arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 19 recordsLinked to original sources

arXiv2026

$\boldsymbol{\chi_{c1}}(3872)$ and its Partners in the Diabatic Born-Oppenheimer Approximation for QCD

In the Born-Oppenheimer approximation for QCD, the exotic hidden-charm tetraquark meson $\chi_{c1}(3872)$ is a near-threshold bound state in Born-Oppenheimer potentials associated with an isospin-0 adjoint meson. The $\chi_{c1}(3872)$ is the $1^{++}$ member of a heavy-quark spin-symmetry multiplet whose other members have $J^{PC}$ quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$. We introduce a simple model for the Born-Oppenheimer potentials that interpolates between the adjoint-meson potential at short distances and the triplet-meson-pair potential at large distances. We take into account the spin splittings of charm mesons nonperturbatively for the first time by solving the diabatic Schr\"odinger equation. We also take into account the spin splittings of the adjoint meson as well as a narrow avoided crossing with the quarkonium potential. We tune the energy of $\chi_{c1}(3872)$ to the $D^* \bar{D}$ threshold and then calculate the spin splittings of the other members of the multiplet and their decay widths into charm-meson pairs. We also calculate the energies and decay widths of the corresponding multiplet of hidden-bottom tetraquarks. These calculations provide a template for the quantitative analysis of all hidden-heavy hadrons using the Born-Oppenheimer approximation for QCD.

hep-ph↗

arXiv2025

Hidden-Heavy Pentaquarks and Where to Find Them

We provide a simple explanation for the observed hidden-charm pentaquarks as bound states in Born-Oppenheimer potentials. We identify $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4440)^+$, and $P_{c\bar{c}}(4457)^+$ as heavy-quark spin states in a quartet of $c \bar{c}$ pentaquarks with $J^P$ quantum numbers $\frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$. The quantum numbers of $P_{c\bar{c}}(4457)^+$ differ from most previous predictions. We also predict a fourth $c\bar{c}$ pentaquark with quantum numbers $\frac{3}{2}^-$ near the $\Sigma_c^\ast\bar{D}$ threshold. We identify $P_{c\bar{c}s}(4338)^0$ and $P_{c\bar{c}s}(4459)^0$ as heavy-quark spin states in a triplet of $c \bar{c}s$ pentaquarks with quantum numbers $\frac{1}{2}^-$ and either $\frac{1}{2}^-$ or $\frac{3}{2}^-$. We also predict a third $c\bar{c}s$ pentaquark with quantum numbers either $\frac{3}{2}^-$ or $\frac{1}{2}^-$ near the $\Xi_c\bar{D}^\ast$ threshold. We explain why the observed hidden-charm pentaquarks have narrow widths.

hep-ph↗

arXiv2025

Explaining Snowball-in-hell Phenomena in Heavy-ion Collisions Using a Novel Thermodynamic Variable

A loosely bound hadronic molecule produced by a relativistic heavy-ion collision has been described as a ``snowball in hell'' since it emerges from a hadron resonance gas whose temperature is orders of magnitude larger than the binding energy of the molecule. This remarkable phenomenon can be explained in terms of a novel thermodynamic variable called the ``contact'' that is conjugate to the binding momentum of the molecule. The production rate of the molecule can be expressed in terms of the contact density at the kinetic freezeout of the hadron resonance gas. It approaches a nonzero limit as the binding energy goes to 0.

hep-ph↗

arXiv2025

Exotic Hidden-heavy Hadrons and Where to Find Them

The Born-Oppenheimer potentials for QCD with light quarks include adjoint-hadron potentials that are repulsive at short distances and heavy-hadron-pair potentials that approach thresholds at large distances. The adjoint-hadron potentials must connect smoothly to the heavy-hadron-pair potentials at intermediate distances. We identify exotic hidden-heavy hadrons as bound states and resonances in adjoint-hadron potentials that cross below a heavy-hadron-pair threshold before approaching it. This explains why many exotic hidden-charm and hidden-bottom hadrons have energies near heavy-hadron-pair thresholds. The remarkable properties of some exotic hidden-heavy mesons can be explained by fine tunings of adjoint-meson energies in QCD.

hep-ph↗

arXiv2024

Born-Oppenheimer Potentials for $SU(3)$ Gauge Theory

We develop parameterizations of 8 of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation $r$ of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure $SU(3)$ lattice gauge theory. The parameterizations have the correct limiting behavior at small $r$, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large $r$, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-$r$ region between two potentials with the same Born-Oppenheimer quantum numbers.

