arXiv subjects
Publications and source records attributed to M. B. Voloshin.
We consider transitions from the resonance X(3872) to the chi_{cJ} states of charmonium with emission of one or two pions as a means of studying the structure of the X resonance. We find that the relative rates for these transitions to the final states with different J significantly depend on whether the initial state is a pure charmonium state or a four-quark/molecular state.
We point out some properties of the amplitude of the dipion transition $Υ(3S) \to Υ(1S) ππ$ in relation to the recently reported results of a CLEO analysis of form factors in this amplitude. We find that the reported significant complex phase between two of the form factors under the assumption that the third form factor is zero, is not consistent with the picture where the phase shifts arise due to the final state interaction in the $ππ$ channel. It is also shown that in an analysis that uses no information on the polarization of both the initial and the final $Υ$ resonances it is impossible in principle to determine all the relevant terms. We suggest that a study of a simple correlation between the direction of the total momentum of the two pions and the axis of the initial beams is sufficient to resolve the ambiguity in the fit for the form factors.
The $D {\bar D}^*$ scattering amplitude and the production of the final states $π^+ π^- J/ψ$ and $π^+ π^- π^0 J/ψ$ near the $D^0 {\bar D}^{*0}$ threshold are discussed following the recent suggestion that the observed peaks X(3872) and X(3875) in the decays $B \to X K$ are due to a virtual state $X$ in the $D^0 {\bar D}^{*0}$ channel. The strong interaction is treated using the small interaction radius approximation. It is shown that the mass difference between the charged and neutral $D^{(*)}$ mesons results in a distinctive behavior of the relevant isotopic amplitudes. In particular, the shape of the peak in the $π^+ π^- J/ψ$ channel should be significantly narrower than in the $π^+ π^- π^0 J/ψ$ channel, which property can be used for an experimental test of the virtual state hypothesis.
We revisit the problem of interplay between the strong and the Coulomb interaction in the charged-to-neutral yield ratio for $B {\bar B}$ and $D {\bar D}$ pairs near their respective thresholds in $e^+e^-$ annihilation. We consider here a realistic situation with a resonant interaction in the isospin I=0 channel and a nonresonant strong scattering amplitude in the I=1 state. We find that the yield ratio has a smooth behavior depending on the scattering phase in the I=1 channel. The same approach is also applicable to the $K {\bar K}$ production at the $ϕ(1020)$ resonance, where the Coulomb effect in the charged-to-neutral yield ratio is generally sensitive to the scattering phases in both the isoscalar and the isovector channels. Furthermore, we apply the same approach to the treatment of the effect of the isotopic mass difference between the charged and neutral mesons and argue that the strong-scattering effects generally result in a modification to the pure kinematical effect of this mass difference.
We evaluate the cross section of the process $e^+e^- \to γX(3872)$ in terms of the content of the $D^{*0} {\bar D}^0$ `molecular' component in the wave function of the resonance X(3872). If this component is dominating, the cross section of the reaction $e^+e^- \to γX(3872)$ can reach up to about $10^{-3}$ of that for $e^+e^- \to D^* {\bar D}^*$ at energy slightly above the $D^* {\bar D}^*$ threshold, and the considered process can be a realistic source of the X(3872) particles for the studies of this resonance.
We argue that the recent CLEO-c data on $e^+e^-$ annihilation into pairs of charmed mesons at c.m. energy around 4.0 GeV are not well described by a single resonance $ψ(4040)$, but can be better understood if there is an additional narrow resonance with mass within few MeV from the $D^* {\bar D}^*$ threshold.
Two-pion transitions in charmonium and bottomonium are considered with the leading relativistic effects taken into account. The contribution of the chromo- magnetic interaction of the charmed quarks to the amplitude of the decay $ψ(2S) \to ππJ/ψ$ is estimated from the available data. This contribution is enhanced by a factor of three in the decay $η_c(2S) \to ππη_c$ and should produce a noticeable modification of the rate and the spectrum in the latter decay. It is argued that the peculiar observed spectrum in the decay $Υ(3S) \to ππΥ$ arises due to a dynamical suppression of the leading nonrelativistic quarkonium amplitude and thus enhanced prominence of the relativistic terms. Also discussed are the effects of the final state interaction between the pions.
I discuss topics related to four-quark states of the `molecular quarkonium' type, i.e. resonances that could be considered as (dominantly) made from a heavy meson and antimeson. Of the so far observed resonances such picture is very likely applicable to the state X(3872), and I also discuss its possible relevance to the peak near the $D^* {\bar D}^*$ threshold in $e^+e^-$ annihilation.
A threshold singularity in a heavier meson channel, e.g. $D^* {\bar D}^*$, generally reflects in the amplitudes of $e^+e^-$ annihilation into lighter meson pairs, such as $D^* {\bar D}$, $D {\bar D}$, and $D_s {\bar D}_s$, due to the channel coupling. The behavior of the cross section of the $e^+e^-$ annihilation into each channel in this situation is considered using general properties of the amplitudes near the new threshold. It is argued that the effects of the channel coupling can be quite significant in the observable cross section, in particular near the $D^* {\bar D}^*$ threshold.
We revisit the problem of decay of a metastable vacuum induced by the presence of a particle. For the bosons of the `master field' the problem is solved in any number of dimensions in terms of the spontaneous decay rate of the false vacuum, while for a fermion we find a closed expression for the decay rate in (1+1) dimensions. It is shown that in the (1+1) dimensional case an infrared problem of one-loop correction to the decay rate of a boson is resolved due to a cancellation between soft modes of the field. We also find the boson decay rate in the `sine-Gordon staircase' model in the limits of strong and weak coupling.
