In this work, we present a thorough analysis of scalar $P$-wave $χ_{Q0}$, $Q=c,b$ quarkonia electromagnetic form factors for the $γ^* γ^* \to χ_{Q0}$ couplings, as well as their hadroproduction observables in $k_\perp$-factorisation using the light-front potential approach for the quarkonium wave function. The electromagnetic form factors are presented as functions of photon virtualities. We discuss the role of the Melosh spin-rotation and relativistic corrections estimated by comparing our results with those in the standard nonrelativistic QCD (NRQCD) approach. Theoretical uncertainties of our approach are found by performing the analysis with two different unintegrated gluon densities and with five distinct models of the $Q\bar Q$ interaction potentials consistent with the meson spectra. The results for the rapidity and transverse momentum distributions of $χ_{Q0}$ produced in high-energy $pp$ collisions at $\sqrt{s} = 13 \, \rm{TeV}$ are shown.
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…
We compute NRQCD long-distance matrix elements that appear in the inclusive production cross sections of $P$-wave heavy quarkonia in the framework of potential NRQCD. The formalism developed in this work applies to strongly coupled charmonia and bottomonia. This makes possible the determination of color-octet NRQCD long-distance matrix elements without relying on measured cross section data, which has not been possible so far. We obtain results for inclusive production cross sections of $χ_{cJ}$ and $χ_{bJ}$ at the LHC, which are in good agreement with measurements.
Recent results on the hadroproduction of charm and beauty are discussed in the context of the current theoretical and experimental status. The areas covered include production of open charm and beauty particles and charm and beauty quarkonia. Experimental results from both fixed target and colliding beam experiments are presented and compared to theoretical predictions. Predictions based on QCD perturbation theory are generally successful in explaining the shapes of differential cross sections but underestimate the scale of the cross section by factors of 2-3. An exception is production of the…
We compute the color-singlet and color-octet nonrelativistic QCD (NRQCD) long-distance matrix elements for inclusive production of $P$-wave quarkonia in the framework of potential NRQCD. In this way, the color-octet NRQCD long-distance matrix element can be determined without relying on measured cross section data, which has not been possible so far. We obtain inclusive cross sections of $χ_{cJ}$ and $χ_{bJ}$ at the LHC, which are in good agreement with data. In principle, the formalism developed in this Letter can be applied to all inclusive production processes of heavy quarkonia.
Hadroproductions of charmonium and bottomonium $χ_J$ in polarized $pp$ collisions at RHIC energies are studied. Two--spin asymmetries $A_{LL}^{χ_J}(pp)$ for these reactions are very good parameters for examining the polarized gluon distributions in a proton.
We extend our previous analysis on inclusive heavy quarkonia hadroproduction to the whole Upsilon(nS) (n=1,2,3) resonance family. We use a Monte Carlo framework with the colour-octet mechanism implemented in the PYTHIA event generator. We include in our study higher order QCD effects such as initial-state emission of gluons and Altarelli-Parisi evolution of final-state gluons. We extract some NRQCD colour-octet matrix elements relevant for Upsilon(nS) (n=1,2,3) hadroproduction from CDF data at the Fermilab Tevatron. Then we extrapolate to LHC energies to predict prompt bottomonia production ra…
In this paper we review the hadroproduction mechanisms of double-charm baryons for the different experimental environments and reinterpret the SELEX and LHCb results.
We derive a light-front Schrodinger-type equation of motion for the quark-antiquark wave function of heavy quarkonia imposing constraints from the holographic soft-wall model.
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…
This talk is based on results obtained for masses and wave functions of heavy quarkonia in a light-front Hamiltonian formulation of QCD with just one flavor of quarks using an ansatz for the mass-gap for gluons. Since the calculated spectra compare reasonably well with data, some further steps one can make are discussed.
We study inclusive processes involving two heavy quarkonia in nonrelativisitic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay $Υ\to χ_{cJ}+X$ via $b\bar{b}({}^3P_{J_b}^{[8]})\to c\bar{c}({}^3P_J^{[1]})+gg$ and the production process $e^+e^-\to J/ψ+χ_{cJ}+X$ via $e^{+}e^{-}\to c\bar{c}({}^3P_{J_1}^{[8]})+c\bar{c}({}^3P_J^{[1]})+g$. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-lea…
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 constituent parton picture of hadrons with logarithmic confinement arises naturally in light-front QCD when the hamiltonian is computed using a perturbative renormalization group; however, rotational symmetry is not manifest as a simple kinematic symmetry. Relevant operators must typically be fine-tuned when a perturbative renormalization group is used, and in light-front field theory such operators contain functions of longitudinal momenta. We explore the possibility that a gluon mass operator with simple longitudinal momentum dependence may improve approximate kinematic rotational symmetry…
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.