hep-ph↗

arXiv2023

Thermal Energy of a Charm-meson Molecule in a Pion Gas

The thermal corrections to the propagator of a loosely bound charm-meson molecule in a pion gas are calculated to next-to-leading order in the heavy-meson expansion using a zero-range effective field theory. Ultraviolet divergences in the charm-meson-pair self energy are canceled by corrections to the charm-meson-pair contact vertex. Terms that are singular at the charm-meson-pair threshold can be absorbed into thermal corrections to the rest energies and kinetic masses of the charm-meson constituents. The remaining terms reduce to a thermal correction to the binding momentum that is proportional to the pion number density and suppressed by the pion/charm-meson mass ratio. The correction gives a tiny decrease in the binding energy of the charm-meson molecule relative to the charm-meson-pair threshold in the pion gas and a change in its thermal width that is small compared to the thermal widths of the charm-meson constituents. These results are encouraging for the prospects of observing $X(3872)$ and $T_{cc}^+(3875)$ in the expanding hadron gas produced by heavy-ion collisions.

hep-ph↗

arXiv2023

Charm-Meson $t$-channel Singularities in an Expanding Hadron Gas

We study the time evolution of the numbers of charm mesons after the kinetic freezeout of the expanding hadron gas produced by the hadronization of the quark-gluon plasma from a central heavy-ion collision. The $πD$ reaction rates have contributions from a $D^\ast$ resonance in the $s$ channel. The $πD^\ast$ reaction rates are enhanced by $t$-channel singularities from an intermediate $D$. The contributions to reaction rates from $D^\ast$ resonances and $D$-meson $t$-channel singularities are sensitive to thermal mass shifts and thermal widths. In the expanding hadron gas, the $t$-channel singularities are regularized by the thermal $D$ widths. After kinetic freezeout, the thermal $D$ widths are dominated by coherent pion forward scattering. The contributions to $πD^\ast$ reaction rates from $t$-channel singularities are inversely proportional to the pion number density, which decreases to 0 as the hadron gas expands. The $t$-channel singularities produce small but significant changes in charm-meson ratios from those predicted using the known $D^\ast$-decay branching fractions.

hep-ph↗

arXiv2023

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance.

hep-ph↗

arXiv2023

Point Production of a Nonrelativistic Unparticle Recoiling Against a Particle

A nonrelativistic unparticle can be defined as an excitation created by an operator with a definite scaling dimension in a nonrelativistic field theory with an approximate conformal symmetry. The point production rate of an unparticle has power-law dependence on its total energy with an exponent determined by its scaling dimension. We use the exact result for the 3-point function of primary operators in a nonrelativistic conformal field theory to derive the contribution to the point production rate of the unparticle from its decay into another unparticle recoiling against a particle. In the case where the conformal symmetry is broken by a large positive scattering length, we deduce the exponent of the energy in the point production rate of the loosely bound two-particle state recoiling against a particle with large relative momentum.

hep-th↗

arXiv2022

Evolution of charm-meson ratios in an expanding hadron gas

We study the time evolution of the numbers of charm mesons after the kinetic freeze-out of the hadron gas produced by a central heavy-ion collision. The $πD^\ast \to πD^\ast$ reaction rates have $t$-channel singularities that give contributions inversely proportional to the thermal width of the $D$. The ratio of the $D^0$ and $D^+$ production rates can differ significantly from those predicted using the measured $D^\ast$ branching fractions.

hep-ph↗

arXiv2022

Triangle Singularity in the Production of $T_{cc}^+$(3875) and a Soft Pion

The double-charm tetraquark meson $T_{cc}^+(3875)$ can be produced in high-energy proton-proton collisions by the creation of the charm mesons $D^{*+} D^0$ at short distances followed by their binding into $T_{cc}^+$. The $T_{cc}^+$ can also be produced by the creation of $D^{*+} D^{*+}$ at short distances followed by their rescattering into $T_{cc}^+ π^+$. A charm-meson triangle singularity produces a narrow peak in the $T_{cc}^+ π^+$ invariant mass distribution 6.1 MeV above the threshold with a width of about 1 MeV. Well beyond the peak, the differential cross section decreases with the invariant kinetic energy $E$ of $T_{cc}^+ π^+$ as $E^{-1/2}$. The fraction of $T_{cc}^+$ that are accompanied by $π^+$ with $E< m_π$ is estimated to be roughly 3%. The fraction of $T_{cc}^+$ events with $T_{cc}^+ π^+$ in the narrow peak from the triangle singularity could be comparable.

hep-ph↗

arXiv2022

Interpretation of neutral charm mesons near threshold as unparticles

The existence of the $X(3872)$ resonance extremely close to the $D^{*0} \bar{D}^0$ 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 $K^\pm$ in inclusive decays of $B^\pm$ 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 $X D^{*0}$ in inclusive prompt production at the Large Hadron Collider.

