Based on the nonrelativistic QCD (NRQCD) factorization formalism, we investigate inclusive productions of two spin-triplet S-wave quarkonia pp->2J/psi+X, 2Upsilon+X, and J/psi+Upsilon+X at the CERN Large Hadron Collider. The total production rates integrated over the rapidity (y) and transverse-momentum (p_T) ranges |y|<2.4 and p_T<50 GGeV are predicted to be sigma[pp->2J/psi+X] = 22 (35) nb, sigma[pp->2Upsilon+X] = 24 (49) pb, and sigma[pp->J/psi+Upsilon+X] = 7 (13) pb at the center-of-momentum energy sqrt{s} = 7 (14) TeV. In order to provide predictions that can be useful in both small- and large-p_T regions, we do not employ the fragmentation approximation and we include the spin-triplet S-wave color-singlet and color-octet channels for each quarkonium final state at leading order in the strong coupling. The p_T distributions of pp->2J/psi+X and 2Upsilon+X in the low-p_T region are dominated by the color-singlet contributions. At leading order in the strong coupling, the color-singlet channel is absent for pp->J/psi+Upsilon+X. Therefore, the process pp->J/psi+Upsilon+X may provide a useful probe to the color-octet mechanism of NRQCD.
I review some recent progress, leading to a substantial reduction in the number of non-perturbative parameters, in the calculation of inclusive quarkonium decay widths in the framework of non-relativistic effective field theories.
We report on the current status of knowledge on inclusive quarkonium production in high-energy photon-photon collisions. As a perspective for the LHC, we compute various production cross sections via direct photon-photon fusion in ultra-peripheral pp, pA and AA collisions at the LHC using the tree-level quarkonium amplitude generator MadOnia.
I review recent progress in the calculation of inclusive quarkonium decays in the framework of QCD nonrelativistic effective field theories and in relation to the experimental measurements.
I review some recent progress and open problems in the calculation of heavy-quarkonium inclusive decay widths into light particles in the framework of QCD non-relativistic effective field theories.
The event generator BEEC [Z. Yang, X.G. Wu and X.Y. Wang, Comput. Phys. Commun. 184, 2848 (2013)] was devoted to the simulation of heavy quarkonium production at an unpolarized electron-positron collider. We upgraded it here by adding the generation of quarkonium with polarized electron and positron beams. In addition, the production of color-singlet 2S-wave states were included. Several future electron-positron colliders with high luminosity have been under discussion in the past decade. Especially, their possibility of producing polarized beams is important for providing more insights into t…
In this brief review, I summarize the current theoretical knowledge of heavy quarkonium inclusive decays, with emphasis on recent progress made in the framework of QCD effective field theories. In appendix, I list the imaginary parts of the matching coefficients of the dimension 6 and dimension 8 NRQCD four-fermion operators as presently known.
We briefly summarize some results obtained by potential NRQCD in the non perturbative regime: 1) a systematic procedure to obtain the heavy quarkonium potential in the 1/m expansion (with explicit expressions up to O(1/m^2) in terms of Wilson loops), and 2) a description of the heavy quarkonium inclusive decays to light particles, and of the NRQCD matrix elements (also the octet ones), in terms of the wave-function at the origen and some gluonic field-strength correlators.
