Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3γ$, $3g$ and $γgg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrödinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.
We analyze the relativistic corrections to annihilation rates of S-wave quarkonia within the framework of NRQCD. We show that order v^2 corrections can be expressed in terms of the heavy quark pole mass and the quarkonium mass. The ratio of hadronic to radiative annihilation rates for eta_b and eta_c can therefore be predicted accurately. The contributions of color-octet operators to the hadronic decay rates of spin-triplet quarkonia are shown to be significant, even though they arise at order v^4 in the velocity expansion. We provide a rough estimate of the color-octet contributions and extra…
QCD corrections to all the allowed decays of superheavy groundstate quarkonia into electroweak gauge and Higgs bosons are presented. For quick estimates, approximations that reproduce the exact results within less than at worst two percent are also given.
In the framework of a newly developed factorization formalism which is based on NRQCD, explicit cancellations are shown for the infrared divergences that appeared in the previously calculated hadronic annihilation decay rates of P-wave and D-wave heavy quarkonia. We extend them to a more general case that to leading order in $v^2$ and next-to-leading order in $α_s$, the infrared divergences in the annihilation amplitudes of color-singlet $Q\bar{Q}(^{2S+1}L_J)$ pair can be removed by including the contributions of color-octet operators $Q\bar{Q}(^{2S+1}(L-1)_{J'})$, $Q\bar{Q}(^{2S+1}(L-3)_{J''}…
In this paper we continue previous efforts in the literature to determine phenomenological values for the gluon mass by confronting theoretical results obtained in a theory of massive gluons with experimental values or results directly referring to the nontrivial structure of the Yang-Mills vacuum, e.g. to the presence of the gluon condensate. The decays of heavy quarkonia into 3 gluons and 2 gluons + photon are considered in detail as well as the correlators of the electromagnetic current and the scalar glueball current. Based on the analysis for the latter quantities a value for the gluon ma…
Open-flavour meson studies are the necessary completion to any comprehensive investigation of quarkonia. We extend recent studies of quarkonia in the Dyson-Schwinger-Bethe-Salpeter-equation approach to explore their results for all possible flavour combinations. Within the inherent limitations of the setup, we present the most comprehensive results for meson masses and leptonic decay constants currently available and put them in perspective with respect to experiment and other approaches.
The decay rates of P-wave heavy quarkonia to light hadrons are presented to leading order in $v^2$ and next-to-leading order in $α_s$. They include contributions from both the color-singlet component and the color-octet component of quarkonia. Applying these results to charmonium and using measured decay rates for the $χ_{c1}$ and $χ_{c2}$ by E760, we determine the two nonperturbative decay matrix elements, and then predict the hadronic decay rates of $χ_{c0}$ and $h_c$, and the electromagnetic decay rates of $χ_{c0}$ and $χ_{c2}$. The obtained decay rates of $χ_{c0}\to LH$ and $χ_{c0}\toγγ$ a…
This writeup summarizes recent CMS results on quarkonia measurements in pp, pPb and PbPb collisions at LHC. The excellent muon detection capability of CMS allows measurement of charmonia states at high transverse momentum ($p_T$) while the $Υ$ states can be reconstructed starting at zero $p_T$. The absolute and relative yields of different charmonia and bottomonia states modified in PbPb collisions (over pp collisions) are described. The vertexing capability of CMS enables measurement of B meson energy loss via its decay to J/$ψ$. An overview of these measurements is given. How these measureme…
We investigate the polarization properties of vector quarkonia in lepton anti-lepton annihilation with special attention to effects due to intermediate Z bosons.
In the framework of QCD sum rules one uses a scheme, allowing one to apply the conditions of both nonrelativistic heavy quark motion inside mesons and independence of nonsplitting nS-state density on the heavy quark flavours. In the leading order an analitic expression is derived for leptonic constants of both heavy quarkonia and heavy mesons with a single heavy quark. The expression allows one explicitly to determine scaling properties of the constants.
