arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 109 records · Page 6Linked to original sources

arXiv2007

Line Shapes of the X(3872)

If the quantum numbers of the X(3872) are J^{PC}=1^{++}, the measurement of its mass implies that it is either a loosely-bound hadronic molecule whose constituents are a superposition of the charm mesons pairs D^{*0} Dbar^0 and D^0 Dbar^{*0} or else it is a virtual state of these charm mesons. Its binding energy is small enough that the decay width of a constituent D^{*0} or Dbar^{*0} has a significant effect on the line shapes of the X resonance. We develop a simple approximation to the line shapes that takes into account the effect of the D^{*0} width as well as inelastic scattering channels of the charm mesons. We carry out a simultaneous fit to the line shapes in the J/psi pi^+ pi^- and D^0 Dbar^0 pi^0 channels measured in the decays B^+ to K^+ + X by the Belle Collaboration. The best fit corresponds to the X(3872) being a bound state just below the D^{*0} Dbar^0 threshold, but a virtual state just above the D^{*0} D-ar^0 threshold is not excluded.

hep-ph↗

arXiv2007

Condensates of Strongly-interacting Atoms and Dynamically Generated Dimers

In a system of atoms with large positive scattering length, weakly-bound diatomic molecules (dimers) are generated dynamically by the strong interactions between the atoms. If the atoms are modeled by a quantum field theory with an atom field only, condensates of dimers cannot be described by the mean-field approximation because there is no field associated with the dimers. We develop a method for describing dimer condensates in such a model based on the one-particle-irreducible (1PI) effective action. We construct an equivalent 1PI effective action that depends not only on the classical atom field but also on a classical dimer field. The method is illustrated by applying it to the many-body behavior of bosonic atoms with large scattering length at zero temperature using an approximation in which the 2-atom amplitude is treated exactly but irreducible $N$-atom amplitudes for $N \ge 3$ are neglected. The two 1PI effective actions give identical results for the atom superfluid phase, but the one with a classical dimer field is much more convenient for describing the dimer superfluid phase. The results are also compared with previous work on the Bose gas near a Feshbach resonance.

cond-mat.soft↗

arXiv2007

Weakly-bound Hadronic Molecule near a 3-body Threshold

The X(3872) seems to be a loosely-bound hadronic molecule whose constituents are two charm mesons. A novel feature of this molecule is that the mass difference of the constituents is close to the mass of a lighter meson that can be exchanged between them, namely the pion. We analyze this feature in a simple model with spin-0 mesons only. Various observables are calculated to next-to-leading order in the interaction strength of the exchanged meson. Renormalization requires summing a geometric series of next-to-leading order corrections. The dependence of observables on the ultraviolet cutoff can be removed by renormalizations of the mass of the heaviest meson, the coupling constant for the contact interaction between the heavy mesons, and short-distance coefficients in the operator product expansion. The next-to-leading order correction has an unphysical infrared divergence at the threshold of the two heavier mesons that can be eliminated by a further resummation that takes into account the nonzero width of the heaviest meson.

hep-ph↗

arXiv2006

Universality Constraints on Three-Body Recombination for Cold Atoms: from 4He to 133Cs

For atoms with large scattering length, the dependence of the 3-body recombination rate on the collision energy is determined by the scattering length and the Efimov 3-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the 3-body recombination rate for 4He atoms to constrain the universal functions. We then use those universal functions to calculate the 3-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the 4He results are strong if the scattering length is near the minimum of the 3-body recombination rate at threshold. We apply our results to 133Cs atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.

cond-mat.other↗

arXiv2006

Efimov Physics in Cold Atoms

Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and the scattering length. In this review, we summarize the universal results that are currently known. We also summarize the experimental information that is currently available with an emphasis on 3-atom loss processes.

cond-mat.other↗

arXiv2006

Exclusive Two-Vector-Meson Production from e^+ e^- Annihilation

The exclusive production of pairs of vector mesons with J^{PC} = 1^{--} in e^+ e^- collisions can proceed through e^+ e^- annihilation into two virtual photons. At energies much greater than the meson masses, the cross section is dominated by the independent fragmentation of the virtual photons into the vector mesons. The fragmentation approximation is used to calculate the cross sections and angular distributions for pairs of vector mesons that can be produced at the B factories. The predicted cross sections for rho^0 + rho^0 and rho^0 + phi production agree with recent measurements by the BaBar Collaboration. For the production of two charmonium vector mesons, the nonfragmentation corrections to the cross sections are calculated by using the NRQCD factorization formalism. The predicted cross sections for J/psi + J/psi and J/psi + psi(2S) production are compatible with upper limits set by the Belle Collaboration.

