Nonrelativistic QCD Research Articles

Heavy meson thresholds in Born-Oppenheimer effective field theory

We consider heavy meson-antimeson pairs and their coupling to quarkonium in the context of nonrelativistic EFTs incorporating the adiabatic expansion. We work out all the leading order couplings of quarkonium to heavy meson-antimeson pairs and obtain their contributions to the masses and widths of quarkonia. We match the new potentials terms to NRQCD. Using the available lattice data for the coupled system of quarkonium and the lowest laying heavy meson-antimeson pair, we extract the mixing potential and use it to compute numerically the contributions of $D\bar{D}(B\bar{B})$ and $D_s\bar{D}_s(B_s\bar{B}_s)$ to the masses and widths of the charmonium (bottomonium) states for $l=0,1,2$ and up to $n=6$ covering the states in threshold region. When a quarkonium state and a heavy meson-antimeson pair are separated by small energy gaps, their interactions can be described by a threshold EFT with contact interactions. We work out the matching between the two EFTs obtaining the couplings of the threshold EFT in terms of the mixing potential and quarkonium wave functions.

The high-energy spectrum of QCD from inclusive emissions of charmed B-mesons

We investigate the high-energy behavior of strong interactions through a study on the inclusive hadroproduction of charmed B-mesons (Bc or Bc⁎ states) accompanied by non-charmed b-hadron or light-flavored jet emissions at LHC energies and kinematic configurations. By making use of the hybrid high-energy and collinear factorization, where the standard fixed-order description based on collinear parton densities and fragmentation functions is enhanced via the Balitsky–Fadin–Kuraev–Lipatov (BFKL) resummation of energy logarithms, we perform a full next-to-leading order analysis of distributions differential in rapidities and azimuthal angles calculated by the hands of the JETHAD multi-modular working package. The large observed transverse momenta justify the use of non-relativistic QCD next-to-leading order fragmentation functions to describe the heavy-flavored meson production mechanism. We come out with the conclusion that the study of this process can be included in forthcoming analyses at the (high-luminosity) LHC as a tool to access the QCD dynamics at high energies and to explore possible common ground between different resummation approaches.

Study of Differential Scattering Cross-Section Using Yukawa Term of Medium-Modified Cornell Potential

In the present work, we have studied the differential scattering cross-section for ground states of charmonium and bottomonium in the frame work of the medium-modified form of quark-antiquark potential and Born approximation using the nonrelativistic quantum chromodynamics approach. To reach this end, quasiparticle (QP) Debye mass depending upon baryonic chemical potential ( μ b ) and temperature has been employed, and hence the variation of differential scattering cross-section with baryonic chemical potential and temperature at fixed value of the scattering angle ( θ = 9 0 o ) has been studied. The variation of differential scattering cross-section with scattering angle θ (in degree) at fixed temperature and baryonic chemical potential has also been studied. We have also studied the effect of impact parameter and transverse momentum on differential scattering cross-section at θ = 90 o .

χc production in modified NRQCD

In a previous paper, we had modified Non-Relativistic QCD as it applies to quarkonium production by taking into account the effect of perturbative soft-gluon emission from the colour-octet quarkonium states. We tested the model by fitting the unknown non-perturbative parameter in the model from Tevatron data and using that to make parameter-free predictions for J/ψ and ψ′ production at the LHC. In this paper, we study χc production: we fit as before the unknown matrix-element using data from Tevatron. We, then, extend the results of the previous paper for J/ψ production by calculating the effect of χc feed-down to the J/ψ cross-section, which, by comparing with CMS results at s= 13 TeV, we demonstrate to be small. We have also computed χc1 and χc2 at s=7 TeV and find excellent agreement with data from the ATLAS experiment.

