arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 73 records · Page 4Linked to original sources

arXiv2014

Born-Oppenheimer Approximation for the XYZ Mesons

Many of the XYZ mesons discovered in the last decade can be identified as bound states in Born-Oppenheimer (B-O) potentials for a heavy quark and antiquark. They include quarkonium hybrids, which are bound states in excited flavor-singlet B-O potentials, and quarkonium tetraquarks, which are bound states in flavor-nonsinglet B-O potentials. We present simple parameterizations of the deepest flavor-singlet B-O potentials. We infer the deepest flavor-nonsinglet B-O potentials from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are used to identify XYZ mesons that are candidates for ground-state energy levels in the B-O potentials for charmonium hybrids and tetraquarks. The energies of the lowest-energy charmonium hybrids are predicted by using the results of lattice QCD calculations to calculate the energy splittings between the ground states of different B-O potentials and using the Schroedinger equation to determine the splittings between energy levels within a B-O potential.

hep-ph↗

arXiv2014

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 (B-O) 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 B-O potentials, and quarkonium tetraquarks, which are bound states in flavor-nonsinglet B-O potentials. 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 B-O potentials for charmonium hybrids and tetraquarks.

hep-ph↗

arXiv2014

J/psi and Upsilon Polarization in Hadronic Production Processes

Both charm and bottom quarks form nonrelativistic bound states analogous to positronium. The J/psi and psi(2S) charmonium states and the first three Upsilon(nS) bottomonium states, all spin-triplet S-wave quarkonium states below open-heavy-flavor thresholds, have relatively large branching ratios to e- e+ or mu- mu+ pairs. In hadron collisions, experiments measuring lepton pairs can determine polarization by using angular correlation techniques. The polarization, in turn, can be related theoretically to the production mechanism for the bound state. This review summarizes experimental studies with proton beams at fixed target and colliding beam accelerators, covering a center-of-mass energy range from 39 to 7000 GeV for nucleon and antiproton targets. Analyses using various polarization frames and spin-quantization axes are described and results compared. A pattern emerges that connects experimental results over the whole energy span. The theoretical implications of the pattern are presented and a set of new measurements is proposed.

hep-ex↗

arXiv2014

Universal Relation for the Inelastic Two-Body Loss Rate

Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate. A simple universal relation between the loss rate and the contact is obtained by truncating the expansion after the lowest dimension operator. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel.

cond-mat.quant-gas↗

arXiv2013

Theoretical Interpretations of the XYZ Mesons

The XYZ mesons are unexpected mesons containing a heavy quark-antiquark pair that have been discovered during the last decade. The models for the XYZ mesons that have been proposed include conventional quarkonium, quarkonium hybrids, and quarkonium tetraquarks, whose four constituents can be clustered in several possible ways. None of the models have provided a compelling pattern for the XYZ mesons. The most promising theoretical approaches within QCD are lattice QCD for the c c-bar mesons, lattice NRQCD for the b b-bar mesons, and the Born-Oppenheimer approximation. The additional hints that will be provided by future experiments guarantee the eventual solution of the XYZ puzzle.

hep-ph↗

arXiv2013

Universal Two-body Physics in Dark Matter near an S-wave Resonance

The dark matter annihilation rate at small relative velocities can be amplified by a large boost factor using various mechanisms, including Sommerfeld enhancement, resonance enhancement, and Breit-Wigner enhancement. These mechanisms all involve a resonance near the threshold for a pair of dark matter particles. We point out that if the resonance is in the S-wave channel, the mechanisms are equivalent sufficiently near the resonance and they are constrained by universal two-body physics. The amplified annihilation rate requires a corresponding amplification of the elastic scattering cross section. If the resonance is a bound state below the threshold, it has an increased lifetime that is inversely proportional to the square root of the binding energy. Its spatial structure is that of two dark matter particles whose mean separation is also inversely proportional to the square root of the binding energy.

hep-ph↗

arXiv2013

Quarkonium at the Frontiers of High Energy Physics: A Snowmass White Paper

In this Snowmass White Paper, we discuss physics opportunities involving heavy quarkonia at the intensity and energy frontiers of high energy physics. We focus primarily on two specific aspects of quarkonium physics for which significant advances can be expected from experiments at both frontiers. The first aspect is the spectroscopy of charmonium and bottomonium states above the open-heavy-flavor thresholds. Experiments at e^+ e^- colliders and at hadron colliders have discovered many new, unexpected quarkonium states in the last 10 years. Many of these states are surprisingly narrow, and some have electric charge. The observations of these charged quarkonium states are the first definitive discoveries of manifestly exotic hadrons. These results challenge our understanding of the QCD spectrum. The second aspect is the production of heavy quarkonium states with large transverse momentum. Experiments at the LHC are measuring quarkonium production with high statistics at unprecedented values of p_T. Recent theoretical developments may provide a rigorous theoretical framework for inclusive production of quarkonia at large p_T. Experiments at the energy frontier will provide definitive tests of this framework. Experiments at the intensity frontier also provide an opportunity to understand the exclusive production of quarkonium states.

