NRQCD Factorization Formalism Research Articles

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.

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.

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.

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.

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.

Charmed-Hadron Production in ϒ(1S) Semi-inclusive Decay

In the framework of the NRQCD factorization formalism, we calculate the decay rate for the process ϒ(1S) → cc̄gg to the next-to-leading order (NLO) in the relative velocity v of the b quark in the bottomonium rest frame. We also study the momentum distributions of the charm quark and the charmed-hadron in the decay. The momentum distribution of the charmed-hadron is obtained by convolving the charm quark momentum distribution with a fragmentation function of the charm quark into the hadron. In addition, we fit the nonperturbative NRQCD matrix element ⟨v2⟩ϒ through comparing the theoretical prediction with the measurement from the BaBar collaboration for the decay rate of ϒ(1S) → D*+X. In return, taking this matrix element as an input parameter, we predict the decay rates as well as the momentum distributions for a collection of charmed-hadrons in the process ϒ(1S) → cc̄gg → hX.

Charm-pair rescattering mechanism for charmonium production in high-energy collisions

A new mechanism for heavy quarkonium production in high-energy collisions called the cut was proposed in 2005 by Lansberg, Cudell, and Kalinovsky. We identify this mechanism physically as the production of a heavy quark and anti-quark that are on-shell followed by their rescattering to produce heavy quarkonium. We point out that in the NRQCD factorization formalism this rescattering mechanism is a contribution to the color-singlet model term at next-to-next-to-leading order in perturbation theory. Its leading contribution to the production rate can be calculated without introducing any additional phenomenological parameters. We calculate the charm-pair rescattering (or s-channel cut) contribution to the production of J/psi at the Tevatron and compare it to estimates by Lansberg et al. using phenomenological models. This contribution competes with the leading-order term in the color-singlet model at large transverse momentum but is significantly smaller than the next-to-leading-order term. We conclude that charm-pair rescattering is not a dominant mechanism for charmonium production in high-energy collisions. Comment: 12 pages, 10 figures

Automatic generation of quarkonium amplitudes in NRQCD

We present a simple method to automatically evaluate arbitrary tree-level amplitudes involving the production or decay of a heavy quark pair QQbar in a generic {2S+1}L_J^[1,8] state, i.e., the short distance coefficients appearing in the NRQCD factorization formalism. Our approach is based on extracting the relevant contributions from the open heavy quark-antiquark amplitudes through an expansion with respect to the quark-antiquark relative momentum and the application of suitable color and spin projectors. To illustrate the capabilities of the method and its implementation in MadGraph a few applications to quarkonium collider phenomenology are presented. Comment: 17 pages, 7 figures

Exclusive two-vector-meson production frome+e−annihilation

The exclusive production of pairs of vector mesons with J{sup PC}=1{sup --} in e{sup +}e{sup -} collisions can proceed through e{sup +}e{sup -} annihilation into two virtual photons. At energies much greater than the meson masses, the cross section is dominated by the independent fragmentation of the virtual photons into the vector mesons. The fragmentation approximation is used to calculate the cross sections and angular distributions for pairs of vector mesons that can be produced at the B factories. The predicted cross sections for {rho}{sup 0}+{rho}{sup 0} and {rho}{sup 0}+{phi} production agree with recent measurements by the BABAR Collaboration. For the production of two charmonium vector mesons, the nonfragmentation corrections to the cross sections are calculated by using the NRQCD factorization formalism. The predicted cross sections for J/{psi}+J/{psi} and J/{psi}+{psi}(2S) production are compatible with upper limits set by the Belle Collaboration.

HARD DIFFRACTIVE SCATTERING FACTORIZATION FROM ηc AND γ ASSOCIATED PRODUCTION AT TEVATRON AND LHC

Based on IS model, the cross-sections of associated ηc and γ diffractive production in [Formula: see text] collision are calculated. Under the framework of NRQCD factorization formalism for quarkonia production, the dominant contribution to associated ηc and γ production comes from color octet [Formula: see text] subprocess, the color octet matrix element of [Formula: see text] is related to that of [Formula: see text] of J/ψ by the heavy quark spin symmetry. Because the value of color octet matrix element of [Formula: see text] of J/ψ is determined by the large PTJ/ψ production data, the prediction of ηc and γ is more reliable. The ratio of diffractive to inclusive cross-sections is independent of the values of color octet matrix elements, which is sensitive to the gluon factor of the Pomeron and renormalized Pomeron flux factors. So experimental measurement of this ratio can give us more information of the nature of Pomeron and test the assumption of diffractive hard scattering factorization.

