arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 55 records · Page 3Linked to original sources

arXiv2017

Comment on "Single-inclusive jet production in electron-nucleon collisions through next-to-next-to-leading order in perturbative QCD" [Phys. Lett. B 763, 52--59 (2016)]

In the cross section for single-inclusive jet production in electron-nucleon collisions, the distribution of a quark in an electron appears at next-to-next-to-leading order. The numerical calculations in Ref. [1] were carried out using a perturbative approximation for the distribution of a quark in an electron. We point out that that distribution receives nonperturbative QCD contributions that invalidate the perturbative approximation. Those nonperturbative effects enter into cross sections for hard-scattering processes through resolved-electron contributions and can be taken into account by determining the distribution of a quark in an electron phenomenologically.

hep-ph↗

arXiv2016

Open Effective Field Theories from Highly Inelastic Reactions

The loss of particles due to highly inelastic reactions has previously been taken into account in effective field theories for low-energy particles by adding local anti-Hermitian terms to the effective Hamiltonian. An additional modification is required in the time evolution equation for the density matrix of a multi-particle system. An effective density matrix can be defined by tracing over states containing high-momentum particles produced by the highly inelastic reactions and by a time average that eliminates short-time correlations. The effective density matrix satisfies the Lindblad equation, with local Lindblad operators that are determined by the anti-Hermitian terms in the effective Hamiltonian.

hep-ph↗

arXiv2016

Nonrelativistic Effective Field Theory for Axions

Axions can be described by a relativistic field theory with a real scalar field $ϕ$ whose self-interaction potential is a periodic function of $ϕ$. Low-energy axions, such as those produced in the early universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field $ψ$ whose effective potential is a function of $ψ^*ψ$. We determine the coefficients in the expansion of the effective potential to fifth order in $ψ^*ψ$ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to expand the effective potential in powers of $ψ^*ψ$, we develop a sequence of systematically improvable approximations to the effective potential that include terms of all orders in $ψ^*ψ$.

hep-ph↗

arXiv2016

Wino dark matter annihilation through the radiative formation of bound states

The most dramatic "Sommerfeld enhancements" of neutral-wino-pair annihilation occur when the wino mass is tuned to near critical values where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold. If the wino mass is larger than the critical value, the resonance is a wino-pair bound state. If the wino mass is near a critical value, low-energy winos can be described by a zero-range effective field theory in which the winos interact nonperturbatively through a contact interaction. The parameters of the zero-range effective field theory can be determined by matching wino scattering amplitudes calculated by solving the Schrödinger equation for a nonrelativistic effective field theory in which the winos interact through a potential due to the exchange of electroweak gauge bosons. The utility of the zero-range effective field theory is illustrated by calculating the rate for formation of an S-wave bound state in the collision of two neutral winos through the emission of two soft photons.

hep-ph↗

arXiv2016

Emission of Photons and Relativistic Axions from Axion Stars

The number of nonrelativistic axions can be changed by inelastic reactions that produce photons or relativistic axions. Any odd number of axions can annihilate into two photons. Any even number of nonrelativistic axions can scatter into two relativistic axions. We calculate the rate at which axions are lost from axion stars from these inelastic reactions. In dilute systems of axions, the dominant inelastic reaction is axion decay into two photons. In sufficiently dense systems of axions, the dominant inelastic reaction is the scattering of four nonrelativistic axions into two relativistic axions. The scattering of odd numbers of axions into two photons produces monochromatic radio-frequency signals at odd-integer harmonics of the fundamental frequency set by the axion mass. This provides a unique signature for dense systems of axions, such as a dense axion star or a collapsing dilute axion star.

hep-ph↗

arXiv2016

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 $10^{-14} M_\odot$ 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 $10^{-20} M_\odot$ to about $M_\odot$. 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.

hep-ph↗

arXiv2016

Lindblad Equation for the Inelastic Loss of Ultracold Atoms

The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the local anti-Hermitian terms in the effective Hamiltonian. We use the Lindblad equation to derive the universal relation for the two-atom inelastic loss rate for fermions with two spin states and the universal relation for the three-atom inelastic loss rate for identical bosons.