We analyse inclusive photoproduction of polarized $^3P_1$ quarkonium in the framework of QCD. To separate nonperturbative and perturbative parts in the density matrix of the produced quarkonium we use a method , which is equivalent to the diagramatic expansion widely used in analysing deeply inelastic scatterings. A systematic expansion in a small velocity $v$, with which a heavy quark moves inside the quarkonium in its rest frame, is performed for the nonperturbative parts, and they are expressed as matrix elements in nonrelativistic QCD. At the leading order of $v$ there are four matrix elem…
We analyze higher twist effect in photoproduction of quarkonium, where the quarkonium is a spin-triplet, S-wave state. We find that the nonperturbative effect of next-to-leading twist is contained in three correlation functions related to the initial hadron and some of the effect of next-to-leading twist is only suppressed by the inverse of the mass square of the quarkonium. A naive estimation indicates that the effect can be significant for charmonium. In the analysis we only take the leading order in the small velocity expansion for the nonperturbative parts related to the quarkonium. Possib…
The inclusive $J/Ψ$ production by direct and resolved photoproduction in the $γ$p scattering is calculated based on the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, which is in good agreement with the experimental data of total cross section distribution of heavy quarkonium production at HERA. Then we extend the formalism including the direct and resolved photoproduction processes to resolved pomeron model to study the heavy quarkonium photoproduction at the LHC energies. We present the predictions of rapidity and transverse momentum distributions of the inclusive di…
We discuss the theory of inclusive production of heavy quarkonium, the comparison between theory and experiment, and the expected nuclear effects in cold nuclear targets. We also present predictions, based on Nonrelativistic QCD (NRQCD), for quarkonium production cross sections in the LHC energy range. We find that nuclear effects in the production cross sections are largely independent of the sizes of the NRQCD matrix elements, the charmonium state that is produced and, in the color-octet case, largely independent of the partonic subprocess that produces the heavy quark-antiquark pair.
In this paper, the production rates of quarkonia eta_c, J/psi, eta_b, Upsilon, B_c and B_c^* through W boson decay at the LHC are calculated, at the leading order in both the QCD coupling constant and in v, the typical velocity of the heavy quark inside of mesons. It shows that a sizable number of quarkonia from W boson decay will be produced at the LHC. Comparison with the predictions by using quark fragmentation mechanism is also discussed. Results show that, for the charmonium production through W decay, the difference between predictions by the fragmentation mechanism and complete leading …
We consider a different power counting in potential NRQCD by incorporating the static potential exactly in the leading order Hamiltonian. We compute the leading relativistic corrections to the inclusive electromagnetic decay ratios in this new scheme. The effect of this new power counting is found to be large (even for top). We produce an updated value for the $η_b$ decay to two photons. This scheme also brings consistency between the weak coupling computation and the experimental value of the charmonium decay ratio.
We show that some NRQCD colour-octet matrix elements can be written in terms of (derivatives of) wave functions at the origin and non-perturbative universal constants once the factorization between the soft and ultrasoft scale is achieved by using an effective field theory where only ultrasoft degrees of freedom are kept as dynamical entities. This allows us to derive a new set of relations between inclusive heavy-quarkonium P-wave decays into light hadrons with different principal quantum number and with different heavy flavour. In particular, we can estimate the branching ratios of bottomoni…
The inclusive $J/Ψ$, $Ψ(2S)$ and $Υ(1S)$ direct and resolved photoproduction are investigated by including the quark subprocesses in the framework of non-relativistic quantum chromodynamics (NRQCD). We find that the theoretical total cross section of heavy quarkonium productions are in good agreement with the data available at HERA, once the $γq$, $qg$ and $qq$ subprocesses in the heavy quark pair productions are taken into account. The inclusive diffractive rapidity and transverse momentum distributions of $J/Ψ$, $Ψ(2S)$ and $Υ(1S)$ in $pp$, $pPb$ and $PbPb$ collisions at LHC are also studied…
We show that perturbation theory may give reasonable numbers for the decays of the bottomonium and charmonium ground states to $e^+e^-$ and to $γγ$. To reach this conclusion it is important to perform the resummation of logs. In particular, we obtain the value $Γ(η_b (1S) \to γγ)=0.35 \pm 0.1 ({\rm th.}) \pm 0.05 (\lQ)$ KeV.
In this talk, I briefly review several models of the heavy quarkonium production at collider energies, and discuss the status of QCD factorization for these production models.
The theoretical description of heavy quarkonium production at high-energy p-pbar and e-p colliders is reviewed. Predictions based on non-relativistic QCD factorisation are confronted with recent charmonium and bottomonium data from the Tevatron and HERA. Potential shortcomings of the present theoretical analyses are discussed, and the prospects for quarkonium physics at the upgraded Tevatron and HERA colliders and at the LHC are summarised.
