Interpretation of Neutral Charm Mesons near Threshold as Unparticles.

The existence of the X(3872) resonance extremely close to the D^{*0}D[over ¯]^{0} threshold implies that neutral charm mesons have an approximate nonrelativistic conformal symmetry. Systems consisting of these mesons with small kinetic energies produced in a short-distance reaction are unparticles in the sense that they can be created by operators with definite scaling dimensions in a nonrelativistic conformal field theory. There is a scaling region in which their energy distribution has power-law behavior with an exponent determined by the scaling dimension of the operator. The unparticle associated with two neutral charm mesons produces a peak in the recoil momentum spectrum of K^{±} in inclusive decays of B^{±} that has been observed. The scaling dimensions of the unparticles associated with three neutral charm mesons are calculated. They can be determined experimentally by measuring the invariant mass distributions for XD^{0} or XD^{*0} in inclusive prompt production at the Large Hadron Collider.

Dense Axion Stars.

If the dark matter particles are axions, gravity can cause them to coalesce into axion stars, which are stable gravitationally bound systems of axions. In the previously known solutions for axion stars, gravity and the attractive force between pairs of axions are balanced by the kinetic pressure. The mass of these dilute axion stars cannot exceed a critical mass, which is about 10^{-14}M_{⊙} if the axion mass is 10^{-4} eV. We study axion stars using a simple approximation to the effective potential of the nonrelativistic effective field theory for axions. We find a new branch of dense axion stars in which gravity is balanced by the mean-field pressure of the axion Bose-Einstein condensate. The mass on this branch ranges from about 10^{-20}M_{⊙} to about M_{⊙}. If a dilute axion star with the critical mass accretes additional axions and collapses, it could produce a bosenova, leaving a dense axion star as the remnant.

Association of atoms into universal dimers using an oscillating magnetic field.

In a system of ultracold atoms near a Feshbach resonance, pairs of atoms can be associated into universal dimers by an oscillating magnetic field with a frequency near that determined by the dimer binding energy. We present a simple expression for the transition rate that takes into account many-body effects through a transition matrix element of the contact. In a thermal gas, the width of the peak in the transition rate as a function of the frequency is determined by the temperature. In a dilute Bose-Einstein condensate of atoms, the width is determined by the inelastic scattering rates of a dimer with zero-energy atoms. Near an atom-dimer resonance, there is a dramatic increase in the width from inelastic atom-dimer scattering and from atom-atom-dimer recombination. The recombination contribution provides a signature for universal tetramers that are Efimov states consisting of two atoms and a dimer.

Selection rules for hadronic transitions of XYZ mesons.

Many of the XYZ mesons discovered in the last decade can be identified as bound states of a heavy quark and antiquark in Born-Oppenheimer (BO) potentials defined by the energy of gluon and light-quark fields in the presence of static color sources. The mesons include quarkonium hybrids, which are bound states in excited flavor-singlet BO potentials, and quarkonium tetraquarks, which are bound states in BO potentials with light-quark+antiquark flavor. The deepest hybrid potentials are known from lattice QCD calculations. The deepest tetraquark potentials can be inferred from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are derived and used to identify XYZ mesons that are candidates for ground-state energy levels in the BO potentials for charmonium hybrids and tetraquarks.

Two-body and three-body contacts for identical Bosons near unitarity.

In a recent experiment with ultracold trapped Rb85 atoms, Makotyn et al. studied a quantum-degenerate Bose gas in the unitary limit where its scattering length is infinitely large. We show that the observed momentum distributions are compatible with a universal relation that expresses the high-momentum tail in terms of the two-body contact C2 and the three-body contact C3. We determine the contact densities for the unitary Bose gas with number density n to be C2 ≈ 20 n(4/3) and C3 ≈ 2n(5/3). We also show that the observed atom loss rate is compatible with that from 3-atom inelastic collisions, which gives a contribution proportional to C3, but the loss rate is not compatible with that from 2-atom inelastic collisions, which gives a contribution proportional to C2. We point out that the contacts C2 and C3 could be measured independently by using the virial theorem near and at unitarity, respectively.

How the Z(c)(3900) reveals the spectra of charmonium hybrids and tetraquarks.

The recently discovered Z(c)(3900) meson is a flavor-exotic tetraquark whose constituents consist of a charm quark and antiquark and a light quark and antiquark. We identify such heavy tetraquark mesons as analogs of quarkonium hybrids, with the gluon field replaced by an isospin-1 excitation of the gluon and light-quark fields. Given the identification of Y(4260) as a ground-state charmonium hybrid, lattice QCD calculations of the charmonium spectrum by the Hadron Spectrum Collaboration can be used to estimate the masses of the four lowest spin-symmetry multiplets of charmonium hybrids. We make the assumption that the isospin-1 Born-Oppenheimer potentials, whose energy levels are tetraquarks, have the same shapes as the flavor-singlet Born-Oppenheimer potentials, whose energy levels are hybrids. Given the identification of Z(c)(3900) as a charmonium tetraquark, lattice QCD calculations of the charmonium hybrid spectrum can then be used to estimate the masses of the four lowest spin-symmetry multiplets of charmonium tetraquarks.

