The quarkonium hadroproduction in association with a photon at high energies provides a probe of the dynamics of the strong interactions as it is dependent on the nuclear gluon distribution. Therefore, it could be used to constrain the behavior of the nuclear gluon distribution in proton-nucleus and nucleus-nucleus collisions. Such processes are useful to single out the magnitude of the shadowing/antishadowing effects in the nuclear parton densities. In this work we investigate the influence of nuclear effects in the production of JPsi + photon and Upsilon + photon and estimate the transverse momentum dependence of the nuclear modification factors. The theoretical framework considered in the JPsi (Upsilon) production associated with a direct photon at the hadron collider is the non-relativistic QCD (NRQCD) factorization formalism.
FDCHQHP is a Fortran package to calculate the transverse momentum (p_t) distribution of yield and polarization for heavy quarkonium hadroproduction at next-to-leading-order (NLO) based on non-relativistic QCD(NRQCD) framework. It contains the complete color-singlet and color-octet intermediate states in present theoretical level, and is available to calculate different polarization parameters in different frames. As the LHC running now and in the future, it supplies a very useful tool to obtain theoretical prediction on the heavy quarkonium hadroproduction.
We examine carefully bottomonia hadroproduction in proton colliders, especially focusing on the LHC, as a way of probing the gluon density in protons. To this end we develop some previous work, getting quantitative predictions and concluding that our proposal can be useful to perform consistency checks of the parameterization sets of different parton distribution functions.
The prediction of single spin asymmetry (SSA) in double $\rm J/ψ$ production in proton-proton collision is given out within the framework of non-relativistic QCD, using the recently obtained best fit parameters for the gluon Sivers function extracted from PHENIX data in $\rm p+p^\uparrow\toπ^0+X$. The color singlet state $\rm ^3 S_1^{(1)}$ and color octet state $\rm ^3 S_1^{(8)}$ are considered to the SSA contribution in the double $\rm J/ψ$ hadroproduction. Our result shows that a sizable asymmetry can be estimated as functions of different kinematic variables.
The energy dependence of the total hadroproduction cross section of pseudo-scalar quarkonia is computed via matching Next-to-Leading Order (NLO) Collinear-Factorisation (CF) results with resummed higher-order corrections, proportional to $α_s^{n}\ln^{n-1}(1/z)$, to the CF hard-scattering coefficient, where $z=M^2/\hat{s}$ with $M$ and $\hat{s}$ being the quarkonium mass and the partonic center-of-mass energy squared. The resummation is performed using High-Energy Factorisation (HEF) in the Doubly-Logarithmic (DL) approximation, which is a subset of the leading logarithmic $\ln (1/z)$ approxima…
Double $J/ψ$ production has been observed by the NA3 collaboration in $πN$ and $p N$ collisions with a cross section of the order of 20-30 pb. The $ψψ$ pairs measured in $π^- $ nucleus interactions at 150 and 280 GeV$/c$ are observed to carry an anomalously large fraction of the projectile momentum in the laboratory frame, $x_{ψψ} \geq 0.6$ at 150 GeV$/c$ and $\geq 0.4$ at 280 GeV$/c$. We postulate that these forward $ψψ$ pairs are created by the materialization of Fock states in the projectile containing two pairs of intrinsic $c \overline c$ quarks. We calculate the overlap of the charmonium…
We study nuclear shadowing in $J/ψ$ and $Υ$ production in hadron-nucleus interactions and in nucleus-nucleus collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider. %We define the regions in $x_f$ where nuclear shadowing begins %to set in for \jp\ and \up. As a consequence of the perturbative $Q^2$-dependence of gluon shadowing, we predict that $Υ$ production is less suppressed than the $J/ψ$. We show that antishadowing leads to enhanced \jp\ production at $x_f \lesssim 0$, an effect reduced for $Υ$ production.
