tensor-pomeron approach, incorporating absorption effects at the amplitude level. Model parameters are constrained using WA102 experimental data measured at $\sqrt{s} = 29.1$ GeV. We present cross sections and differential distributions for the LHC energy of $\sqrt{s} = 13$ TeV. For $pp \to pp η$, the upper limit of the total cross section is 2.5 $μ$b for $|η_{M}| < 1$ and 5.6 $μ$b for $2 < η_{M} < 5$. For $pp \to pp η'$, the predicted cross sections are 0.3--0.7 $μ$b and 0.9--2.1 $μ$b in the respective pseudorapidity regions. These results demonstrate the feasibility of studying diffractive flavour singlet pseudoscalar meson production to probe the nature of the pomeron at the LHC.

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arXiv2026

Exclusive production of $π^+ π^-$ pairs in diffractive $γp$ and in $pp$ collisions within the tensor-pomeron approach

We discuss exclusive production of $π^+ π^-$ pairs in diffractive $γp$ and in $pp$ collisions at high energies, considering resonant ($ρ(770)$, $ω$, $f_2(1270)$) and non-resonant (Drell-Söding) contributions within the tensor-pomeron approach. For the $γp \to π^+ π^- p$ reaction, the model describes well the H1 data in the region $M_{ππ} \lesssim 1.2$ GeV. We discuss the important role of the Drell-Söding mechanism in shaping the resonance line. We also predict differential cross sections for the $pp \to pp π^+ π^-$ reaction at $\sqrt{s} = 13$ TeV where at least one proton emits a virtual photon. These findings are relevant for the central exclusive production of $π^+ π^-$ pairs in the context of ALICE, ATLAS, CMS, and LHCb measurements in hadron-hadron collisions at the LHC, especially under experimental selections using only rapidity-gap conditions. Additionally, our results are also applicable to $π^+ π^-$ production in ultraperipheral $p$A/AA collisions at the LHC and to photo- and electroproduction of $π^+ π^-$ at future electron-proton/ion colliders (EIC, LHeC).

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arXiv2026

Addendum: Production of $π^{+} π^{-}$ pairs in diffractive photon-proton and in proton-proton collisions revisited, in particular concerning the Drell-Söding contribution

We update our analyses concerning the non-resonant (Drell-Söding) contribution to the reaction $γ^{(*)} p \to π^{+} π^{-} p$, now including general vertex functions for the coupling of pomeron, $f_{2 \mathbb{R}}$, and $ρ_{\mathbb{R}}$, to pions. This takes into account the off-shellness of the pions. We present a comparison of our tensor-pomeron model, including our new Drell-Söding and $ρ$, $ω$ vector-meson contributions, with data for the $γp \to π^{+} π^{-} p$ reaction measured by the ZEUS and H1 Collaborations. We find very good agreement of our theory with the experimental data for the $π^{+} π^{-}$ invariant mass ($M_{ππ}$) and for angular distributions. Here we restrict our analysis to the region $M_{ππ} \lesssim 1.2$ GeV. For higher values of $M_{ππ}$ we will have to consider production of higher-mass mesons. The purpose of the present article is to show that our tensor-pomeron model gives a very good fit to the so-called skewing of the $ρ$-resonance contribution in photoproduction. In fact, it is an old problem/puzzle to understood the difference of the shapes of the $M_{ππ}$ distributions in the region of the $ρ(770)$ resonance in $e^{+} e^{-}$ annihilation and photoproduction. We think that with our results we have obtained for this problem a solution which is very satisfactory from the Quantum-Field-Theory point of view. Our results are also relevant for central-exclusive $π^{+} π^{-}$ production in ultraperipheral $pp$, A$p$, and AA collisions at the LHC and for photo- and electroproduction of $π^{+} π^{-}$ at future electron-proton/ion colliders, EIC and LeHC.

