arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 91 records · Page 5Linked to original sources

arXiv2010

Efimov Physics in 6Li Atoms

A new narrow 3-atom loss resonance associated with an Efimov trimer crossing the 3-atom threshold has recently been discovered in a many-body system of ultracold 6Li atoms in the three lowest hyperfine spin states at a magnetic field near 895 G. O'Hara and coworkers have used measurements of the 3-body recombination rate in this region to determine the complex 3-body parameter associated with Efimov physics. Using this parameter as the input, we calculate the universal predictions for the spectrum of Efimov states and for the 3-body recombination rate in the universal region above 600 G where all three scattering lengths are large. We predict an atom-dimer loss resonance at (672 +/- 2) G associated with an Efimov trimer disappearing through an atom-dimer threshold. We also predict an interference minimum in the 3-body recombination rate at (759 +/- 1) G where the 3-spin mixture may be sufficiently stable to allow experimental study of the many-body system.

cond-mat.quant-gas↗

arXiv2010

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.

cond-mat.quant-gas↗

arXiv2010

Scattering of an Ultrasoft Pion and the X(3872)

The identification of the X(3872) as a loosely-bound charm-meson molecule allows it to be described by an effective field theory, called XEFT, for the D^* Dbar, D Dbar^* and D Dbar pi sector of QCD at energies small compared to the pion mass. We point out that this effective field theory can be extended to the sector that includes an additional pion and used to calculate cross sections for the scattering of a pion and the X(3872). If the collision energy is much smaller than the pion mass, the cross sections are completely calculable at leading order in terms of the masses and widths of the charm mesons, pion masses, and the binding energy of the X(3872). We carry out an explicit calculation of the cross section for the breakup of the X(3872) into D^{*+} Dbar^{*0} by the scattering of a very low energy pi^+.

hep-ph↗

arXiv2009

Production of the X(3872) at the Tevatron and the LHC

We predict the differential cross sections for production of the X(3872) at the Tevatron and the Large Hadron Collider from both prompt QCD mechanisms and from decays of b hadrons. The prompt cross section is calculated using the NRQCD factorization formula. Simplifying assumptions are used to reduce the nonperturbative parameters to a single NRQCD matrix element that is determined from an estimate of the prompt cross section at the Tevatron. For X(3872) with transverse momenta greater than about 4 GeV, the predicted cross section is insensitive to the simplifying assumptions. We also discuss critically a recent analysis that concluded that the prompt production rate at the Tevatron is too large by orders of magnitude for the X(3872) to be a weakly-bound charm-meson molecule. We point out that if charm-meson rescattering is properly taken into account, the upper bound is increased by orders of magnitude and is compatible with the observed production rate at the Tevatron.

hep-ph↗

arXiv2009

Three-body Recombination of Lithium-6 Atoms with Large Negative Scattering Lengths

The 3-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 semi-analytic 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 Lithium-6 atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.

cond-mat.other↗

arXiv2009

Charm-pair Rescattering Mechanism for Charmonium Production in High-energy Collisions

A new mechanism for heavy quarkonium production in high-energy collisions called the "s-channel cut" was proposed in 2005 by Lansberg, Cudell, and Kalinovsky. We identify this mechanism physically as the production of a heavy quark and anti-quark that are on-shell followed by their rescattering to produce heavy quarkonium. We point out that in the NRQCD factorization formalism this rescattering mechanism is a contribution to the color-singlet model term at next-to-next-to-leading order in perturbation theory. Its leading contribution to the production rate can be calculated without introducing any additional phenomenological parameters. We calculate the charm-pair rescattering (or s-channel cut) contribution to the production of J/psi at the Tevatron and compare it to estimates by Lansberg et al. using phenomenological models. This contribution competes with the leading-order term in the color-singlet model at large transverse momentum but is significantly smaller than the next-to-leading-order term. We conclude that charm-pair rescattering is not a dominant mechanism for charmonium production in high-energy collisions.