Scrutinizing new physics in semi-leptonic B c → J/ψτν decay

We perform a global analysis of the b → cτν data using the recent lattice results on the B c → J/ψ vector and axial-vector form factors. To explore the effects from the tensor operator of new physics beyond the Standard Model, we determine the tensor form factors by using the non-relativistic QCD (NRQCD) relations between tensor and (axial-)vector form factors. Based on the lattice + NRQCD form factors, we fit the Wilson coefficients and the new physics couplings in R 2, S 1 and U 1 leptoquark models by including the recently measured R(Λ c ) and imposing the relaxed constraint in light of the recent studies on LEP1 data and B c lifetime. We give predictions for the experimental observables including R(J/ψ), P τ (J/ψ), F L (J/ψ) and as well as their q 2 distribution in new physics scenarios/models. Our results suggest that the longitudinal τ polarization fraction P τ (J/ψ) and the forward–backward asymmetry are useful for testing the R 2 leptoquark model.

Higher-Order QCD Corrections to ϒ Decay into Double Charmonia

In this Letter, we study the exclusive decay of ϒ into J/ψ in association with η_{c} (χ_{c0,1,2}). The decay widths for different helicity configurations are evaluated up to QCD next-to-leading order within the nonrelativistic QCD framework. We find that the QCD corrections notably mitigate the renormalization scale dependence of the decay widths for all the processes. The branching fraction of ϒ→J/ψ+χ_{c1} is obtained as 3.73_{-2.06-1.19}^{+5.10+0.10}×10^{-6}, which agrees well with the Belle measurement, i.e., Br(ϒ→J/ψ+χ_{c1})=(3.90±1.21±0.23)×10^{-6}. For the other processes, our results of the branching fractions are compatible with the upper limits given by the Belle experiments, except for ϒ(2S)→J/ψ+χ_{c1}, where some tension exists between theory and experiment. Having the polarized decay widths, we study the J/ψ polarization, which turns out to be independent of any nonperturbative parameters. Further, according to our calculation, it is promising to measure all the processes at Super B factory thanks to the high luminosity.

Inclusive J/ψ photoproduction at the ILC within the framework of non-relativistic QCD

Based on the non-relativistic quantum chromodynamics factorization framework, we study the inclusive J/ψ photoproduction at the future high energy e+e− collider, International Linear Collider(ILC), where the initial photons come from the back-scattering of laser and electron (positron). The intermediate states, coverline{c} (3 {S}_1^{left[mathbf{1}right]} ,1 {S}_0^{left[mathbf{8}right]} ,3 {S}_1^{left[mathbf{8}right]} , 3 {P}_{0,1,2}^{left[mathbf{8}right]} ), and resolved photoproduction processes are considered. Numerical results show that the cross section of J/ψ photoproduction at the ILC could be very large, and the single resolved pro- cess via coverline{c} (3 {S}_0^{left[mathbf{8}right]} ) intermediate state dominates primarily the production. We also present various kinematic distributions for J/ψ photoproduction. Combining the high luminosity of the collision, J/ψ photoproduction at the ILC shall provide a good platform to test the NRQCD factorization.

Relations among Bc→ J/ψ, ηc form factors

We analyze the form factors parametrizing the Bc→ J/ψ, ηc matrix elements of the operators in a generalized low-energy b → c semileptonic Hamiltonian. We consider an expansion in nonrelativistic QCD, classifying the heavy quark spin symmetry breaking terms and expressing the form factors in terms of universal functions in a selected kinematical range. Using as an input the lattice QCD results for the Bc → J/ψ matrix element of the SM operator, we obtain information on other form factors. The extrapolation to the full kinematical range is also presented.