We calculate the annihilation decay rates of the $^3D_2(2^{--})$ and $^3D_3(3^{--})$ charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. The wave functions of states with quantum numbers $J^{PC}=2^{--}$ and $3^{--}$ are constructed. By solving the corresponding instantaneous Bethe-Salpeter equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic…
Inclusive production of $χ_{c J}$ in $e^+e^-$ annihilation is an excellent probe of the role of higher Fock states in the production of heavy quarkonia. Within the non-relativistic QCD approach, contributions from the short-distance production of colour-octet $c\bar{c}$ pairs are significantly larger than those from colour-singlet production. At the same time, $χ_{c J}$ production rates are significantly smaller than expected in the colour evaporation approach. Measurements of $χ_{\c J}$ production at CLEO and future B-factories will thus constitute a major test of theoretical approaches to th…
We present the first exact and most general neutralino-neutralino annihilation cross sections in the presence of flavor violation. The existing set of calculations in literature do not include flavour violation. These calculations are important for the calculation of relic density and indirect detection of dark matter in various experiments.
In this work, the non-relativistic asymptotic behavior of the transition $q\overline{q}\rightarrow2g\rightarrow q\overline{q}$ in the $^1S_0$ channel is discussed. Different with the usual calculation which expands the physical amplitude around the quark anti-quark threshold, we take the quark anti-quark pairs as off shell and only expand the expression on the three-dimensional momenta of the quarks and anti-quarks. We calculate the results to order 6. The imagine part of the results after applying the on shell conditions can reproduce the non-relativistic QCD (NRQCD) results in leading order …
In this work, we calculate the nonrelativistic asymptotic behavior of the amplitudes of $q\overline{q}\rightarrow 2g \rightarrow q\overline{q}$ in the leading order of $α_s$ (LO-$α_s$) with $q\overline{q}$ in the $^3P_J$ channels. In the practical calculation we take the momenta of quarks and antiquarks on-shell and expand the amplitudes on the three-momentum of the quarks and antiquarks to order 6 and get three nonzero terms. The imaginary parts of the first term and the second term are the old. The real parts of the results have IR divergence. When applying the results to the heavy quarkonia…
We report on the creation of a database for quarkonium and open heavy-flavour production in hadronic collisions. This database, made as a collaboration between HepData and the ReteQuarkonii network of the integrating activity I3HP2 of the 7th Framework Programme, provides an up-to-date review on quarkonia and open heavy-flavour existing data. We first present the physics motivation for this project, which is connected to the aim of the ReteQuarkonii network, studies of open heavy-flavour hadrons and quarkonia in nucleus-nucleus collisions. Then we give a general overview of the database and de…
It is shown that $BR(χ_{b1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 3.3\cdot 10^{-7}$, $BR(χ_{b1}(2P)\rightarrow Z\rightarrow e^+e^-)\simeq 4.1\cdot 10^{-7}$ and $BR(χ_{c1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 10^{-8}$ that give a good chance to search for the direct production of pseudovector $^3P_1$ heavy quarkonia in $e^+e^-$ collisions ($e^+e^-\rightarrow Z\rightarrow ^3P_1$) even at current facilities not to mention $b$ and $c-τ$ factories. Leading radiative corrections to annihilation of quarkonia in QCD are discussed.
The decay rates of $c\bar{c}$ and $b\bar{b}$ through two-photon or two-gluon annihilations are obtained by using totally relativistic decay amplitudes and a sophisticated quantum-chromodynamic potential model for heavy quarkonia. Our results for the photonic and gluonic widths of the 1S0, 3P0, and the 3P2 states are in excellent agreement with the available experimental data. The procedures and mathematical techniques used by us for the treatment of the fermion-antifermion bound states are also applicable to other decay processes.
