We report on our recent evaluation of the two-photon width of the pseudoscalar quarkonia, eta_c(nS) and eta_b(nS) in an approach based on Heavy-Quark Spin Symmetry (HQSS). To what concerns the 1S state eta_c, our parameter-free computation agrees with experiments, as well as most of other theoretical works. On the other hand, our computation for the 2S-state looks 2S like a confirmation that there may exist an anomaly related to the decay of eta_c(2S), especially in the light of the new preliminary result of the Belle collaboration. We also point out that the essentially model-independent ratio of eta_b two-photon width to the Upsilon leptonic width and the eta_b two-photon width could be used to extract the strong coupling constant alpha_s.
In this work we study the radiative decay widths of vector quarkonia for the process of $J/ψ(nS)\rightarrowη_{c}(nS)γ$ and $Υ(nS)\rightarrowη_{b}(nS)γ$ (for principal quantum numbers $n=1, 2, 3$) in the framework of Bethe-Salpeter equation under the covariant instantaneous ansatz using a $4\times 4$ form of BSE. The parameters of the framework were determined by a fit to the mass spectrum of ground states of pseudoscalar and vector quarkonia, such as; $η_{c}$, $η_{b}$, $J/ψ$ and $Υ$. These input parameters so fixed were found to give good agreements with data on mass spectra of ground and exci…
We present the quarkonia correlators for charmonium and bottomonium systems in the pseudoscalar, vector and scalar channels. For the description of quark-antiquark interaction we adopt the temperature dependant colour screening potential of the power law form. The spectroscopic parameters defined from the model are employed in the spectral functions to compute the quarkonia correlators. We find considerable medium modifications to the effective masses of the quarkonia as well as in the behaviour of the respective radial wave functions. These modifications are then reflected in the computed cor…
The Kawai model describing the glueball-quarkonia mixing is modified. The mixing of $η$, $η^\prime$ and $η(1410)$ is re-investigated based on the modified Kawai model. The glueball-quarkonia content of the three states is determined from a fit to the data of the electromagnetic decays involving $η$, $η^\prime$. Some predictions about the electromagnetic decays involving $η(1410)$ are presented.
This work is an extension of our previous work in \cite{bhatnagar20} to calculate M1 transitions, $0^{-+}\rightarrow 1^{--} γ$, and E1 transitions involving axial vector mesons such as, $1^{+-} \rightarrow 0^{-+}γ$, and $0^{-+}\rightarrow 1^{+-} γ$ for which very little data is available as of now. We make use of the general structure of the transition amplitude, $M_{fi}$ derived in our previous work \cite{bhatnagar20} as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadrons. In the present work,…
Preliminary calculations using the Covariant Spectator Theory (CST) employed a scalar linear confining interaction and an additional constant vector potential to compute the mesonic mass spectra. In this work we generalize the confining interaction to include more general structures, in particular a vector and also a pseudoscalar part, as suggested by a recent study. A one-gluon-exchange kernel is also implemented to describe the short-range part of the interaction. We solve the simplest CST approximation to the complete Bethe-Salpeter equation, the one-channel spectator equation, using a nume…
Two-photon decay rates of pseudoscalar, scalar and tensor states of charmonium and bottomonium are calculated in the framework of the relativistic quark model. Both relativistic effects and one-loop radiative corrections are taken into account. The obtained results are compared with other theoretical predictions and available experimental data.
I discuss recent theoretical results for inclusive decays of quarkonia into a photon plus hadrons, and summarize the status of perturbative calculations.
The pseudoscalar quarkonium state, eta_4 1^S_0, formed by the Standard Model (SM) fourth generation quarks, is the best candidate among the fourth generation quarkonia to be produced at the LHC and VLHC. The production of this J^{PC} = 0^{-+} resonance is discussed and the background processes are studied to obtain the integrated luminosity limits for the discovery, depending on its mass.
The supernumerous eta(1405) is considered a strong candidate for the pseudoscalar glueball. In a phenomenological chiral approach, we consider a mixing scenario of bare pseudoscalar (n bar n) and (s bar s) quarkonia with the glueball. We study the decay properties and point out the peculiarities of this scenario in order to support the possible identification of the J(PC) = 0(-+) glueball.