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arXiv2026

Two photon decay width of the fully charmed tetraquarks: revisiting prospects for ultraperipheral collisions

We discuss the role of fully heavy tetraquarks in ultraperipheral collisions $AA\to AA\, J/ψJ/ψ$ and $AA \to AA\, γγ$. Two-photon couplings to scalar and tensor tetraquarks are considered. We use relatively recent results of four-body calculation of fully heavy tetraquark wave function within the extended relativized quark model. The corresponding radiative decay widths for different tetraquark states are evaluated using NRQCD factorisation, with LDMEs extracted from the four-body wave functions at the origin. The results are collected in tables. The cross sections for production of pairs of $J/ψ$ mesons and diphotons in UPC of $^{208}Pb + {^{208}Pb}$ collisions are presented. While the couplings for $T_{4c}\left(0^{++}, 2^{++}\right) \to γγ$ are calculated based on the model wave functions, simplified couplings are used for $T_{4c}\left(0^{++}, 2^{++}\right) \to J/ψJ/ψ$. When calculating the energy dependence of the resonant $γγ\to J/ψJ/ψ$ and $γγ\to γγ$ cross section, we employ the total decay widths measured at $Γ_{\rm{tot}}=0.446\,\rm{GeV}$ for $X(6600)$ while $Γ_{\rm{tot}}=0.135\,\rm{GeV}$ for $X(6900)$ in latest CMS data. The resonant terms are compared with continuum contributions for both considered channels. While for the $J/ψJ/ψ$ channel the resonant contributions are larger than continuum ones, for the $γγ$ channels the situation is reversed. The latter result is in clear disagreement with the result obtained from the näive use of vector dominance picture.

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arXiv2026

Probing GPDs in exclusive electroproduction of dijets

We summarize the formalism for calculating the exclusive dijet production in $e p \to e^{\prime} jj p$ in collinear QCD factorization, using generalized parton distributions as the soft hadronic input modeled in the double distribution approach. We include all leading-order contributions coming from light sea and valence quark exchanges, and gluon exchanges for both light quark-antiquark ($q\bar{q}$) production and also the heavy $c\bar{c}$ final state. We present results for several differential distributions for the cross section evaluated over a broad region of phase space, covering a wide range of inelasticity and photon virtuality. The gluon and sea contributions exhibit similar shapes, whereas the valence contribution, though relatively small, shows a markedly different behavior. The latter becomes particularly noticeable at large $x_{\mathbb{P}}$, a kinematic region not explored at HERA, but potentially accessible in future measurements at the Electron Ion Collider. This requires further feasibility studies. We also present the azimuthal angle modulation between the leptonic and the outgoing dijet planes for the general case, as well as for the ZEUS kinematic region where we see reasonable agreement with the data for diffractive deep inelastic scattering parameter $β\gtrsim 0.4$.

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arXiv2026

Phenomenology developments in UPC: $γγ\to γγ$ scattering

We discuss several possible extensions of present studies of $γγ\to γγ$ scattering in ultraperipheral heavy ion collisions. One of the possible extensions are studies for lower diphoton invariant masses (smaller transverse momenta). There new mechanisms may show up. This includes possible studies with future FOCAL and ALICE 3 detectors. So far only coherent $γγ\to γγ$ processes, when initial photons couple to nuclei, were sudied theoretically. Recently we proposed to study also inelastic processes, when initial photons couple to individual nucleons. Without special cuts the corresponding processes are of the order of 20 - 30 \%. A study to which extent the inelastic processes survive with the present cuts used for the $γγ\to γγ$ studies is an interesting question. They can be of interest by itself and dedicated studies are suggested. We calculate also cross section for associated neutron production. Deviation from our predictions could signal presence of the inelastic contribution. Finally we discuss production of single photons in UPC ($A A \to A A γ$). Corresponding cross sections for selected mechanisms are presented.

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arXiv2026

Exclusive $D \bar{D}$ pair production with low invariant mass in ultraperipheral Pb-Pb collisions at the LHC

We present predictions for the ultraperipheral heavy-ion reaction ${\rm Pb} {\rm Pb} \to {\rm Pb} {\rm Pb} D \bar{D}$, where $D$ refers to either $D^0$ or $D^+$, limiting to low invariant mass of $D \bar{D}$ and at energies available at the LHC. The calculation of the $γγ\to D \bar{D}$ subprocess is done including the continuum mechanisms and the $χ_{c0}(3860)$ and $χ_{c2}(3930)$ resonant contributions. These states are considered as candidates for the first excited $P$-wave charmonia $χ_{c0}(2P)$ and $χ_{c2}(2P)$. We compare our results for the $γγ\to D \bar{D}$ process with the $D \bar{D}$ invariant mass and angular distributions measured by the Belle and BaBar experiments in $e^{+}e^{-}$ collisions. Then, we present first calculations for ultraperipheral Pb-Pb collisions (UPCs) within the equivalent photon approximation in the impact-parameter space. Both, the total cross section and several differential distributions for experimental cuts corresponding to the ALICE, ATLAS, CMS, and LHCb experiments are presented. For instance, the nuclear cross sections for the $D^{0} \bar{D}^{0}$ and $D^{+} D^{-}$ channel at $\sqrt{s_{NN}} = 5.02$ TeV are found to be approximately 100--132 $μ$b and 29 $μ$b, respectively, taking into account the cuts on pseudorapidities and transverse momenta of the final state charmed mesons ($|η_{D}| < 2.5$, $p_{t,D} > 0.2$ GeV) and for $M_{D \bar{D}} < 4.3$ GeV. Results for $\sqrt{s_{NN}} = 5.36$ TeV are also presented. Cross section for the ${\rm Pb} {\rm Pb} \to {\rm Pb} {\rm Pb} (γγ\to χ_{c0,2}(2P) \to D \bar{D})$ processes is sufficiently large for experimental studies. The back-to-back correlation between charm mesons can be used to separate the exclusive process under consideration from other background processes, and could provide valuable insight into the properties of the excited quarkonia.