cond-mat.quant-gas↗

arXiv2016

Open Effective Field Theories from Deeply Inelastic Reactions

Effective field theories have often been applied to systems with deeply inelastic reactions that produce particles with large momenta outside the domain of validity of the effective theory. The effects of the deeply inelastic reactions have been taken into account in previous work by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-particle systems are considered, an additional modification is required in equations governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum particles, and show that it satisfies a Lindblad equation, with local Lindblad operators determined by the anti-Hermitian terms in the effective Hamiltonian density.

hep-ph↗

arXiv2015

Towards a Theoretical Understanding of the XYZ Mesons from QCD

The XYZ mesons are mesons that contain a heavy quark and antiquark but have properties that seem to require additional constituents. Some of them are electrically charged, so they must be tetraquark mesons whose additional constituents are a light quark and antiquark. The list of XYZ mesons has grown to about two dozen over the last decade. A promising approach to understanding these mesons within QCD is the Born-Oppenheimer approximation, which reduces the problem to the solution of the Schrodinger equation in potentials that can be calculated using lattice QCD. The Born-Oppenheimer approximation has not yet revealed the pattern of the XYZ mesons, but it provides a compelling framework for understanding them from the fundamental theory.

hep-ph↗

arXiv2015

Inclusive Higgs Production at Large Transverse Momentum

We present a factorization formula for the inclusive production of the Higgs boson at large transverse momentum $P_T$ that includes all terms with the leading power of $1/P_T^2$. The cross section is factorized into convolutions of parton distributions, infrared-safe hard-scattering cross sections for producing a parton, and fragmentation functions that give the distribution of the longitudinal momentum fraction of the Higgs relative to the fragmenting parton. The infrared-safe cross sections and the fragmentation functions are perturbatively calculable. The factorization formula enables the resummation of large logarithms of $P_T/M_H$ due to final-state radiation by integrating evolution equations for the fragmentation functions. By comparing the cross section for the process $q\bar{q}\to H t\bar t$ from the leading-power factorization formula at leading order in the coupling constants with the complete leading-order cross section, we infer that the error in the factorization formula decreases to less than 5% for $P_T>600$ GeV at a future $100$ TeV collider.

hep-ph↗

arXiv2015

Inclusive Higgs Production at Large Transverse Momentum

We present a factorization formula for the inclusive production of the Higgs boson at large transverse momentum $P_T$ that includes all terms with the leading power of $1/P_T^2$. The cross section is factorized into convolutions of parton distributions, infrared-safe hard-scattering cross sections for producing a parton, and fragmentation functions that give the distribution of the longitudinal momentum fraction of the Higgs relative to the fragmenting parton. The infrared-safe cross sections and the fragmentation functions are perturbatively calculable. The most important fragmentation functions are those for which the fragmenting parton is the top quark, gluon, $W$, $Z$, and the Higgs itself. We calculate the fragmentation functions at leading order in the Standard Model coupling constants. The factorization formula enables the resummation of large logarithms of $P_T/M_H$ due to final-state radiation by integrating evolution equations for the fragmentation functions. By comparing the cross section for the process $q\bar{q}\to H t\bar t$ from the leading-power factorization formula at leading order in the coupling constants with the complete leading-order cross section, we infer that the error in the factorization formula decreases to less than 5\% for $P_T>600$ GeV at a future $100$ TeV collider.

hep-ph↗

arXiv2015

Universal Relations for Range Corrections to Efimov Features

In a three-body system of identical bosons interacting through a large S-wave scattering length $a$, there are several sets of Efimov features related by discrete scale invariance. Effective field theory was recently used to derive universal relations between these Efimov features that include the first-order correction due to a nonzero effective range $r_s$. We reveal a simple pattern in these range corrections that had not been previously identified. The pattern is explained by the renormalization group for the effective field theory, which implies that the Efimov three-body parameter runs logarithmically with the momentum scale at a rate proportional to $r_s/a$. The running Efimov parameter also explains the empirical observation that range corrections can be largely taken into account by shifting the Efimov parameter by an adjustable parameter divided by a. The accuracy of universal relations that include first-order range corrections is verified by comparing with various theoretical calculations using models with nonzero range.

