The presented paper is devoted to theoretical analysis of charmonium mesons $η_c$, $J/ψ$, $χ_{c0,1,2}$, and $h_c$ production in exclusive radiative $Z$ boson decays in the frameworks of Nonrelativistic Chromodynamic and amplitude expansion on the light-cone. In the framework of light-cone expansion amplitudes and widths of all processes are described with one universal relation. It is interesting to note that from this relation it follows automatically which component of $Z$ boson (either vector or axial) gives contribution to the width of the particular decay. It is shown that the effect of internal quark motion almost doubles theoretical predictions for production of $S$-wave charmonia and $χ_{c1}$ meson.
We show that the twist-2 light-cone wave-functions of eta_c and J/ψcan be factorized with nonrelativistic QCD(NRQCD) at one-loop level, where the nonperturbative effects are represented by NRQCD matrix elements. The factorization is achieved by expanding the small velocity v, which the c- or \bar c- quark moves inside a rest quarkonium with. At leading order of v the twist-2 light-cone wave-functions of eta_c and J/ψcan be factorized as the product of a perturbative function and a NRQCD matrix element. The perturbative function is calculated at one-loop level and free from any soft divergence.…
This work presents the differential charmonia production cross sections in high energy p+p collisions calculated using NRQCD formalism. The NRQCD formalism, factorizes the quarkonia production cross sections in terms of short distance QCD cross sections and long distance matrix elements (LDMEs). The short distance cross sections are calculated in terms of perturbative QCD and LDMEs are obtained by fitting the experimental data. Measured transverse momentum distributions of $χ_{\rm c}$, $ψ$(2S) and J/$ψ$ in p +{$\bar {\rm p}$} collisions at $\sqrt{s}=$ 1.8, 1.96 TeV and in p+p collisions at $\s…
We study the semileptonic differential decay rates of $B_c$ meson to S-wave charmonia, $η_c$ and $J/Ψ$, at the next-to-leading order accuracy in the framework of NRQCD. In the heavy quark limit, $m_b \to \infty$, we obtain analytically the asymptotic expression for the ratio of NLO form factor to LO form factor. Numerical results show that the convergence of the ratio is perfect. At the maximum recoil region, we analyze the differential decay rates in detail with various input parameters and polarizations of $J/ψ$, which can now be checked in the LHCb experiment. Phenomenologically, the form f…
This article is devoted to systematic analysis of double charmonium production in exclusive $Z$ boson decays in the framework of Nonrelativistic Quantum Chromodynamic (NRQCD) and leading twist light-cone (LC) models. Theoretical predictions for branching fractions of all considered decays are presented. According to obtained results in the case of allowed by helicity suppression rule processes the effect of internal quark motion increases the branching fraction by a factor 1.5, while for forbidden reactions LC predictions are strictly zero, while NRQCD ones are significantly smaller than for a…
In the framework of $k_T$-factorization approach, the production and polarization of prompt $J/ψ$ mesons at the LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. Both the direct production mechanism and feed-down contributions from $χ_c$ and $ψ(2S)$ decays are taken into account. The transverse momentum dependent (or unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Ki…
In the framework of kt-factorization approach,the production of prompt $χ_c$ mesons in pp collisions at the LHC energies is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses $g^*g^*\toχ_{cJ}$ and non-relativistic QCD formalism for bound states. The transverse momentum dependent (unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. Taking into account both color singlet and color octet contributions, we de…
In the presented paper production of charmonium state $\mathcal{Q}$ in exclusive $W\to\mathcal{Q} D_{s}^{(*)}$ decays is analyzed in the framework of both leading order Nonrelativistic Quantum Chromodynamics (NRQCD) and light-cone expansion (LC) models. Analytical and numerical predictions for the branching fractions of these decays in both approaches are given. The typical value of the branching fractions is $\sim 10^{-11}$ and it turns out the LC results are about 4 times lager than NRQCD ones, so the effect of internal quark should be taken into account. Some estimates of color-octet contri…
In the framework of kt-factorization approach, the production and polarization of prompt psi(2S) mesons in pp collisions at the LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. The transverse momentum dependent (unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. The non-perturbative color-octet matrix elements were first deduced from …
We perform a detailed study of semileptonic form-factors for the doubly heavy baryons in the framework of three-point NRQCD sum rules. The analyis of spin symmetry relations as well as numerical results on various exclusive decay modes of doubly heavy baryons are given.