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arXiv2026

Competition of $χ_{c}(2P)$ quarkonia and continuum in $e^+ e^- \to e^+ e^- D \bar{D}$

We discuss the production of $D \bar{D}$ pairs in $e^+ e^-$ collisions, where $D$ refers to either $D^0$ or $D^+$. The continuum mechanism with the $t/u$-channel vector-meson $D^*$ exchanges are considered. The results of the calculation depend on the parameter of the off-shell form-factor for the virtual $D^*$ mesons. The $D^* D γ$ coupling constants are found from the $D^* \to D γ$ decays. We find relatively large contribution for the $D^0 {\bar D}^0$ channel and much smaller contribution in the $D^+ D^-$ channel. In the second case we consider also the $D^{\pm}$ exchanges. We conclude that the bump at $M_{D^0 {\bar D}^0} = 3.8$ GeV observed by the Belle and BaBar Collaborations has rather continuum origin than it corresponds to the broad resonance $χ_{c0}(3860)$. We discuss also production of the $χ_{c2}(3930)$ resonance which is a candidate for the $χ_{c2}(2P)$ state. This state can decay into both $D \bar{D}$ channels, however the branching fractions are not well known at present. From a comparison of our model results to the BaBar data we find $B(χ_{c2}(3930) \to D \bar{D}) = 0.58 \pm 0.13$ using the two-photon width $Γ_{γγ} = 0.544$ keV (obtained for the Buchmüller-Tye potential) evaluated within the light-front approach (NRQCD limit). Our finding of $Γ_{γγ} \times B(χ_{c2}(3930) \to D \bar{D}) = 0.32 \pm 0.07$ keV is close to the Belle and BaBar results. Realistic predictions of the differential distributions in several variables and integrated cross-sections are given for the Belle II kinematics.

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arXiv2026

Central exclusive production of $η$ and $η'$ mesons in diffractive proton-proton collisions at the LHC and the nature of the pomeron

Central exclusive production (CEP) of $η$ and $η'$ mesons in proton-proton collisions at high-energies is discussed. At the LHC the main mechanism for the production of these mesons should be double-pomeron ($\rm I\!P$-$\rm I\!P$) exchange, that is, the fusion reactions ${\rm I\!P I\!P} \to η, η'$. We show that for a scalar pomeron these fusion reactions are not possible. In contrast, in the tensor-pomeron model CEP of $η$ and $η'$ mesons via double-pomeron exchange is allowed. We discuss these reactions for the c.m. energy $\sqrt{s} = 29.1$ GeV realised at the WA102 experiment and for $\sqrt{s} = 13$ TeV corresponding to the LHC experiments. Cross sections and distributions are presented and discussed.

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arXiv2026

Charm associated production of the pseudoscalar Higgs boson $h''$ in the MCPM' at the LHC