Double $J/ψ$ production on the order of 20-30 pb has been observed by the NA3 collaboration. These $ψψ$ pairs, measured in $π^- N$ interactions at 150 and 280 GeV$/c$ and in $pN$ interactions at 400 GeV$/c$, carry a large fraction of the projectile momentum, $x_{ψψ} \geq 0.6$ for the 150 GeV$/c$ beam and $\geq 0.4$ at 280 GeV$/c$. We examine several sources of $ψψ$ pair production within QCD, including ${\cal O}(α_s^4)$ $ψψ$ production, leading-twist $b \overline b$ production and decay, and the materialization of heavy-quark Fock states in the projectile. We estimate the production cross sect…
The photonuclear production of vector mesons in ultraperipheral heavy ion collisions is investigated within the collinear approach using different parameterizations for the nuclear gluon distribution. The integrated cross section and the rapidity distribution for the $AA \to V AA$ ($V = J/Ψ, Υ$) process are computed for energies of RHIC and LHC. A comparison with the recent PHENIX data on coherent production of $J/Ψ$ mesons is also presented. We demonstrate that the study of the exclusive quarkonium photoproduction can be used to constrain the nuclear effects in the gluon distribution.
We discuss the various mechanisms potentially at work in hadroproduction of heavy quarkonia in the light of computations of higher-order QCD corrections both in the Colour-Singlet (CS) and Colour-Octet (CO) channels and the inclusion of the contribution arising from the s-channel cut in the CS channel. We also discuss new observables meant to better discriminate between these different mechanisms.
Quarkonium production in proton-proton collision is interesting in profiling the partons inside the nucleon. Recently, the impact of double parton scatterings (DPSs) was suggested by experimental data of associated quarkonium production (J/psi+Z, J/psi+W, and J/psi+J/psi) at the LHC and Tevatron, in addition to single parton scatterings (SPSs). In this proceedings contribution, we review the extraction of the effective parameter of the DPS through the evaluation of the SPS contributions under quark-hadron duality.
We present a study of heavy quarkonium production in hard diffractive process by the Pomeron exchange for Tevatron and LHC energies. The numerical results are computed using recent experimental determination of the diffractive parton density functions in Pomeron and are corrected by unitarity corrections through gap survival probability factor. We give predictions for single as well as central diffractive ratios. These processes are sensitive to the gluon content of the Pomeron at small Bjorken-x and may be particularly useful in studying the small-x physics. They may also be a good place to t…
Quarkonium data suggest an enhancement of the hadroproduction rate from interactions of the heavy quark pair with a comoving color field generated in the hard gg -> Q\bar{Q} subprocess. We review the motivations and principal consequences of this comover enhancement scenario (CES).
Complete NLO BFKL impact factors for quarkonium hadroproduction in NRQCD: the case of ${}^1S_0^{[1]}$, ${}^1S_0^{[8]}$, and ${}^3S_1^{[8]}$ states
National Centre for Nuclear Research（国家核研究中心）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学，法国国家科学研究中心/欧洲核子研究组织，IJCLab）；Physics Department, Ben-Gurion University of the Negev（内盖夫本古里安大学物理系）
We compute fragmentation corrections to hadroproduction of the quarkonium states $J/ψ$, $χ_{cJ}$, and $ψ(2S)$ at leading power in $m_c^2/p_T^2$, where $m_c$ is the charm-quark mass and $p_T$ is the quarkonium transverse momentum. The computation is carried out in the framework of nonrelativistic QCD. We include corrections to the parton-production cross sections through next-to-leading order in the strong coupling $α_s$ and corrections to the fragmentation functions through second order in $α_s$. We also sum leading logarithms of $p_T^2/m_c^2$ to all orders in perturbation theory. We find that…
We explore how the positivity of the P_T-integrated eta_c-hadroproduction cross-section computed at NLO in alpha_s can set up constraints on the x-dependence of gluon PDFs at low scales.
Soft-gluon resummation within the framework of heavy quarkonium hadroproduction is considered. A few selected cases are studied in detail. A sizeable increase of the cross sections with respect to the next-to-leading order predictions with central factorization/renormalization scale choice can generally be observed. Improvements in the dependence of the cross sections on the two scales, especially when they are kept equal, are also found.
