NRQCD Factorization Research Articles

Improved analysis of double J/ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J/\\psi $$\\end{document} production in Z-boson decay

In this paper, we present an improved calculation for the decay rate of the rare Z-boson decay into 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}$$J/\\psi + J/\\psi .$$\\end{document} This decay is dominated by the photon fragmentation mechanism, i.e., the transition Z→J/ψ+γ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z\\rightarrow J/\\psi + \\gamma ^{*}$$\\end{document} followed by the fragmentation γ∗→J/ψ.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ^{*}\\rightarrow J/\\psi .$$\\end{document} In our calculation, the amplitude of γ∗→J/ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ^{*}\\rightarrow J/\\psi $$\\end{document} is extracted from the measured value of Γ(J/ψ→e+e-),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma (J/\\psi \\rightarrow e^+ e^-),$$\\end{document} and the amplitude of Z→J/ψ+γ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z\\rightarrow J/\\psi + \\gamma ^{*}$$\\end{document} is calculate through the light-cone approach. The higher-order QCD and relativistic corrections in the amplitude of γ∗→J/ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ^{*}\\rightarrow J/\\psi $$\\end{document} and the large logarithms of mZ2/mc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{_Z}^2/m_c^2$$\\end{document} that appear in the amplitude of Z→J/ψ+γ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z\\rightarrow J/\\psi + \\gamma ^{*}$$\\end{document} are resummed in our calculation. Besides, the non-fragmentation amplitude is calculated based on the NRQCD factorization, and the next-to-leading order QCD and relativistic corrections are included. The obtained branching fraction for this Z decay channel is 8.66-0.69+1.48×10-11.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$8.66 ^{+1.48} _{-0.69}\ imes 10^{-11}.$$\\end{document}

Gluon TMD fragmentation function into quarkonium

We compute the gluon transverse-momentum-dependent fragmentation function (TMDFF) at next-to-leading order (NLO) into heavy quarkonium in the color-octet S183\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {}^3{S}_1^{\\left[8\\right]} $$\\end{document} channel, based on the NRQCD factorization approach. The spurious rapidity divergences are explicitly shown to cancel in a well-defined TMDFF, which incorporates the needed soft factor. We also compute the integrated gluon FF at NLO in the same S183\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {}^3{S}_1^{\\left[8\\right]} $$\\end{document} channel, and show that the matching coefficient of the TMDFF onto the FF at large transverse momentum is the expected one. These results are relevant to perform precise and sensible phenomenological studies of transverse-momentum spectra of quarkonium production, for which the production mechanism through fragmentation plays a relevant role, like in the future Electron-Ion Collider.

Further study on the production of P-wave doubly heavy baryons from Z-boson decays

In this paper, we carried out a systematic investigation for the excited doubly heavy baryons production in Z-boson decays within the NRQCD factorization approach. Our investigation accounts for all the P-wave intermediate diquark states, i.e.〈cc〉[P11]3¯, 〈cc〉[PJ3]6, 〈bc〉[P11]3¯/6, 〈bc〉[PJ3]3¯/6, 〈bb〉[P11]3¯, and 〈bb〉[PJ3]6 with J=(0,1,2). The results show that contributions from all diquark states in P-wave were 7%, 8%, and 3% in comparing with S-wave for the production of Ξcc, Ξbc and Ξbb via Z-boson decay, respectively. Based on these results, we predicted about 0.539×103(106) events for Ξcc, 1.827×103(106) events for Ξbc, and 0.036×103(106) events for Ξbb can be produced annually at the LHC (CEPC). Additionally, we plot the differential decay widths of Ξcc, Ξbc and Ξbb as a function of the invariant mass s23 and energy function z distributions, and analyze the theoretical uncertainties in decay width arising from the mass parameters of heavy quark.

