Nonrelativistic QCD Research Articles

Baryons, multihadron systems, and composite dark matter in nonrelativistic QCD

Baryons, multihadron systems, and composite dark matter in nonrelativistic QCD

Analysis of double-J/ψ production in Z decay at next-to-leading-order QCD accuracy

In this article, we study in detail the double-J/ψ yield through Z decay at the next-to-leading-order (NLO) QCD accuracy within the nonrelativistic QCD factorization. At the tree level, the pure QCD diagrams predict a branching ratio of BZ→J/ψ+J/ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{B}}_{Z\ o J/\\psi +J/\\psi } $$\\end{document} ~ 10−12; however, the inclusion of the QED diagrams would augment this prediction by approximately 2–3 orders of magnitude. After incorporating the QCD corrections, the QCD results exhibit a considerable increase, whereas the QED results undergo a substantial reduction. Combining the QCD and QED contributions at NLO in αs, it is observed that the prediction of BZ→J/ψ+J/ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{B}}_{Z\ o J/\\psi +J/\\psi } $$\\end{document} = (1.110−0.241−0.001+0.334+0.054\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {1.110}_{-0.241-0.001}^{+0.334+0.054} $$\\end{document}) × 10−10, which displays a fairly steady dependence on the renormalization scale, is significantly lower than the upper limits released by CMS.

Exclusive J/Psi plus jet associated production in ultraperipheral PbPb collisions

The study of exclusive processes in ultraperipheral collisions at the Large Hadron Collider (LHC) has allowed us to test several aspects of the Standard Model and to search for New Physics. In this letter, we investigate the possibility of using these processes to improve our understanding of the quarkonium production mechanism through the study of the exclusive J/Psi plus jet associate production in ultraperipheral PbPb collisions. We estimate the transverse-momentum and rapidity distributions considering that the gamma gamma rightarrow J/Psi + X(X = gamma , , g) subprocess is described by the Non-Relativistic QCD (NRQCD) formalism and present predictions for the rapidity ranges covered by central and forward detectors. The experimental separation of these events is discussed and the results indicate that a future experimental analysis is, in principle, feasible in future runs of the LHC and the Future Circular Collider (FCC).

Production of excited doubly heavy baryons at the super-Z factory

In the framework of nonrelativistic QCD, the excited doubly heavy baryons are thoroughly studied via the channel e^{+} e^{-}rightarrow langle QQ^{prime }rangle [n] rightarrow Xi _{QQ^{prime }} +bar{Q^{prime }} +{bar{Q}}, which takes place at the collision energy Z-pole. Q^{(prime )} represents b or c quark for the production of Xi _{cc}, Xi _{bc}, and Xi _{bb}, respectively. All of the intermediate diquark states langle QQ'rangle [n] in P-wave, langle ccrangle [^{1}P_{1}]_{{bar{textbf{3}}}}, langle ccrangle [^{3}P_{J}]_{{textbf{6}}}, langle bcrangle [^{1}P_{1}]_{{bar{textbf{3}}}/ {textbf{6}}}, langle bcrangle [^{3}P_{J}]_{{bar{textbf{3}}}/ {textbf{6}}}, langle bb rangle [^{1}P_{1}]_{{bar{textbf{3}}}}, and langle bbrangle [^{3}P_{J}]_{{textbf{6}}} with J=0, 1, or 2, are taken into account. The cross sections and differential distributions, including the transverse momentum, rapidity, angular, and invariant mass, are discussed for the excited baryons production. We find that the contributions of langle cc rangle , langle bc rangle , and langle bb rangle in P-wave are found to be 3.97%, 5.08%, and 5.89%, respectively, compared to S-wave. Supposing that all excited states can decay into the ground state 100%, the total events N_{Xi _{cc}}=8.48 times 10^{4-6}, N_{Xi _{bc}}=2.26times 10^{5-7}, and N_{Xi _{bb}}=4.12 times 10^{3-5} would be produced at the Super-Z Factory with a high luminosity up to {{mathcal {L}}} simeq 10^{34-36}textrm{cm}^{-2} textrm{s}^{-1}.

Transverse momentum dependent shape function for J/ψ production in SIDIS

It has been shown previously that the transverse momentum dependent (TMD) factorization of heavy quarkonium production requires a TMD shape function. Its perturbative tail can be extracted by matching the cross sections valid at low and high transverse momenta. In this article we compare the order-αs TMD expressions with the order- {alpha}_s^2 collinear ones for J/ψ production in semi-inclusive deep inelastic scattering (SIDIS), employing nonrelativistic QCD in both cases. In contrast to previous studies, we find that the small transverse momentum limit of the collinear expressions contains discontinuities. We demonstrate how to properly deal with them and include their finite contributions to the TMD shape functions. Moreover, we show that soft gluon emission from the low transverse momentum Born diagrams provide the same leading order TMD shape functions as required for the matching. Their revised perturbative tails have a less divergent behavior as compared to the TMD fragmentation functions of light hadrons. Finally, we investigate the universality of TMD shape functions in heavy quarkonium production, identify the need for process dependent factorization and discuss the phenomenological implications.

