Color-octet Long-distance Matrix Elements Research Articles

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 $J/\psi$.

Global analysis of ψ(2S) inclusive hadroproduction at next-to-leading order in nonrelativistic-QCD factorization

Working in the nonrelativistic-QCD factorization framework at next-to-leading order in $\alpha_s$, we fit the relevant color octet (CO) long-distance matrix elements (LDMEs) of the $\psi(2S)$ meson, $\langle {\cal O}^{\psi(2S)}({^1S}_0^{[8]})\rangle$, $\langle {\cal O}^{\psi(2S)}({^3S}_1^{[8]})\rangle$, and $\langle {\cal O}^{\psi(2S)}({^3P}_0^{[8]})\rangle$, to 1001 data points of upolarized and polarized $\psi(2S)$ inclusive hadroproduction. We do four different fits, with filters on polarization and low to middle transverse momentum $p_T$. We find that a successful description of the data is only possible with a large low-$p_T$ cut. Our results are one order of magnitude more precise than previous determinations of these color octet long-distance matrix elements.

TMD evolution study of the cos2ϕ azimuthal asymmetry in unpolarized J/ψ production at EIC

Semi-inclusive $J/\psi$ production in electron-proton collisions is a promising process to study gluon transverse momentum distributions (TMDs) at the future Electron-Ion Collider. In this article, we improve on previous studies of the $\cos 2 \phi$ azimuthal asymmetry that arises from the linear polarization of gluons inside unpolarized protons by including TMD evolution. We find that in the TMD regime the asymmetry grows monotonically with increasing transverse momentum of the outgoing $J/\psi$, in contrast to tree level calculations with Gaussian TMDs. Our predictions for the asymmetry at EIC can become very large at larger $x$, $Q$, and transverse momenta, even larger than the positivity bound. This problem stems from the very small $b$ region and implies a range of validity of TMD factorization that is more restricted than usually expected. We also include an estimate of the nonperturbative uncertainty from the large $b$ region and we conclude that it is smaller than the largest source of uncertainty, which stems from the choice of Color Octet Long-Distance Matrix Elements.

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.

ψ(2S)andϒ(3S)hadroproduction in the parton Reggeization approach: Yield, polarization, and the role of fragmentation

The hadroproduction of the radially excited heavy-quarkonium states $\psi(2S)$ and $\Upsilon(3S)$ at high energies is studied in the parton reggeization approach and the factorization formalism of nonrelativistic QCD at lowest order in the strong-coupling constant $\alpha_s$ and the relative heavy-quark velocity $v$. A satisfactory description of the $\psi(2S)$ transverse-momentum ($p_T$) distributions measured by ATLAS, CMS, and LHCb at center-of-mass energy $\sqrt{S}=7$ TeV is obtained using the color-octet long-distance matrix elements (LDMEs) extracted from CDF data at $\sqrt{S}=1.96$ TeV. The importance of the fragmentation mechanism and the scale evolution of the fragmentation functions in the upper $p_T$ range, beyond 30 GeV, is demonstrated. The $\Upsilon(3S)$ $p_T$ distributions measured by CDF at $\sqrt{S}=1.8$ TeV and by LHCb at $\sqrt{S}=7$ TeV and forward rapidities are well described using LDMEs fitted to ATLAS data at $\sqrt{S}=7$ TeV. Comparisons of polarization measurements by CDF and CMS at large $p_T$ values with our predictions consolidate the familiar problem in the $\psi(2S)$ case, but yield reasonable agreement in the $\Upsilon(3S)$ case.

Yields and polarizations of prompt J/ψ and ψ(2S) production in hadronic collisions

We give predictions of J/ψ and ψ(2S) yields and polarizations in prompt production at hadron colliders based on non-relativistic QCD factorization formula. We calculate short-distance coefficients of all important color-octet intermediate channels as well as color-singlet channels up to $$ \mathcal{O}\left({\alpha}_S^4\right) $$ , i.e. next-to-leading order in α S . For prompt J/ψ production, we also take into account feeddown contributions from χ cJ (J=0,1,2) and ψ(2S) decays. Color-singlet long-distance matrix elements (LDMEs) are estimated by using potential model, and color-octet LDMEs are extracted by fitting the Tevatron yield data only. The predictions are satisfactory for both yields and polarizations of prompt J/ψ and prompt ψ(2S) production at the Tevatron and the LHC. In particular, we find our predictions for polarizations of prompt J/ψ production have only a little difference from our previous predictions for polarizations of direct J/ψ production.