We give a short and basic introduction to our covariant Dyson-Schwinger-Bethe-Salpeter-equation approach using a rainbow-ladder truncated model of QCD, in which we investigate the leptonic decay properties of heavy quarkonium states in the pseudoscalar and vector channels. Comparing the magnitudes of decay constants, we identify radial 1-- excitations in our calculation with experimental excitations of J/Ψand Υ. Particular attention is paid to those states regarded as D-wave states in the quark model. We predict e+e- decay width of the Υ(1^3D_1) and Υ(2^3D_1) states of the order of ca. 15 eV o…
In this article we propose standard model strictly forbidden decay modes, quarkonia (QQ(1^{--}) = J/psi, Upsilon) decays into two photons, as a possible signature of the space-time non-commutativity. An experimental discovery of J/psi -> gamma gamma and/or Upsilon -> gamma gamma processes would certainly indicate a violation of the Landau-Pomeranchuk-Yang theorem and a definitive appearance of new physics.
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.
Two types of pseudoscalar quarkonium electromagnetic decay processes, i.e. decay to a lepton pair, and to a lepton pair plus a photon (Dalitz decay), are analyzed at the leading order in NRQCD expansion. The former type of processes, highly suppressed in the Standard Model, have been hoped to act as the sensitive probes of the possible new physics. The latter type of processes generally possess much greater decay rates than the former, owing to several conspiring factors. The recently launched BES-III program, with $10^8$ $η_c$ samples to be anticipated in the coming years, may be able to obse…
In this work we calculate the mass spectrum, weak decay constants, two photon decay widths, and two gluon decay widths of ground (1S), and radially excited (2S,3S,...) states of pseudoscalar charmoniuum and bottomonium such as $η_{c}$ and $η_{b}$, as well as the mass spectrum and leptonic decay constants of ground state (1S), excited (2S,1D,3S,2D,4S,and 3D) states of vector charmonium and bottomonium such as $J/ψ$, and $Υ$, using the formulation of Bethe-Salpeter equation under covariant Instantaneous Ansatz (CIA). Our results are in good agreement with data (where ever available) and other mo…
We investigate the associated production of heavy quarkonia, with angular-momentum quantum numbers ^{2S+1}L_J = ^1S_0, ^3S_1, ^1P_1, ^3P_J (J = 0, 1, 2), and photons, Z bosons, and W bosons in photon-photon, photon-hadron, and hadron-hadron collisions within the factorization formalism of nonrelativistic quantum chromodynamics providing all contributing partonic cross sections in analytic form. In the case of photoproduction, we also include the resolved-photon contributions. We present numerical results for the processes involving J/psi and chi_{cJ} mesons appropriate for the Fermilab Tevatro…
We consider the inclusive radiative decays quarkonium -> gamma + hadrons and examine the effects of soft QCD radiation on the photon energy spectrum near the endpoint.
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…
We show that quarkonia-like states of a hidden SU(N) gauge group can account for the 750 GeV diphoton excess observed by ATLAS and CMS, even with constituents carrying standard model hypercharge only. The required hypercharge is modest, varying between about 1.3-1.6 for strong SU(N) coupling, to 2-3 for weak SU(N) coupling, for N=3, 4. This scenario predicts a variety of diphoton and multi-photon resonances, as well as photons from continuum pair production, and possibly exotic decays into standard model fermions, with no multi-jet resonances.
In this article, we investigate the structures of the pseudoscalar charmonium and bottomonium in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential (infrared modified flat bottom potential). As the current masses are very large, the dressing or renormalization for the $c$ and $b$ quarks are tender, however, mass poles in the timelike region are absent. The Euclidean time fourier transformed quark propagator has no mass poles in the timelike region which naturally implements confinement. The Bethe-Salpeter wave…
The two photon transition of $\bar{c}c$ quarkonia are studied within a covariant approach based on the consistent truncation scheme of the quantum chromodynamics Dyson-Schwinger equation for the quark propagator and the Bethe--Salpeter equation for the mesons. We find the decay widths of $η_{c}^{} \to γγ$ and $χ_{c0,2}^{} \to γγ$ in good agreement with experimental data. The obtained transition form factor of $η_{c}^{} \to γγ^{\ast}$ for a wide range of space-like photon momentum transfer squared is also in agreement with the experimental findings of the BABAR experiment. As a by-product, the …
recently proposed strictly phenomenological static quark-antiquark potential belonging to the generality $V(r)=-Ar^{-α}+κr^β+V_{0}$ is tested with heavy quarkonia in the context of the shifted large N-expansion method. This nonrelativistic potential model fits the spin-averaged mass spectra of the $c\bar{c},$ $b\bar{b}$ and $c% \bar{b}$ quarkonia within a few ${\rm MeV}$ and also the five experimentally known leptonic decay widths of the $c\bar{c}$ and $b% \bar{b}$ vector states. Further, we compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittin…
The effective interaction of a pseudoscalar particle with photon in plasma with the presence of a constant uniform magnetic field is investigated. It is shown that under some physical conditions the effective coupling between pseudoscalar particle and photon does not depend on medium parameters and particles momentum. The probability of the familon decay into photon pair in a strongly magnetized degenerate ultrarelativistic plasma is calculated.