Considering the possibility to build an $e^+e^-$ collider at the energies around $Z$-boson resonance with a luminosity so high as ${\cal L} \propto 10^{34}cm^{-2}s^{-1}$ (even higher) and the abilities of a modern synthesis detector, we systematically calculate the exclusive two body processes: $e^+e^-$ annihilates into a heavy quarkonium and a photon (initiate state radiation i.e. ISR is involved), at the energies around the $Z$-boson resonance. Since the couplings of $Z$-boson to quarks contain axial vector as well as vector, so here the produced heavy quarkonium may stand for a charmonium s…
I present a short review of recent studies of quarkonium production in proton-proton and proton-nucleus collisions at collider energies in Small-$x$ formalism.
In the paper, the inclusive production of heavy quarkonium $η_Q$ ($Q=b$ or $c$) via $Z$ boson decays within the framework of nonrelativistic QCD effective theory are studied. The contributions from the leading color-singlet and color-octet Fock states are considered. Total and differential decay widths for the inclusive decays $Z \to η_Q+X$ are presented. It is found that the decays $Z\to η_Q +X$ are dominated by the $^3S_1^{[8]}$ component, so the decays can be inversely adopted to determine the values of the long-distance matrix elements $\langle {\cal O}^{η_{c}}(^{3}S_{1}^{[8]})\rangle$ and…
The inclusive diffractive quarkonium photoproduction in $pp$ and $pA$ collisions is investigated considering the Resolved Pomeron Model to describe the diffractive interaction. We estimate the rapidity and transverse momentum distributions for the $J/Ψ$, $Ψ(2S)$ and $Υ$ photoproduction in hadronic collisions at the LHC and present our estimate for the total cross sections at the Run 2 energies. A comparison with the predictions associated to the exclusive production also is presented. Our results indicate that the inclusive diffractive production is a factor $\gtrsim 10$ smaller than the exclu…
The studies of heavy quarkonium inclusive production and polarization at LHC are becoming crucial to solve the puzzle of hadron formation. The results by CMS and the other LHC experiments are compactly presented for the five S-wave states J/Psi, Psi(2S) and Y(nS) (n=1,2,3) and briefly discussed especially in comparison to the theoretical predictions provided by Non Relativistic QCD.
The pseudoscalar quarkonium state, eta_4 1^S_0, formed by the Standard Model (SM) fourth generation quarks, is the best candidate among the fourth generation quarkonia to be produced at the LHC and VLHC. The production of this J^{PC} = 0^{-+} resonance is discussed and the background processes are studied to obtain the integrated luminosity limits for the discovery, depending on its mass.
Inclusive P-wave Quarkonium Decay Widths from Lattice QCD and pNRQCD
Technical University of Munich（慕尼黑工业大学）；University of Southern Denmark（南丹麦大学）；RWTH Aachen University（亚琛工业大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）
We review our recent understanding of quarkonium production at $e^+e^-$ and hadronic colliders from the point of view of potential non-relativistic QCD, and apply it to $P$-wave charmonium and bottomonium inclusive production.
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.
After an introduction motivating the study of quarkonium production, we review the recent developments in the phenomenology of quarkonium production in inclusive scatterings of hadrons and leptons. We naturally address data and predictions relevant for the LHC, the Tevatron, RHIC, HERA, LEP, B factories and EIC. An up-to-date discussion of the contributions from feed downs within the charmonium and bottomonium families as well as from b hadrons to charmonia is also provided. This contextualises an exhaustive overview of new observables such as the associated production along with a Standard Mo…
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.