Hc production at hadron colliders

In this paper, we present the study of the hadroproduction rate of hc at next-to-leading order in under the nonrelativisitic QCD (NRQCD) factorization framework, using color-octet long-distance matrix elements obtained from a global fit of experimental measurements on yield and the ratio from the CDF, LHCb, CMS, and ATLAS Collaborations. This paper considers the problem of NRQCD scale dependence for the first time, and finds that, for some experimental conditions, the choice of this scale can significantly affect the final results, which indicates that, for these conditions, theoretical evaluation up to next-to-leading order cannot provide sufficiently precise predictions. We also present a brief analysis on the NRQCD scale dependence problem, and provide a criterion to determine in which case next-to-leading order prediction would be ruined by the scale dependence.

Next-to-leading-order study of the associated production ofJ/ψ+γat the LHC

The associate $J/\ensuremath{\psi}+\ensuremath{\gamma}$ production at the LHC is studied completely at next-to-leading order within the framework of nonrelativistic QCD. By using three sets of color-octet long-distance matrix elements obtained in previous prompt $J/\ensuremath{\psi}$ studies, we find that only one of them can result in a positive transverse momentum (${p}_{t}$) distribution of $J/\ensuremath{\psi}$ production rate at the large ${p}_{t}$ region. Based on reasonable consideration to cut down background, our estimation is measurable up to ${p}_{t}=50\text{ }\text{ }\mathrm{GeV}$ with the present data sample collected at 8 TeV LHC. All the color-octet long-distance matrix elements in $J/\ensuremath{\psi}$ production could be fixed sensitively by including this proposed measurement and our calculation, and then a confident conclusion on the $J/\ensuremath{\psi}$ polarization puzzle could be achieved.

Complete Next-to-Leading-Order Study on the Yield and Polarization ofΥ(1S,2S,3S)at the Tevatron and LHC

Based on the nonrelativistic QCD factorization scheme, we present the first complete next-to-leading-order study on the yield and polarization of Υ(1S,2S,3S) hadroproduction. By using the color-octet long-distance matrix elements obtained from fits of the experimental measurements on Υ yield and polarization at the Tevatron and LHC, our results can explain the measurements on the yield very well, and for the polarizations of Υ(1S,2S,3S), they are in (good, good, bad) agreement with recent CMS measurement, but still have some distance from the CDF measurement.

Polarization for prompt J/ψ and ψ(2s) production at the Tevatron and LHC.

With nonrelativistic QCD factorization, we present the first complete next-to-leading order study on the polarization of prompt J/ψ hadroproduction by including feeddown from χ(c)((3)P(J)(1),(3)S(1)(8)) and ψ(2s) which turn out to be very important parts. By using the color-octet long-distance matrix elements obtained from a combined fit of the measurements at the Tevatron and LHC for J/ψ, ψ(2s) and χ(c), the prompt J/ψ polarization predictions are presented, and the results are in agreement with the CDF run I data (except two points), but in conflict with the CDF run II data, while they are close to the ALICE data (inclusive J/ψ). The measurements at the LHC are expected to clarify the situation.

J/ψPolarization at the Tevatron and the LHC: Nonrelativistic-QCD Factorization at the Crossroads

We study the polarization observables of J/ψ hadroproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics. We complete the present knowledge of the relativistic corrections by also providing the contribution due to the intermediate (3)P(J)([8]) color-octet states at this order, which turns out to be quite significant. Exploiting the color-octet long-distance matrix elements previously extracted through a global fit to experimental data of unpolarized J/ψ production, we provide theoretical predictions in the helicity and Collins-Soper frames and compare them with data taken by CDF at Fermilab Tevatron I and II and by ALICE at CERN LHC. The notorious CDF J/ψ polarization anomaly familiar from leading-order analyses persists at the quantum level, while the situation looks promising for the LHC, which is bound to bring final clarification.