cond-mat.quant-gas↗

arXiv2015

Harmonic and Subharmonic Association and Dissociation of Universal Dimers in a Thermal Gas

In a gas of ultracold atoms whose scattering length is controlled by a magnetic Feshbach resonance, atoms can be associated into universal dimers by an oscillating magnetic field. In addition to the harmonic resonance with frequency near that determined by the dimer binding energy, there is a subharmonic resonance with half that frequency. If the thermal gas contains dimers, they can be dissociated into unbound atoms by the oscillating magnetic field. We show that the transition rates for association and dissociation can be calculated by treating the oscillating magnetic field as a sinusoidal time-dependent perturbation proportional to the contact operator. Many-body effects are taken into account through transition matrix elements of the contact operator. We calculate both the harmonic and subharmonic transition rates analytically for association in a thermal gas of atoms and dissociation in a thermal gas of dimers.

cond-mat.quant-gas↗

arXiv2015

Galilean-Invariant XEFT

XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the X(3872) resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly conserved in the transition D*0 --> D0 pi0. The transitions D*0 --> D0 pi0 and X --> D0 D0-bar pi0 are described explicitly in XEFT. The effects of the decay D*0 --> D0 gamma and of short-distance decay modes of the X(3872), such as J/psi --> pi+ pi-, can be taken into account by using complex on-shell renormalization schemes for the D*0 propagator and for the D*0 D0-bar propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the D*0 D0-bar scattering length to next-to-leading order. Galilean invariance ensures the cancellation of ultraviolet divergences without the need for truncating an expansion in powers of the ratio of the pion and charm meson masses.

hep-ph↗

arXiv2014

Gluon fragmentation into quarkonium at next-to-leading order

We present the first calculation at next-to-leading order (NLO) in $α_s$ of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of $z$, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction terms in $4-2ε$ dimensions. We also extract the divergences in the virtual NLO corrections analytically, and detail the cancellation of all divergences after renormalization. The NLO corrections have a dramatic effect on the shape of the fragmentation function, and they significantly increase the fragmentation probability.

hep-ph↗

arXiv2014

Two-body and Three-body Contacts for Identical Bosons near Unitarity

In a recent experiment with ultracold trapped Rb-85 atoms, Makotyn et al. have 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 2-body and the 3-body contacts. We determine the 2- and 3-body contact densities for the unitary Bose gas with number density n to be approximately 20n^{4/3} and 2n^{5/3}, respectively. We also show that the observed atom loss rate is compatible with that from 3-atom inelastic collisions, which gives a contribution proportional to the 3-body contact, but the loss rate is not compatible with that from 2-atom inelastic collisions, which gives a contribution proportional to the 2-body contact. We point out that the contacts could be measured independently by using the virial theorem near and at unitarity.

cond-mat.quant-gas↗

arXiv2014

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 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.

cond-mat.quant-gas↗

arXiv2014

Direct detection of dark matter in universal bound states

We study the signatures for internal structure of dark matter in direct detection experiments in the context of asymmetric self-interacting dark matter. The self-interaction cross section of two dark matter particles at low energies is assumed to come close to saturating the S-wave unitarity bound, which requires the presence of a resonance near their scattering threshold. The universality of S-wave near-threshold resonances then implies that the low-energy scattering properties of a two-body bound state of dark matter particles are completely determined by its binding energy, irrespective of the underlying microphysics. The form factor for elastic scattering of the bound state from a nucleus and the possibility of breakup of the bound state produce new signatures in the nuclear recoil energy spectrum. If these features are observed in experiments, it will give a smoking-gun signature for the internal structure of dark matter.

hep-ph↗