A rigorous QCD analysis of the inclusive annihilation decay rates of heavy quarkonium states is presented. The effective-field-theory framework of nonrelativistic QCD is used to separate the short-distance scale of annihilation, which is set by the heavy quark mass $M$, from the longer-distance scales associated with quarkonium structure. The annihilation decay rates are expressed in terms of nonperturbative matrix elements of 4-fermion operators in nonrelativistic QCD, with coefficients that can be computed using perturbation theory in the coupling constant $α_s(M)$. The matrix elements are o…
In this contribution we review the status of inclusive jet cross sections at hadron colliders in perturbative QCD, studying in particular the renormalisation and factorisation scale dependence of the one-jet inclusive cross section at NNLO.
I present an introduction to the NRQCD factorization method for calculating annihilation rates and inclusive production rates for heavy quarkonium. Using this method, annihilation decay rates and sufficiently inclusive cross sections are factored into long-distance NRQCD matrix elements and perturbative short-distance coefficients. I derive the velocity-scaling rules that are used to estimate the magnitudes of the nonperturbative NRQCD matrix elements and I describe perturbative matching methods for calculating their short-distance coefficients. Some simple applications for which NRQCD factori…
Recent data from the Tevatron has revealed that the production rate of prompt charmonium at large transverse momentum is orders of magnitude larger than the best theoretical predictions of a few years ago. These surprising results can be understood by taking into account two recent developments that have revolutionized the theoretical description of heavy quarkonium production. The first is the realization that fragmentation must dominate at large transverse momentum, which implies that most charmonium in this kinematic region is produced by the hadronization of individual high-$p_T$ partons. …
We derive the imaginary part of the potential NRQCD Hamiltonian up to order 1/m^4, when the typical momentum transfer between the heavy quarks is of the order of Lambda_{QCD} or greater, and the binding energy E much smaller than Lambda_{QCD}. We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to O(mv^3 x (Lambda_{QCD}^2/m^2,E/m)) and O(mv^5) times a short-distance coefficient, for S- and P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown non-perturbative parameters and, therefore, we obta…
This thesis can be divided into several parts. The first one consists in a detailed historical review of quarkonium physics, centered on the different production models successively introduced. Then comes a review of the currently available data on high-energy hadronic production of J/psi, psi' and Upsilon's. In a third part, we concentrate on the extension of the Colour-Singlet Model beyond the static approximation. In this extension, we emphasise that a simple generalisation of the static case is not sufficient and new 4-point vertices are to be introduced to restore gauge invariance. Since …
The inclusive $Υ(1S,2S,3S)$ photoproduction at the future Circular-Electron-Positron-Collider (CEPC) is studied based on the non-relativistic QCD (NRQCD). Including the contributions from both direct and resolved photons, we present different distributions for $Υ(1S,2S,3S)$ production and the results show there will be considerable events, which means that a well measurements on the $Υ$ photoprodution could be performed to further study on the heavy quarkonium physics at electron-positron collider in addition to hadron colliders. This supplement study is very important to clarify the current s…
In this work we investigate the coherent photoproduction of psi(1S), psi(2S) and Upsilon (1S) states in the proton-nucleus collisions in the LHC energies. Predictions for the rapidity distributions are presented using the color dipole formalism and including saturation effects that are expected to be relevant at high energies. Calculations are done at the energy 5.02 TeV and also for the next LHC run at 8.8 TeV in proton-lead mode. Discussion is performed on the main theoretical uncertainties associated to the calculations.
I describe the NRQCD factorization approach to the inclusive production of heavy quarkonium, contrasting it with the color-singlet and color evaporation models. These approaches differ dramatically in their assumptions about the roles played by color and spin in the production process. They also differ dramatically in their predictions for the production of charmonium at large transverse momentum.
We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to $γ+γ\to η_c+c+\bar{c}$, $γ+γ\to η_b+b+\bar{b}$ and $γ+γ\to B_c+b+\bar{c}$ processes in the framework of non-relativistic QCD (NRQCD) factorization formalism. The cross sections at the SuperKEKB electron-positron collider, as well as the future collider like the Circular Electron Positron Collider (CEPC), are evaluated. Numerical results indicate that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are reduced as expected. Due to the high luminosity…
We discuss spin physics, Guido Altarelli's contribution to it, and what we still have to learn. We set out in particular a programme for incorporating constraints from semi-inclusive data into global fits of polarized PDFs, and discuss the need for the EIC to increase the precision and kinematic coverage of current measurements.