Investigation of Z-boson decay into and baryons within the NRQCD factorization approach* *Supported in part by the Natural Science Foundation of China (12265010) and the Project of Guizhou Provincial Department of Education (KY[2021]030)

Z-boson decay provides a good opportunity to search for the baryon because a large number of its events can be collected at high energy colliders. In this paper, we perform a complete investigation of the indirect production of the and baryons via the Z-boson decay process with a quark under the NRQCD factorization approach. After considering the contribution from the diquark states , , , and , the calculated branching fractions are and . Furthermore, the and production events are predicted to be of the order of and at the LHC collider, and the order of and for the CEPC collider. We then estimate the production ratio for with in Z-boson decay, that is, and , respectively. Finally, we present the differential decay widths of and with respect to and z distributions and analyze the uncertainties.

Next-to-next-to-leading-order QCD corrections to J/ψ plus ηc production at the B factories

In this paper, we calculate the next-to-next-to-leading-order (NNLO) QCD corrections to e+e− → J/ψ + ηc at the B factories. After including the NNLO corrections, the cross section of e+e−→ J/ψ +ηc is enhanced by about 17%, and the perturbative series of the prediction shows the convergent behavior. It is also found that the contributions from bottom quark starts at the {alpha}_s^3 -order, which is about 2.4% of the total prediction. The renormalization scale μR dependence of the cross section is reduced at the NNLO level, but the prediction is sensitive to the charm quark mass mc. By considering the uncertainties caused by renormalization scale μR, charm quark mass mc and the NRQCD factorization scale μΛ, our prediction shows agreement with the BABAR and BELLE measurements within errors.

Next-to-leading-order QCD corrections to gluon fragmentation into quarkonia* *F. F. is supported by the National Natural Science Foundation of China (12275353 and 11875318). Y. J. is supported in part by the National Natural Science Foundation of China (11475188) and CRC110 by DGF and NSFC (11621131001)

Within the NRQCD factorization framework, we compute the next-to-leading-order QCD corrections to the gluon fragmentation into the Fock components of a quarkonium, at the lowest order in velocity expansion. We follow the operator definition of the fragmentation function advanced by Collins and Soper. The key technique underpinning our calculation is the sector decomposition method widely used in the area of multi-loop computation. It is found that the NLO QCD corrections have significant effects, and qualitatively modify the profiles of the corresponding leading-order fragmentation functions.

Probing the Hγγ coupling via Higgs boson exclusive decay into quarkonia plus a photon at the HL-LHC

It is well know that the precise measurement of $H\to\gamma\gamma$ can generate two degenerate parameter spaces of $H\gamma\gamma$ anomalous coupling. We propose to utilize the exclusive Higgs rare decays $H\to\Upsilon(ns)+\gamma$ to break above mentioned degeneracy and further to constrain the $H\gamma\gamma$ anomalous coupling at the HL-LHC. We demonstrate that the branching ratios of $H\to\Upsilon(ns)+\gamma$ can be significantly enhanced in the non-SM-like parameter space from $H\to\gamma\gamma$ measurement, due to the destructive interference between the direct and indirect production of $\Upsilon(ns)$ in the SM. By applying the NRQCD factorization formalism, we calculate the partial decay widths of $H\to\Upsilon(ns)+\gamma$ at the NLO accuracy of $\alpha_s$. We show that it is hopeful to break such degenerate parameter space at the HL-LHC if we can further highly suppress the background and enhance the signal efficiency compared to the ATLAS preliminary simulation.

Gluon fragmentation into Bc(*) in NRQCD factorization

The universal fragmentation functions of gluon into the flavored quarkonia $B_c$ and (polarized) $B_c^*$ are computed within NRQCD factorization framework, at the lowest order in velocity expansion and strong coupling constant. It is mandatory to invoke the DGLAP renormalization program to render the NRQCD short-distance coefficients UV finite in a point-wise manner. The calculation is facilitated with the sector decomposition method, with the final results presented with high numerical accuracy. This knowledge is useful to enrich our understanding toward the large-$p_T$ behavior of $B_c^{(*)}$ production at LHC experiment.

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.