In this paper we show that the intrinsic heavy-quark QCD mechanism for the hadroproduction of heavy hadrons at large $x_F$ can resolve the apparent conflict between measurements of double-charm baryons by the SELEX fixed-target experiment and the LHCb experiment at the LHC collider. We show that both experiments are compatible, and that both results can be correct. The observed spectroscopy of double-charm hadrons is in agreement with the predictions of supersymmetric light front holographic QCD.
We revisit the calculation of the width for the radiative decay of a $1^{+-}$ heavy $Q \bar Q$ meson via the channel $1^{+-} \to 0^{-+} +γ$ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy qua…
The light-front wave functions of hadrons allow us to calculate a wide range of physical observables; however, the wave functions themselves cannot be measured. We discuss recent results for quarkonia obtained in basis light-front quantization using an effective Hamiltonian with a confining model in both the transverse and longitudinal directions and with explicit one-gluon exchange. In particular, we focus on the numerical convergence of the basis expansion, as well as the asymptotic behavior of the light-front wave functions. We also illustrate that, for mesons with unequal quark masses, the…
We calculate the electromagnetic (charge, magnetic and quadrupole) form factors and the associated static moments of heavy quarkonia (charmonia and bottomonia) using the Basis Light Front Quantization (BLFQ) approach. For this work, we adopt light front wavefunctions (LFWFs) generated by a holographic QCD confining potential and a one-gluon exchange interaction with fixed coupling. We compare our BLFQ results with the limiting case of a single BLFQ basis state description of heavy quarkonia and with other available results. These comparisons provide insights into relativistic effects. Using th…
A constituent parton picture of hadrons with logarithmic confinement naturally arises in weak coupling light-front QCD. Confinement provides a mass gap that allows the constituent picture to emerge. The effective renormalized Hamiltonian is computed to ${\cal O}(g^2)$, and used to study charmonium and bottomonium. Radial and angular excitations can be used to fix the coupling $α$, the quark mass $M$, and the cutoff $Λ$. The resultant hyperfine structure is very close to experiment.
The perturbative renormalization group for light-front QCD Hamiltonian produces a logarithmically rising interquark potential already in second order, when all gluons are neglected. There is a question if this approach produces also color van der Waals forces between heavy quarkonia and of what kind. This article shows that such forces do exist and estimates their strength, with the result that they are on the border of exclusion in naive approach, while more advanced calculation is possible in QCD.
We present calculations of radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach. The valence sector light-front wavefunctions of heavy quarkonia are obtained from the Basis Light-Front Quantization (BLFQ) approach in a holographic basis. We study the transition form factor with both the traditional "good current" $J^+$ and the transverse current $\vec J_\perp$ (in particular, $J^R=J^x+i J^y$). This allows us to investigate the role of rotational symmetry by considering vector mesons with different magnetic projections ($m_j=0,\pm 1$). We use t…
This is the third paper on hadronic light front wave functions (LFWFs). We derive a light front Hamiltonian from first principles using the key features of the QCD vacuum at low resolution. In the first approximation, it gives transverse oscillator and longitudinal harmonic modes and yields the correct Regge trajectories. For heavy quarkonia, we compare its spectrum to that obtained from the usual Schroedinger equation in the rest frame. We use the same approach for light quarks, and investigate the role of confinement and chiral symmetry breaking in the quark-antiquark sector. We then study s…
The ladder kernel of the Bethe-Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the $D_u$, $D_s$, $B_u$, $B_s$ and $B_c$ mesons and the heavy quarkonia $η_c$ and $η_b$ within the same framework at a physical pion mass. The corresponding Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full…
In this work we compare mass spectra and decay constants obtained from two recent, independent, and fully relativistic approaches to the quarkonium bound-state problem: the Hamiltonian basis light-front quantization (BLFQ) approach, where light-front wave functions are naturally formulated; and, the covariant spectator theory (CST), based on a reorganization of the Bethe-Salpeter equation. Even though conceptually different, both solutions are obtained in Minkowski space. Comparisons of decay constants for more than ten states of charmonium and bottomonium show favorable agreement between the …
In this paper, we study fully differential quarkonia photoproduction observables in ultraperipheral collisions (UPCs) as functions of momentum transfer squared. We employ the dipole picture of the QCD part of the scattering with proton and nucleus targets, with the projectile being a quasi-real photon flux emitted by an incoming hadron. We analyse such observables for ground $J/ψ$, $Υ(1S)$ and excited $ψ'$, $Υ(2S)$ states whose light-front wave functions are obtained in the framework of interquark potential model incorporating the Melosh spin transformation. Two different low-$x$ saturation mo…
We study the charmonium 2S states $ψ'$ and $η_c'$, and the bottomonium 2S states $Υ'$ and $η_b'$, using the light-front quark model and the 2S state wave function of harmonic oscillator as the approximation of the 2S quarkonium wave function. The decay constants, transition form factors and masses of these mesons are calculated and compared with experimental data. Predictions of quantities such as Br$(ψ' \to γη_c')$ are made. The 2S wave function may help us learn more about the structure of these heavy quarkonia.