We reproduce masses of the self-conjugate and non-self-conjugate mesons in the context of the spinless Salpeter equation taking into account the relativistic kinematics and the quark spins. The hyperfine splittings for the ${\rm 2S}$ charmonium and ${\rm 1S}$ bottomonium are also calculated. Further, the pseudoscalar and vector decay constants of the $B_{c}$ meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form $…
The possibility to constrain the meson distribution amplitude from the transitions of virtual photons to pseudoscalar mesons is investigated. It is shown that for a large range in the two photon virtualities the transition form factors are essentially independent of the distribution amplitudes. This in turn entails parameter-free predictions of QCD.
In this talk it is reported on an analysis of the form factors for the transitions from a photon to one of the pseudoscalar mesons pi0, eta, eta', etac within the modified perturbative approach in which quark transverse degrees of freedom are retained. The report is focused on the discussion of the surprising features the new BaBar data exhibit, namely the sharp rise of the pi-gamma form factor with the photon virtuality and the strong breaking of flavor symmetry in the sector of pseudoscalar mesons.
We present a relativistic calculation of two-photon decays for heavy and light mesons in the framework of the Salpeter equation for quark-antiquark states. The meson-photon-photon vertex is computed by reconstructing the Bethe-Salpeter vertex function and evaluating the four-dimensional Feynman diagram with off-shell quark amplitudes. The two-photon width for light and heavy quarkonia up to spin equal six are calculated with different parameter sets taken from the literature thus giving a complete overview on the mesonic two-photon physics. We find that relativistic effects including the negat…
We consider the minimal coupling of two photons to neutral scalar and pseudoscalar fields, as for instance in the case of the Higgs boson and axion, respectively. In this framework, we analyze the photon dispersion relations in the presence of static and homogeneous external magnetic and electric fields, by taking into account the contribution of the imaginary part of the scalar/pseudoscalar self-energy. We show that this contribution cannot be neglected when it is of the same order as the photon-scalar/pseudoscalar mixing term. In addition to the usual light-like photon propagation mode, with…
Strong decays of vector ($^3S_1$) mesons to the pair of pseudoscalar ($^1S_0$) mesons are considered in the framework of the microscopic decay mechanism and the relativistic quark model based on the quasipotential approach. The quark-antiquark potential, which was previously used for the successful description of meson spectroscopy and electroweak decays, is employed as the source of the $q\bar q$ pair creation. The relativistic structure of the decay matrix element, relativistic contributions and boosts of the meson wave functions are comprehensively taken into account. The calculated rates o…
We study infrared QCD effects in radiative quarkonia decays. We examine the endpoint region z -> 1 of the photon spectrum. We point out a cancellation mechanism for the corrections in $α_s^n \ln^{m} (1-z)$, $m \leq 2 n$, in the short-distance coefficient for the color-singlet Fock state in the quarkonium. The cancellation is due to the coherence of the color radiation, and applies even though logarithmic contributions are present in the jet distributions associated with the decay. We comment on the implications of our results for the modeling of hadronization in the endpoint region and for the…
The Operator Product Expansion, in conjunction with the power counting of non-relativistic field theory, is used to examine the end-point region of the radiative decay of heavy quark bound states with $^3S_1$ quantum numbers, $Q\bar{Q}\rightarrow γ+X$. We identify an infinite class of operators that determine the shape of the photonic end-point spectrum. These operators can be resummed to form an octet structure function which parameterizes the energy of the dynamical gluon content of the leading octet Fock state component of the quarkonium. This color-octet contribution is important when the …
We present a calculation of the two-photon and two-gluon widths for the equal mass quarkonium states $^1S_0$, $^3P_0$ and $^3P_2$ of the charmonium and upsilon systems. The approach taken is based on using the full relativistic $q\bar{q}\to\ga\ga$ amplitude together with a wave function derived from the instantaneous Bethe-Salpeter equation. Momentum space radial wave functions obtained from an earlier fit of the charmonium and upsilon spectra are used to evaluate the necessary integrals.
The effects of an external time-dependent magnetic field in the conversion probability of photon-to-axion-like particles are studied. Our findings show that for a certain time regime, the amplitude of the produced axion-like field can be enlarged with respect to the static case, thus, enhancing the probability of conversion.
