NRQCD Factorization Research Articles

Semi-analytical calculation of gluon fragmentation into 1S0[1,8] quarkonia at next-to-leading order

We calculate the NLO corrections for the gluon fragmentation functions to a heavy quark-antiquark pair in 1S0[1] or 1S0[8] state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of z (light-cone momentum fraction carried by the quark-antiquark pair), which can not only give FFs results with very high precision at any value of z, but also provide fully analytical structure at these singularities. We find that the NLO corrections are significant, with K-factors larger than 2 in most regions. The NLO corrections may have important impact on heavy quarkonia (e.g. ηc and J/ψ) production at the LHC.

O(αs) corrections to e+e−→J/ψ+ηc2(χc1′) at B factories

We investigate the $\mathcal{O}({\ensuremath{\alpha}}_{s})$ correction to ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c2}$ in the NRQCD factorization approach. A detailed comparative study between ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c2}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\chi}}_{c1}^{\ensuremath{'}}$ at the $B$ factory energy is also carried out. After incorporating the $\mathcal{O}({\ensuremath{\alpha}}_{s})$ correction, we predict the cross section for the former process to be around 0.3 fb, while that of the latter is about 6 times greater. The outgoing $J/\ensuremath{\psi}$ is found to be dominantly transversely polarized in the former process, while longitudinally polarized in the latter. These features may provide valuable guidance for the Belle 2 experiment to establish the ${\ensuremath{\chi}}_{c1}^{\ensuremath{'}}$ or ${\ensuremath{\eta}}_{c2}$ states. In the Appendix, we also identify the coefficients of the double logarithms of form ${\mathrm{ln}}^{2}(s/{m}_{c}^{2})$ associated with all the relevant next-to-leading-order Feynman diagrams, for the helicity-suppressed double-charmonium production channels ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c2}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\chi}}_{c0,1,2}$.

Proof of factorization of heavy quarkonium production in non-equilibrium QCD at RHIC and LHC

Recently we have proved the NRQCD factorization in heavy quarkonium production at high energy colliders at all orders in coupling constant. In this paper we extend this to non-equilibrium QCD and prove the NRQCD factorization in heavy quarkonium production at all orders in coupling constant in non-equilibrium QCD. This proof is necessary to study heavy quarkonium production from quark gluon plasma at RHIC and LHC.

NNLO QCD corrections to \u03b3 + \u03b7c(\u03b7b) exclusive production in electron-positron collision

Based on the NRQCD factorization formalism, we calculate the next-to-next-to-leading order QCD corrections to the heavy quarkonium ηc(ηb) production associated with a photon at electron-positron colliders. By matching the amplitudes calculated in full QCD theory to a series of operators in NRQCD, the short-distance coefficients up to NNLO QCD radiative corrections are determined. It turns out that the full set of master integrals that we obtained could be analytically expressed in terms of Goncharov Polylogarithms, integrals over polylogarithms and complete elliptic integrals, which mostly do not exist in the literature and could be employed in the analyses of other physical processes. In phenomenology, numerical calculations of NNLO K-factors and cross sections of e+e− → γ + ηc(ηb) processes in BESIII and B-factory experiments are performed, which may stand as a test of the NRQCD higher order calculation while confronting to the data.

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium.

We compute the next-to-next-to-leading-order QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of nonrelativistic QCD (NRQCD) factorization for inclusive quarkonium decay process, for the first time, is verified to relative order α_{s}^{2}. As a by-product, the renormalization group equation of the leading NRQCD four-fermion operator O_{1}(^{1}S_{0}) is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured η_{c} hadronic width and, in particular, the branching fraction of η_{c}→γγ. NRQCD appears to be capable of accounting for η_{b} hadronic decay to a satisfactory degree, and our most refined prediction is Br(η_{b}→γγ)=(4.8±0.7)×10^{-5}.

Production of ψ(2S) and ϒ(3S) mesons in the parton Reggeization approach: Polarization observables and fragmentation

Production of the ψ(2S) and ϒ(3S) mesons is considered in the framework of the leading order parton Reggeization approach and within the NRQCD factorization hypothesis. A self-consistent description of the p T spectra at low p T (fusion model) and high p T (fragmentation model) is obtained. The fusion model predictions for polarization observables agree with experiment for ϒ(3S) and are at variance with experiment for ψ(2S).