In the framework of QCD factorization, we study the $B$ meson exclusive decays $B\to χ_{cJ}K$ where the spin-triplet P-wave charmonium states $χ_{cJ}(J=0,1,2)$ are described by the color-singlet non-relativistic wave functions. We find that for these decays (except $χ_{c1}$) there are infrared divergences arising from nonfactorizable vertex corrections as well as logarithmic end-point singularities arising from nonfactorizable spectator interactions at leading-twist order. The infrared divergences due to vertex corrections will explicitly break down QCD factorization within the color-singlet m…
In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of non-relativistic Schrödinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and few low-lying P and D waves. The resultant wave functions at zero inter quark separation as well as some finite separation are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states by using the conventiona…
We discuss the power scaling rules along the lines of a complete Heavy Quark Effective Field Theory (HQEFT) for the description of heavy quarkonium production through a color-octet mechanism. To this end, we firstly derive a tree-level heavy quark effective Lagrangian keeping both particle-antiparticle mixed sectors allowing for heavy quark-antiquark pair annihilation and creation, but describing only low-energy modes around the heavy quark mass. Then we show the consistency of using HQEFT fields in constructing four-fermion local operators a la NRQCD, to be identified with standard color-octe…
In a typical exclusive quarkonium production process, when the center-of-mass energy, $\sqrt{s}$, is much greater than the heavy quark mass $m$, large kinematic logarithms of $s/m^2$ will unavoidably arise at each order of perturbative expansion in the short-distance coefficients of the nonrelativistic QCD (NRQCD) factorization formalism, which may potentially harm the perturbative expansion. This symptom reflects that the hard regime in NRQCD factorization is too coarse and should be further factorized. We suggest that this regime can be further separated into "hard" and "collinear" degrees o…
We study exclusive production of scalar $χ_{c0}\equiv χ_c(0^{++})$ and pseudoscalar $η_c$ charmonia states in proton-proton collisions at the LHC energies. The amplitudes for $gg \to χ_{c0}$ as well as for $gg \to η_c$ mechanisms are derived in the $k_{T}$-factorization approach. The $p p \to p p η_c$ reaction is discussed for the first time. We have calculated rapidity, transverse momentum distributions as well as such correlation observables as the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The latter two observables are very different for $χ_{c0}$ and $η_c$ case…
Within the framework of nonrelativisitic QCD factorization formalism, we present the next-to-leading-order relativistic corrections to $Υ$ exclusive decay into $η_c$ plus $J/ψ$. The double charmonia can be produced through several immediate channels, i.e. $Υ\to g^*g^*g^*\to η_c+J/ψ$, $Υ\to g^*g^*γ^*\to η_c+J/ψ$, and $Υ\to γ^*\to η_c+J/ψ$. The amplitudes of these three channels are obtained accurate up to ${\cal O}(α_s^3 v^2)$, ${\cal O}(αα_s^2 v^2)$, and ${\cal O}(αα_s^2 v^2)$ respectively, where $v$ indicates the typical heavy quark velocity in bottomonium and/or charmonium rest frame. The de…
The importance of the color octet component in P-wave charmonia is discussed in the context of exclusive decay processes. It is vital to include this contribution already at the level of the two-body decay channels. The ππand proton-antiproton channels are used as examples.
Predictions for $e^+e^-\to J/ψη_c$ from previous studies are made by taking charmonia as a nonrelativistic bound state and by using nonrelativistic QCD(NRQCD) approach. The predicted cross-section is smaller by an order of magnitude than the experimentally observed. We study the process by taking charm quark as a light quark and use light-cone wave-functions to parameterize nonperturbative effects related to charmonia. The total cross section of $e^+e^-\to J/ψη_c$ can be predicted, if these wave-functions are known. Motivated by studies of light-cone wave-functions of light hadrons, we make a …
We consider exclusive double diffractive production of polarised axial-vector $χ_c(1^+)$ and tensor $χ_c(2^+)$ charmonia in proton-(anti)proton collisions at Tevatron energy. The corresponding amplitudes for these processes are derived within the $k_t$-factorisation approach. Contributions from different polarisation states of axial-vector and tensor charmonia are quantified. Corresponding experimental consequences are discussed.