Probing the [formula omitted] anomalous couplings via exclusive Z boson decay

We propose to utilize the exclusive Z-boson rare decays Z→ϒ(ns)+γ to constrain the Zbb¯ couplings at the HL-LHC and 100 TeV proton-proton collider. We demonstrate that the event yield of the proposed processes is sensitive to the axial-vector component of the Zbb¯ coupling and can provide complementary information to the jet-charge weighted single-spin asymmetry measurement at the EIC and the gg→Zh production rate measurement at the LHC. By applying the NRQCD factorization formalism, we calculate the partial decay width of Z→ϒ(ns)+γ to the NLO accuracy in strong interaction, which is found to agree with those obtained from the light-cone distribution amplitude approach. We show that the HL-LHC can break the degeneracy of the Zbb¯ couplings, as implied by the precision electroweak data at LEP and SLC, if the signal efficiency can be improved by a factor of 1.7 from the present ATLAS analysis at the 13 TeV LHC with an integrated luminosity of 36.1fb−1.

Color-octet contributions for J/ψ inclusive production at B factories in soft gluon factorization

We have studied color-octet contributions for J/ψ inclusive production at B factories, i.e., e+e− → J/ψ(3 {P}_J^{left[8right]} ,1 {S}_0^{left[8right]} ) + {X}_{mathrm{non}-coverline{c}} , using the soft gluon factorization (SGF) approach, in which the J/ψ energy spectrum is expressed in a form of perturbatively calculable short-distance hard parts convoluted with one-dimensional soft gluon distributions (SGDs). The series of velocity corrections originated from kinematic effect can be naturally resummed in this approach. Short-distance hard parts have been calculated analytically to next-to-leading order in αs. Renormalization group equations for SGDs have been derived and solved, which resums Sudakov logarithms originated from soft gluon emissions. Our final result gives a upper bound for color-octet matrix elements consistent with that extracted from hadron colliders. This may relieve the well-known universality problem in the NRQCD factorization.As a comparison, we also analytically calculated short-distance hard parts in the NRQCD factorization, with Sudakov logarithms resummed by using soft collinear effective theory. The comparison shows that velocity corrections from kinematic effect, which have been resummed in SGF, are significant for phenomenological study. Furthermore, it is found that Sudakov logarithms originated from soft gluon emissions are very important, while it is not the case for Sudakov logarithms originated from jet function. Therefore, the partial Sudakov resummation in SGF has already captured the main physics.

Subleading power corrections to heavy quarkonium production in QCD factorization approach

We report the current understanding of heavy quarkonium production at high transverse momentum (pT) in hadronic collisions in terms of QCD factorization. In this presentation, we highlight the role of subleading power corrections to heavy quarkonium production, which are essential to describe the pT spectrum of quarkonium at a relatively lower pT. We also introduce prescription to match QCD factorization to fixed-order NRQCD factorization calculations for quarkonium production at low pT.

Gluon fragmentation into 3 {P}_J^{left[1,8right]} quark pair and test of NRQCD factorization at two-loop level

The next-to-leading order (NLO) ( mathcal{O} ( {alpha}_s^3 )) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in 3 {P}_J^{left[1,8right]} states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and mathcal{O} ( {alpha}_s^2 ) perturbative NRQCD matrix elements ⟨ {mathcal{O}}^3{P}_J^{left[1,8right]} (3 {S}_1^{left[8right]} )⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

Next-to-leading-order QCD corrections to heavy quark fragmentation into {}^1S^{(1,8)}_0 quarkonia

Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the {}^1S_0^{(1,8)} components of a heavy quarkonium. Starting from the Collins and Soper’s operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.

Fragmentation function of g \u2192 Qoverline{Q} (3 {S}_1^{left[8right]} ) in soft gluon factorization and threshold resummation

We study the fragmentation function of the gluon to color-octet 3S1 heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet 3S1 soft gluon distribution (SGD). The short distance hard part is calculated to the next-to-leading order in αs and all orders in velocity expansion. By deriving and solving the renormalization group equation of the SGD, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study.

Fragmentation function of gluon into spin-singlet P -wave quarkonium

Following the operator definition of the fragmentation function developed by Collins and Soper, we compute the gluon-to-$h_c$ fragmentation function at the lowest order in the velocity expansion in NRQCD factorization approach. Utilizing some modern technique developed in the area of multi-loop calculation, we are able to analytically deduce the infrared-finite color-singlet short-distance coefficient associated with the fragmentation function. The fragmentation probability for gluon into $h_c$ is estimated to be order $10^{-6}$.