Heavy quarkonium dynamics at next-to-leading order in the binding energy over temperature

Using the potential non-relativistic quantum chromodynamics (pNRQCD) effective field theory, we derive a Lindblad equation for the evolution of the heavy-quarkonium reduced density matrix that is accurate to next-to-leading order (NLO) in the ratio of the binding energy of the state to the temperature of the medium. The resulting NLO Lindblad equation can be used to more reliably describe heavy-quarkonium evolution in the quark-gluon plasma at low temperatures compared to the leading-order truncation. For phenomenological application, we numerically solve the resulting NLO Lindblad equation using the quantum trajectories algorithm. To achieve this, we map the solution of the three-dimensional Lindblad equation to the solution of an ensemble of one-dimensional Schrödinger evolutions with Monte-Carlo sampled quantum jumps. Averaging over the Monte-Carlo sampled quantum jumps, we obtain the solution to the NLO Lindblad equation without truncation in the angular momentum quantum number of the states considered. We also consider the evolution of the system using only the complex effective Hamiltonian without stochastic jumps and find that this provides a reliable approximation for the ground state survival probability at LO and NLO. Finally, we make comparisons with our prior leading-order pNRQCD results and experimental data available from the ATLAS, ALICE, and CMS collaborations.

Study of χbJ(nP ) → ωΥ(1S) at Belle

We report preliminary results from a study of hadronic transitions of the χbJ (nP) states of bottomonium at Belle. The P-wave states are reconstructed in transitions to the Υ(1S) with the emission of an ω meson. The transitions of the n = 2 triplet states provide a unique laboratory in which to study nonrelativistic quantum chromodynamics, as the kinematic threshold for production of an ω and Υ(1S) lies between the J = 0 and J = 1 states. A search for the χbJ (3P) states is also reported.

BEEC2.0: An upgraded version for the production of heavy quarkonium at electron-positron collider

The event generator BEEC (Yang et al. (2013) [11]) 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 the underlying physics. This upgraded version offers a useful tool for the feasibility study on quarkonium from the experimental side. New version program summaryProgram title: BEEC version 2.0CPC Library link to program files:https://doi.org/10.17632/bvtwwm22tj.1Licensing provisions: GNU General Public License 3Programming language: FORTRAN 77/90Journal Reference of previous version: Comput. Phys. Commun. 184 (2013) 2848Does the new version supersede the previous version?: YesReasons for the new version: The proposed electron-positron colliders could possibly produce polarized beams, with which it would be helpful to provide more insights into the structure of the underlying physics in heavy quarkonium. Thus, it is essential to simulate the quarkonium production through polarized beams. In addition, the Bc(2S) state attracted more and more interests since its discovery, which makes it necessary to produce the 2S-wave excited states.Summary of revisions: Two polarized amplitudes of leptonic scattering are computed theoretically. The relevant codes of the formula are included in BEEC2.0. Meanwhile, new parameters for the 2S-excited states are also included.Nature of problem: Although PYTHIA can generate events for many processes, a dedicated event generator is also necessary. Especially, PYTHIA does not internally produce events with polarized beams. BEEC is implemented into PYTHIA as an external process for simulating heavy quarkonium events with high efficiency. Further hadronization and decay simulation can be done by using PYTHIA subroutine.Solution method: Two projection operators are used to calculate the polarized leptonic scattering amplitudes with the help of improved trace technology [1,2]. The code with option can generate events through unpolarized and polarized initial beams. In addition to the (QQ′¯)-quarkonium (Q,Q′=b,c) in color-singlet 1S-wave states, 1P-wave states, and the color-octet 1S-wave states in the last version, BEEC 2.0 also deal with the production of 2S-wave excited states within the framework of non-relativistic QCD [3].Additional comments including restrictions and unusual features: About the running time, it depends on which option one chooses to match PYTHIA when generating the heavy quarkonium events. Typically, for the production of the S-wave quarkonium states, if setting IDWTUP=1 (unweighted events), then it takes about 21 minutes on a 3.22 GHz Apple M1 Pro Processor machine to generate 105 events; if setting IDWTUP=3 (weighted events), it takes only ∼5 minutes to generate 105 events. While for the production of the P-wave quarkonium states, the time will be almost one hundred times longer than the case of the S-wave quarkonium.

