Nonrelativistic QCD Research Articles

Kinematic distributions of the \u03b7c leptoproduction in association with light hadrons

The ηc meson leptoproduction is calculated within the nonrelativistic QCD framework for the first time. It is found that the colour-singlet channel, although suppressed by a factor of αs relative to the colour-octet ones, provides important contribution for almost all the experimental conditions, which disagrees with some of the expectations before computation. We present the differential cross sections with respect to {p}_t^2 , {p}_t^{bigstar 2} , Q2, W, and z, for both HERA and EIC experimental conditions as a reference for future studies. The scale dependence and long-distance-matrix-element dependence are also investigated in this paper.

Bottomonium production and polarization in the NRQCD with k_T-factorization. III: Upsilon (1S) and chi _b(1P) mesons

The Upsilon (1S) meson production and polarization at high energies is studied in the framework of the k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for a bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative chi _b(mP) decays and contributions from Upsilon (3S) and Upsilon (2S) decays are taken into account. The transverse momentum dependent (TMD) gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation and the Kimber-Martin–Ryskin prescription. Treating the non-perturbative color octet transitions in terms of multipole radiation theory, we extract the corresponding non-perturbative matrix elements for Upsilon (1S) and chi _b(1P) mesons from a combined fit to transverse momenta distributions measured at various LHC experiments. Then we apply the extracted values to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (1S) spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.

Bottomonium production in heavy-ion collisions using quantum trajectories: Differential observables and momentum anisotropy

We report predictions for the suppression and elliptic flow of the $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ as a function of centrality and transverse momentum in ultra-relativistic heavy-ion collisions. We obtain our predictions by numerically solving a Lindblad equation for the evolution of the heavy-quarkonium reduced density matrix derived using potential nonrelativistic QCD and the formalism of open quantum systems. To numerically solve the Lindblad equation, we make use of a stochastic unraveling called the quantum trajectories algorithm. This unraveling allows us to solve the Lindblad evolution equation efficiently on large lattices with no angular momentum cutoff. The resulting evolution describes the full 3D quantum and non-abelian evolution of the reduced density matrix for bottomonium states. We expand upon our previous work by treating differential observables and elliptic flow; this is made possible by a newly implemented Monte-Carlo sampling of physical trajectories. Our final results are compared to experimental data collected in $\sqrt{s_{NN}} = 5.02$ TeV Pb-Pb collisions by the ALICE, ATLAS, and CMS collaborations.

Cos(2ϕh) asymmetry in J/ψ production in unpolarized ep collision

We present a calculation of the $cos (2 \phi_h)$ asymmetry in $J/\psi$ production in electron-proton collision at the future electron-ion collider (EIC), a useful channel to probe the gluon TMDs. We calculate the asymmetry at next-to-leading order (NLO) in $\alpha_s$ in the framework of generalized factorization. The dominating sub-process is $\gamma^* +g \rightarrow J/\psi+g$. The production of $J/\psi$ is calculated in the non-relativistic QCD(NRQCD) framework with the inclusion of both color singlet and color octet contributions. Numerical estimates of the $cos(2\phi_h)$ asymmetry are given in the kinematical region to be accessed by the future EIC. The asymmetry depends on the parameterization of the gluon TMDs, as well as on the long distance matrix elements (LDMEs). We use both Gaussian-type parameterization and McLerran-Venugopalan model for the TMDs in the kinematical region of small-$x$, where the gluons play a dominant role. We obtain sizable asymmetry, which may be useful to probe the ratio of the linearly polarized and the unpolarized gluon distribution in the proton.

Inclusive production of heavy quarkonium ηQ via Z boson decays within the framework of nonrelativistic QCD

In the paper, the inclusive production of heavy quarkonium $\eta_Q$ ($Q=b$ 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 $Z \to \eta_Q+X$ are presented. It is found that the decays $Z\to \eta_Q +X$ 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 $\langle {\cal O}^{\eta_{c}}(^{3}S_{1}^{[8]})\rangle$ and $\langle {\cal O}^{\eta_{b}}(^{3}S_{1}^{[8]})\rangle$, respectively. Our numerical results show that at an $e^+e^-$ collider running at the $Z$ pole with a high luminosity around $10^{35}{\rm cm}^{-2}{\rm s}^{-1}$ (a super $Z$ factory), there are about $4.5\times 10^7$ $\eta_c$ meson events and $6.1\times 10^5$ $\eta_b$ meson events to be produced per operation year, and the inclusive decays may be used for clarifying some problems on the heavy quarkonium $\eta_Q$ and nonrelativistic QCD.