We present a new approach for the prompt production of quarkonia which is based on the $k_T$-factorization method. The production of even C-parity quarkonia proceeds via the fusion of two (off-shell) gluons. Especially in the kinematics of the LHCb experiment these processes are thus expected to be a sensitive probe of the small-$x$ gluon distribution. We calculate the relevant off-shell matrix elements in terms of the light-front wave functions of the quarkonium states. We present our results for scalar and pseudoscalar charmonia and discuss photon transition form factors as well as cross sec…
The three-gluon contribution to $J/ψ$ hadroproduction is calculated within perturbative QCD in the $k_T$ factorization framework. This mechanism involves double gluon density and enters at a non-leading twist, but it is enhanced at large energies due to large double gluon density at small $x$. We obtain results for differential $p_T$-dependent cross-sections for all $J/ψ$ polarisations. The rescattering contribution is found to provide a significant correction to the standard leading twist cross-section at the energies of the Tevatron or the LHC at moderate $p_T$. We also discuss a possible co…
We examine angular distributions of leptons arising from the decay of J/psi in inclusive hadroproduction. Taking into account feed-down contributions from chi_{1,2}, a flat distribution emerges without fine tuning parameters. Changes in the ratio of direct to total J/psi cross sections would change this distribution significantly. Such angular distributions are, therefore, confirmatory tests of the J/psi suppression signal for the production of a quark-gluon plasma. Related effects are predicted for the Upsilon.
In this paper hadroproduction of charmonium states in polarized pp collisions is discussed. A thermal picture for the gluonic cloud of comovers is given making contact between the formalism and the measured unpolarized cross sections. The experimentally observed non-polarization of the final J/psi states leads to the consequence that no correlations between the initial proton spin and the final charmonium spin should be existent. Hence the single spin asymmetries vanish to leading order in that model.
We study the Single-Parton-Scattering (SPS) production of double quarkonia (J/psi+J/psi, J/psi+Upsilon, and Upsilon+Upsilon) in pp and pp(bar) collisions at the LHC and the Tevatron as measured by the CMS, ATLAS, LHCb, and D0 experiments in the Colour-Evaporation Model (CEM), based on the quark-hadron-duality, including Next-to-Leading Order (NLO) QCD corrections up to alpha_s^5. To do so, we also perform the first true NLO --up to alpha_s^4-- study of the p_T-differential cross section for single-quarkonium production. This allows us to fix the non-perturbative CEM parameters at NLO accuracy …
We extend to large transverse momentum pt an approach to quarkonium hadroproduction previously suggested for low pt. The dynamics involves a perturbative rescattering of the heavy quark pair off a comoving color field which originates from gluon radiation prior to the heavy quark production vertex. Assuming simple properties of the comoving field we find the rescattering scenario to be in reasonable agreement with data. At large pt, psi' is predicted to be unpolarized, and chi1 production is favoured compared to chi2. We predict the chi1 polarization to be transverse at low pt, and to get a lo…
We compute the relativistic corrections to the color-singlet contribution to gluon fragmentation into a J/psi at relative order v^4, making use of the nonrelativistic QCD (NRQCD) factorization approach. The corresponding full-QCD process exhibits infrared divergences that manifest themselves as single and double poles in epsilon in 4-2epsilon dimensions. We isolate the infrared-divergent contributions and treat them analytically. In the matching of full QCD to NRQCD, the pole contributions are absorbed into long-distance NRQCD matrix elements. The renormalizations of the ultraviolet divergence…
In this work, we present a thorough analysis of $η_c(1S,2S)$ quarkonia hadroproduction in $k_\perp$-factorisation in the framework of the light-front potential approach for the quarkonium wave function. The off-shell matrix elements for the $g^* g^* η_c(1S,2S)$ vertices are derived. We discuss the importance of taking into account the gluon virtualities. %We discuss the role of relativistic corrections, the Melosh spin-rotation and theoretical uncertainties by comparing our results with the standard NRQCD approach. We present the transverse momentum distributions of $η_c$ for several models of…
Quarkonium production is a sensitive probe of the dynamics of hard scattering, which can `measure' the environment of the heavy quark pair after it is created in a hard process. Quarkonium hadroproduction data indicates that the produced pair experiences a secondary, hard interaction and then ceases to interact at a stage when the pair is still compact (compared to the size of the quarkonium wave function). These features differ from scenarios mostly discussed so far. An approach which relies on an early, perturbative rescattering of the pair with a comoving color field can explain many observ…
Recent measurements of J/psi production in e^+ e^- colliders pose a challenge to the NRQCD factorization theorem for quarkonium production. Discrepancies between leading order calculations of color-octet contributions and the momentum distribution of J/psi observed by Belle and BaBar are resolved by resumming large perturbative and nonperturbative corrections that are enhanced near the kinematic endpoint. The large cross sections for J/psi + c + \bar c and double quarkonium production remain poorly understood. Nonperturbative effects in fixed-target hadroproduction of open charm are also discu…
In this contribution we study the photoproduction of quarkonium in coherent proton-proton and nucleus-nucleus interactions at the LHC. The integrated cross sections and rapidity distributions are estimated using the Color Glass Condensate (CGC) formalism, which takes into account the parton saturation effects at high energies. Nuclear shadowing effects are also taken into account.