Unraveling gluon jet quenching through [formula omitted] production in heavy-ion collisions

Jet quenching has long been regarded as one of the key signatures for the formation of quark-gluon plasma in heavy-ion collisions. Despite significant efforts, the separate identification of quark and gluon jet quenching has remained as a challenge. Here we show that J/ψ in high transverse momentum (pT) region provides a uniquely sensitive probe of in-medium gluon energy loss since its production at high pT is particularly dominated by gluon fragmentation. Such gluon-dominance is first demonstrated for the baseline of proton-proton collisions within the framework of leading power non-relativistic quantum chromodynamics factorization formalism. We then use the linear Boltzmann transport model combined with hydrodynamics for the simulation of jet-medium interaction in nucleus-nucleus collisions. The satisfactory description of experimental data on both nuclear modification factor RAA and elliptic flow v2 reveals, for the first time, that the gluon jet quenching is the driving force for high pTJ/ψ suppression. This novel finding is further confirmed by the data-driven Bayesian analyses of relevant experimental measurements, from which we also obtain the first quantitative extraction of the gluon energy loss distribution in the quark-gluon plasma.

Vector Quarkonia at the LHC with Jethad: A High-Energy Viewpoint

In this review, we discuss and extend the study of the inclusive production of vector quarkonia, J/ψ and Υ, emitted with large transverse momenta and rapidities at the LHC. We adopt the novel ZCW19+ determination of fragmentation functions to depict the quarkonium production mechanism at the next-to-leading level of perturbative QCD. This approach is based on the nonrelativistic QCD formalism well adapted to describe the formation of a quarkonium state from the collinear fragmentation of a gluon or a constituent heavy quark at the lowest energy scale. We rely upon the NLL/NLO+ hybrid high-energy and collinear factorization for differential cross-sections, where the collinear formalism is enhanced by the BFKL resummation of next-to-leading energy logarithms arising in the t-channel. We employ the method to analyze the behavior of the rapidity distributions for double-inclusive vector quarkonium and inclusive vector quarkonium plus jet emissions. We discover that the natural stability of the high-energy series, previously seen in observables sensitive to the emission of hadrons with heavy flavor detected in the rapidity acceptance of LHC barrel calorimeters, becomes even more manifest when these particles are tagged in forward regions covered by endcaps. Our findings present the important message that vector quarkonia at the LHC via hybrid factorization offer a unique chance to perform precision studies of high-energy QCD, as well as an intriguing opportunity to shed light on the quarkonium production puzzle.

Formula omitted] corrections to J/ψ + χc0,1,2 production at B factories

We compute the O(αs2) corrections to the exclusive channels e+e−→J/ψ+χcJ (J=0,1,2) at s=10.58 GeV within the nonrelativistic QCD (NRQCD) factorization framework. The validity of NRQCD factorization at O(αs2) has been confirmed for these double-charmonium exclusive production processes. We analyze the impact of the O(αs2) corrections on the polarized and unpolarized cross sections, as well as the J/ψ angular distributions, which largely reduce the renormalization scale dependence but increase the O(αs) NRQCD predictions to some extent for χc0,1. With high numerical accuracy, our predictions for σ(J/ψ+χc1,2) through O(αs2) are compatible with the upper limit of the Belle measurement. Although the theoretical prediction for σ(J/ψ+χc0) is consistent with both Belle and BaBar measurements within uncertainties, there still exists serious tension between the predicted and the measured profiles for the J/ψ angular distribution. Regarding the bright observation prospect of the e+e−→J/ψ+χc1,2 channels in Belle 2 experiment, it is interesting to compare the future measurements with our NRQCD predictions. The more accurate measurement of e+e−→J/ψ+χ0 at Belle 2 will also help to clarify the long-standing puzzle of J/ψ angular distribution.

Resummation and renormalization of kinematical effects in inclusive P-wave quarkonium production

We investigate the renormalization properties of the shape function formalism for inclusive production of P-wave heavy quarkonia, which arises from resumming a class of corrections coming from kinematical effects associated with the motion of the heavy quark and antiquark pair relative to the quarkonium. Such kinematical effects are encoded in the nonperturbative shape functions, which are normalized to the corresponding nonrelativistic QCD long-distance matrix elements. By using the known ultraviolet divergences in the matrix elements, we derive the large-momentum asymptotic behavior of the shape functions. This strongly constrains the form of the shape functions and significantly reduces the dependence on the nonperturbative model. Based on these results we show that the shape function formalism at loop level can be useful in taming the threshold logarithms at large transverse momentum, and at small transverse momentum the kinematical corrections reduce the sizes of χc and χb cross sections which may improve agreement with measurements.