We discuss charm associated production of the pseudoscalar Higgs boson $h''$ in the MCPM'. In our analysis we assume $m_{h''}$ = 95.4 GeV, which corresponds to an enhancement observed by the CMS collaboration in the $γγ$ channel. As discussed recently, the MCPM' is consistent with the CMS enhancement. In this model the $h''$ Higgs boson of this mass decays dominantly into $c \bar c$ jets. The cross section for the associated $h''$ production in $p p \to h'' c \bar c$ is found to be almost as big as that for the Drell-Yan (DY) $c \bar c \to h''$ production, much larger than that for two-gluon fusion $g g \to h''$. Since in the MCPM' the dominant $h''$ decay is into the $c \bar c$ channel we have to deal with the $p p \to c \bar c c \bar c$ process with $c$ and $\bar c$ jets. In addition to the signal processes, we have sizeable single parton scattering (SPS) and double parton scattering (DPS) nonresonant background. In our analysis we include diagrams of gluon-gluon fusion $g g \to h''$ which lead to the $c \bar c c \bar c$ final state. We discuss also the possible role of the reaction $p p \to h'' h''$. Assuming 100\% c and $\bar c$ jet tagging we discuss in detail how to improve the signal-to-background ratio. Our analysis shows promising resonance-like enhancements and relatively large cross sections in the $c \bar c c \bar c$ channel within the MCPM'. In an appendix we discuss the total cross section for $h''$ production at the LHC. We also compare distributions for the reactions $p p \to h'' X$ and $p p \to Z X$ with $h''$ and $Z$ decaying to $c\bar c$ and $μ^{+}μ^{-}$. We hope that the LHC collaborations will in the future perform the experimental studies corresponding to the theoretical studies discussed here.

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arXiv2026

Transition Form-Factor for $η_Q$ at NNLO in the strong coupling $α_s$ and with all-order $v^2$ resummation

In this work, we discuss both relativistic and perturbative QCD corrections to the transition form-factor ${\cal F}_{η_Q}{(t_1,t_2)}$ for the process $γ^*(q_1) γ^*(q_2) \leftrightarrow η_Q(P)$ with dependencies on the normalised photon virtualities $t_1=q_1^2/m_Q^2$ and $t_2=q_2^2/m_Q^2$, where $m_Q$ is the heavy quark mass. We resum a class of relativistic corrections to all orders in the relativistic parameter $\langle v^2 \rangle_{η_Q}$. In addition, we include perturbative QCD corrections up to Next-to-Next-to-Leading Order (NNLO) in the strong coupling constant $α_s$. This involves the computation of two-loop amplitudes with two off-shell photons. We explore three different phenomenological applications of our transition form-factors for the charmonium case. We first study the ratio $\vert {\cal F}_{η_c}{(t_1,0)} \vert/ \vert {\cal F}_{η_c}{(0,0)} \vert$ for the single space-like photon case and compare our results with the existing $η_c$ measurements from the BaBar collaboration. Secondly, we consider observables for the case of double space-like photons and discuss the impact of the different corrections. The NNLO corrections for this case are presented here for the first time in the literature. Finally, we revisit the decay width $Γ[η_c \rightarrow γγ]$ and compare it with the existing PDG value.

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arXiv2025

From photons to dikaon -- theoretical insights into $K^+K^-$ production in nuclear collisions

The production of charged kaon pairs in ultraperipheral heavy-ion collisions can proceed via photoproduction (gamma-Pomeron interaction) or via photon-photon fusion. An important contribution to this process arises from the decays of scalar, tensor and vector mesons. This study provides a consistent description of K+K- production at both the elementary level (gamma gamma -> meson -> K+K-) and the nuclear level (Pb Pb -> Pb Pb K+K-). The gamma gamma fusion cross section is compared with experimental results from Belle, TPC/Two-Gamma and ARGUS. A comparison with existing midrapidity measurements is presented, together with theoretical predictions for ultraperipheral Pb-Pb collisions at sqrt(sNN) = 5.02 TeV.

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arXiv2025

Light-by-Light scattering in ultraperipheral heavy ion collisions: Estimating inelastic contributions

The current state-of-the-art theoretical estimations lead to cross-sections for $AA \to γγAA$ which are somewhat smaller than the measured ones by the ATLAS and CMS Collaborations, which motivates the searching and calculation of subleading corrections disregarded in these previous studies. In this paper, we estimate for the first time the contribution of inelastic channels to the Light-by-Light (LbL) scattering in ultraperipheral collisions of heavy ions (UPHICs), in which one or both of the incident nuclei dissociate ($A A \to γγX Y$ where $X, Y = A, A'$) due to the photon emission. These new mechanisms are related to extra emissions that are rather difficult to identify at the LHC and may be misinterpreted as enhanced $γγ\to γγ$ scattering compared to the Standard Model result. We include processes of coupling of photons to individual nucleons (protons and neutrons) in addition to coherent coupling to the whole nuclei (called standard approach here). Both elastic (nucleon in the ground state) and inelastic (nucleon in an excited state) in the couplings of photons to nucleons are taken into account. The inelastic nucleon fluxes are calculated using CT18qed photon in nucleon PDFs. The inelastic photon fluxes are shown and compared to standard photon fluxes in the nucleus. In addition, we show the ratio of the inelastic corrections to the standard contribution as a function of diphoton invariant mass and photon rapidity difference. We find that for the ATLAS acceptance region the inelastic corrections grow with $M_{γγ}$ and rapidity difference. Our results indicate that the inelastic contributions can be of the order of 20-40 \% of the traditional (no nuclear excitation) predictions. Uncertainties due to factorization scale choice are quantified.