Search for b¯b¯us and b¯c¯ud tetraquark bound states using lattice QCD

We use lattice QCD to investigate the existence of strong-interaction-stable antiheavy-antiheavy-light-light tetraquarks. We study the $\overline{b}\overline{b}us$ system with quantum numbers ${J}^{P}={1}^{+}$ as well as the $\overline{b}\overline{c}ud$ systems with quantum numbers $I({J}^{P})=0({0}^{+})$ and $I({J}^{P})=0({1}^{+})$. We carry out computations on five gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass. The bottom quarks are implemented using lattice nonrelativistic QCD, and the charm quarks using an anisotropic clover action. In addition to local diquark-antidiquark and local meson-meson interpolating operators, we include nonlocal meson-meson operators at the sink, which facilitates the reliable determination of the low-lying energy levels. We find clear evidence for the existence of a strong-interaction-stable $\overline{b}\overline{b}us$ tetraquark with binding energy $(\ensuremath{-}86\ifmmode\pm\else\textpm\fi{}22\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$ and mass $(10609\ifmmode\pm\else\textpm\fi{}22\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$. For the $\overline{b}\overline{c}ud$ systems we do not find any indication for the existence of bound states, but cannot rule out their existence either.

Reformulation of the twist-3 gluon Sivers effect toward an application to heavy quarkonium production

In this paper, we propose a new calculation method for the twist-3 gluon Sivers effect within the collinear factorization approach. The method called pole calculation has been used to derive the cross section formula for the single transverse-spin asymmetry as a standard method. We point out that we encounter a problem when we try to apply the pole calculation to the single transverse-spin asymmetry in the heavy quarkonium production whose hadronization mechanism is described by nonrelativistic QCD framework. We show that the new calculation method solves this problem and successfully reproduces known results derived by the pole calculation. Our new method extends the applicability of the twist-3 calculation technique to heavy quarkonium productions that are ideal observables for the investigation of the gluon Sivers effect.

Cos2ϕt azimuthal asymmetry in back-to-back J/ψ -jet production in ep→eJ/ψ jet X at the EIC

In this article, we investigate the $\cos2\phi_t$ azimuthal asymmetry in $e ~p\rightarrow e ~J/\psi ~Jet~ X$, where the $J/\psi$-jet pair is almost back-to-back in the transverse plane, within the framework of the generalized parton model(GPM). We use non-relativistic QCD(NRQCD) to calculate the $J/\psi$ production amplitude and incorporate both color singlet(CS) and color octet(CO) contributions to the asymmetry. We estimate the asymmetry using different parameterizations of the gluon TMDs in the kinematics that can be accessed at the future electron-ion collider (EIC) and also investigate the impact of transverse momentum dependent (TMD) evolution on the asymmetry. We present the contributions coming from different states to the asymmetry in NRQCD.

Higgs boson decay to charmonia via c-quark fragmentation

We calculate the decay branching fractions of the Higgs boson to J/ψ and ηc via the charm-quark fragmentation mechanism for the color-singlet and color-octet states in the framework of non-relativistic QCD. The decay rates are governed by the charm-quark Yukawa coupling, unlike the decay H → J/ψ + γ, which is dominated by the γ∗-J/ψ mixing. We find that the decay branching fractions can be about 2×10−5 for Hto coverline{c}+J/psi , and 6 × 10−5 for Hto coverline{c}+{eta}_c . We comment on the perspective of searching for the Higgs boson to J/ψ transition at the High-Luminosity LHC for testing the charm-quark Yukawa coupling.

Sivers asymmetry in inelastic $J/ψ$ leptoproduction at the EIC

We study the Sivers asymmetry in inelastic J/\psiJ/ψ leptoproduction, ep^\uparrow \to e+ J/\psi+Xep↑→e+J/ψ+X, within a transverse momentum dependent scheme, the so-called generalized parton model (GPM). The effects of final-state interactions are properly taken into account by employing the color-gauge invariant GPM (CGI-GPM). For the J/\psiJ/ψ formation the non-relativistic QCD (NRQCD) framework is adopted. Predictions for unpolarized cross sections and maximized Sivers asymmetries at EIC energies are given.