We improve the pNRQCD approach to annihilation processes of heavy quarkonium and make first pNRQCD predictions for exclusive electromagnetic production of heavy quarkonium. We consider strongly coupled quarkonia, i.e., quarkonia that are not Coulombic bound states. Possible strongly coupled quarkonia include excited charmonium and bottomonium states. For these, pNRQCD provides expressions for the decay and exclusive electromagnetic production NRQCD matrix elements that depend on the wavefunctions at the origin and few universal gluon field correlators. We compute electromagnetic decay widths a…
We present the results from the heavy quarks and quarkonia working group. This report gives benchmark heavy quark and quarkonium cross sections for $pp$ and $pA$ collisions at the LHC against which the $AA$ rates can be compared in the study of the quark-gluon plasma. We also provide an assessment of the theoretical uncertainties in these benchmarks. We then discuss some of the cold matter effects on quarkonia production, including nuclear absorption, scattering by produced hadrons, and energy loss in the medium. Hot matter effects that could reduce the observed quarkonium rates such as color …
Proton-proton collisions at the LHC provide the ground for tests of the strong interactions through the study of the production mechanisms for quarkonia and hadrons containing charm or beauty flavours. This review addresses recent results and includes studies of kinematical correlations, polarisation and associated production. QCD-based models are briefly discussed and compared to measurements.
Fitting $Z^0$-pole data from ALEPH and SLD, and TPC data at a lower c.m.s.\ energy, we fix the boundary condition for NLO parton$\to$hadron (hadron$=π^\pm, K^\pm, \sum_h h^\pm$) fragmentation functions (FFs) at the low resolution scale of the radiative parton model of Glück, Reya and Vogt (GRV). Perturbative LO$\leftrightarrow$NLO stability is investigated. The emphasis of the fit is on information on the fragmentation process for individual light ($u,d,s$) and heavy ($c,b$) quark flavours where we comment on the factorization scheme for heavy quarks in $e^+e^-$ annihilations as compared to de…
Valuable data on quarkonia (the bound states of a heavy quark Q=c,b and the corresponding antiquark) have recently been provided by a variety of sources, mainly e+ e- collisions, but also hadronic interactions. This permits a thorough updating of the experimental and theoretical status of electromagnetic and strong transitions in quarkonia. We discuss QQbar transitions to other QQbar states, with some reference to processes involving QQbar annihilation.
Here we present the two-photon and two-gluon decay widths of the S-wave ($η_{Q\in c,b}$) and P-wave ($χ_{Q\in c,bJ}$) charmonium and bottonium states and the radiative transition decay widths of $c\bar c$, $b\bar b$ and $c\bar b$ systems based on Coulomb plus power form of the inter-quark potential ($CPP_ν$) with exponent $ν$. The Schr$\ddot{o}$dinger equation is solved numerically for different choices of the exponent $ν$. We employ the masses of different states and their radial wave functions obtained from the study to compute the two-photon and two-gluon decay widths and the E1 and M1 radi…
In the framework of nonrelativistic QCD, we compute the leading double-logarithmic corrections of order alpha_s^3 ln^2(1/alpha_s) to the heavy-quark-antiquark bound-state wave function at the origin, which determines the production and annihilation rates of heavy quarkonia. The phenomenological implications for the top-antitop and Upsilon systems are discussed.