The hadronic decays of quarkonium and the B meson inclusive decay into J/Psi + X, if treated in the zero-binding approximation, suggest a value of the strong coupling constant much smaller than the value implied in the standard model by running from measurements at the Z. Thus, assuming the standard model is correct in the low energy region, there must be very substantial relativistic binding corrections to these processes. We discuss the wave function factor appearing in covariant treatments of quarkonium production and decay processes with special attention to the way in which the spin of th…
The Belle II experiment at the SuperKEKB energy-asymmetric $e^+e^-$ collider is a substantial upgrade of the B factory facility at KEK in Tsukuba, Japan. It aims to record a factor of 50 times more data than its predecessor. The experiment completed a commissioning run in 2018, and began full operation in early 2019. Belle II is uniquely capable of studying the so-called XYZ particles: heavy exotic hadrons consisting of more than three quarks. First discovered by Belle, these now number in the dozens, and represent the emergence of a new category within quantum chromodynamics. This talk will p…
We investigate the pair production of S-wave heavy quarkonium at the LHC in the color-singlet mechanism (CSM) and estimate the contribution from the gluon fragmentation process in the color-octet mechanism (COM) for comparison. With the matrix elements extracted previously in the leading order calculations, the numerical results show that the production rates are quite large for the pair production processes at the LHC. The $p_t$ distribution of double $J/ψ$ production in the CSM is dominant over that in the COM when $p_t$ is smaller than about 8GeV. For the production of double $Υ$, the contr…
We present a systematic study of the production of the heavy quarkonium, i.e., $|(c\bar{c})[n] \rangle$ , $|(b\bar{c})[n] \rangle$ (or $|(c\bar{b})[n] \rangle$), and $|(b\bar{b})[n] \rangle$ quarkonium [$|(Q\bar{Q'})[n]\rangle$ quarkonium for short], through $Z^0$ boson semi-exclusive decays with new parameters \cite{lx} for the heavy quarkonium under the framework of the NRQCD, where $[n]$ stands for $n^1S_0$, $n^3S_1$, $n^1P_0$, $n^3P_J$ ($n=1, \cdots, 6$; $J=(0, 1, 2)$). "Improved trace technology" is adopted to derive the simplified analytic expressions at the amplitude level, which shall …
The rates for diffractive quarkonium plus prompt-photon associated production at the LHC are estimated. The theoretical framework considered in the J/Psi (or Upsilon) production associated with a direct photon at the hadron collider is the non-relativistic QCD (NRQCD) factorization formalism. The corresponding single diffractive cross section is computed based on the hard diffractive scattering factorization supplemented by absorptive corrections. Such processes are sensitive to the gluon content of the Pomeron at small Bjorken-x and they may also be a good place to test the different availabl…
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 …
Dimensional regularization is incompatible with the standard covariant projection methods that are used to calculate the short-distance coefficients in inclusive heavy quarkonium production and annihilation rates. A new method is developed that allows dimensional regularization to be used consistently to regularize the infrared and ultraviolet divergences that arise in these perturbative calculations. We illustrate the method by calculating the leading color-octet terms and the leading color-singlet terms in the gluon fragmentation functions for arbitrary quarkonium states. We resolve a discre…
We calculate the ${\cal O}(α_s^3)$ short-distance, QCD collinear-factorized coefficient functions for all partonic channels that include the production of a heavy quark pair at short distances. This provides the first power correction to the collinear-factorized inclusive hadronic production of heavy quarkonia at large transverse momentum, $p_T$, including the full leading-order perturbative contributions to the production of heavy quark pairs in all color and spin states employed in NRQCD treatments of this process. We discuss the role of the first power correction in the production rates and…