hep-ph↗

arXiv2013

How the Z_c(3900) Reveals the Spectra of Quarkonium Hybrid and Tetraquark Mesons

Flavor-exotic tetraquark mesons have recently been observed in the heavy-quark pair sectors of QCD, including two isospin multiplets in the b b-bar sector, Z_b(10610) and Z_b(10650), and one isospin multiplet in the c c-bar sector, Z_c(3900). We identify Z_b and Z_c as tetraquark mesons that are analogs of quarkonium hybrids with the gluon field replaced by an isospin-1 excitation of the light-quark fields. Given the identification of Y(4260) and Z_c(3900) as a ground-state charmonium hybrid and tetraquark, respectively, lattice QCD calculations of the charmonium spectrum can be used to estimate the masses of the lowest four spin-symmetry multiplets of charmonium hybrids and tetraquarks. The Z_b(10610) and Z_b(10650) can be assigned to excited-state multiplets of bottomonium tetraquarks, resulting in estimates of the masses of the ground-state multiplets of bottomonium hybrids and tetraquarks.

hep-ph↗

arXiv2013

The J/ψ ω Decay Channel of the X(3872) Charm Meson Molecule

Analyses of the J/ψ π+ π- decay channel of the X(3872) resonance by the CDF, Belle, and LHCb collaborations have established its J^{PC} quantum numbers as 1^{++}. An analysis of the π+ π- π0 invariant mass distribution in the J/ψ π+ π- π0 decay channel by the Babar collaboration indicated a preference for 2^{-+} over 1^{++}. We point out that a proper evaluation of the chi^2 in that analysis increases the probability for 1^{++} from 7.1% to about 18.7%. In the case of quantum numbers 1^{++}, where the X has an S-wave coupling to J/ψ ω, the proximity of the J/ψ ω threshold to D^* Dbar thresholds and the narrow width of the ω suggest that the effects of scattering between J/ψ ω and charm meson pairs could be significant. We derive invariant mass distributions for J/ψ π+ π- and π+ π- π0 that take into account S-wave scattering between the D^{*0} Dbar^0, D^{*+} D^-, and J/ψ ω channels. We also analyze the effects of scattering through the chi_{c1}(2P) charmonium resonance. We find that scattering effects are unable to produce significant changes in the shape of the π+ π- π 0 invariant mass distribution.

hep-ph↗

arXiv2013

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.

cond-mat.quant-gas↗

arXiv2012

Avalanche Mechanism for the Enhanced Loss of Ultracold Atoms

In several experiments with ultracold trapped atoms, a narrow loss feature has been observed near an {\it atom-dimer resonance}, at which there is an Efimov trimer at the atom-dimer threshold. The conventional interpretation of these loss features is that they are produced by the {\it avalanche mechanism}, in which the energetic atom and dimer from 3-body recombination undergo secondary elastic collisions that produce additional atoms with sufficient energy to escape from the trapping potential. We use Monte Carlo methods to calculate the average number of atoms lost and the average heat generated by recombination events in a Bose-Einstein condensate and in a thermal gas. We improve on previous models by taking into account the energy-dependence of the cross sections, the spacial structure of the atom cloud, and the elastic scattering of the atoms. We show that the avalanche mechanism cannot produce a narrow loss feature near the atom-dimer resonance. The number of atoms lost from a recombination event can be more than twice as large as the 3 that would be obtained in the absence of secondary collisions. However the resulting loss feature is broad and its peak is at a scattering length that is larger than the atom-dimer resonance and depends on the trap depth.

cond-mat.quant-gas↗

arXiv2012

Clock shift in a strongly interacting two-dimensional Fermi gas

We derive universal relations for the radio-frequency (rf) spectroscopy of a two-dimensional Fermi gas consisting of two spin states with a resonant S-wave interaction. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like $1/(ω^2 \ln^2 ω)$. Its coefficient is proportional to $\ln^2(a_{2D}'/a_{2D})$, where $a_{2D}$ and $a_{2D}'$ are the 2-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 $|\ln(a_{2D}'/a_{2D})| \gg 1$, the clock shift arises as a cancellation between much larger contributions proportional to $\ln^2(a_{2D}'/a_{2D})$ from bound-bound and bound-free rf transitions.