We discuss the partial width of the pseudoscalar charmonium state eta_c and bottomonium state eta_b into two photons. Predictions from potential models are examined and compared with experimental values for the eta_c case. Through the NRQCD factorisation procedure results for eta_c are also compared with those from J/psi data, and results for eta_b to the Upsilon decay data.
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…
We argue that the photon spectra in radiative decays of various heavy quarkonium states provide important information on their nature. If two of these states are in the strong coupling regime, we are able to produce a parameter-free model independent formula, which holds at next-to-leading order and includes both direct and fragmentation contributions. When the formula is checked against recent CLEO data it favors Upsilon (2S) and Upsilon (3S) in the strong coupling regime and disfavors Upsilon (1S) in it.
Within the standard model, we have investigated rare $Z$-boson decays into double heavy quarkonia, $Z\to VV$ and $Z\to VP$ with $V$ denoting vector and $P$ denoting pseudoscalar quarkonia, respectively. It is assumed that the leading-order QCD diagrams would give the dominant contributions to these processes, and the corresponding branching fractions, for instance, ${\cal B}(Z\to J/ΨJ/Ψ)$ has been estimated to be around $10^{-13}$ in the literature. However, these decays could also happen through the electromagnetic transition $Z\to Vγ^*$ and $Z\to Pγ^*$, with the virtual photon transforming i…
The key assumption used recently by Feldmann, Kroll and Stich [Phys.Rev. D58, 114006 (1998)] that the decay constants f_η, and f_η' of the respective eta and eta ' mesons in the quark flavor basis follow the pattern of strange and non--strange quarkonia mixing in their wave functions, is reproduced in identifying the non-isotriplet part of the strong neutral axial current with the genuine axial hypercharge current J_{μ, 5}^Y =\bar q γ_μγ_5 Y/2 q, where Y=C+S+B is defined by the Gell-Mann-Nakano-Nishijima relation as the sum of charm (C), strangeness (S), and baryon (B) quark quantum numbers. T…
The paper is devoted to vector or pseudoscalar heavy quarkonia production J/ψ, ψ(2S), B_{s} or B_s^* in association with five charged π-mesons in exclusive B_c-meson decays. Using available formfactors parameterizations and spectral functions of $W \to 5 π$ transition we obtain branching fractions of these decays and distributions over invariant mass of (5π)-system.
By means of the universal unitary and analytic model of electromagnetic structure of hadrons the two-photon decay rates of P=pi^0, eta, eta' mesons are determined in an alternative way from data on their transition form factors.
The extrapolation of the decay amplitudes of the pseudoscalar mesons into two photons from the soft meson limit where it is obtained from the axial-anomaly to the mass shell involves the contribution of the 0^ - continuum. These chiral symmetry breaking corrections turn out to be large. The effects of these corrections on the calculated pi ^0 decay rate, on the values of the singlet-octet mixing angle and on the ratios f_8 / f_pi and f_0 / f_pi are discussed. The implications for the transition form factors gamma gamma* --> pseudoscalars are also evaluated and confronted with the available exp…
We investigate the possibility to constrain the pion distribution amplitude from the gamma* gamma* -> pi transition. For a surprisingly large range in the two photon virtualities we find that the transition form factor is essentially independent of the distribution amplitude. This in turn entails a parameter-free prediction of QCD. The gamma* gamma* -> eta, eta' form factors are also briefly discussed. We estimate that experimental studies might be feasible at the existing e+ e- experiments BaBar, Belle, and CLEO.