Sunrise Integral in Non-Relativistic QCD with Elliptics

Sunrise Integral in Non-Relativistic QCD with Elliptics

J/ψ polarization in large- PT semi-inclusive deep-inelastic scattering at the EIC

We present a detailed phenomenological study of $J/\psi$ polarization in semi-inclusive deep inelastic scattering processes, focusing on the kinematics accessible at the future Electron-Ion Collider. We show theoretical estimates for the standard polarization parameters for different frames usually adopted in the literature, in the large $P_T$ region, namely $P_T\gg \Lambda_\text{QCD}$, where collinear factorization is expected to hold. We adopt both the Color Singlet Model and the Nonrelativistic QCD approach, paying special attention to the role of different sets of Long Distance Matrix Elements. Finally we present a preliminary analysis of some frame independent polarization invariants.

Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications

Within the framework of non-relativistic QCD (NRQCD) factorization, we compute the matching coefficients between full Quantum Chromodynamics (QCD) and NRQCD for the heavy flavor-changing vector, axial-vector, scalar and pseudo-scalar currents up to next-to-next-to-next-to-leading order (N3LO). We accomplish the analytical expressions for the three-loop renormalization constants and the corresponding anomalous dimensions for all of the four NRQCD currents with two different heavy flavors. The three-loop QCD corrections to the matching coefficients turn out to be significantly larger than lower order corrections. By employing the scale relation, we approximately simulate the N3LO correction to the wave functions at the origin for the vector {B}_c^{ast } meson and the pseudo-scalar Bc meson from the known result for the equal-mass heavy quarkonium in potential NRQCD (pNRQCD). We find large cancellations at the third order between the matching coefficients and the wave functions at the origin, and obtain the convergent decay constants of {B}_c^{ast } and Bc up to N3LO. We present the complete perturbative QCD predictions for the decay constants, leptonic decay widths, and branching ratios of the beauty-charmed mesons.

Resolution of the LHCb ηc anomaly

Due to the heavy-quark symmetry of Non-Relativistic Quantum Chromodynamics (NRQCD), the cross-section for the production of ηc can be predicted. This NRQCD prediction when confronted with data from the LHCb is seen to fail miserably. We address this LHCb ηc anomaly in this paper using a new approach called modified NRQCD, an approach that has been shown to work extremely well for studying J/ψ, ψ′ and χc production at the LHC. We show, in the present paper, that the predictions for ηc production agrees very well with LHCb measurements at the three different values of energy that the experiment has presented data for. Modified NRQCD also explains the intriguing agreement of the LHCb ηc data with the colour-singlet prediction. The remarkable agreement of the theoretical predictions with the LHCb data suggests that modified NRQCD is closer to apprehending the true dynamics of quarkonium production.

X(3860) production in association with J/psi via e^{+}e^{-} annihilation at Belle

In this paper, we study the X(3860) production associated with J/psi via e^{+}e^{-} annihilation at the next-to-leading-order (NLO) accuracy in alpha _s, within the nonrelativistic QCD (NRQCD) framework. With the hypothesis of J^{PC}_{X(3860)}=0^{++}, the predictions of sigma _{e^{+}e^{-} rightarrow J/psi +X(3860)} agree well with the Belle measurements, whereas the results following the 2^{++} assignment significantly undershoot the data. This is consistent with the Belle’s conclusion that the 0^{++} hypothesis is favored over the 2^{++} hypothesis for X(3860). Despite fitting the data of the total cross section, the NRQCD predictions seem to be incompatible with the measured J/psi angular distributions. We simultaneously calculate the cross section of e^{+}e^{-} rightarrow J/psi +X(3940) under the assumption of J^{PC}_{X(3940)}=0^{-+}, discovering the consistency of the NRQCD predictions with the light-cone results as well as the experiment.

Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark

We compute the matching coefficient between the quantum chromodynamics (QCD) and the non-relativistic QCD (NRQCD) for the flavor-changing scalar current involving the heavy charm and bottom quark, up to the three-loop order within the NRQCD factorization. For the first time, we obtain the analytical expressions for the three-loop renormalization constant tilde{Z}_s(x,R_f) and the corresponding anomalous dimension tilde{gamma }_s(x,R_f) for the NRQCD scalar current with the two heavy bottom and charm quark. We present the precise numerical results for those relevant coefficients (C_{FF}(x_0), ldots , C_{FBB}(x_0)) with an accuracy of about thirty digits. The three-loop QCD correction turns out to be significantly large. The obtained matching coefficient C_s(mu _f,mu ,m_b,m_c) is helpful to analyze the threshold behaviours when two different heavy quarks are close to each other and form the double heavy B_c meson family.