NRQCD: Fundamentals and Applications to Quarkonium Decay and Production

I discuss NRQCD and, in particular, the NRQCD factorization formalism for quarkonium production and decay. I also summarize the current status of the comparison between the predictions of NRQCD factorization and experimental measurements.

Inclusive production of theX(3872)

If the $X(3872)$ is a loosely-bound ${D}^{*0}{\overline{D}}^{0}/{D}^{0}{\overline{D}}^{*0}$ molecule, its inclusive production rate can be described by the NRQCD factorization formalism that applies to inclusive quarkonium production. We argue that if the molecule has quantum numbers ${J}^{PC}={1}^{++}$, the most important term in the factorization formula should be the color-octet $^{3}S_{1}$ term. This is also one of the two most important terms in the factorization formulas for ${\ensuremath{\chi}}_{cJ}$. Since the color-octet $^{3}S_{1}$ term dominates ${\ensuremath{\chi}}_{cJ}$ production for many processes, the ratio of the inclusive direct production rates for $X$ and ${\ensuremath{\chi}}_{cJ}$ should be roughly the same for these processes. The assumption that the ratio of the production rates for $X$ and ${\ensuremath{\chi}}_{cJ}$ is the same for all processes is used to estimate the inclusive production rate of $X$ in $B$ meson decays, ${Z}^{0}$ decays, and in $p\overline{p}$ collisions.

Relativistic corrections to gluon fragmentation into spin-tripletS-wave quarkonium

We use the NRQCD factorization formalism to calculate the relativistic corrections to the fragmentation function for a gluon fragmenting into a spin-triplet S-wave heavy quarkonium. We make use of the gauge-invariant formulation of the fragmentation function of Collins and Soper. The color-octet contribution receives a large, negative relativistic correction, while the color-singlet contribution receives a large, positive relativistic correction. The considerable decrease in the color-octet contribution requires a corresponding increase in the phenomenological value of the leading color-octet matrix element in order to maintain a fit to the Fermilab Tevatron data.

Nonrelativistic QCD analysis of bottomonium production at the Fermilab Tevatron

Recent data from the CDF collaboration on the production of spin-triplet bottomonium states at the Tevatron p \bar p collider are analyzed within the NRQCD factorization formalism. The color-singlet matrix elements are determined from electromagnetic decays and from potential models. The color-octet matrix elements are determined by fitting the CDF data on the cross sections for Upsilon(1S), Upsilon(2S), and Upsilon(3S) at large p_T and the fractions of Upsilon(1S) coming from chi_b(1P) and chi_b(2P). We use the resulting matrix elements to predict the cross sections at the Tevatron for the spin-singlet states eta_b(nS) and h_b(nP). We argue that eta_b(1S) should be observable in Run II through the decay eta_b -> J/psi + J/psi.

Quarkonium production and NRQCD matrix elements

Most recent calculations of quarkonium production are based on the NRQCD factorization formalism. This formalism is reviewed. To make predictions about specific cross section, universal NRQCD matrix elements need to be extracted from experiments. Extractions from different experimental situations are compared, with some emphasis on the extraction from LEP.

Two-spin asymmetry forψ′photoproduction with the color-octet mechanism

We study the photoproduction of ${\ensuremath{\psi}}^{\ensuremath{'}}$ in the forward regions in polarized $\ensuremath{\gamma}p$ collisions at relevant (DESY) HERA energies. We find that this reaction is very effective to test the color-octet mechanism which is based on the NRQCD factorization formalism. Furthermore we find that the value of the NRQCD matrix elements can be severely constrained by measuring the two-spin asymmetry, though the process depends on the polarized gluon distribution $\ensuremath{\Delta}g(x).$

D-wave heavy quarkonium production in fixed target experiments

We calculate the D-wave heavy quarkonium production at fixed target experiments under the NRQCD factorization formalism. We find that the color-octet contributions are two orders of magnitude larger than color-singlet contributions if color-octet matrix elements are taken according to the NRQCD velocity scaling rules. Within theoretical uncertainties, the prediction for the production rate of a ${2}^{\ensuremath{-}\ensuremath{-}}$ D-wave charmonium state agrees with the preliminary result of E705 and other experiments. Searching for the ${1}^{\ensuremath{-}\ensuremath{-}}$ D-wave state $\ensuremath{\psi}(3770)$ is further suggested.

Photoproduction ofhc

Using the NRQCD factorization formalism, we calculate the total cross section for the photoproduction of h_c mesons. We include color-octet and color-singlet mechanisms as well as next-to-leading order perturbative QCD corrections. The theoretical prediction depends on two nonperturbative matrix elements that are not well determined from existing data on charmonium production. For reasonable values of these matrix elements, the cross section is large enough that the h_c may be observable at the E831 experiment and at the HERA experiments.