hep-ph↗

arXiv2009

Optimal spin-quantization axes for quarkonium with large transverse momentum

The gluon collision process that creates a heavy-quark-antiquark pair with small relative momentum and large transverse momentum predicts at leading-order in the QCD coupling constant that the transverse polarization of the pair should increase with its transverse momentum. Measurements at the Fermilab Tevatron of the polarization of charmonium and bottomonium states with respect to a particular spin-quantization axis are inconsistent with this prediction. However the predicted rate of approach to complete transverse polarization depends on the choice of spin-quantization axis. We introduce axes that maximize and minimize the transverse polarization from the leading-order gluon collision process. They are determined by the direction of the jet that provides most of the balancing transverse momentum.

hep-ph↗

arXiv2009

Resonant Dimer Relaxation in Cold Atoms with a Large Scattering Length

Efimov physics refers to universal phenomena associated with a discrete scaling symmetry in the 3-body problem with a large scattering length. The first experimental evidence for Efimov physics was the recent observation of a resonant peak in the 3-body recombination rate for 133Cs atoms with large negative scattering length. There can also be resonant peaks in the atom-dimer relaxation rate for large positive scattering length. We calculate the atom-dimer relaxation rate as a function of temperature and show how measurements of the relaxation rate can be used to determine accurately the parameters that govern Efimov physics.

cond-mat.other↗

arXiv2009

Optimal spin-quantization axes for the polarization of dileptons with large transverse momentum

The leading-order parton processes that produce a dilepton with large transverse momentum predict that the transverse polarization should increase with the transverse momentum for almost any choice of the quantization axis for the spin of the virtual photon. The rate of approach to complete transverse polarization depends on the choice of spin quantization axis. We propose axes that optimize that rate of approach. They are determined by the momentum of the dilepton and the direction of the jet that provides most of the balancing transverse momentum.

hep-ph↗

arXiv2008

Three-Body Recombination of Identical Bosons with a Large Positive Scattering Length at Nonzero Temperature

For identical bosons with a large scattering length, the dependence of the 3-body recombination rate on the collision energy is determined in the zero-range limit by universal functions of a single scaling variable. There are six scaling functions for angular momentum zero and one scaling function for each higher partial wave. We calculate these universal functions by solving the Skorniakov--Ter-Martirosian equation. The results for the 3-body recombination as a function of the collision energy are in good agreement with previous results from solving the 3-body Schroedinger equation for 4He atoms. The universal scaling functions can be used to calculate the 3-body recombination rate at nonzero temperature. We obtain an excellent fit to the data from the Innsbruck group for 133Cs atoms with a large positive scattering length.

cond-mat.other↗

arXiv2008

Exotic c c-bar Mesons

A surprising number of new c c-bar mesons with masses above the D D-bar threshold have been discovered at the B factories. Some of them are ordinary charmonium states, but others are definitely exotic mesons. The current theoretical status of the new c c-bar mesons is summarized.

hep-ph↗

arXiv2008

Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance

A set of universal relations between various properties of any few-body or many-body system consisting of fermions with two spin states and a large but finite scattering length have been derived by Shina Tan. We derive generalizations of the Tan relations for a two-channel model for fermions near a Feshbach resonance that includes a molecular state whose detuning energy controls the scattering length. We use quantum field theory methods, including renormalization and the operator product expansion, to derive these relations. They reduce to the Tan relations as the scattering length is made increasingly large.

cond-mat.other↗

arXiv2008

Scattering Models for Ultracold Atoms

We present a review of scattering models that can be used to describe the low-energy behavior of identical bosonic atoms. In the simplest models, the only degrees of freedom are atoms in the same spin state. More elaborate models have other degrees of freedom, such as atoms in other spin states or diatomic molecules. The parameters of the scattering models are specified by giving the S-wave phase shifts for scattering of atoms in the spin state of primary interest. The models are formulated as local quantum field theories and the renormalization of their coupling constants is determined. Some of the parameters can be constrained by renormalizability or by the absence of negative-norm states. The Green's functions that describe the evolution of two-atom states are determined analytically. They are used to determine the T-matrix elements for atom-atom scattering and the binding energies of diatomic molecules. The scattering models all exhibit universal behavior as the scattering length in a specific spin state becomes large.

cond-mat.other↗

arXiv2008

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/k^4 at large momentum k, as pointed out by Shina 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.