We study eta_c and J/psi hadroproduction induced by multiple scattering off fixed centres in the target. We determine the minimum number of hard scatterings required and show that additional soft scatterings may be factorized, at the level of the production amplitude for the eta_c and of the cross section for the J/psi. The J/psi provides an interesting example of soft rescattering effects occurring inside a hard vertex. We also explain the qualitative difference between the transverse momentum broadening of the J/psi and of the Upsilon observed in collisions on nuclei. We point out that resca…
The necessicity of the color-octet mechanism in describing heavy quarkonium production is a longstanding puzzle. Compared to the yields of heavy quarkonium, its polarizations should be a sensitive observable to pin down the color-octet contributions. In this talk, I will focus on the $χ_c$ polarization in hadroproduction processes, which may provide a unique test for the color-octet mechanism in nonrelativistic QCD.
In this paper, we investigate the inclusive diffractive hadroproduction for $\rm η_{c}$ and $\rm η_{b}$ at the LHC energies. Based on the NRQCD factorization formalism and the resolved-Pomeron model for the quarkonium production mechanism, we estimate the rapidity, momentum fraction loss dependence of the cross section. We give prediction ratios for single and central diffractive processes with respect to non diffractive process. These inclusive processes are sensitive to gluon content of Pomeron for small-$x$ and Reggeon for large-$x$, useful to study small and large-$x$ physics and good to t…
We calculate the fragmentation function for charm quark into J/psi at the QCD next-to-leading-order (NLO) and find that the produced J/psi is of larger momentum fraction than it is at the leading-order. Based on the fragmentation function and partonic processes calculated at the NLO, the transverse momentum distribution on J/psi hadroproduction associated with a charm c (or \bar{c}) jet are predicted. We find that the distribution is enhanced by a factor of 2.0--3.3 at the NLO as p_t increased from 10 GeV to 100 GeV and it is measurable at the LHC with charm tagger. The measurement at the LHC …
We proceed to the first study of $η_c'$ prompt hadroproduction at next-to-leading order in $α_s$. Based on heavy-quark-spin symmetry, which is systematically used in quarkonium-production phenomenology, we demonstrate that prompt $η_c'$ can be studied at the LHC with the existing data. We emphasize its relevance to constrain $ψ'$ production, in the same way as the first prompt $η_c'$ data at the LHC lately strongly impacted the phenomenology of $J/ψ$ studies.
We address the unphysical energy dependence of quarkonium-hadroproduction cross sections at Next-to-Leading Order (NLO) in alpha_S which we attribute to an over-subtraction in the factorisation of the collinear singularities inside the PDFs in the MSbar scheme. Such over- or under-subtractions have a limited phenomenological relevance in most of the scattering processes in particle physics. On the contrary, it is particularly harmful for P_T-integrated charmonium hadroproduction which renders a wide class of NLO results essentially unusable. Indeed, in such processes, alphaS is not so small, t…
We describe a light-cone wave function formalism for hadroproduction of heavy-flavors via gluon-gluon fusion. The developed approach is well suited to address coherence effects in heavy-quark production on nuclei at small $x_{2} \lsim 0.1\cdot A^{-1/3}$. Nuclear attenuation in hadroproduction of heavy-flavors is found to be similar to shadowing effects for heavy-flavor structure functions in deep-inelastic scattering from nuclei. Nevertheless, remaining differences in the theoretical formulation of both processes imply corrections to factorization theorems.