Revisit prompt J/ψ production in associated with Higgs boson via gluon fusion at the LHC

The production of charmonium associated with Higgs boson via gluon fusion has been investigated by Kniehl, Palisoc, and Zwirner [Phys. Rev. D 66, 114002 (2002)] in which they considered the contribution of the final Higgs boson radiation off the charm quark at tree level and found that this process is far too rare to be observable in any of the considered experiments. In this paper, the production of prompt $J/\ensuremath{\psi}$ associated with the Higgs boson via gluon fusion at the 14 TeV LHC within the factorization formalism of nonrelativistic quantum chromodynamics is revisited. After considering the contribution from the final Higgs boson radiation off the top quark in the loop, which is more than 3 orders of magnitudes higher than the charm quark at tree level, the production of prompt $J/\ensuremath{\psi}$ associated with the Higgs boson has great potential to be detected. The prompt $J/\ensuremath{\psi}$ production includes the direct production and indirect production via radiative or hadronic decays of high excited charmonium states. For the direct $J/\ensuremath{\psi}+H$ production via loop-induced gluon fusion, the ${^{3}S}_{1}^{(8)}$ Fock state gives the dominant contribution to the cross section, which is about 95% of the total direct production. The indirect loop-induced contribution is appreciable, since the summation of $\ensuremath{\psi}(2S)+H$, ${\ensuremath{\chi}}_{c1}+H$ and ${\ensuremath{\chi}}_{c2}+H$ is about 34% of the total cross section of prompt $J/\ensuremath{\psi}+H$. The indirect contribution from ${\ensuremath{\chi}}_{c0}+H$ is tiny and can be neglected. With great potential to be detected, prompt $J/\ensuremath{\psi}$ production associated with the Higgs boson can help us to further understand the mechanism of the color octet, as well as being useful to further investigate the coupling of the Higgs boson and fermions.

Inclusive production of heavy quarkonia in pNRQCD

We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories. Our formalism applies to strongly coupled quarkonia, which include excited charmonium and bottomonium states. Analogously to heavy quarkonium decay processes, we express nonrelativistic QCD long-distance matrix elements in terms of quarkonium wavefunctions at the origin and universal gluonic correlators. Our expressions for the long-distance matrix elements are valid up to corrections of order 1/{N}_c^2 . These expressions enhance the predictive power of the nonrelativistic effective field theory approach to inclusive production processes by reducing the number of nonperturbative unknowns, and make possible first-principle determinations of long-distance matrix elements once the gluonic correlators are known. Based on this formalism, we compute the production cross sections of P-wave charmonia and bottomonia at the LHC, and find good agreement with measurements.

Next-to-leading-order study of J/\u03c8 angular distributions in e+e\u2212\u2192 J/\u03c8 + \u03b7c, \u03c7cJ at sqrt{s} \u2248 10.6 GeV

In this paper, we present a detailed next-to-leading-order (NLO) study of J/ψ angular distributions in e+e−→ J/ψ + ηc, χcJ (J = 0, 1, 2) within the nonrelativistic QCD factorization (NRQCD). The numerical NLO expressions for total and differential cross sections, i.e., frac{dsigma}{dcos theta } = A + B cos2θ, are both derived. With the inclusion of the newly-calculated QCD corrections to A and B, the αθ (= B/A) parameters in J/ψ + χc0 and J/ψ + χc1 are moderately enhanced, while the magnitude of αθJ/ψ+χc2 is significantly reduced; regarding the production of J/ψ + ηc, the αθ value remains unchanged. By comparing with experiment, we find the predicted αθJ/ψ+ηc is in good agreement with the Belle measurement; however, αθJ/ψ+χc0 is still totally incompatible with the experimental result, and this discrepancy seems to hardly be cured by proper choices of the charm-quark mass, the renormalization scale, and the NRQCD matrix elements.