cond-mat.other↗

arXiv2008

An Estimate of the Partial Width for X(3872) into p p-bar

We present an estimate of the partial width of X(3872) into p p-bar under the assumption that it is a weakly-bound hadronic molecule whose constituents are a superposition of the charm mesons D^{*0} D-bar^0 and D^{0} D-bar^{*0}. The p p-bar partial width of X is therefore related to the cross section for p p-bar to D^{*0} D-bar^0 near the threshold. That cross section at an energy well above the threshold is estimated by scaling the measured cross section for p p-bar to K^{*-} K^+. It is extrapolated to the D^{*0} D-bar^0 threshold by taking into account the threshold resonance in the 1^{++} channel. The resulting prediction for the p p-bar partial width of X(3872) is proportional to the square root of its binding energy. For the current central value of the binding energy, the estimated partial width into p p-bar is comparable to that of the P-wave charmonium state chi_{c1}.

hep-ph↗

arXiv2007

Line Shapes of the Z(4430)

The Belle Collaboration recently discovered the first manifestly exotic meson: Z^+(4430), which decays into psi' pi^+ and therefore has quark content c c-bar u d-bar. The proximity of its mass to the D_1 D-bar^* threshold has motivated the interpretation of the Z^+ as a charm meson molecule whose constituents are an S-wave superposition of D_1^+ D-bar^{*0}$ and D^{*+} D-bar_1^0$. If this interpretation is correct, the small ratio of the binding energy of the Z^+ to the width Gamma_1 of its constituent D_1 can be exploited to predict properties of its line shapes. Its full width at half maximum in the channel psi' pi^+ should be approximately sqrt{3} Gamma_1 = 35 MeV, which is consistent with the measured width of the Z^+. The Z^+ should also decay into D^* D-bar^* pi through decay of its constituent D_1. The peak in the line shape for D^* D-bar^* pi should be at a higher energy than the peak in the line shape for psi' pi^+ by about Gamma_1/sqrt{12} = 6 MeV. The line shape in D^* D-bar^* pi should also be broader and asymmetric, with a shoulder on the high energy side that can be attributed to a threshold enhancement in the production of D_1 D-bar^*.

hep-ph↗

arXiv2007

The Effects of Charged Charm Mesons on the Line Shapes of the X(3872)

The quantum numbers J^PC = 1++ of the X(3872) and the proximity of its mass to the D*0 anti-D0 threshold imply that it is either a loosely-bound hadronic molecule whose constituents are a superposition of D*0 anti-D0 and D0 anti-D*0 or it is a virtual state of charm mesons. The line shapes of the X(3872) can discriminate between these two possibilities. At energies within a few MeV of the D*0 anti-D0 threshold, the lines shapes of the X produced in B -> K transitions are determined by its binding energy and its width. Their normalizations are determined by a short-distance constant that is different for B+ -> K+ and B0 -> K0. At energies comparable to the 8 MeV splitting between the D*0 anti-D0 and D*+ D- thresholds, the charged meson channels D*+ D- and D+ D*- have a significant effect on the line shapes of the X. We calculate the line shapes taking into account the resonant coupling between the charged and neutral 1++ channels. The line shapes and their normalizations depend on one additional scattering parameter and two additional short-distance constants associated with the B -> K transitions. The line shapes of the X resonance depend on its decay channel; they are different for J/psi pi+ pi-, J/psi pi+ pi- pi0, and D0 anti-D0 pi0. The line shapes are also different for X produced in B+ decays and in B0 decays. Some conceptual errors in previous work on this problem are pointed out.

hep-ph↗

arXiv2007

Inclusive Charm Production in chi_b Decays

We calculate the inclusive decay rate of the spin-triplet bottomonium states chi_{bJ} into charm hadrons, including the leading-order color-singlet and color-octet bb-bar annihilation mechanisms. We also calculate the momentum distribution of the charm quark from the decay of chi_{bJ}. The infrared divergences from the color-singlet process bb-bar -> cc-bar g are factored into the probability density at the origin for a bb-bar pair in a color-octet state. That probability density can be determined phenomenologically from the fraction of decays of chi_{bJ} that include charm hadrons. It can then be used to predict the partial widths into light hadrons for all four states in the P-wave bottomonium multiplet.

hep-ph↗