We review the status of theoretical evaluations of heavy quark and heavy quarkonium hadroproduction cross sections and their comparisons with experimental data.
Background: Proton-nucleus collisions have been used as a intermediate baseline for the determination of cold medium effects. They lie between proton-proton collisions in vacuum and nucleus-nucleus collisions which are expected to be dominated by hot matter effects. Modifications of the quark densities in nuclei relative to those of the proton are well established although those of the gluons in the nucleus are not well understood. We focus on the effect of these on quarkonium production in proton-lead collisions at the LHC at a center of mass energy of 5.02 TeV.
We present a phenomenological study of the $x_F$ dependence of quarkonium production in high energy proton-nucleus collisions. The \xf~dependence of comover contributions is introduced to account for the observed quarkonium suppression at low $x_F$. Combining comover contributions, nuclear shadowing effect, energy loss mechanism and nuclear absorption together we reproduce the overall \xf~dependence of E772/E789 data.
We study contributions from color-octet quarkonium formation mechanisms to $J/ψ$ hadroproduction at low $p_\perp$. We include transitions of color-octet $c\bar{c}$ states into ``direct'' $J/ψ$ and into $χ_{1,2}$ which decay radiatively into a $J/ψ$. Together with earlier work, this calculation constitutes a complete analysis of $p_\perp$-integrated $J/ψ$ production at leading twist. We find that the leading-twist contribution is not sufficient to reproduce the observed production rates and polarization of the $J/ψ$ and $χ_{1,2}$. Hence there must exist other important quarkonium production mec…
This talk presents a review of recent results for quarkonium production at the LHC from ATLAS, CMS, LHCb, and ALICE. Production cross sections for $J/ψ$, $ψ(2S)$, and $Υ(mS)$, and production ratios for $χ_{c,bJ}$ are found to be in good agreement with predictions from non-relativistic QCD. In contrast, spin-alignment (polarization) measurements seem to disagree with all theoretical predictions. Some other production channels useful for investigating quarkonium hadroproduction mechanisms are also considered.
We suggest the measurement of Drell-Yan (DY) lepton pairs in p-Pb collisions at the LHC (sqrt(s)=5.02 TeV) in order to disentangle the relative contributions of shadowing and coherent energy loss in quarkonium production off nuclei. The nuclear modification of low mass DY production is computed at NLO using various sets of nuclear parton densities. It is then observed that shadowing effects strongly cancel out in the J/psi over DY suppression ratio R_{pA}^{J/psi}(y) / R_{pA}^{DY}(y), unlike the effect of coherent energy loss. Such a measurement could be performed at forward rapidity by the ALI…
The aim of this paper is to introduce a general way to stabilize the perturbative QCD computations of heavy quarkonium production in the boosted or high-momentum transferring region with tree-level generators only. Such an approach is possible by properly taking into account the power-enhanced perturbative contributions in a soft and collinear safe manner without requiring any complete higher-order computations. The complicated NLO results for inclusive quarkonium hadroproduction can be well reproduced within our approach based on a tree-level generator {\sc\small HELAC-Onia}. We have applied …
A model for the production of quarkonium states in the midrapidity region at RHIC and LHC energy range is presented which explores well understood properties of QCD only. An increase of the quarkonium hadronisation time with the initial energy leads to a gradual change of the most important phenomena from fixed target- to collider-energies. We evaluate nuclear effects in the quarkonium production due to medium modification of the momentum distribution of the heavy quarks produced in the hard interactions, i.e. due to the broadening of the transverse momentum distribution. Other nuclear effects…
The charmonium yields are expected to be considerably suppressed if a deconfined medium is formed in high-energy heavy-ion collisions. In addition, the bottomonium states, with the possible exception of the Upsilon(1S) state, are also expected to be suppressed in heavy-ion collisions. However, in proton-nucleus collisions the quarkonium production cross sections, even those of the Upsilon(1S), are also suppressed. These "cold nuclear matter" effects need to be accounted for before signals of the high density QCD medium can be identified in the measurements made in nucleus-nucleus collisions. W…