Atom loss resonances in a Bose-Einstein condensate.

Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near two-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions.

Clock shift in a strongly interacting two-dimensional Fermi gas.

We derive universal relations for the rf spectroscopy of a two-dimensional Fermi gas consisting of two spin states interacting through an S-wave scattering length. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like 1/(ω2ln2ω). Its coefficient is proportional to ln2'(a'(2D)/a(2D)), where a(2D) and a'(2D) are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to ln(a'(2D)/a(2D)). If |ln(a'(2D)/a(2D))| >> 1, the clock shift arises as a cancellation between much larger contributions proportional to ln2(a'(2D)/a(2D)) from bound-bound and bound-free rf transitions.

Universal relations for identical bosons from three-body physics.

Systems consisting of identical bosons with a large scattering length satisfy universal relations determined by 2-body physics that are similar to those for fermions with two spin states. They require the momentum distribution to have a large-momentum 1/k(4) tail and the radio-frequency transition rate to have a high-frequency 1/ω(3/2) tail, both of which are proportional to the 2-body contact. Identical bosons also satisfy additional universal relations that are determined by 3-body physics and involve the 3-body contact, which measures the probability of 3 particles being very close together. The coefficients of the 3-body contact in the 1/k(5) tail of the momentum distribution and in the 1/ω(2) tail of the radio-frequency transition rate are log-periodic functions of k and ω that depend on the Efimov parameter.

Short-time operator product expansion for rf spectroscopy of a strongly interacting Fermi gas.

Universal relations that hold for any state provide powerful constraints on systems consisting of fermions with two spin states interacting with a large scattering length. In radio-frequency (rf) spectroscopy, the mean shift in the rf frequency and the large-frequency tail of the rf transition rate are proportional to the contact, which measures the density of pairs with small separations. We show that these universal relations can be derived and extended by using the short-time operator product expansion of quantum field theory. This is a general method for identifying aspects of many-body physics that are controlled by few-body physics.

Three-body recombination of 6Li atoms with large negative scattering lengths.

The three-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex-valued. We provide semianalytic expressions for the cases of 2 or 3 equal scattering lengths, and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three lowest hyperfine states of 6Li atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.

Exact relations for a strongly interacting fermi gas from the operator product expansion.

The momentum distribution in a Fermi gas with two spin states and a large scattering length has a tail that falls off like 1/k4 at large momentum k, as pointed out by Tan. He used novel methods to derive exact relations between the coefficient of the tail in the momentum distribution and various other properties of the system. We present simple derivations of these relations using the operator product expansion for quantum fields. We identify the coefficient as the integral over space of the expectation value of a local operator that measures the density of pairs.

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.

An infrared renormalization group limit cycle in QCD.

We use effective field theories to show that small increases in the up and down quark masses would move QCD very close to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. We conjecture that QCD can be tuned to the critical trajectory by adjusting the quark masses independently. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner would be tuned to zero and the triton would have infinitely many excited states with an accumulation point at the 3-nucleon threshold. The ratio of the binding energies of successive states would approach a universal constant that is close to 515.

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.

e+ e- annihilation into J/psi + J/psi.

Recent measurements by the Belle Collaboration of the exclusive production of two charmonia in e(+)e(-) annihilation differ substantially from theoretical predictions. We suggest that a significant part of the discrepancy can be explained by the process e(+)e(-)-->J/psi+J/psi. Because the J/psi+J/psi production process can proceed through fragmentation of two virtual photons into two cc pairs, its cross section may be larger than that for J/psi+eta(c) by about a factor of 3.7, in spite of a suppression factor alpha(2)/alpha(2)(s) that is associated with the QED and QCD coupling constants.

Leading-particle effect from heavy-quark recombination.

The leading particle effect in charm hadroproduction is an enhancement of the cross section for a charmed hadron D in the forward direction of the beam when the beam hadron has a valence parton in common with the D. The large D(+)/D(-) asymmetry observed by the E791 experiment is an example of this phenomenon. We show that the heavy-quark recombination mechanism provides an economical expla-nation for this effect. In particular, the D(+)/D(-) asymmetry can be fit reasonably well using a single parameter whose value is consistent with a recent determination from charm photoproduction.

Dilute Bose-Einstein condensate with large scattering length.

We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density E of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda* that determines the low-energy observables in the three-body sector. The second-order correction to E has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative a, we calculate the coefficient of the three-body mean-field term in E in terms of a and Lambda*. It can be very large if there is an Efimov state near threshold.

Convergence of the linear delta expansion in the critical O(N) field theory.

The linear delta expansion is applied to the three-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for (2)> converges, with errors decreasing as a power of the order n in delta. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with n.