We present the main results of our recent analyses of exclusive production of vector charmonia ($J/ψ$ and $ψ'$) in $k_t$-factorization approach and for $γγ$ production of charged dilepton pairs in exclusive and semiinclusive processes in a new approach, similar in spirit to $k_t$-factorization. The results for charmonia are compared with recent results of the LHCb collaboration. We include some helicity flip contributions and quantify the effect of absorption correction. The effect of $c \bar c$ wave function is illustrated. We present uncertainties related to $F_2$ structure function which ar…
This paper is devoted to the leading twist exclusive bottomonia decays with double charmonium in the final state. Using models of the twist-2 charmonia distribution amplitudes the widths of these decays are calculated within light cone formalism. In addition, the processes under consideration are studied within nonrelativistic QCD. In our analysis we have found that the production of some of the $P$-wave charmonia mesons with $L_z \neq 0$ is allowed already at the leading twist approximation. This means that the selection rules which predict the suppression of such decays are violated. The mec…
We apply the newly developed NRQCD factorization formula to analyze the exclusive production of the fully-charmed tetraquark $T_{4c}$ plus a hard photon at $B$ factory. For simplicity, in this work we have concentrated on the associated production of the $0^{++}$ and $2^{++}$ tetraquarks with a photon. With some rough estimates about the size of the unknown nonperturbative NRQCD matrix elements, we predict the production rates of these types of exclusive channels at $\sqrt{s}=10.6$ GeV and also assess their observation prospect at {\tt Belle 2} experiment.
As a test of the color-singlet mechanism of the nonrelativistic QCD (NRQCD) factorization approach, we consider the exclusive two-quarkonium productions in electron-positron annihilation e+ e- -> eta_c + gamma and e+ e- -> J/psi + J/psi at B factories. The cross sections are computed to the next-to-leading order in alpha_s and are resummed to all orders in half the relative velocity v of the charm quark in each meson rest frame. The available theoretical prediction of the cross section for e+ e- -> J/psi + eta_c at the same level of theoretical accuracies is consistent with the available exper…
In this paper, we calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the exclusive processes $B_c^+\to χ_{cJ}(h_c)π^+$ in the framework of the nonrelativistic QCD (NRQCD) factorization formalism. The results show that NLO QCD corrections markedly enhance the branching ratios with $K$ factors of about 2.5. In combination with the study of $B_c^+\to J/ψπ^+$, we find that the NLO NRQCD prediction for the ratio of branching fractions $\frac{\mathcal{B}(B_c^+\to χ_{c0}π^+)}{\mathcal{B}(B_c^+\to J/ψπ^+)}$ is then compatible with the experimental measurement.