Probing a new strongly interacting sector via composite diboson resonances

Diphoton resonance was a crucial discovery mode for the 125 GeV SM Higgs boson at the LHC. This mode or the more general diboson modes may also play an important role in probing for new physics beyond the SM. In this paper, we consider the possibility that a diphoton resonance is due to a composite (pseudo)scalar boson, whose constituents are either new hyperquarks Q or scalar hyperquarks tilde{Q} confined by a new hypercolor force at a confinement scale Lambda_h. Assuming the mass m_Q (or m_{tilde Q}) >> Lambda_h, a diphoton resonance could be interpreted as either a Q bar{Q} state eta_Q with J^{PC} = 0^{-+} or a tilde{Q} tilde{Q}^dagger state eta_{tilde Q} with J^{PC}=0^{++}. For the Q bar{Q} scenario, there will be a spin-triplet partner psi_Q which is slightly heavier than eta_Q due to the hyperfine interactions mediated by hypercolor gluon exchange; while for the tilde{Q} tilde{Q}^dagger scenario, the spin-triplet partner chi_{tilde Q} arises from higher radial excitation with nonzero orbital angular momentum. We consider productions and decays of eta_Q, eta_{tilde Q}, psi_Q, and chi_{tilde Q} at the LHC using the NRQCD factorization approach. We discuss how to test these scenarios by using the DY process and the forward dijet azimuthal angular distributions to determine the J^{PC} quantum number of the diphoton resonance. Constraints on the parameter space can be obtained by interpreting some of the small diphoton excesses reported by the LHC as the composite scalar or pseudoscalar of the model. Another important test of the model is the presence of a nearby hypercolor-singlet but color-octet state like the eta^8_Q or eta^8_{tilde Q}, which can also be constrained by dijet or monojet+monophoton data. Both possibilities of a large or small width of the resonance can be accommodated, depending on whether the hyper-glueball states are kinematically allowed in the final state or not.

Relativistic correction to gluon fragmentation function into pseudoscalar quarkonium**Supported by National Natural Science Foundation of China (11475188, 11261130311, 11575202, 11222549), IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors

Inspired by the recent measurements of the ηc meson production at LHC experiments, we investigate the relativistic correction effect for the fragmentation functions of gluon/charm quark fragmenting into ηc, which constitute the crucial nonperturbative element for the ηc production at high pT. Employing three distinct methods, we calculate the next-to-leading-order (NLO) relativistic correction to g → ηc fragmentation function in the NRQCD factorization framework, as well as verifying the existing NLO result for the c → ηc fragmentation function. We also study the evolution behavior of these fragmentation functions with the aid of the DGLAP equation.

Next-to-leading order QCD corrections to Higgs boson decay to quarkonium plus a photon **Supported by National Natural Science Foundation of China (11305001, 11105083, 11205003)

In this paper, we investigate the decay of the Higgs boson to J/ψ(ϒ) plus a photon based on NRQCD factorization. For the direct process, we calculate the decay width up to QCD NLO. We find that the decay width for process H → J/ψ(ϒ) + γ direct production at the LO is significantly reduced by the NLO QCD corrections. For the indirect process, we calculate the H → γ*γ with virtual γ substantially decaying to J/ψ(ϒ), including all the SM Feynman diagrams. The decay width of indirect production is much larger than the direct decay width. Since it is very clean in experiment, the H → J/ψ(ϒ) + γ decay could be observable at a 14 TeV LHC and it also offers a new way to probe the Yukawa coupling and New Physics at the LHC.

Proof of NRQCD factorization at all orders in the coupling constant in heavy quarkonium production

Recently the proof of factorization in heavy quarkonium production in NRQCD color octet mechanism is given at next-to-next-to-leading order (NNLO) in coupling constant by using diagrammatic method of QCD. In this paper we prove factorization in heavy quarkonium production in NRQCD color octet mechanism at all order in coupling constant by using path integral method of QCD. Our proof is valid to all powers in the heavy quark relative velocity. We find that the gauge invariance and the factorization at all order in coupling constant require gauge-completed non-perturbative NRQCD matrix elements that were introduced previously to prove factorization at NNLO.

Cancellation of infrared divergence in inclusive production of heavy quarkonia

A scheme is presented here to cancel out the topologically unfactorized infrared divergences in the inclusive production of heavy quarkonia, which affect the NRQCD factorization of these processes. The heavy quarkonia are defined as resonance states of QCD instead of color singlet heavy quark pair. Thus the final heavy quark pair is nor necessarily to be color singlet. In addition, the heavy quarkonia are reconstructed by their decay products. As the result, transition between states containing containing heavy quarks caused by exchanges of soft gluons are also taken into account here. Such cancellation is crucial for the NRQCD factorization of these processes.