Recently, several surprising experimental observations in the production of heavy quarkonium have been reported. In $e^+e^-$ annihilation at $\sqrt{s}=10.6$ GeV, Belle Collaboration finds that $J/ψ$ mesons are predominantly produced in association with an extra $\bar{c}c$ pair, with $σ(e^+e^- \to J/ψ\bar{c}c) / σ(e^+e^- \to J/ψX) = 0.59^{+0.15}_{-0.13}\pm 0.12$, and the BaBar collaboration reports that the produced $J/ψ$'s have mostly longitudinal polarization. In $\bar{p}p$ collisions at the Tevatron, the CDF Collaboration reported an excess of $J/ψ$ and $ψ^{\prime}$ mesons at high $p_{\perp}…
The recent theory developments and latest experimental results on heavy-flavour production in Deep Inelastic Scattering and at hadron colliders are summarized. Models of heavy quarkonia production, non-perturbative corrections to fragmentation, theory of heavy-hadron production in heavy-ion collisions, and interpretation of new exotic hadrons are discussed. Progress in event generators development is reported. Most recent experimental results from HERA and e+e- colliders as well as from proton-(anti)proton and heavy ion experiments are presented and the role of charm and beauty quarks in the a…
We compare QCD theoretical predictions for heavy flavoured mesons fragmentation spectra in e+ e- annihilation with data from CLEO, BELLE and LEP. We include several effects in our calculation: next-to-leading order initial conditions, evolution and coefficient functions. Soft-gluon effects are resummed at next-to-leading-log accuracy. A matching condition for the crossing of the bottom threshold in evolution is also implemented at next-to-leading order accuracy. Important initial-state electromagnetic radiation effects in the CLEO and BELLE data are accounted for. We find that, with reasonably…
Uncertainties in the next-to-leading-order calculations of heavy-quark ($Q$) production are investigated. Predictions for total cross sections, single-inclusive distributions of heavy quarks and heavy flavoured hadrons, as well as for $Q\bar{Q}$ correlations, are compared with charm and bottom data. The description of heavy-quarkonium production requires a separation of the short-distance scale of $Q\bar{Q}$ production, which is set by the heavy-quark mass from the longer-distance scales associated with the bound-state formation. Various factorization approaches are compared, in particular wit…
Before wondering about the quark-gluon plasma (QGP), one has to take into account various cold (normal) nuclear matter effects, that can be probed through p+A like collisions. This article aims at reviewing the current results (and understanding) of these effects on heavy quarks and quarkonia production.
We calculate the annihilation decay widths of spin-singlet heavy quarkonia $h_c, h_b$ and $η_b$} into light hadrons with both QCD and relativistic corrections at order $O(α_{s}v^{2})$ in nonrelativistic QCD. With appropriate estimates for the long-distance matrix elements by using the potential model and operator evolution method, we find that our predictions of these decay widths are consistent with recent experimental measurements. We also find that the $O(α_{s}v^{2})$ corrections are small for $b\bar{b}$ states but substantial for $c\bar{c}$ states. In particular, the negative contribution …
New double ratios of exponential moments of different two-point functions, which are less sensitive to the heavy quark mass and to the continuum effects than the commonly used ratio of moments, are presented for a more refined analysis of the mass-splittings between the different heavy quarkonia states. We show that at the $c$ and $b$ quark mass scales the $1/m$-expansion does not converge for these quarkonia channels, while a connection of our mass and width formulae, with the potential model ones is done. Using the present value of the QCD coupling $α_s$, we deduce the value: $<α_s G^2> = (7…
In this work we study the process $e^{+}+e^{-}\longrightarrow J/Ψ+η_{c} $ at energy $\sqrt{s}= 10.6 GeV$ observed recently at B-factories whose measurements were made by Babar and Belle groups. We calculate the cross section for this process in the Bethe-salpeter formalism under Covariant Instantaneous Anstaz (CIA). To simplify our calculation, the heavy quark approximation $(q<<M, P M)$ is employed in the quark and gluon propagators. In the exclusive process of $e^{+}e^{-}$ annihilation into two heavy quarkonia, the cross section calculated in this scenario is compatible with the experimental…
It is shown that specific spin-flavour properties of the nonperturbative interaction between quarks induced by instantons allow us to explain the peculiarities of the OZI rule violation in $N \bar N$ annihilation. New experiments to test the instanton mechanism of the OZI rule violation are proposed.