Inclusive diffractiveηcproduction in pp, pA, and AA modes at the LHC

In this paper, the inclusive Pomeron-Pomeron, Reggeon-Reggeon, Pomeron-Reggeon as well as gluon-Pomeron(-Reggeon) and photon-Pomeron(-Reggeon) interactions for the $\rm \eta_{c}$ at the LHC energies have been examined in proton-proton, proton-nucleus and nucleus-nucleus collision modes. The cross section has been computed based on the NRQCD factorization and Regge theory formalism. The cross exchange of Pomeron-Reggeon contribution is important in $\rm pp$ and $\rm pA$ modes. The Pomeron-Pomeron contribution is significant in $\rm AA$ mode. The Pomeron contribution is considerable for $\rm AA$ and $\rm pA$ modes in single diffractive process where $\rm A$ undergoes the diffractive process. Reggeon contribution is sizable in $\rm pp$ and $\rm pA$ modes where $\rm p$ only undergoes the diffractive process. The Pomeron and Reggeon contributions in photon-Pomeron and-Reggeon process remain smaller than that of gluon-Pomeron and-Reggeon processes. Our results show that the experimental study of Reggeon, Pomeron and their cross exchange can be carried out in certain kinematic windows with the specific choice of the mode at the LHC. The investigation can be useful to better constrain the Reggeon and Pomeron parton content. The inclusive process serves as the background to related exclusive processes which should be predicted.

Hard diffractive ηc,b hadroproduction at the LHC

In this paper, we investigate the inclusive diffractive hadroproduction for $\rm \eta_{c}$ and $\rm \eta_{b}$ at the LHC energies. Based on the NRQCD factorization formalism and the resolved-Pomeron model for the quarkonium production mechanism, we estimate the rapidity, momentum fraction loss dependence of the cross section. We give prediction ratios for single and central diffractive processes with respect to non diffractive process. These inclusive processes are sensitive to gluon content of Pomeron for small-$x$ and Reggeon for large-$x$, useful to study small and large-$x$ physics and good to test different mechanism for $\rm \eta_{c}$ and $\rm \eta_{b}$ production at the LHC. They also serve as the background to related exclusive processes thus should be predicted. Our results demonstrate that the Reggeon contribution of diffractive processes can be sizable, even sometimes dominant over Pomeron, and that its study can be useful to better constrain the Reggeon parton content. The experimental study of Reggeon can be carried out in certain kinematic windows.

Relativistic effect of J/\U0001d713 hadroproduction in large pT region

By combining NRQCD factorization and collinear factorization, we compute a series of relativistic corrections for J/\U0001d713 hadroproduction to all orders in \U0001d7102 at large pT limit. The \U0001d7102 expansion converges well for all channels. We find that the ratio of relativistic correction term to the corresponding leading term is independent of kinematic variables for any channel, which generalizes the proportional relations found in previous works to all orders.

W radiative decay to heavy-light mesons in HQET factorization through O(αs)

Analogous to NRQCD factorization for heavy quarkonium exclusive production, in this work we propose to employ the heavy-quark-effective-theory (HQET) factorization, which has been predominantly applied to account for exclusive $B$ decays, to study the exclusive production of the heavy-flavored mesons. We take $W\to B(D_s)+\gamma$ as a prototype process. The validity of the HQET factorization rests upon the presumed scale hierarchy: $m_W\sim m_b\gg \Lambda_{\rm QCD}$. Through an explicit analysis at next-to-leading order in $\alpha_s$ yet at leading order in $1/m_b$, we verify that the decay form factors can indeed be expressed as the convolution between perturbatively calculable hard-scattering kernel and the $B$ meson light-cone distribution amplitude (LCDA) defined in HQET. It is observed that the factorization scale dependence becomes reduced after incorporating the NLO perturbative correction. An interesting future investigation is to identify and resum large collinear logarithms of $m_W/m_b$ that arise ubiquitously in the fixed-order expressions of the hard-scattering kernel in HQET factorization.