cond-mat.quant-gas↗

arXiv2012

Renormalization in the Three-body Problem with Resonant P-wave Interactions

Resonant P-wave interactions can be described by a minimal zero-range model defined by a truncated effective range expansion, so that the only 2-body interaction parameters are the inverse scattering volume 1/a_P and the P-wave effective range r_P. This minimal model can be formulated as a local quantum field theory with a P-wave interaction between atom fields and a molecular field. In the two-atom sector, the model is renormalizable, but it has unphysical behavior at high energies, because there are negative-probability states with momentum scale r_P. In the sector with three atoms, two of which are identical, renormalization in some parity and angular-momentum channels involves an ultraviolet limit cycle, indicating asymptotic discrete scale invariance. The Efimov effect occurs in the unitary limit a_P^(-1/3), r_P \to 0, but this limit is unphysical because there are low-energy states with negative probability. The minimal model can be of physical relevance only at energies small compared to the energy scale set by r_P, where the effects of negative-probability states are suppressed.

cond-mat.quant-gas↗

arXiv2012

The Avalanche Mechanism for Atom Loss near an Atom-Dimer Efimov Resonance

An Efimov trimer near the atom-dimer threshold can increase the atom loss rate in ultracold trapped atoms through the {\it avalanche mechanism} proposed by Zaccanti et al. A 3-body recombination event creates an energetic atom and dimer, whose subsequent elastic collisions produce additional atoms with sufficient energy to escape from the trapping potential. We use Monte Carlo methods to calculate the average number of atoms lost and the average heat generated by recombination events in both a Bose-Einstein condensate and a thermal gas. We take into account the energy-dependence of the cross sections and the spatial structure of the atom cloud. We confirm that the number of atoms lost can be much larger than the naive value 3 if there is an Efimov trimer near the atom-dimer threshold. This does not produce a narrow loss feature, but it can significantly affect the determination of Efimov parameters.

cond-mat.quant-gas↗

arXiv2011

Universal Relations for Identical Bosons from 3-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/omega^{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/omega^2 tail of the radio-frequency transition rate are log-periodic functions of k and omega that depend on the Efimov parameter.

cond-mat.quant-gas↗

arXiv2011

Estimating the Production Rate of Loosely-bound Hadronic Molecules using Event Generators

We examine the use of hadronic event generators, such as Pythia or Herwig, to estimate the production rate of loosely-bound hadronic molecules, such as the deuteron and the X(3872). In the case of the deuteron, we point out that there are large uncertainties in the normalization of the predictions using event generators, because baryon pair distributions are not among the inputs used to tune the event generators. Predictions using Pythia for anti-deuteron production in Upsilon decay are compared to measurements by the CLEO Collaboration. They suggest that Pythia overpredicts the probability of producing pairs of baryons, at least in Upsilon decay into three gluons, and that the standard value of the coalescence parameter underpredicts the probability for formation of a deuteron from a neutron and proton with small relative momentum. In the case of the X(3872), we discuss a proposed upper bound on the prompt cross section at the Tevatron that has been used as an argument against the X(3872) being a loosely-bound charm meson molecule. We demonstrate that this proposed upper bound is invalid by showing that the analogous upper bound for the anti-deuteron would be smaller than the observed anti-deuteron cross section.

hep-ph↗

arXiv2010

Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872)

We construct line shapes for the X(3872) that generalize the Flatte and zero-range line shapes that have been considered previously. These line shapes are associated with scattering amplitudes that are exactly unitary for real values of the interaction parameters and can be derived from a renormalizable quantum field theory. The new line shapes can be used to discriminate between the alternative binding mechanisms in which the X(3872) is generated either dynamically by charm meson interactions or by a resonance near the D^{*0} Dbar^0 threshold. If the resonance is identified with the P-wave charmonium state chi'_{c1}, the interaction parameters can be constrained by using charmonium phenomenology. We analyze data on the X(3872) and also data from the Belle and Babar Collaborations on the invariant mass distribution of the charm mesons from the decay B -> K + D^{*0} Dbar^0 up to 4000 MeV. Our analysis is compatible with the mechanism for the X(3872) being either a fine-tuning of charm meson interactions or the fine-tuning of the chi'_{c1} to the D^{*0} Dbar^0 threshold. In particular, the data do not exclude a separate chi'_{c1} resonance between the D^{*+} D^- threshold and 4000 MeV.

hep-ph↗

arXiv2010

Universal Relations for Fermions with Large Scattering Length

The behavior of fermions with two spin states that interact with a large scattering length is constrained by universal relations that hold for any state of the system. These relations involve a central property of the system called the contact, which measures the number of pairs of fermions with different spins that have small separations. The contact controls the thermodynamics of the system as well as the large-momentum and high-frequency tails of correlation functions. This review summarizes the current theoretical and experimental status of these universal relations.

cond-mat.quant-gas↗