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arXiv2025

Neutron emission associated with $γγ\toγγ$ scattering in UPC of heavy ions at the LHC

We calculate cross sections for the production of different neutron classes $0n 0n$, $0nXn+Xn0n$ and $Xn Xn$, possible to measure in Zero Degree Calorimeters (ZDCs), associated with photon-photon scattering in UPC of lead on lead. The calculations are performed for the ATLAS kinematics. Our calculations for neutron classes are tested against existing data for $ρ^0$ production in UPC. We get a good agreement for absolute cross section as well as very good results for fractional cross section which gives confidence to the analogous calculation for diphoton production, corresponding to $γγ\to γγ$ scattering. We present both absolute as well as fractional cross sections for the different neutron classes. We also show different distributions in impact parameter, photon rapidity, transverse momentum, diphoton invariant mass and photon rapidity difference. The shapes of the photon distributions depend on the neutron classes which we quantify in this paper. It would be valuable to test our predictions using the ATLAS main detector and the ATLAS ZDCs.

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arXiv2025

Central exclusive production of $η$ and $η'$ mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach

We present a study of the central exclusive production (CEP) of $η$ and $η'(958)$ mesons in diffractive proton-proton collisions at high energies. The amplitudes, including pomeron and $f_{2 \mathbb{R}}$ reggeon exchanges, are calculated within the tensor-pomeron model. Absorption effects are also taken into account at the amplitude level. We fit some undetermined model parameters (coupling constants and cutoff parameters in form factors) to the WA102 experimental data and then make predictions for the LHC energy $\sqrt{s} = 13$ TeV. Both, total cross sections and several differential distributions are presented. For $pp \to pp η$, we find an upper limit for the total cross section of 2.5 $μ$b for pseudorapidity of the $η$ meson $|η_{M}| < 1$ and 5.6 $μ$b for $2 < η_{M} < 5$. For $pp \to pp η'$, we predict the cross section to be in the range of 0.3-0.7 $μ$b for pseudorapidity of the $η'$ meson $|η_{M}| < 1$ and 0.9-2.1 $μ$b for $2 < η_{M} < 5$. This opens the possibility to study diffractive production of pseudoscalar mesons in experiments at the LHC. We discuss if there are arguments from SU(3)-flavor symmetry which would forbid pomeron-pomeron fusion giving an $η$ meson. In our opinion such arguments do not exist. We also consider CEP of the pseudoscalars $η$ and $η'(958)$ and the pseudovector meson $f_{1}(1285)$ in diffractive proton-proton collisions in a theory with a scalar pomeron. We show that none of these particles can be produced in this way in the scalar-pomeron theory. Thus, experimental observation of any of these particles in the above CEP processes at the LHC would give striking evidence against a scalar character of the pomeron.

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arXiv2025

Production of open and hidden charm in fixed-target experiments at the LHC

We discuss the production of $D$ mesons and $J/ψ$ quarkonia in proton-nucleus collisions in the fixed-target LHCb experiment. We consider gluon-gluon fusion within $k_t$-factorization, processes initiated by intrinsic charm in the nucleon and perturbative recombination mechanism. All the mechanisms seem to be necessary to describe the LHCb experimental data. We get an upper limit for the probability of the large-$x$ $c \bar c$ Fock component in the nucleon, which is slightly less than 1 \%. The recombination mechanism allows the description of $D^0$ and $\bar D^0$ asymmetry observed by the LHCb collaboration.\\ We also discuss the production of $J/ψ$ quarkonia, including color singlet mechanisms. We include $g^* g^* \to J/ψg$ and $g^* g^* \to χ_c(1^+,2^+)(\to J/ψγ)$ within $k_t$-factorization approach. Different unintegrated gluon distributions from the literature are used. A reasonable agreement is achieved with some distributions from the literature.

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