Formula omitted] production in NRQCD: A global analysis of yield and polarization

We present a rigorous next-to-leading order analysis of J/psi yield and polarization within the factorization theorem of nonrelativistic QCD (NRQCD). To the orders considered, this framework depends on three free parameters, the color-octet long-distance matrix elements. We extract their values in a global fit to inclusive J/psi production data from various hadroproduction, photoproduction, two-photon scattering and electron-positron annihilation experiments. We show that this fit is constrained and stable and describes all data sufficiently well. We then make predictions for J/psi polarization in photo- and hadroproduction and compare them to the currently available data. As for photoproduction, HERA data is not precise enough to draw definite conclusions. But as for hadroproduction, CDF data measured at Tevatron run II is in strong conflict with NRQCD predictions. With early ALICE data being however compatible with NRQCD, the future, more precise polarization measurements at the LHC will thus have the potential to clearly confirm or dismiss LDME universality.

Probing Nonrelativistic QCD Factorization in PolarizedJ/ψPhotoproduction at Next-to-Leading Order

We analyze the polarization observables of J/ψ photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD). This is a complete next-to-leading-order study of heavy-quarkonium polarization including the full relativistic corrections due to the intermediate (1)S(0)([8]), (3)S(1)([8]), and (3)P(J)([8]) color-octet states closing a gap in the worldwide endeavor to test NRQCD factorization at the quantum level. We present theoretical predictions in the helicity, target, and Collins-Soper frames of DESY HERA, evaluated using the color-octet long-distance matrix elements previously extracted through a global fit to experimental data of unpolarized J/ψ production, and confront them with recent measurements by the H1 and ZEUS Collaborations. We find the overall agreement to be satisfactory but the case for NRQCD to be not as strong as for the J/ψ yield.

World data ofJ/ψproduction consolidate nonrelativistic QCD factorization at next-to-leading order

We calculate the cross sections of inclusive J/psi production in photoproduction and two-photon scattering, involving both direct and resolved photons, and in e^+e^- annihilation at next-to-leading order (NLO) within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the full relativistic corrections due to the intermediate ^1S_0^{[8]}, ^3S_1^{[8]}, and ^3P_J^{[8]} color-octet (CO) states. Exploiting also our previous results on hadroproduction, we perform a combined fit of the respective CO long-distance matrix elements (LDMEs) to all available high-quality data of inclusive J/psi production, from KEKB, LEP~II, RHIC, HERA, the Tevatron, and the LHC, comprising a total of 194 data points from 26 data sets.

ReconcilingJ/ψProduction at HERA, RHIC, Tevatron, and LHC with Nonrelativistic QCD Factorization at Next-to-Leading Order

We calculate the cross section of inclusive direct J/ψ hadroproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics, including the full relativistic corrections due to the intermediate 1S(0)[8], 3S(1)[8], and 3P(J)[8] color-octet states. We perform a combined fit of the color-octet long-distance matrix elements to the transverse-momentum (p(T)) distributions measured by CDF at the Fermilab Tevatron and H1 at DESY HERA and demonstrate that they also successfully describe the p(T) distributions from PHENIX at BNL RHIC and CMS at the CERN LHC as well as the photon-proton c.m. energy and (with worse agreement) the inelasticity distributions from H1. This provides a first rigorous test of nonrelativistic QCD factorization at next-to-leading order. In all experiments, the color-octet processes are shown to be indispensable.

Complete Next-to-Leading-Order Corrections toJ/ψPhotoproduction in Nonrelativistic Quantum Chromodynamics

We calculate the cross section of inclusive direct J/psi photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics for the first time including the full relativistic corrections due to the intermediate {1}S{0}{[8]}, {3}S{1}{[8]}, and {3}P{J}{[8]} color-octet states. A comparison of our results to recent H1 data suggests that the color-octet mechanism is indeed realized in J/psi photoproduction, although the predictivity of our results still suffers from uncertainties in the color-octet long-distance matrix elements.