hep-ph↗

arXiv2006

Universality in Few-body Systems with Large Scattering Length

Particles with short-range interactions and a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-body sector, the universal properties are familiar and depend only on the scattering length a. In the 3-body sector for identical bosons, the universal properties include the existence of a sequence of shallow 3-body bound states called "Efimov states" and log-periodic dependence of scattering observables on the energy and the scattering length. The spectrum of Efimov states in the limit a -> +/- infinity is characterized by an asymptotic discrete scaling symmetry that is the signature of renormalization group flow to a limit cycle. In this review, we present a thorough treatment of universality for the system of three identical bosons and we summarize the universal information that is currently available for other 3-body systems. Our basic tools are the hyperspherical formalism to provide qualitative insights, Efimov's radial laws for deriving the constraints from unitarity, and effective field theory for quantitative calculations. We also discuss topics on the frontiers of universality, including its extension to systems with four or more particles and the systematic calculation of deviations from universality.

cond-mat.other↗

arXiv2006

Inclusive Production of the X(3872)

If the X(3872) is a loosely-bound D^{*0} Dbar^0 / D^0 Dbar^{*0} molecule, its inclusive production rate can be described by the NRQCD factorization formalism that applies to inclusive quarkonium production. We argue that if the molecule has quantum numbers J^{PC} = 1^{++}, the most important term in the factorization formula should be the color-octet ^3S_1 term. This is also one of the two most important terms in the factorization formulas for chi_{cJ}. Since the color-octet ^3S_1 term dominates chi_{cJ} production for many processes, the ratio of the inclusive direct production rates for X and chi_{cJ} should be roughly the same for these processes. The assumption that the ratio of the production rates for X and chi_{cJ} is the same for all processes is used to estimate the inclusive production rate of X in B meson decays, Z^0 decays, and in p pbar collisions.

hep-ph↗

arXiv2006

Operator Product Expansion in the Production and Decay of the X(3872)

The X(3872) seems to be a weakly-bound hadronic molecule whose constituents are two charm mesons. Its binding energy is much smaller than all the other energy scales in QCD. This separation of scales can be exploited through factorization formulas for production and decay rates of the X. In a low-energy effective field theory for the constituents of the X, the factorization formulas can be derived using the operator product expansion. The derivations are carried out explicitly for the simplest effective theory in which the constituents interact through a contact interaction that produces a large scattering length. The long-distance factors in the operator product expansions for various observables are calculated nonperturbatively in the interaction strength of the contact interaction. After renormalization of the coupling constant, all remaining ultraviolet divergences can be absorbed into the short-distance factors in the operator product expansions.

hep-ph↗

arXiv2006

Factorization in Break-up and Recombination Processes for Atoms with a Large Scattering Length

Break-up and recombination processes for loosely-bound molecules composed of atoms with a large scattering length $a$ necessarily involve interactions that are nonperturbative in the exact 2-body interaction. If these processes involve atoms with relative momenta much larger than $\hbar/|a|$, the leading contributions to their rates can be separated into short-distance factors that are insensitive to $a$ and long-distance factors that are insensitive to the range of the interaction. These factorization contributions can be obtained from the leading term in a perturbation expansion in the exact atom-atom scattering amplitude. The short-distance factors are atom-atom cross sections at a lower collision energy. In the special case of inclusive break-up cross sections for atom-molecule scattering, the long-distance factors simply count the number of atoms in the molecule.

cond-mat.other↗

arXiv2005

Exclusive Double-Charmonium Production from e^+ e^- Annihilation into Two Virtual Photons

We calculate the contributions from QED processes involving two virtual photons to the cross sections for e^+ e^- annihilation into two charmonium states with the same C-parity. Generically, the cross sections are three orders of magnitude smaller than those for charmonia with opposite C-parity because they are suppressed by a factor of alpha^2/alpha_s^2. However, if both charmonia have quantum numbers J^{PC} = 1^{--}, then there is a contribution to the cross section that involves the fragmentation of each photon into a charmonium. The fragmentation contribution is enhanced by powers of E_{beam}/m_c, the ratio of the beam energy to the charm-quark mass, and this enhancement can compensate for the suppression factor that is associated with the coupling constants. In particular, the predicted cross section for J/psi + J/psi at the B factories is larger than that for J/psi + eta_c.