Based on the NRQCD factorization formalism, we calculate the next-to-next-to-leading order QCD corrections to the heavy quarkonium $η_c (η_b)$ 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, Chen's iterated integrals, and elliptic functions, which mostly do not exi…
Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35,%. Among the various processes, the relativistic c…
We investigate two exclusive processes, e+ e- -> eta_c + gamma and e+ e- -> J/psi + J/psi, at the center-of-momentum energy sqrt{s}=10.58 GeV within the framework of the nonrelativistic QCD factorization approach. A class of relativistic corrections is resummed to all orders in the heavy-quark velocity v and the corrections are large negative. We further improve the prediction by including available QCD next-to-leading-order corrections and the interference between the QCD and relativistic corrections. The prediction for sigma[e+ e- -> eta_c + gamma] is about 50 fb. In the case of e+ e- -> J/p…
The amplitude for $γp \to J/ψp$ ($γp \to ψ' p$) is calculated in a pQCD $k_{T}$-factorization approach. The total cross section for this process is calculated for different unintegrated gluon distributions and compared with the HERA data and the data extracted recently by the LHCb collaboration. The amplitude for $γp \to J/ψp$ ($γp \to ψ' p$) is used to predict the cross section for exclusive photoproduction of $J/ψ$ ($ψ'$) meson in proton-proton collisions. Compared to earlier calculations we include both Dirac and Pauli electromagnetic form factors. The effect of Pauli form factor is quantif…
We calculate the contributions from QED processes involving two virtual photons to the cross sections for e^+ e^- annihilation into two charmonium states with the same C-parity. Generically, the cross sections are three orders of magnitude smaller than those for charmonia with opposite C-parity because they are suppressed by a factor of alpha^2/alpha_s^2. However, if both charmonia have quantum numbers J^{PC} = 1^{--}, then there is a contribution to the cross section that involves the fragmentation of each photon into a charmonium. The fragmentation contribution is enhanced by powers of E_{be…
After the great triumph of the Higgs discovery in 2012, the next target at the energy frontier will be to study the Higgs properties and to search for the next scale beyond the SM. Experimentally, the $H\to c \bar{c}$ channel would be extremely difficult to dig out because of both the weak Yukawa coupling and the daunting SM di-jet background. We propose to test the charm-quark Yukawa coupling at the LHC and future hadron colliders with the Higgs boson decay to $J/ψ$ via the charm-quark fragmentation. Using the non-relativistic quantum chromodynamics (NRQCD), we study the charmonia production …
We analyze B -> K H_c (where H_c = eta_c, J/psi, chi_{cJ(J=0,1)}) decays estimating nonfactorizable contributions from the light-cone sum rules (LCSR). Nonfactorizable contributions are sizable for B -> K J/psi and particularly for B -> K chi_{c1} decay. For the B decays into a (pseudo)scalar charmonia we find small nonfactorizable contributions which cannot accommodate relatively large branching ratios obtained by measurements. This specially concerns the puzzling B -> K chi_{c0} decay.
Recent measurements of the Belle Collaboration of the exclusive production of two charmonia in the $e^+e^-$ annihilation differ substantially from theoretical predictions. Recently it was suggested that a significant part of this discrepancy can be explained by the process $e^2e^- --> 2J/psi$ and value for its cross-section was published. In this paper it is shown, that these results are incorrect and the values for the cross-sections of the production of different vector charmonia are presented.
In this paper, we calculate twist-2 light-cone distribution amplitudes (LCDAs) of the S-wave and P-wave quarkonia (namely $^1S_0$ state $η_{Q}$, $^3S_1$ state $J/ψ(Υ)$, $^1P_1$ state $h_{Q}$ and $^3P_J$ states $χ_{QJ}$ with $J=0,1,2$ and $Q=c,b$) to the next-leading order of the strong coupling $α_s$ and leading order of the velocity expansion $v$ in the non-relativistic QCD (NRQCD). We apply these LCDAs to some single quarkonium exclusive productions at large center-of-mass energy, such as $γ^*\to η_Qγ, χ_{QJ}γ~(J=0,1,2)$, $Z\to η_Qγ, χ_{QJ}γ~(J=0,1,2), J/ψ(Υ)γ, h_Qγ$ and $h\to J/ψγ$, by adop…
We present numerical results for the dissociation cross sections of ground-state, orbitally- and radially-excited charmonia in collisions with light mesons. Our results are derived using the nonrelativistic quark model, so all parameters are determined by fits to the experimental meson spectrum. Examples of dissociation into both exclusive and inclusive final states are considered. The dissociation cross sections of several C=(+) charmonia may be of considerable importance for the study of heavy ion collisions, since these states are expected to be produced more copiously than the J/psi. The r…
Recent advances in our understanding of the higher-wave quarkonia have generated much interests in quarkonium physics. However most are devoted to inclusive decays and productions. Experimental data of several two-body exclusive decay channels of P-wave charmonia such as ππand p \bar p are available and some have recently been re-measured by the BES collaboration. It is not clear from the outset that color octet is needed for these exclusive channels. Indeed only color singlet has been used in the past and reasonable agreement with data was found. Contrary to these old results, we provide theo…
The next-to-leading order QCD corrections for $χ_{bJ}$, the p-wave bottomonium, to $J/ψ$ pair decay processes are evaluated utilizing NRQCD factorization formalism. The scale dependence of $χ_{b2}\rightarrow J/ψJ/ψ$ 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 $χ_{bJ}\rightarrow J/ψJ/ψ$ processes, indicating that they are observable in the LHC and super-B experiments.