The isosinglet scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$ and their mixing are studied. Two recent lattice results are employed as the starting point; one is the approximate SU(3) symmetry in the scalar sector above 1 GeV for the connected insertion part without $q\bar q$ annihilation, and the other is the scalar glueball mass at 1710 MeV in the quenched approximation. In the SU(3) symmetry limit, $f_0(1500)$ becomes a pure SU(3) octet and is degenerate with $a_0(1450)$, while $f_0(1370)$ is mainly an SU(3) singlet with a slight mixing with the scalar glueball which is the primary com…
Using a quite accurate flavour-independence of $nS$-level mass differences in heavy quarkonia and a corresponding quasiclassical expression for the heavy quark binding energy, one shows that experimental data on masses of mesons with heavy quarks allow one to make the estimate $\bar Λ= 0.63\pm 0.03$ GeV.
We present a dynamical lattice calculation with 2 flavours for bottomonium states with an additional gluonic excitation. Using improved actions for the quarks and gauge fields at a lattice spacing of $a \approx 0.1$ fm, we find 10.977(61)(62) GeV for the energy of the lowest lying $b\bar bg$-hybrid, where the first error is statistical and the second denotes the systematic uncertainty due to the determination of scale. In a parallel quenched simulation we demonstrate explicitly that vacuum polarisation effects are less than 10% of the splitting with the ground state.
We present new sets of next-to-leading order fragmentation functions for the production of K0short and Lambda particles from the gluon and from each of the quarks, obtained by fitting to all relevant data sets from e+e- annihilation. The individual light quark flavour fragmentation functions are constrained phenomenologically for the first time by including in the data the light quark tagging probabilities measured by the OPAL Collaboration.
We present new sets of next-to-leading order fragmentation functions describing the production of charged pions, kaons and protons from the gluon and from each of the quarks, obtained by fitting to all relevant data sets from e+ e- annihilation. The individual light quark flavour fragmentation functions are obtained phenomenologically for the first time by including in the data the light quark tagging probabilities obtained by the OPAL Collaboration.
Starting with two coupled Bethe-Salpeter equations for the quark-antiquark, and for the quark-glue-antiquark component of the quarkonium, we solve the bound state equations perturbatively. The resulting admixture of glue can be partially understood in a semiclassical way, one has, however, to take care of the different use of time ordered versus retarded Green functions. Subtle questions concerning the precise definition of the equal time wave function arise, because the wave function for the Coulomb gluon is discontinuous with respect to the relative time of the gluon. A striking feature is t…
We show that both the multiplicity distribution and the ratio of factorial cumulants over factorial moments for 2-jet events in e+e- annihilation at the Z^0 peak can be well reproduced by the weighted superposition of two negative binomial distributions, associated to the contribution of $b\bar b$ and light flavoured events respectively. The negative binomial distribution is then suggested to describe the multiplicity distribution of 2-jet events with fixed flavour.
Next-to-leading order calculations for heavy quark three-jet production in e+e- annihilation are reviewed. Their applications for the measurement of the b-quark mass at LEP/SLC and for the test of flavour independence of the strong coupling constant are discussed.
Exploiting an interplay of the Bethe-Salpeter equation enabling us to regard mesons as bound states of quark and antiquark and the Dyson-Schwinger equation controlling the dressed quark propagator, we amend existing studies of quarkonia by a comprehensive description of open-flavour mesons composed of all conceivable combinations of quark flavour. Employing throughout a fixed set of model parameters, we predict some basic characteristics of these mesons, i.e., their masses, leptonic decay constants and corresponding in-hadron condensates entering in a generalized formulation of the Gell-Mann-O…
We extract the strong coupling constants of three mesons, each of which is composed of either two charm quarks or one charm quark and one light (i.e., $u$, $d$, or $s$) quark, from the matrix elements for the transitions of two of these mesons induced by appropriate quark currents within the framework of a relativistic dispersion approach to the constituent-quark picture of mesons. Among others, we also analyse the impact of the violation of the SU(3) flavour symmetry by the quark masses. In the case of mesons containing one light quark, we observe, in two respects, discrepancies between our f…
The ampitude of the $B\toργ$ decay induced by the flavour-changing neutral currents contains the penguin contribution and the weak-annihilation contribution generated by the 4-quark operators in the effective Hamiltonian. The penguin contribution is known quite well. We analyse the weak-annihilation which is suppressed by the heavy-quark mass compared to the penguin contribution. In the factorization approximation, the weak annihilation amplitude is represented in terms of the leptonic decay constants and the meson-photon matrix elements of the weak currents. The latter contain the $Bγ$, $ργ$ …
The cross section for Higgs+jet production in bottom quark annihilation is calculated through NLO QCD. The five-flavour scheme is used to derive this contribution to the Higgs+jet production cross section which becomes numerically important in the MSSM for large values of tan(beta). We present numerical results for a proton collider with 14 TeV center-of-mass energy. The NLO matrix elements for d(sigma)/d(pT) are then combined with the total inclusive cross section in order to derive the integrated cross section with a maximum cut on pT at next-to-next-to-leading order.