An updated study of ϒ production and polarization at the Tevatron and LHC**Supported by National Nature Science Foundation of China (11475183) and Youth Innovation Promotion Association of CAS (2014010)

Following the nonrelativistic QCD factorization scheme, by taking the latest available measurements of χbJ(3P) into consideration, we present an updated study on the yield and polarization of ϒ(1S, 2S, 3S) hadroproduction, and the fractions of χbJ(mP) feed-down in ϒ(nS) production at QCD next-to-leading order. In the fitting, three schemes are applied with different choices of χbJ(mP) feed-down ratios and NRQCD factorization scale. The results can explain the measurements of yield very well. The polarization puzzle to ϒ(3S) is now solved by considering the χbJ(3P) feed-down contributions. The ratio of σ[χb2(1P)]/σ[χb1(1P)] measured by the CMS experiment can also be reproduced in our prediction. Among the different schemes, the results show little difference, but there are sizeable differences for the fitted long-distance color-octet matrix elements. This may bring large uncertainties when the values are applied in theoretical predictions for other experiments such as those at ee, ep colliders.

Can Nonrelativistic QCD Explain the γγ^{*}→η_{c} Transition Form Factor Data?

Unlike the bewildering situation in the γγ^{*}→π form factor, a widespread view is that perturbative QCD can decently account for the recent BABAR measurement of the γγ^{*}→η_{c} transition form factor. The next-to-next-to-leading-order perturbative correction to the γγ^{*}→η_{c,b} form factor, is investigated in the nonrelativistic QCD (NRQCD) factorization framework for the first time. As a byproduct, we obtain, by far, the most precise order-α_{s}^{2} NRQCD matching coefficient for the η_{c,b}→γγ process. After including the substantial negative order-α_{s}^{2} correction, the good agreement between NRQCD prediction and the measured γγ^{*}→η_{c} form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of the NRQCD approach to hard exclusive reactions involving charmonium.

α s v 2 corrections to η c and χ cJ production recoiled with a photon at e + e − colliders

We consider the production of the $\eta_c$ and $\chi_{cJ}$ states recoiled with a photon up to $\mathcal{O}(\alpha_s v^2)$ at BESIII and B-factories within the frame of NRQCD factorization. With the corrections, we revisit the numerical calculations to the cross sections for the $\eta_c(nS)$ and the $\chi_{cJ}(mP)$ states. We argue that the search for $XYZ$ states with even charge conjugation such as $X(3872)$, $X(3940)$, $X(4160)$, and $X(4350)$ recoiled with a photon at BESIII may help clarify the nature of these states. For completeness, the production of charmonium with even charge conjugation recoiled with a photon at B factories is also discussed.

χ c J Associated Production with b b ̄ $b\bar {b}$ from SM Higgs Boson Decay

In this work, we investigate the associated production of χcJ associated production with \(b\bar {b}\) from SM Higgs boson decay in the nonrelativistic factorization formalism. At leading order, the \(c\bar {c} \left [{~}^{3}S_{1}^{(8)} \right ]\) state give the main contribution for this process. From our work, we find that the production rates of these processes are not too small, makes these processes have the potential to be detected at the LHC since we can get enough Higgs events at the LHC. Such a production model of χcJ in Higgs decay provided a possible channel to study color-octet mechanism. Detailly studing this process will be useful for testing the NRQCD factorization formalism.

NLO corrections toχbJto two-J/ψexclusive decay processes

The next-to-leading order QCD corrections for $\chi_{bJ}$, the p-wave bottomonium, to $J/\psi$ pair decay processes are evaluated utilizing NRQCD factorization formalism. The scale dependence of $\chi_{b2}\rightarrow J/\psi J/\psi$ process is depressed with NLO corrections, and hence the uncertainties in the leading order results are greatly reduced. The total branch ratios are found to be the order of $10^{-5}$ for all three $\chi_{bJ}\rightarrow J/\psi J/\psi$ processes, indicating that they are observable in the LHC and super-B experiments.