This work aims at illustrating that, for a class of leading-twist hard exclusive reactions involving two heavy quarkonia, the light-cone approach, when equipped with the strategy of refactorization of the light-cone distribution amplitude of quarkonium, can be employed to elegantly reproduce the corresponding predictions made in the nonrelativistic QCD (NRQCD) factorization approach, order by order in perturbative expansion. Taking the electromagnetic form factor of the $B_c$ meson at large momentum transfer, $Q^2$, as a concrete example, we compare the results obtained from both NRQCD-based a…
Using the fact that the c-quark inside a charmonium moves with a small velocity v in the charmonium rest-frame, one can employ an expansion in v to study decays of charmonia and results at the leading order for chi_{c0,2} --> gamma gamma exist in the literature. We study corrections at the next-to-leading order in the framework of nonrelativistic QCD(NRQCD) factorization. The study presented here is different than previous approaches where chi_{c0,2} is taken as a bound-state of a c cbar pair and a nonrelativistic wave-function is used for the pair. We find that the corrections are consist not…
We derive relations among branching fractions in the exclusive decay of charmonia to light flavour meson pairs assuming factorization between the quark spin and spatial degrees of freedom. With the further assumption that these amplitudes can be described by flux-tube models, we assess prospects for production of hybrid mesons in charmonium decays.
We discuss our ongoing effort to calculate form factors for several B and Bs semileptonic decays. We have recently completed the first unquenched calculation of the form factors for the rare decay B -> K ll. Extrapolated over the full kinematic range of q^2 via model-independent z expansion, these form factor results allow us to calculate several Standard Model observables. We compare with experiment (Belle, BABAR, CDF, and LHCb) where possible and make predictions elsewhere. We discuss preliminary results for Bs -> K l nu which, when combined with anticipated experimental results, will provid…
We study hadronic decays $χ_{cJ}\rightarrow K^*(892)\bar{K} $ within the effective field theory framework. We consider the colour-singlet and colour-octet contributions and study their properties using (p)NRQCD effective theory. We show that infrared singularities in collinear integrals of the colour-singlet amplitudes can be absorbed into the renormalisation of the colour-octet matrix elements. The heavy quark spin symmetry allows us to establish a relation between the colour-octet matrix elements and to define the spin symmetry breaking corrections which are free from infrared singularities.…
We generalize results of lattice QCD to determine the spin-dependent symmetries and factorization properties of meson production in OZI allowed processes. This explains some conjectures previously made in the literature about axial meson decays and gives predictions for exclusive decays of vector charmonia, including ways of establishing the structure of Y(4260) and Y(4325) from their S-wave decays. Factorization gives a selection rule which forbids $e^+e^- \to D^* D_2$ near threshold with the tensor meson in helicity 2. The relations among amplitudes for double charmonia production $\e^+e^-\t…
We analyze the exclusive charmonium $J/ψ+η_c$ pair production in $e^+e^-$ annihilation using the nonfactorized perturbative QCD and the light-front quark model(LFQM) that goes beyond the peaking approximation. We effectively include all orders of higher twist terms in the leading order of QCD coupling constant and compare our nonfactorized analysis with the usual factorized analysis in the calculation of the cross section. We also calculate the quark distribution amplitudes, the Gegenbauer moments, and the decay constants for $J/ψ$ and $η_c$ mesons using our LFQM. Our nonfactorized result enha…
We study the exclusive decay of $J/Ψ$ into a lepton pair combined with light hadrons in the kinematic region, specified by that the total energy of the light hadrons is much smaller than $m_c$, the mass of the $c$-quark. In this region, the nonperturbaive effect related to $J/Ψ$ and that related to the light hadrons can be separated, the former is represented by a NRQCD matrix element, while the later is represented by a matrix element of a correlator of electric chromofields. The results are obtained in a axial gauge by assumming that contributions from two-gluon emmssion are dominant. But we…