In this work we provide all the missing ingredients for calculating parity-violating 3-jet observables in e^+e^- collisions at next-to-leading order (NLO) including the full quark mass dependence. In particular we give explicit results for the one-loop corrections and for the singular contributions from real emission processes. Our formulae allow for the computation of the NLO 3-jet contributions to the forward-backward asymmetry for heavy flavours, which is -- and will be -- an important observable for electroweak physics at present and future e^+e^- colliders.
We discuss the $p\bar{p}$ annihilation into a pair of charmed $D$ mesons not far from the threshold of the reaction. An interesting interference pattern in the differential cross section is predicted to arise from the existence of both $t$-channel charmed-baryon exchange and $s$-channel $Ψ^{''}$ charmonium resonance amplitudes. We argue that the experimental study of this process would provide new and valuable information about the unknown $p\bar{p}Ψ^{''}$ and $Λ_c N D$ couplings. These are important to know to solve the long-standing puzzle of the heavy flavour contents of baryons and to test…
We show how a precise knowledge of parton distribution functions, in particular those of the u and d quarks, can be used to constrain a certain class of New Physics models in which new heavy charged resonances couple to quarks and leptons. We illustrate the method by considering a left-right symmetric model with a W' from a SU(2)_R gauge sector produced in quark-antiquark annihilation and decaying into a charged lepton and a heavy Majorana neutrino. We discuss a number of quark and lepton mixing scenarios, and simulate both signals and backgrounds in order to determine the size of the expected…
We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top lim…
We estimate the non-perturbative power-suppressed corrections to heavy flavour fragmentation and correlation functions in e^+e^- annihilation, using a model based on the analysis of one-loop Feynman graphs containing a massive gluon. This approach corresponds to the study of infrared renormalons in the large-n_f limit of QCD, or to the assumption of an infrared-finite effective coupling at low scales. We find that the leading corrections to the heavy quark fragmentation function are of order $λ/M$, where $λ$ is a typical hadronic scale ($λ\sim 0.4$ GeV) and M is the heavy quark mass. The inclu…
Recently, we completed a comprehensive investigation of a huge part of the entire meson spectrum by considering both quarkonia and open-flavour mesons by means of a single common framework which unites the homogeneous Bethe-Salpeter equation that describes mesons as quark-antiquark bound states and the Dyson-Schwinger equation that governs the full quark propagator: Adopting two (as a matter of fact, not extremely diverse) models that attempt to grasp all principal aspects of the effective strong interactions entering identically in both these equations, we derived within this unique setup, fo…
We present factorization theorems for two exclusive heavy-quarkonium production processes: production of two quarkonia in e^+e^- annihilation and production of a quarkonium and a light meson in B-meson decays. We describe the general proofs of factorization and supplement them with explicit one-loop analyses, which illustrate some of the features of the soft-gluon cancellations. We find that violations of factorization are generally suppressed relative to the factorized contributions by a factor v^2m_c/Q for each S-wave charmonium and a factor m_c/Q for each L-wave charmonium with L>0. Here, v…