HELAC-Onia: An automatic matrix element generator for heavy quarkonium physics

By the virtues of the Dyson–Schwinger equations, we upgrade the published code HELAC to be capable to calculate the heavy quarkonium helicity amplitudes in the framework of NRQCD factorization, which we dub HELAC-Onia. We rewrote the original HELAC to make the new program be able to calculate helicity amplitudes of multi P-wave quarkonium states production at hadron colliders and electron–positron colliders by including new P-wave off-shell currents. Therefore, besides the high efficiencies in computation of multi-leg processes within the Standard Model, HELAC-Onia is also sufficiently numerical stable in dealing with P-wave quarkonia (e.g. hc,b,χc,b) and P-wave color-octet intermediate states. To the best of our knowledge, it is a first general-purpose automatic quarkonium matrix elements generator based on recursion relations on the market. Program summaryProgram title: HELAC-Onia.Catalogue identifier: AEPR_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 114595No. of bytes in distributed program, including test data, etc.: 1555550Distribution format: tar.gzProgramming language: Fortran 90.Computer: Any.Operating system: Windows, Unix.Classification: 4.4, 11.1, 11.2, 11.5.Nature of problem:An important way to explore the law of the nature is to investigate the heavy quarkonium physics at B factories and hadron colliders. However, its production mechanism is still unclear, though NRQCD can explain its decay mechanism in a sufficiently satisfactory manner. The substantial K-factor in heavy quarkonium production processes also implies that the associated production of quarkonium and a relatively large number of particles may play a crucial role in unveiling its production mechanism.Solution method:A labor-saving and efficient way is to make the tedious amplitudes calculation automatic. Based on a recursive algorithm derived from the Dyson–Schwinger equations, the goal of automatic calculation of heavy quarkonium helicity amplitudes in NRQCD has been achieved. Inheriting from the virtues of the recursion relations with the lower computational cost compared to the traditional Feynman-diagram based method, the multi-leg processes (with or without multi-quarkonia up to P-wave states) at colliders are also accessible.Running time:It depends on the process that is to be calculated. However, typically, for all of the tested processes, they take from several minutes to tens of minutes.

Exclusive decay ofΥintoJ/ψ+χc0,1,2

We study the $\Upsilon$ exclusive decay into double charmonium, specifically, the $S$-wave charmonium $ J/\psi$ plus the $P$-wave charmonium $\chi_{c0,1,2}$ in the NRQCD factorization framework. Three distinct decay mechanisms, i.e., the strong, electromagnetic and radiative decay channels are included and their interference effects are investigated. The decay processes $\Upsilon(1S,2S,3S)\to J/\psi+\chi_{c1,0}$ are predicted to have the branching fractions of order $10^{-6}$, which should be observed in the prospective Super $B$ factory.

Formula omitted] production in proton–proton collisions at 7 TeV with CMS experiment

This article presents the cross-section ratio σ(χc2)/σ(χc1) for prompt χc production as a function of J/ψpT in pp collisions at 7 TeV, using 2011 data collected by CMS experiment. The total integrated luminosity corresponds to 4.62fb−1. The measurement is performed by reconstructing the χc radiative decays to J/ψ+γ, where J/ψ decays into two muons. The photons are reconstructed through their conversions into electron-positron pairs in the tracker. The results are compared with two theory predictions, NLO NRQCD and kT factorization models.

Order-v4relativistic corrections toΥinclusive decay into a charm pair

In this work, we determine the short-distance coefficients for $\Upsilon$ inclusive decay into a charm pair through relative order $v^4$ within the framework of NRQCD factorization formula. The short-distance coefficient of the order-$v^4$ color-singlet NRQCD matrix element is obtained through matching the decay rate of $b\bar{b}(^3S^{[1]}_1)\to c\bar{c}gg$ in full QCD to that in NRQCD. The double and single IR divergences appearing in the decay rate are exactly canceled through the next-to-next-to-leading-order renormalization of the operator ${\mathcal O}(^3S^{[8]}_1)$ and the next-to-leading-order renormalization of the operators ${\mathcal O}(^3P^{[8]}_J)$. To investigate the convergence of the relativistic expansion arising from the color-singlet contributions, we study the ratios of the order-$v^2$ and -$v^4$ color-singlet short-distance coefficients to the leading-order one. Our results indicate that though the order-$v^4$ color-singlet short-distance coefficient is quite large, the relativistic expansion for the color-singlet contributions in the process $\Upsilon\to c\bar{c}+X$ is well convergent due to a small value of $v$. In addition, we extrapolate the value of the mass ratio of the charm quark to the bottom quark, and find the relativistic corrections rise quickly with increase of the mass ratio.