This is the first of a sequence of papers that address the non-perturbative origin of the central, and spin-dependent forces between quarks. Its main thrust is a focus on meson spectroscopy in the center of mass frame. We suggest a "dense instanton ensemble" model for the QCD vacuum, to explain the interquark forces in mesons, from quarkonia to heavy-light and light-light ones, to the extent it is possible. The sequels will show how to export these interactions to the light front, and derive the corresponding Hamiltonians and mesonic wavefunctions.
In this work we use the framework of the Dyson-Schwinger and Bethe-Salpeter equations to compute Light-Cone Distribution Amplitudes of heavy-light mesons and quarkonia. In studying the meson properties, we introduce a flavor dependence in the heavy-quark sector of the Bethe-Salpeter ladder kernel which yields improved numerical results for masses and leptonic decay constants of the pseudoscalar $D$, $D_s$, $B$ and $B_s$ mesons. Finally, the corresponding heavy-light Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the …
We study the radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach, and investigate the effects of using different current component and different reference frames. In practical calculations with truncated Fock spaces, transition form factors may acquire current component dependence and frame dependence, and such dependences could serve as a measure for the Lorentz symmetry violation. We suggest using the transverse current with $m_j=0$ state of the vector meson, since this procedure employs the dominant spin components of the light-front wavef…
We investigate the inclusive hadroproduction of a heavy quarkonium ($J/ψ$ or $Υ$), in association with a light-flavored jet, as a testing ground for the semi-hard regime of QCD. Our theoretical setup is the hybrid high-energy and collinear factorization, where the standard collinear approach is supplemented by the $t$-channel resummation of leading and next-to-leading energy logarithms à la BFKL. We present predictions for rapidity and azimuthal-angle differential distributions, hunting for stabilizing effects of the high-energy series under higher-order corrections. Our reaction represents an…
In this paper we study the relation between the light-front (infinite momentum) and rest-frame descriptions of quarkonia. While the former is more convenient for high-energy production, the latter is usually used for the evaluation of charmonium properties. In particular, we discuss the dynamics of a relativistically moving system with nonrelativistic internal motion and give relations between rest frame and light-front potentials used for the description of quarkonium states. We consider two approximations, first the small coupling regime, and next the nonperturbative small binding energy app…
University of Science and Technology of China（中国科学技术大学）；Anhui Center for Fundamental Sciences in Theoretical Physics, University of Science and Technology of China（中国科学技术大学理论物理基础科学中心）；State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子科学和技术国家重点实验室）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；Huazhong University of Science and Technology（华中科技大学）
The masses and vertex functions of heavy and heavy-light mesons, described as quark-antiquark bound states, are calculated with the Covariant Spectator Theory (CST). We use a kernel with an adjustable mixture of Lorentz scalar, pseudoscalar, and vector linear confining interaction, together with a one-gluon-exchange kernel. A series of fits to the heavy and heavy-light meson spectrum were calculated, and we discuss what conclusions can be drawn from it, especially about the Lorentz structure of the kernel. We also apply the Brodsky-Huang-Lepage prescription to express the CST wave functions fo…
In this paper, a study of two-photon and two-gluon decays in the context of p-wave heavy quarkonia is presented. Within the covariant light-front framework, the annihilation rates of scalar and tensor quarkonium states are derived. In the absence of free parameters in this case, the results for the charmonium decay widths are consistent with the experimental data. However, in comparison to other theoretical calculations, there are large discrepancies in our results regarding bottomonia.