Within the nonrelativistic QCD (NRQCD) factorization framework, we have computed the ${\mathcal O}(α_s^2)$ corrections to the exclusive production of $P$-wave spin-triplet charmonia $χ_{cJ}(J=0,1,2)$ accompanied by a hard photon at $B$ factories. For the first time, we have explicitly verified the validity of NRQCD factorization for exclusive $P$-wave quarkonium production at two-loop order. Unlike the $χ_{cJ}$ electromagnetic decay processes, the $\mathcal{O}(α_s^2)$ corrections are found to be smaller than the $\mathcal{O}(α_s)$ corrections in all three channels $e^+e^-\to χ_{c0,1,2}+γ$. In …
Unlike the bewildering situation in the $γγ^*\to π$ form factor, a widespread view is that perturbative QCD can decently account for the recent \textsc{BaBar} measurement of $γγ^*\to η_c$ transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the $γγ^*\to η_{c,b}$ form factor, is investigated in the 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 $η_{c,b}\to γγ$ process. After including the substantial negative order-$α_s^2$ correction, the good agreement be…
In this paper, we study double charmonia production in Upsilon peaks, especially, a S-wave charmonium $η_c$ and a P-wave charmonium $h_c(^1P_1)$, or a S-wave charmonium $J/ψ$ and the $X(3940)$ and $X(4160)$ within the nonrelativistic QCD (NRQCD) approach which is a powerful tool to realize the factorization of double charmonia production in electron-positron annihilation. The $J^{PC}=1^{--}$ state $Υ(nS)$ can provide an ideal laboratory for studying the properties of double-heavy quarkonium and also can separate the perturbative and nonperturbative parts due to the large heavy quark mass compa…
The pseudoscalar quarkonia exclusive decays to light mesons still poses a challenge to the theoretical understanding of quarkonium properties in decay. In this work, we evaluate the processes of pseudoscalar heavy quarkonium decays into vector meson pairs, especially the helicity suppressed processes of $η_b\rightarrow J/ψJ/ψ$ and $η_c\rightarrow VV$. In the frame of NRQCD, the branching fraction of $Br[η_b\rightarrow J/ψJ/ψ]$ are evaluated at the next-to-leading order of perturbative QCD; and within the light-cone distribution formalism, we calculate also the higher twist effects in these pro…
The light-cone distribution amplitudes (LCDAs) serve as important non-perturbative inputs for the study of hard exclusive processes. In this paper, we calculate ten LCDAs at twist-2 for the S-wave and P-wave $B_c$ mesons up to the next-to-leading order (NLO) of the strong coupling $α_s$ and leading order of the velocity expansion. Each one of these ten LCDAs is expressed as a product of a perturbatively calculable distribution and a universal NRQCD matrix-element. By use of the spin symmetry, only two NRQCD matrix-elements will be involved. The reduction of the number of non-perturbative input…
We analyze the recent LHCb measurement of the distribution of the fraction of the transverse momentum, $z(J/ψ)$, carried by the $J/ψ$ within a jet. LHCb data is compared to analytic calculations using the fragmenting jet function (FJF) formalism for studying $J/ψ$ in jets. Logarithms in the FJFs are resummed using DGLAP evolution. We also convolve hard QCD partonic cross sections, showered with PYTHIA, with leading order Non Relativistic Quantum Chromodynamics (NRQCD) fragmentation functions and obtain consistent results. Both approaches use Madgraph to calculate the hard process that creates …
We compute the cross section for exclusive production of a photon associated with a heavy quarkonium H of charge-conjugation parity C=+1 from e+ e- annihilation into a virtual photon at the center-of-momentum energy root-s=10.58 GeV. The NRQCD factorization formulas for the differential and total cross sections are obtained at leading order in the strong coupling and in the relative velocity of the heavy quark in the quarkonium rest frame. The predicted cross sections for the S-wave spin-singlet cases are about 80 fb and 50 fb for H = eta_c and eta_c(2S), respectively. Among P-wave spin-triple…
The exclusive production of pairs of vector mesons with J^{PC} = 1^{--} in e^+ e^- collisions can proceed through e^+ e^- 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^0 + rho^0 and rho^0 + phi production agree with recent measurements by the Ba…