hep-ph↗

arXiv2005

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-bar pairs, its cross section may be larger than that for J/psi +eta_c by about a factor 1.8, in spite of a suppression factor alpha^2/alpha_s^2 that is associated with the QED and QCD coupling constants.

hep-ph↗

arXiv2005

Exclusive Double-Charmonium Production from e^+ e^- Annihilation into a Virtual Photon

We calculate the exclusive cross sections for e^+ e^- annihilation into two charmonium states through a virtual photon. Purely electromagnetic contributions are surprisingly large, changing the cross sections by as much as 21%. The predicted cross section for J/psi + eta_c is about an order of magnitude smaller than a recent measurement by the BELLE Collaboration, although part of the discrepancy can be attributed to large relativistic corrections. The cross sections for S-wave + P-wave, P-wave + P-wave, and S-wave + D-wave charmonium states are also calculated. It may be possible to discover the D-wave state eta_{c2}(1D) at the B factories through the mode J/psi+η_{c2}, whose cross section is predicted to be about a factor of 10 smaller than J/psi + eta_c.

hep-ph↗

arXiv2005

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^0 \bar D^{*0} and D^{*0} \bar D^0, it can decay through the decay of a constituent in a hadronic channel with a nearby threshold, such as J/ψωor J/ψρ. The differential decay rates of the X into J/ψπ^+π^-, J/ψπ^+π^-π^0, J/ψπ^0 γ, and J/ψγare calculated in terms of X J/ψρand X J/ψωcoupling constants using an effective lagrangian that reproduces the decay rates of the ωand the ρ. 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/ψπ^+π^-π^0 as a function of the binding energy and the total width of the X.

hep-ph↗

arXiv2005

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^0 \bar D^{*0} and D^{*0} \bar D^0. The decays imply that the large D^0 \bar D^{*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^0 \bar D^{*0} and D^{*0} \bar D^0 near threshold. They also imply that the line shape of X differs significantly from that of a Breit-Wigner resonance.

hep-ph↗

arXiv2005

Comparison of the color-evaporation model and the NRQCD factorization approach in charmonium production

We compare the color-evaporation model (CEM) and nonrelativistic QCD (NRQCD) factorization predictions for inclusive quarkonium production. Using the NRQCD factorization formulas for quarkonium production and for perturbative QQ-bar production, we deduce relationships that are implied by the CEM between the nonperturbative NRQCD matrix elements that appear in the factorization formula for quarkonium production. These relationships are at odds with the phenomenological values of the matrix elements that have been extracted from the Tevatron data for charmonium production at large transverse momentum. A direct comparison of the CEM and NRQCD factorization predictions with the CDF charmonium production data reveals that the CEM fits to the data are generally unsatisfactory, while the NRQCD factorization fits are generally compatible with the data. The inclusion of k_T smearing improves the CEM fits substantially, but significant incompatibilities remain. The NRQCD factorization fits to the chi_c data indicate that multiple gluon radiation is an essential ingredient in obtaining the correct shape of the cross section as a function of p_T.

hep-ph↗

arXiv2005

Exclusive Production of the X(3872) in B Meson Decay

If the recently-discovered charmonium-like state X(3872) is a loosely-bound S-wave molecule of the charm mesons D^0 \bar D^{*0} or D^{*0} \bar D^0, it can be produced through the weak decay of the B meson into D^0 \bar D^{*0} K or D^{*0} \bar D^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 \to XK are determined by the binding energy of X, while the short-distance factors are essentially determined by the amplitudes for B \to D^0 \bar D^{*0} K and B \to D^{*0} \bar D^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\to \bar D^{(*)} D^{(*)} K using a factorization assumption, heavy quark symmetry, and isospin symmetry. The resulting order-of-magnitude estimate of the branching fraction for B^+ \to X K^+ is compatible with observations provided that J/ψπ^+ π^- is a major decay mode of the X. The branching fraction for B^0 \to X K^0 is predicted to be suppressed by more than an order of magnitude compared to that for B^+ \to X K^+.

hep-ph↗

arXiv2004

Production of the X(3870) at the Upsilon(4S) by the Coalescence of Charm Mesons

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 Υ(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.

hep-ph↗