We study the light-unflavored mesons as relativistic bound states in the nonperturbative Hamiltonian formalism of the basis light-front quantization (BLFQ) approach. The dynamics for the valence quarks of these mesons is specified by an effective Hamiltonian containing the one-gluon exchange interaction and the confining potentials both introduced in our previous work on heavy quarkonia, supplemented additionally by a pseudoscalar contact interaction. We diagonalize this Hamiltonian in our basis function representation to obtain the mass spectrum and the light-front wave functions (LFWFs). Bas…
We study exclusive production of scalar $χ_{c0}\equiv χ_c(0^{++})$ and pseudoscalar $η_c$ charmonia states in proton-proton collisions at the LHC energies. The amplitudes for $gg \to χ_{c0}$ as well as for $gg \to η_c$ mechanisms are derived in the $k_{T}$-factorization approach. The $p p \to p p η_c$ reaction is discussed for the first time. We have calculated rapidity, transverse momentum distributions as well as such correlation observables as the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The latter two observables are very different for $χ_{c0}$ and $η_c$ case…
We study charmonium and bottomonium as relativistic bound states in a light-front quantized Hamiltonian formalism. The effective Hamiltonian is based on light-front holography. We use a recently proposed longitudinal confinement to complete the soft-wall holographic potential for the heavy flavors. The spin structure is generated from the one-gluon exchange interaction with a running coupling. The adoption of asymptotic freedom improves the spectroscopy compared with previous light-front results. Within this model, we compute the mass spectroscopy, decay constants and the r.m.s. radii. We also…
We present a novel study on the inclusive production of a heavy quarkonium ($J/ψ$ or $Υ$), in association with a light-flavored jet, as a test field of the high-energy QCD dynamics. The large transverse momenta at which the two final-state objects are detected permits us to perform an analysis in the spirit of the variable-flavor number scheme (VFNS), in which the cross section for the hadroproduction of a light parton is convoluted with a perturbative fragmentation function that describes the transition from a light quark to a heavy hadron. The quarkonium collinear fragmentation function is b…
We develop a unified algebraic model which satisfactorily describes the internal structure of pion and kaon as well as heavy quarkonia ($η_c$ and $η_b$). For each of these mesons, we compute their generalized parton distributions (GPDs), built through the overlap representation of their light-front wave function, tightly constrained by the modern and precise knowledge of their quark distribution amplitudes. From this three-dimensional knowledge of mesons, we deduce parton distribution functions (PDFs) as well as electromagnetic form factors and construct the impact parameter space GPDs. The PD…
University of Science and Technology of China（中国科学技术大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Anhui Center for Fundamental Sciences in Theoretical Physics（安徽理论物理基础科学中心）；School of Mechanics and Physics, Anhui University of Science and Technology（安徽理工大学力学与光电学院）
We derive the light-front wave function (LFWF) representation of the $γ^{\star} γ^{\star} \to η_{c} (1S),η_{c}(2S)$ transition form factor $F(Q^2_1,Q^2_2)$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schrödinger equation for a variety of $c\bar{c}$ potentials. We compare our results to the BaBar experimental data for the $η_{c}(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massle…
Near-threshold heavy quarkonium photoproduction in a light-front spectator model
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所高精度核谱学重点实验室）；Department of Physics, Indian Institute of Technology Kanpur（坎普尔印度理工学院物理系）；University of Science and Technology of China（中国科学技术大学）
We analyze the validity of a commonly used identification between structures of the virtual photon $γ^*\to Q\bar Q$ and vector meson $V\to Q\bar Q$ transitions. In the existing studies of $S$-wave vector-meson photoproduction in the literature, such an identification is typically performed in the light-front (LF) frame while the radial component of the meson wave function is rather postulated than computed from the first principles. The massive photon-like $V\to Q\bar Q$ vertex, besides the $S$-wave component, also contains an extra $D$-wave admixture in the $Q\bar Q$ rest frame. However, the …
The study of the dynamics of strong interactions in the high-energy regime is a core line of frontier researches at the LHC as well as at new-generation colliding facilities. Here, the enhancement of energy logarithms due to diffractive semi-hard final states spoils the convergence of the perturbative series in the QCD running coupling, thus calling for an improvement of the pure collinear factorization that accounts for an all-order resummation of these large logarithmic contributions. Motivated by the recent discovery that inclusive emissions of heavy-flavored particles allow for clear signa…
As a sequel of our preceding work [1] we carry out a comprehensive comparative study between the quasi parton distribution functions (PDFs), distribution amplitudes (DAs) and their light-cone counterparts for various flavor-neutral mesons, in the context of the 't Hooft model, that is, the two-dimensional QCD in the large $N$ limit. In contrast to the original derivation via diagrammatic techniques exemplified by Dyson-Schwinger and Bethe-Salpeter equations, here we employ the Hamiltonian operator approach to reconstruct the celebrated 't Hooft equation in light-front quantization, and Bars-Gr…