J/ψ polarization in high multiplicity pp and pA collisions: CGC + NRQCD approach

Quarkonium production mechanism in high multiplicity small collision systems has recently been pursued in the color-glass-condensate (CGC) effective theory combined with non-relativistic QCD (NRQCD) factorization, allowing to study initial state interactions. Quarkonium polarization, potentially measured in future experiments, would help elucidate the quarkonium production mechanism at high multiplicities. In this paper, we provide predictions on $J/\psi$ polarization parameters in high multiplicity proton-proton ($pp$) and proton-nucleus ($pA$) collisions within the CGC+NRQCD framework. Theoretical predictions are given for $J/\psi$ rapidity $2.5< y_{J/\psi}<4$, charged-particle multiplicity pseudorapidity $|\eta_{ch} | <1$ and energies $\sqrt{S}=13\mathrm{~TeV}$ for $pp$, $\sqrt{S}=8.16\mathrm{~TeV}$ for $pA$ collisions. Considering two leptonic frame choices (Collins - Soper and helicity) we find a weak polarization of $J/\psi$ that additionally decreases with growing event activities. No significant system size dependence between $pp$ and $pA$ collisions is obtained - this could be a new constraint to initial state interactions in small collision systems.

Non-relativistic and potential non-relativistic effective field theories for scalar mediators

Yukawa-type interactions between heavy Dirac fermions and a scalar field are a common ingredient in various extensions of the Standard Model. Despite of that, the non-relativistic limit of the scalar Yukawa theory has not yet been studied in full generality in a rigorous and model-independent way. In this paper we intend to fill this gap by initiating a series of investigations that make use of modern effective field theory (EFT) techniques. In particular, we aim at constructing suitable non-relativistic and potential non-relativistic EFTs of Yukawa interactions (denoted as NRY and pNRY respectively) in close analogy to the well known and phenomenologically successful non-relativistic QCD (NRQCD) and potential non-relativistic QCD (pNRQCD). The phenomenological motivation for our study lies in the possibility to explain the existing cosmological observations by introducing heavy fermionic dark matter particles that interact with each other by exchanging a light scalar mediator. A systematic study of this compelling scenario in the framework of non-relativistic EFTs (NREFTs) constitutes the main novelty of our approach as compared to the existing studies.

Inclusive diffractive heavy quarkonium photoproduction including quark subprocesses

The inclusive $J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ 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 $\gamma q$, $qg$ and $qq$ subprocesses in the heavy quark pair productions are taken into account. The inclusive diffractive rapidity and transverse momentum distributions of $J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ in $pp$, $pPb$ and $PbPb$ collisions at LHC are also studied by our quark improved NRQCD model combined with the resolved pomeron model. We find that the contributions from the quark involved subprocesses can reach to $8\%$ in the rapidity distribution and $6\%$ in the transverse momentum distribution. The numerical results show that the contributions from quark involved subprocesses are significant in heavy quarkonium photoprodution.

Bc meson exclusive decays to a P -wave charmonium and a pion at NLO accuracy

In this paper, we calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the exclusive processes $B_c^+\to \chi_{cJ}(h_c)\pi^+$ in the framework of the nonrelativistic QCD (NRQCD) factorization formalism. The results show that NLO QCD corrections markedly enhance the branching ratios with $K$ factors of about 2.5. In combination with the study of $B_c^+\to J/\psi\pi^+$, we find that the NLO NRQCD prediction for the ratio of branching fractions $\frac{\mathcal{B}(B_c^+\to \chi_{c0}\pi^+)}{\mathcal{B}(B_c^+\to J/\psi \pi^+)}$ is then compatible with the experimental measurement.

Inclusive production of fully-charmed 1+− tetraquark at B factory * *The work of Y.-S. H., Y. J. and J.-Y. Z. is supported in part by the National Natural Science Foundation of China (11925506, 11875263, 12070131001 (CRC110by DFG and NSFC)). The work of F. F. is supported by the National Natural Science Foundation of China (11875318, 11505285) and by the Yue

Inspired by the recent discovery of the meson in the experiment, we investigate the inclusive production rate of the -odd fully-charmed tetraquarks associated with light hadrons at the factory within the nonrelativistic QCD (NRQCD) factorization framework. The short-distance coefficient is computed at the lowest order of velocity and . Employing two different kinds of phenomenological models to approximately estimate the long-distance NRQCD matrix element, we predict the rate for the inclusive production of the state and discuss the observation prospect of the experiment.

Bc → J/ψ tensor form factors at large momentum recoil

We present a next-to-leading order (NLO) relativistic correction to [Formula: see text] tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears [Formula: see text] with [Formula: see text] matrices [Formula: see text] in the [Formula: see text] transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for [Formula: see text] meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil.