Bottomonium suppression and elliptic flow in heavy-ion collisions

In this proceedings contribution I review recent progress concerning the suppression of bottomonium production in the quark-gluon plasma. Making use of open quantum system methods applied to potential non-relativistic quantum chromodynamics one can show that the dynamics of heavy-quarkonium bound states satisfying the scale hierarchy 1/a0 » πT ∼ mD » E obey a Lindblad equation whose solution provides the quantum evolution of the heavy-quarkonium reduced density matrix. To solve the resulting Lindblad equation we use a quantum trajectories algorithm which allows one to include all possible angular momentum states of the quark-antiquark probe in a scalable manner. We solve the Lindblad equation using a tuned 3+1D dissipative hydrodynamics code for the background temperature evolution. We then consider a large number of Monte-Carlo sampled bottomonium trajectories embedded in this background. This allows us to extract the centrality- and pT-dependence of the nuclear suppression factor RAA[Υ] and elliptic flow v2[Υ]. We find good agreement between our model predictions and available √ sNN = 5.02 TeV = 5.02 TeV Pb-Pb collision experimental data from the ALICE, ATLAS, and CMS collaborations.

Impact of heavy quark and quarkonium data on nuclear gluon PDFs

A clear understanding of nuclear parton distribution functions (nPDFs) plays a crucial role in the interpretation of collider data taken at the Relativistic Heavy Ion Collider (RHIC), the Large Hadron Collider (LHC) and in the near future at the Electron-Ion Collider (EIC). Even with the recent inclusions of vector boson and light meson production data, the uncertainty of the gluon PDF remains substantial and limits the interpretation of heavy ion collision data. To obtain new constraints on the nuclear gluon PDF, we extend our recent nCTEQ15WZ+SIH analysis to inclusive quarkonium and open heavy-flavor meson production data from the LHC. This vast new data set covers a wide kinematic range and puts strong constraints on the nuclear gluon PDF down to $x\lesssim 10^{-5}$. The theoretical predictions for these data sets are obtained from a data-driven approach, where proton-proton data are used to determine effective scattering matrix elements. This approach is validated with detailed comparisons to existing next-to-leading order (NLO) calculations in non-relativistic QCD (NRQCD) for quarkonia and in the general-mass variable-flavor-number scheme (GMVFNS) for the open heavy-flavored mesons. In addition, the uncertainties from the data-driven approach are determined using the Hessian method and accounted for in the PDF fits. This extension of our previous analyses represents an important step toward the next generation of PDFs not only by including new data sets, but also by exploring new methods for future analyses.

Production and polarization of S -wave quarkonia in potential nonrelativistic QCD

Based on the potential nonrelativistic QCD formalism, we compute the nonrelativistic QCD long-distance matrix elements (LDMEs) for inclusive production of $S$-wave heavy quarkonia. This greatly reduces the number of nonperturbative unknowns and brings in a substantial enhancement in the predictive power of the nonrelativistic QCD factorization formalism. We obtain improved determinations of the LDMEs and find cross sections and polarizations of $J/\ensuremath{\psi}$, $\ensuremath{\psi}(2S)$, and excited $\mathrm{\ensuremath{\Upsilon}}$ states that agree well with LHC data. Our results may have important implications in pinning down the heavy quarkonium production mechanism.

Next-to-leading order QCD calculation of Bc to charmonium tensor form factors

We present a next-to-leading order (NLO) QCD corrections to $B_c\to \eta_c$ and $B_c\to J/\psi$ tensor form factors within nonrelativistic QCD (NRQCD) framework. The full analytical results for $B_c$ to S-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviours of tensor form factors in hierarchy heavy quark limit, i.e. $m_b\to\infty,~ m_c\to\infty, ~\mathrm{and }~m_c/m_b\to0$. A compact expression for tensor form factors are given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed especially at large momentum recoil point. The numerical results for the $B_c$ to charmonium tensor form factors in all the physical region are given in the end.