Constraints on the decay rates of quarkonium

We derive inequalities between the leptonic decay rates of 1S and 2S states of quarkonium, when the binding potential is an increasing concave (convex) function of the inter-quark distance in a framework where some relativistic corrections have been made to the Van Royen-Weisskopf formula for these rates. Experimental decay rates of the γ and γ′ rule out the convex increasing potential.     

On the corrections of the wave function in weakly bound quarkonium

A non-relativistic quark-antiquark system with perturbative gluonic interactions (quarkonium) is considered, which allows a systematic expansion in the strong coupling constant α_s. In a non-abelian gauge theory, non-trivial corrections of the wave function already occur to O(α_s). We emphasize the existence of a renormalization, which is “natural” for such a system leaving only little freedom in the choice of the renormalization point Λ. The general corrections to O(α_s) including coulombic binding are presented. An explicit application to the lowest-order gluonic corrections of the leptonic decay of quarkonium is made. In this process the new term is sometimes much larger than the gluonic correction at the photon vertex and it varies greatly between different coulombic (S-wave) bound states.     

Gluonic corrections to the decay rate of heavy quarkonium states into lepton pairs

We calculate one-gluon corrections to the decay rate of heavy quarkonium states into lepton pairs. We find that the correction due to one-gluon exchange is not very significant for charmonium, and for practical purposes only the relativistic kinematical effects need to be taken into account. For theY family the gluonic corrections are, relatively, of greater importance.     

Decay properties of 2++ glueballs,quarkonia and their mixtures

We study the decay branching ratios of 1P and 2P quarkonia using quark pair creation model. We conclude that θ(1640) cannot be understood as a pure quarkonium. Considering then quarkonium-glueball mixing we conclude that a 2P \(q\bar q\) -glueball interpretation is unlikely. A 1P \(q\bar q\) -glueball interpretation is better. We also study the quarkonium interpretation of the particle found in π^? P→g _T (2160)n→φφn.     

Pseudoscalar quarkonium exclusive decays to vector meson pair

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 ηb→J/ψJ/ψ and ηc→VV. In the framework of NRQCD, the branching fraction of Br[ηb→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 processes. Numerical results show that the higher twist terms contribute more than what from the NLO QCD corrections in the process of ηb→J/ψJ/ψ. It is found that the experimental results on ηc→VV are hard to be understood by merely the quark model and perturbative QCD calculation.     

Soft photon spectrum in orthopositronium and vector quarkonium decays

QED gauge invariance, when combined with analyticity, leads to constraints on the low energy end of the emitted photon spectra. This is known as Low's theorem. It is shown that the Ore–Powell result, as well as further developments for the orthopositronium differential decay rate, are in contradiction with Low's theorem, i.e., that their predicted soft photon spectra are incorrect.A solution to this problem is presented. The implications for the orthopositronium lifetime puzzle, the charmonium ρ–π puzzle, the prompt photon spectrum in inclusive quarkonium decays and the extraction of α_S from quarkonium annihilation rates are briefly commented.     

Gluon condensate effects on the fine structure of heavy quarkonium spectra

We compute the effects of <G _μν G_μν> condensate on the fine structure of 1S, 2S, 2P states in heavy quarkonium systems. Large perturbative corrections are found. The inapplicability of perturbation theory is a clear signal that models based on a random background field without any spatial cut-off are too naive to be reliable.     

Meson decays in the non-relativistic quark model

Treating light as well as heavy pseudoscalar and vector mesons as non-relativistic quarkonia, we calculate various decay modes, including lowest QCD corrections. All decay modes studied are in good agreement with experiment, indicating that the quarkonium treatment is applicable to light mesons η, η′, π, also. Consistency of the quarkonium and current algebra treatments for the process π⁰ → 2λ leads to $\text{f}{}_{\mathrm{\pi }}\text{= (}\text{3}\text{2π}\text{)m}{}_{\mathrm{<mtext>u</mtext>}}\text{{1 ? (0.62/4π)α}{}_{\mathrm{<mtext>s</mtext>}}\text{(μ)},}\text{where}\text{m}{}_{\mathrm{<mtext>u</mtext>}}$ is the constituent u-quark mass, and $\text{f}{}_{\mathrm{\pi }}\text{? 93}\text{MeV}$.     

Holographic hadro-quarkonium

We consider the recently suggested model for some resonances near the open charm threshold as bound states of charmonium inside excited light mesons. It is argued in the soft-wall holographic model of QCD that such states of heavy quarkonium necessarily exist at sufficiently large spin of the light meson. The bound state is provided by the dilaton exchange through the 5D bulk. We also argue that the decay of such bound systems into mesons with open heavy flavors due to splitting of the heavy quarkonium can be treated as semiclassical tunneling and is suppressed. This behavior is in agreement with the known relative suppression of the decay of the discussed charmonium-like resonances into channels with D mesons.     

Radiative decays of quarkonia into Goldstone fermions

We consider the decay of³ S ₁ quarkonia into a photon and two Goldstone fermions in a model realizing supersymmetry in a nonlinear way. We derive a lower bound of 3.5 GeV for the scale of spontaneous supersymmetry breaking from Υ-decays. We show that the decay of a³ S ₁ quarkonium into two Goldstone fermions is forbidden in the order we consider.     