Double prompt J/ψ production at hadron colliders

In this paper, we give a brief review of recent theoretical studies of double prompt [Formula: see text] production at the FNAL Tevatron and the CERN LHC, to which both single- and double-parton-scattering processes contribute. In single parton scattering, we mainly present the results computed within the framework of non-relativistic quantum chromodynamics factorization combined with one of the two approaches to describe the parton inside the (anti)proton, the collinear parton model and the parton Reggeization approach. The contributions from double parton scattering calculated with different values of [Formula: see text] are also discussed. We conclude that, in double prompt [Formula: see text] hadroproduction, there remain some differences between theoretical predictions and experimental measurements.

NRQCD analysis of charmonium production with pion and proton beams at fixed-target energies

We present an analysis of hadroproduction of J∕ψ and ψ(2S) at fixed-target energies in the framework of non-relativistic QCD (NRQCD). Using both pion- and proton-induced data, a new determination of the color-octet long-distance matrix elements (LDMEs) is obtained. Compared with previous results, the contributions from the qq̄ and color-octet processes are significantly enhanced, especially at lower energies. A good agreement between the pion-induced J∕ψ production data and NRQCD calculations using the newly obtained LDMEs is achieved. We find that the pion-induced charmonium production data are sensitive to the gluon density of pions, and favor pion PDFs with relatively large gluon contents at large x.

Bottomonia production in p + p collisions under NRQCD formalism

In this work, we present the calculation of the production cross sections of bottomonia states using Non-Relativistic Quantum Chromodynamics (NRQCD) formalism. The direct production cross-section of a resonance can be factorised in terms of short distance Quantum Chromodynamics (QCD) cross sections and long distance matrix elements (LDMEs) under NRQCD. We use a large set of measured ϒ(nS) production data at Tevatron and LHC energies in both central and forward rapidity regions to extract the LDMEs with better precision. The feed down contributions from the higher states including the χb(3P) state are taken into account for the LDME extraction. The formalism provides a good description of the bottomonia data in wide transverse momentum range at different collision energies.

Toward accurate form factors for B -to-light meson decay from lattice QCD

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\to\eta_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f = 2 + 1 + 1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays.

Fragmentation functions for a quark into a spin-singlet quarkonium: Different flavor case

In the paper, we calculate the fragmentation functions for a quark to fragment into a spin-singlet quarkonium, where the flavor of the initial quark is different from that of the constituent quark in the quarkonium. The ultraviolet divergences in the phase space integral are removed through the operator renormalization under the modified minimal subtraction scheme. The fragmentation function $D_{q \to \eta_Q}(z,\mu_F)$ is expressed as a two-dimensional integral. Numerical results for the fragmentation functions of a light quark or a bottom quark to fragment into the $\eta_c$ are presented. As an application of those fragmentation functions, we study the processes $Z \to \eta_c+q\bar{q}g(q=u,d,s)$ and $Z \to \eta_c+b\bar{b}g$ under the fragmentation and the direct nonrelativistic QCD approaches.

Exploring J/ψ Production Mechanism at the Future Electron-Ion ColliderH. X. is supported by Guangdong Major Project of Basic and Applied Basic Research (Grant No. 2020B0301030008), and the National Natural Science Foundation of China (Grant Nos. 12022512 and 12035007), as well as the Science and Technology Program of Guangzhou (Grant No. 2019050001). J.-W.Q. is supported by the U.S. Department of Energy

We propose to use transverse momentum p T distribution of J/ψ production at the future Electron Ion Collider (EIC) to explore the production mechanism of heavy quarkonia in high energy collisions. We apply QCD and QED collinear factorization to the production of a pair at high p T, and non-relativistic QCD factorization to the hadronization of the pair to a J/ψ. We evaluate J/ψ p T-distribution at both leading and next-to-leading order in strong coupling, and show that production rates for various color-spin channels of a pair in electron-hadron collisions are very different from that in hadron-hadron collisions, which provides a strong discriminative power to determine various transition rates for the pair to become a J/ψ. We predict that the J/ψ produced in electron-hadron collisions is likely unpolarized, and the production is an ideal probe for gluon distribution of colliding hadron (or nucleus). We find that the J/ψ production is dominated by the color-octet channel, providing an excellent probe to explore the gluon medium in large nuclei at the EIC.