Higgs boson decays to Bc meson in the fragmentation-function approach

In the paper, we present a calculation of the decay widths for the Higgs boson decays to the $B_c$, $B_c^*$, $B_c(2^1S_0)$ and $B_c^*(2^3S_1)$ mesons using the fragmentation-function approach. In the calculation, the fragmentation functions up to order $\alpha_s^3$ based on the nonrelativistic QCD factorization theory are used, and the decay widths for $H\to Q+X$ and $H \to g+X$ at the partonic level are calculated up to order $\alpha_s$. The large logarithms of $m_H^2/m_{Bc}^2$ are resummed up to next-to-leading logarithmic accuracy by solving the evolution equations for the running quark masses and the fragmentation functions. Compared to the leading-order decay widths based on the nonrelativistic QCD approach, the decay widths based on the fragmentation-function approach that include the higher-order QCD corrections are reduced significantly. Our numerical results show that there are about $1.2\times 10^5$ $B_c$ events via the Higgs decays to be produced at the HL-LHC with $3ab^{-1}$, and about $1.6\times 10^6$ $B_c$ events via the Higgs decays to be produced at the HE-LHC with $15ab^{-1}$.

Matching the Standard Model to heavy-quark effective theory and nonrelativistic QCD

We find the leading electroweak corrections to the Lagrangians of heavy-quark effective theory and nonrelativistic QCD. These corrections appear in the Wilson coefficients of the two- and four-quark operators and are considered here at one-loop order through O(1/m3) and O(1/m2), respectively. The two-quark operators through this order include new parity violating terms, which we derive analogously to the parity preserving QCD result at one-loop order.

Inclusive production of J/ψ, ψ(2S), and Υ states in pNRQCD

Under some assumptions on the hierarchy of relevant energy scales, we compute the nonrelativistic QCD (NRQCD) long-distance matrix elements (LDMEs) for inclusive production of J/ψ, ψ(2S), and Υ states based on the potential NRQCD (pNRQCD) effective field theory. Based on the pNRQCD formalism, we obtain expressions for the LDMEs in terms of the quarkonium wavefunctions at the origin and universal gluonic correlators, which do not depend on the heavy quark flavor or the radial excitation. This greatly reduces the number of nonperturbative unknowns and substantially enhances the predictive power of the nonrelativistic effective field theory formalism. We obtain improved determinations of the LDMEs for J/ψ, ψ(2S), and Υ states thanks to the universality of the gluonic correlators, and obtain phenomenological results for cross sections and polarizations at large transverse momentum that agree well with measurements at the LHC.

Fixed-target charmonium production and pion parton distributions

We investigate how charmonium hadroproduction at fixed-target energies can be used to constrain the gluon distribution in pions. Using nonrelativistic QCD (NRQCD) formulation, the $J/\psi$ and $\psi(2S)$ cross sections as a function of longitudinal momentum fraction $x_F$ from pions and protons colliding with light targets, as well as the $\psi(2S)$ to $J/\psi$ cross section ratios, are included in the analysis. The color-octet long-distance matrix elements are found to have a pronounced dependence on the pion parton distribution functions (PDFs). This study shows that the $x_F$ differential cross sections of pion-induced charmonium production impose strong constraints on the pion's quark and gluon PDFs. In particular, the pion PDFs with larger gluon densities provide a significantly better description of the data. It is also found that the production of the $\psi(2S)$ state is associated with a larger quark-antiquark contribution, compared with $J/\psi$.

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

In this work, we obtain solutions of the deformed Schrödinger equation (DSE) with improved internal energy potential at a finite temperature model in a 3-dimensional nonrelativistic noncommutative phase-space (3D-NRNCPS) symmetries framework, using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). The modified bound state energy spectra are obtained for the heavy quarkonium system such as charmonium cc- and bottomonium bb- at finite temperature. It is found that the perturbative solutions of the discrete spectrum are sensible to the discreet atomic quantum numbers (j,l,s,m) of the ( QQ- (Q=c,b)) state, the parameters of internal energy potential (T,αs(T), mD (T),β,c), which are the Debye screening mass mD (T), the running coupling constant αs(T) the critical temperature β, the free parameter c in addition to noncommutativity parameters (Θ,θ-). The new Hamiltonian operator in 3D-NRNCPS symmetries is composed of the corresponding operator in commutative phase-space and three additive parts for spin-orbit interaction, the new magnetic interaction, and the rotational Fermi-term. The obtained energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium systems (cc- and bb-). The total complete degeneracy of the new energy levels of the improved internal energy potential changed to become equal to the new value 3n2 in 3D-NRNCPS symmetries instead of the value n2 in the symmetries of 3D-NRQM. Our non-relativistic results obtained from DSE will possibly be compared with the Dirac equation in high-energy physics.