These lectures present an overview of the current status of the QCD based phenomenology for open and hidden heavy flavor production at high energies. A unified description based on the light-cone color-dipole approach is employed in all cases. A good agreement with available data is achieved without fitting to the data to be explained, and nontrivial predictions for future experiments are made. The key phenomena under discussion are: (i) formation of the wave function of a heavy quarkonium; (ii) quantum interference and coherence length effects; (iii) Landau-Pomeranchuk suppression of gluon ra…
The hadroproduction of the radially excited heavy-quarkonium states $ψ(2S)$ and $Υ(3S)$ at high energies is studied in the parton reggeization approach and the factorization formalism of nonrelativistic QCD at lowest order in the strong-coupling constant $α_s$ and the relative heavy-quark velocity $v$. A satisfactory description of the $ψ(2S)$ transverse-momentum ($p_T$) distributions measured by ATLAS, CMS, and LHCb at center-of-mass energy $\sqrt{S}=7$ TeV is obtained using the color-octet long-distance matrix elements (LDMEs) extracted from CDF data at $\sqrt{S}=1.96$ TeV. The importance of…
We update the study of the QCD corrections to direct J/psi and Upsilon hadroproduction in association with a photon in the QCD-based approach of the Colour-Singlet (CS) Model. After comparison with the recent full next-to-leading-order (NLO) computation for this process, we provide an independent confirmation to the inclusive case that NLO QCD corrections to quarkonium-production processes whose LO exhibits a non-leading P_T behaviour can be reliably computed at mid and large P_T by considering only the real emission contributions accompanied with a kinematical cut. In turn, we evaluate the le…
Used in the fixed-target mode, the multi-TeV LHC proton and lead beams allow for studies of heavy-flavour hadroproduction with unprecedented precision at backward rapidities - far negative Feyman-x - using conventional detection techniques. At the nominal LHC energies, quarkonia can be studies in detail in p+p, p+d and p+A collisions at sqrt(s_NN) ~ 115 GeV as well as in Pb+p and Pb+A collisions at sqrt(s_NN) ~ 72 GeV with luminosities roughly equivalent to that of the collider mode, i.e. up to 20 fb-1 yr-1 in p+p and p+d collisions, up to 0.6 fb-1 yr-1 in p+A collisions and up to 10 nb-1 yr-1…
We study prompt hadroproduction of the charged bottomonium-like states $Z_b^\pm (10610)$ and $Z_b^\pm (10650)$, and the charged charmonium-like states $Z_c^\pm (3900)$ and $Z_c^\pm (4020)$, at the Tevatron and the LHC, provided that these states are $S$-wave hadronic molecules. Using two Monte Carlo event generators, Herwig and Pythia, to simulate the production of heavy meson pairs, we derive an order-of-magnitude estimate of the production rates for these four particles. Our estimates yield a cross section at the nb level for the $Z_b(10610)$ and $Z_b(10650)$. The results for the $Z_c(3900)$…
Heavy quarkonium production in ultra-peripheral nuclear collisions (UPC) is described within the QCD dipole formalism. Realistic quarkonium wave functions in the $Q\bar Q$ rest frame are calculated by solving the Schrödinger equation with a subsequent Lorentz boost to high energy. We rely on several realistic $Q\bar Q$ potentials, which allow to describe well the quarkonium masses and decay widths, as well as data on diffractive electroproduction of quarkonia on protons. Nuclear effects are calculated with the phenomenological dipole cross sections fitted to DIS data. The higher twist quark sh…
Coherent photoproduction of heavy quarkonia on nuclear targets is studied within the QCD color dipole formalism including several main phenomena: i) The correlation between impact parameter of a collision $\vec b$ and dipole orientation $\vec r$; ii) The higher-twist nuclear shadowing related to the $\bar QQ$ Fock state of the photon; iii) The leading-twist gluon shadowing corresponding to higher Fock components of the photon containing gluons; iv) Reduced effects of quantum coherence in a popular Balitsky-Kovchegov equation compared to calculations, which are frequently presented in the liter…