It is pointed out that in the decays $X(3872) \to D {\bar D} γ$ the possible `molecular' component of the X(3872) should give rise essentially only to a $D^0 {\bar D}^0 γ$ final state with a predictable spectrum, and should yield virtually no contribution to decays into $D^+D^- γ$. The latter final state with charged $D$ mesons should however arise from the radiative decays of the short-distance core of the X(3872) through the transition $X(3872) \to ψ(3770) γ$. Thus an observation of the radiative decays of X(3872) to pairs of neutral and charged $D$ mesons would provide an insight into the internal dynamics of the X(3872) resonance.
It is suggested that the resonance $ψ(3770)$ may contain a sizeable ($O(10%)$ in terms of the probability weight factor) four-quark component with the up- and down- quarks and antiquarks in addition to the $c {\bar c}$ pair, which component in itself has a substantial part with the isospin I=1. Furthermore such four-quark part of the wave function should also affect the properties of the $ψ'$ charmonium resonance through the $ψ(3770) - ψ'$ mixing previously considered in the literature. It is argued that an admixture of extra light quark pairs can explain a possible discrepancy between the theoretical expectations and the recent data on the non-$D {\bar D}$ decay width of the $ψ(3770)$ and the ratio of the yield of charged and neutral $D$ meson pairs in its decays, as well as on the extra rate of the $ψ'$ direct decay into light hadrons and the rate of the decay $ψ' \to π^0 J/ψ$. It is further argued that the suggested four-quark component of the wave function of the $ψ(3770)$ should give rise to a measurable rate of the decays $ψ(3770) \to ηJ/ψ$ and $ψ(3770) \to π^0 J/ψ$.
The interaction of the charmonium resonances J/psi and psi' with nucleons at low energies is considered using the multipole expansion and low-energy theorems in QCD. A lower bound is established for the relevant gluonic operator average over the nucleon. As a result we find the discussed interaction to be significantly stronger than previously estimated in the literature. In particular we conclude that the cross section of the J/psi - nucleon elastic scattering at the threshold is very likely to exceed 17 millibarn and that existence of bound states of the J/psi in light nuclei is possible. For the psi' resonance we estimate even larger elastic scattering cross section and also a very large cross section of the process psi'+N -> psi+N giving rise to the decay width of tens of MeV for the psi' resonance in heavy nuclei.
It is argued that the branching ratio for the decay chi_{b0}(2P) -> eta eta_b can reach few permil as a result of the enhancement of the eta emission by the axial anomaly in QCD. This might make the discussed process practical for an experimental search for the eta_b.
The properties of the resonance X(3872) are discussed under the assumption that this resonance is dominantly a `molecular' $J^{PC}=1^{++}$ state of neutral $D$ and $D^*$ mesons. It is argued that in these properties should dominate the states with the total spin of the charmed quark-antiquark pair equal to one. As a practical application of this observation the ratio of the rates of the decays $X \to π^0 χ_{cJ}$ for different $J$ is predicted. It is also pointed out that the total rate of these decays is likely to be comparable to that of the observed transitions $X \to π^+ π^- Jψ$ and $X \to π^+ π^- π^0 Jψ$. The decays of the X into light hadrons and its production in hadronic processes are also briefly discussed.
The pre-exponential factor in the probability of decay of a metastable vacuum is calculated for a generic (2+1) dimensional model in the limit of small difference $ε$ of the energy density between the metastable and the stable vacua. It is shown that this factor is proportional to $ε^{-7/3}$ and that the power does not depend on details of the underlying field theory. The calculation is done by using the effective Lagrangian method for the relevant soft (Goldstone) degrees of freedom in the problem. Unlike in the (1+1) dimensional case, where the decay rate is completely determined by the parameters of the effective Lagrangian and is thus insensitive to the specific details of the underlying (microscopic) theory, in the considered here (2+1) dimensional case the pre-exponential factor is found up to a constant, which does depend on specifics of the underlying short-distance dynamics, but does not depend on the energy asymmetry parameter $ε$. Thus the functional dependence of the decay rate on $ε$ is universally determined in the considered limit of small $ε$.
The subject of the charged-to-neutral yield ratio for B{\bar B} and D{\bar D}pairs near their respective thresholds in e^+e^- annihilation is revisited. As previously argued for the B mesons, this ratio should exhibit a substantial variation across the Upsilon(4S) resonance due to interference of the resonance scattering phase with the Coulomb interaction between the charged mesons. A simple alternative derivation of the expression describing this effect is presented here, and the analysis is extended to include the D meson production in the region of the psi(3770) resonance. The available data on Kaon production at the phi(1020) resonance are also discussed in connection with the expected variation of the charged-to-neutral yield ratio.
It is pointed out that the diagonal amplitude of the $E1-E1$ chromo-electric interaction with soft gluon fields (chromo-polarizability) can be measured directly for the $J/ψ$ and $Υ$ resonances in the decays $J/ψ\to ππ\ell^+ \ell^-$ and $Υ\to ππ\ell^+ \ell^-$ with soft pions. For the $J/ψ$ this amplitude is often discussed in connection with the $J/ψ$ interaction with nuclear matter, while for the $Υ$ the chromo-polarizability enters the estimates of the non-perturbative mass shift of the resonance relevant to precision determination of the $b$ quark mass from the $Υ$ mass.