Masaoki Kusunoki

Low-energy universality and the new charmonium resonance at 3870 MeV

The recently-discovered narrow charmonium resonance near 3870 MeV is interpreted as a hadronic molecule whose constituents are the charm mesons D^0 and \bar D^{*0} or \bar D^0 and D^{*0}. Because of an accidental fine-tuning of the molecule to very near the D^0 \bar D^{*0} threshold, it has some universal properties that are completely determined by the unnaturally large D^0 \bar D^{*0} scattering length a. Its narrow width can be explained by the suppression by a factor of 1/a of decay modes other than the decay of a constituent \bar D^{*0} or D^{*0}. Its production rates are also suppressed by a factor of 1/a. A particularly predictive mechanism for generating the large scattering length is the accidental fine-tuning of a P-wave charmonium state to the D^0 \bar D^{*0} threshold.

Exclusive production of the X(3872) in B meson decay

If the recently discovered charmoniumlike state X(3872) is a loosely bound S-wave molecule of the charm mesons D{sup 0}D*{sup 0} or D*{sup 0}D{sup 0}, it can be produced through the weak decay of the B meson into D{sup 0}D*{sup 0}K or D*{sup 0}D{sup 0}K followed by the coalescence of the charm mesons at a long-distance scale set by the scattering length of the charm mesons. The long-distance factors in the amplitude for the decay B{yields}XK are determined by the binding energy of X, while the short-distance factors are essentially determined by the amplitudes for B{yields}D{sup 0}D*{sup 0}K and B{yields}D*{sup 0}D{sup 0}K near the thresholds for the charm mesons. We obtain a crude determination of the short-distance amplitudes by analyzing data from the BABAR Collaboration on the branching fractions for B{yields}D{sup (}*{sup )}D{sup (}*{sup )}K using a factorization assumption, heavy-quark symmetry, and isospin symmetry. The resulting order-of-magnitude estimate of the branching fraction for B{sup +}{yields}XK{sup +} is compatible with observations provided that J/{psi}{pi}{sup +}{pi}{sup -} is a major decay mode of the X. The branching fraction for B{sup 0}{yields}XK{sup 0} is predicted to be suppressed by more than an order of magnitude compared to that for B{sup +}{yields}XK{sup +}.

Production of the X(3872) in B-Meson Decay by the Coalescence of Charm Mesons

If the recently discovered charmonium state X( 3872) is a loosely bound S-wave molecule of the charm mesons D0 D(*0) or D(*0) D0, it can be produced in B-meson decay by the coalescence of charm mesons. If this coalescence mechanism dominates, the ratio of the differential rate for B+ -->D(0) D(* 0)K+ near the D0 D(*0) threshold and the rate for B+ -->XK+ is a function of the D0 D(*0) invariant mass and hadron masses only. The identification of the X( 3872) as a D0 D(*0)/D(*0)D0 molecule can be confirmed by observing an enhancement in the D0 D(*0) invariant mass distribution near the threshold. An estimate of the branching fraction for B+ -->XK+ is consistent with observations if X has quantum numbers J(PC)=1(++ ) and if J/psi pi(+) pi(-) is one of its major decay modes.

Efimov States in a Bose-Einstein Condensate near a Feshbach Resonance

Recent experiments with Bose-Einstein condensates of 85Rb atoms near a Feshbach resonance have produced evidence for a condensate of diatomic molecules coexisting with the atom condensate. It should also be possible to create condensates of the triatomic molecules predicted by Efimov coexisting with the atom and dimer condensates. The smoking gun for the trimer condensate would be oscillatory dependence of observables on the binding energy of the trimer. It may also be possible to deduce the existence of the trimer condensate from the spectra of the bursts of atoms and dimers created in the disappearance of the trimers.

Decays of the X(3872) into J/psi and light hadrons

If the X(3872) is a loosely bound molecule of the charm mesons D{sup 0}D*{sup 0} and D*{sup 0}D{sup 0}, it can decay through the decay of a constituent in a hadronic channel with a nearby threshold, such as J/{psi}{omega} or J/{psi}{rho}. The differential decay rates of the X into J/{psi}{pi}{sup +}{pi}{sup -}, J/{psi}{pi}{sup +}{pi}{sup -}{pi}{sup 0}, J/{psi}{pi}{sup 0}{gamma}, and J/{psi}{gamma} are calculated in terms of XJ/{psi}{rho} and XJ/{psi}{omega} coupling constants using an effective Lagrangian that reproduces the decay rates of the {omega} and the {rho}. The dependence of the coupling constants on the binding energy and the total width of the X is determined by a factorization formula. Results from a model by Swanson are used to predict the partial width of X into J/{psi}{pi}{sup +}{pi}{sup -}{pi}{sup 0} as a function of the binding energy and the total width of the X.

Factorization in the production and decay of the X ( 3872 )

The production and decay of the X(3872) are analyzed under the assumption that the X is a weakly bound molecule of the charm mesons D{sup 0}D*{sup 0} and D*{sup 0}D{sup 0}. The decays imply that the large D{sup 0}D*{sup 0} scattering length has an imaginary part. An effective field theory for particles with a large complex scattering length is used to derive factorization formulas for production rates and decay rates of X. If a partial width is calculated in a model with a particular value of the binding energy, the factorization formula can be used to extrapolate to other values of the binding energy and to take into account the width of the X. The factorization formulas relate the rates for production of X to those for production of D{sup 0}D*{sup 0} and D*{sup 0}D{sup 0} near threshold. They also imply that the line shape of X differs significantly from that of a Breit-Wigner resonance.

Universal equation for Efimov states

Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of

Production of the X(3870) at the Y(4S) by the coalescence of charm mesons

{}^{4}\mathrm{He}

Λ+c/Λ-c asymmetry in hadroproduction from heavy-quark recombination

atoms. We also extend Efimovs theory to include the effects of deep two-body bound states, which give widths to the Efimov states.

{Lambda}{sub c}{sup +}/{Lambda}{sub c}{sup -} Asymmetry in Hadroproduction from Heavy-Quark Recombination

If the recently-discovered charmonium state X(3870) is a loosely-bound molecule of the charm mesons D^0 and \bar D^{*0} or \bar D^0 and D^{*0}, it can be produced in e^+ e^- annihilation at the \Upsilon(4S) resonance by the coalescence of charm mesons produced in the decays of B^+ and B^- mesons. Remarkably, in the case of 2-body decays of the B mesons, the leading contribution to the coalescence probability depends only on hadron masses and on the width and branching fractions of the B meson. As the binding energy E_b of the molecule goes to zero, the coalescence probability scales as E_b^{1/2} log(E_b). Unfortunately, the coalescence probability is also suppressed by two powers of the ratio of the width to the mass of the B meson, and is therefore many orders of magnitude too small to be observed in current experiments at the B factories.