We consider exclusive $π^0$ production in ep-scattering. At high energies odderon and photon exchange contribute. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-diquark structure as suggested by the small odderon amplitude in pp and $p \bar{p}$ forward scattering. We show that odderon exchange leads to a much larger inelastic than elast…
We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to $γ+γ\to η_c+c+\bar{c}$, $γ+γ\to η_b+b+\bar{b}$ and $γ+γ\to B_c+b+\bar{c}$ processes in the framework of non-relativistic QCD (NRQCD) factorization formalism. The cross sections at the SuperKEKB electron-positron collider, as well as the future collider like the Circular Electron Positron Collider (CEPC), are evaluated. Numerical results indicate that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are reduced as expected. Due to the high luminosity…
The decays of a light scalar meson into a vector meson and a photon ($S\to Vγ)$ are evaluated in the tetraquark and quarkonium assignments of the scalar states. A link with the radiative decays $ϕ\to Sγ$ is established: experimental results for $S\to Vγ$ will allow to understand if the direct, quark-loop contribution to $ϕ\to Sγ$ or the kaon-loop contribution is dominant. Also strong decays $S\to PP$ -where $P$ denotes a pseudoscalar meson- are investigated: the tetraquark assignment works better than the quarkonium one. It is then also discussed why the tetraquark assignment is favoured with …
Non-relativistic QCD (NRQCD) predicts colour octet contributions to be significant not only in many production processes of heavy quarkonia but also in their radiative decays. We investigate the photon energy distributions in these processes in the endpoint region. There the velocity expansion of NRQCD breaks down which requires a resummation of an infinite class of colour octet operators to so-called shape functions. We model these non-perturbative functions by the emission of a soft gluon cluster in the initial state. We found that the spectrum in the endpoint region is poorly understood if …
In this paper we discuss decays of the Higgs boson to quarkonia in association with a photon. We identify a new mechanism for producing such final states in Higgs decays that leads to predictions for the decay rates that differ by an order of magnitude from previous estimates. Although the branching ratios for these processes are still small, the processes are experimentally clean, and the H \to J/ψ+gamma decay should be observable at a 14 TeV LHC. We point out that quantum interference between two different production mechanisms makes the decay rates sensitive to the HQQbar couplings. Consequ…
Exclusive pseudoscalar meson production in ep scattering at high energies is a direct probe for a possible "odderon" exchange in soft hadronic processes. Using a simple phenomenological ansatz for the odderon, we demonstrate how it can be separated from the contribution due to photon-photon fusion, and the relevant parameters be measured. Total cross sections and differential distributions are presented for pi0, eta, eta', and eta_c production. Results are given from both a full calculation and one using the equivalent photon approximation. The accuracy of the latter is discussed.
In this study, the direct pair production of the pseudoscalar Higgs boson at a photon-photon collision is analyzed in the context of two Higgs doublet model, taking account the complete one-loop contributions. In order to illustrate the effect of the new physics, four benchmark points scenarios, which are consistent with theoretical and current experimental constraints, are chosen in the type-I of THDM with an exact alignment limit. In these benchmark points, the CP even lightest Higgs boson ($h^0$) have the Standard Model like couplings to the gauge bosons. The effect of individual contributi…
It is well know that the precise measurement of $H\toγγ$ can generate two degenerate parameter spaces of $Hγγ$ anomalous coupling. We propose to utilize the exclusive Higgs rare decays $H\toΥ(ns)+γ$ to break above mentioned degeneracy and further to constrain the $Hγγ$ anomalous coupling at the HL-LHC. We demonstrate that the branching ratios of $H\toΥ(ns)+γ$ can be significantly enhanced in the non-SM-like parameter space from $H\toγγ$ measurement, due to the destructive interference between the direct and indirect production of $Υ(ns)$ in the SM. By applying the NRQCD factorization formalism…
We present the dominant two-loop electroweak corrections to the partial decay widths to gluon jets and prompt photons of the neutral CP-odd Higgs boson A^0, with mass M_{A^0} < 2 M_W, in the two-Higgs-doublet model for low to intermediate values of the ratio tan(beta) = v_2/v_1 of the vacuum expectation values. They apply as they stand to the production cross sections in hadronic and two-photon collisions, at the Tevatron, the LHC, and a future photon collider. The appearance of three gamma_5 matrices in closed fermion loops requires special care in the dimensional regularization of ultraviole…
We study the associated production of a very light pseudoscalar Higgs boson with a pair of charginos. The novel signature involves a pair of charged leptons from chargino decays and a pair of photons from the pseudoscalar Higgs boson decay, plus large missing energy at the LHC and ILC. The signal may help us to distinguish the NMSSM from MSSM, provided that the experiment can resolve the two photons from the decay of the pseudoscalar Higgs boson.
We investigate the reaction $e p \to e PS X$ where PS denotes a pseudoscalar meson $π^0, η, η'$, or $η_c$ and X either a proton or resonance or continuum states into which the proton can go by diffractive excitation. At high energies photon and odderon exchange contribute to the reaction. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-d…
The heavy quarkonia (Charmonium \(c\bar{c}\) and Bottomonium \(b\bar{b}\)) are investigated in the framework of the instantaneous BS-equation (Salpeter equation). We parametrize confinement alternatively by a linearly rising scalar or a vector interaction kernel and take into account the one-gluon-exchange (OGE) interaction in the instantaneous approximation. Mass spectra as well as leptonic, two-photon, E1 and M1 decay widths are calculated. Our results show that a reasonable description of the experimental data can be obtained with both spin structures for the confining kernel. The relativis…