On duality in e+e- annihilation

With the help of a relativistic generalization of a formula for the leptonic width of quarkonium in the quasiclassical approximation it is shown that the sum of a sufficiently large number of total cross sections for the production of the quarkonium state (Q$\text{Q}$)_n in e⁺e^- annihilation is equal to the total cross section for production of a quasi-free quark- antiquark pair Q$\text{Q}$.     

Heavy quarks as color sextets

It is suggested that heavy quarks, e.g. the constituents of ?(9.6),may be color sextets. Consequences for the spectrum of quarkonium states are discussed. The new particles are long-lived and possibly stable. They can decay only via new types of weak interactions.     

Studies of unitarity at small x using the dipole formulation

Mueller's dipole formulation of onium-onium scattering is used to study unitarity corrections to the BFKL power growth at high energies. After a short discussion of the spatial distribution of colour dipoles in a heavy quarkonium and the associated fluctuations, results are presented showing that the one- and two-pomeron contributions to the total cross section are the same at a rapidity Y ≅ 14. Above this rapidity the large fluctuations in the onium wave function cause the multiple pomeron series to diverge. Resumming the series allows one to show that unitarity corrections set in gradually for the total cross section, which is dominated by rare, large, configurations of the onia. The elastic cross section comes mostly from much smaller impact parameters and has significant unitarity corrections starting at a rapidity Y ≅ 8.     

Quarkonium mass splitting revisited: effects of closed mesonic channels

Modifications of the quarkonium mass spectrum induced by its virtual dissociation into a pair of heavy mesons are considered. Coupling between quark and mesonic channels results in noticeable corrections to spin-dependent mass splitting. In particular, accounting for the dissociation effect allows one to reproduce the observable hierarchy of mass splittings in the χ_c, χ_b and χ′_b multiplets.     

Small QCD corrections in inclusive 0−+ quarkonium decay for the bound-state renormalization scheme

A consistent field theoretic computation of the first-order correction to the total decay of a non-relativistic heavy quarkonium state must consider contributions from the annihilation amplitude, with a typical scale of the order of the quark mass m, and from the bound-state wave function, where the typical scale is of the order of the Bohr momentum α_sm. Therefore, not only the latter smaller scale is the one to be taken for the total decay rate, but also a quite specific renormalization, the “bound-state renormalization scheme”, must be used for a computation of the total inclusive decay rate of 0^?+→hadrons. Due to important cancellations between large individual contributions, the net result turns out to be small, encouraging the use of pure perturbative QCD in such systems.     

Perturbative QCD and the exclusive decay of heavy quarkonium into a photon and two mesons

We consider the radiative decays of the ³S₁ ground state Q$\text{Q}$ into a real photon and two light pseudoscalar or vector mesons. For sufficiently large mass of the heavy quark Q, the decay, e.g. ? → γππ, can be calculated in perturbative QCD, provided that the photon does not carry away a predominant fraction of the available energy. We present differential and integrated Dalitz plot distributions and, for quarkonium states produced with transverse polarization in e⁺e^? annihilation, angular distributions of the orientation of the decay triangle relative to the beam direction.     

Effective field theories for the heavy quarkonium

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field-theory-derived quantum-mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and α _s ) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low-energy QCD dynamics is also discussed.     

Calculations of the excitation functions and isomer ratios of the K(α, n)Sc reaction in the equilibrium and pre-equilibrium statistical models

Angular-momentum effects are incorporated in the pre-equilibrium statistical model using Williams' spin-dependent level density as a function of the particle and hole numbers. Excitation functions and isomer ratios for the ⁴¹K(α, n)⁴⁴Sc reaction are analyzed both in the equilibrium and pre-equilibrium models in the energy range 8 to 40 MeV. Conventional pairing-energy corrections are introduced and their influence on the pre-equilibrium decay is investigated. The results are compared with published experimental data. The best fit was obtained for almost-pure pre-equilibrium decay with the initial excited-particle-plus-hole number n_o = 5 when pairing corrections were taken into account. No success was achieved in fitting the decrease of the isomer ratios at high energies, which is probably caused by the contribution from direct processes.     

Electromagnetic corrections to the s-wave scattering lengths in pionic hydrogen

Motivated by the recently performed X-ray precision experiments on pionic hydrogen (preceding paper), we reconsider the problem of electromagnetic corrections to the π - N scattering lengths. Based on a relativistic two-channel approach, we find corrections to the π⁻p elastic and single-charge-exchange (SCE) scatering lengths due to the point-Coulomb interaction, the finite-size Coulomb interaction (including the pion size), the first-order vacuum polarization (Uehling potential) and the (π⁻p) - (π⁰n) mass difference (mass difference effect). We also estimate the contribution due to the (γ,n) decay channel. The total corrections to the elastic and the SCE scattering lengths are found to be δ_ε = −(2.1 ± 0.5) × 10⁻² and δ_Γ = −(1.3 ± 0.5) × 10⁻². Previously published values for the corrections are critically compared with our results.