hep-ph↗

arXiv2021

Masses of Doubly Heavy Tetraquarks with Error Bars

In the heavy-quark limit, the two heavy quarks in a doubly heavy baryon or a doubly heavy tetraquark are bound by their color-Coulomb potential into a compact diquark. The doubly heavy hadrons are related by the approximate heavy-quark--diquark symmetry of QCD to the heavy hadrons obtained by replacing the heavy diquark by a heavy antiquark. Effective field theories can be used to expand the masses of singly heavy hadrons and doubly heavy hadrons in inverse powers of the heavy quark masses. The coefficients in the expansions for doubly heavy tetraquarks can be determined from those for heavy mesons, heavy baryons, and doubly heavy baryons using heavy-quark--diquark symmetry. We predict the masses of the ground-state doubly heavy tetraquarks with error bars using as inputs the masses of heavy mesons and heavy baryons measured in experiments and the masses of doubly heavy baryons calculated using lattice QCD. The only doubly heavy tetraquarks predicted to be stable with respect to strong decays are $bb$ tetraquarks with light flavor $\bar u \bar d$, $\bar s \bar u$ and $\bar s \bar d$.

hep-ph↗

arXiv2020

Production of $X(3872)$ at High Multiplicity

The dependence of the production of the $X(3872)$ meson on the hadron multiplicity in $pp$ collisions has been used as evidence against $X$ being a charm-meson molecule. The argument is based in part on the incorrect assumption that the cross section for the breakup of $X$ by scattering with comovers can be approximated by a geometric cross section inversely proportional to the binding energy of $X$. The breakup cross section should instead be approximated by the probability-weighted sum of the cross sections for the scattering of comoving pions from the charm-meson constituents of $X$, which is insensitive to the binding energy. A simple modification of the comover interaction model gives excellent fits to the data from the LHCb collaboration on the multiplicity dependence of the production of $X$ and $ψ(2S)$ using parameters compatible with $X$ being a loosely bound charm-meson molecule.

hep-ph↗

arXiv2020

Galilean-Invariant XEFT at Next-to-Leading Order

XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the $X(3872)$ resonance. To simplify calculations beyond leading order, we introduce a new formulation of XEFT with a dynamical field for a pair of charm mesons in the resonant channel. We simplify the renormalization of XEFT by introducing a new renormalization scheme that involves the subtraction of amplitudes at the complex $D^{*0} \bar D^0$ threshold. The new formulation and the new renormalization scheme are illustrated by calculating the complex pole energy of $X$ and the $D^{*0} \bar D^0$ scattering amplitude to next-to-leading order using Galilean-invariant XEFT.

hep-ph↗

arXiv2020

Charm-meson Triangle Singularity in ${e^+e^-}$ Annihilation into ${ D^{*0} \bar{D}^0 + γ}$

We calculate the cross section for $e^+ e^-$ annihilation into $D^{*0} \bar D^0 +γ$ at center-of-mass energies near the $D^{*0} \bar D^{*0}$ threshold under the assumption that $X(3872)$ is a weakly bound charm meson molecule. The Dalitz plot has a $\bar D^{*0}$ resonance band in the squared invariant mass $t$ of $\bar D^0 γ$. In the limit as the decay width of the $D^{*0}$ goes to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$ of $D^{*0} \bar D^0$ from a charm-meson triangle singularity. At the physical value of the $D^{*0}$ width, the narrow band reduces to a shoulder. Thus the triangle singularity cannot be observed directly as a peak in a differential cross section as a function of $u$. It may however be observed indirectly as a local minimum in the $t$ distribution for events with $u$ below the triangle singularity. The minimum is produced by the Schmid cancellation between triangle loop diagrams and a tree diagram. The observation of this minimum would support the identification of $X(3872)$ as a weakly bound charm meson molecule.

hep-ph↗

arXiv2019

Production of $X(3872)$ and a Photon in $e^+e^-$ Annihilation

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced in $e^+ e^-$ annihilation by the creation of $D^{*0} \bar D^{*0}$ from a virtual photon followed by the rescattering of the P-wave charm-meson pair into the $X$ and a photon. A triangle singularity produces a narrow peak in the cross section for $e^+ e^- \to X γ$ 2.2 MeV above the $D^{*0} \bar{D}^{*0}$ threshold. We predict the normalized cross section in the region of the peak. We show that the absorptive contribution to the cross section for $e^+ e^- \to D^{*0} \bar D^{*0} \to X γ$, which was calculated previously by Dubynskiy and Voloshin, does not give a good approximation to the peak from the triangle singularity.

hep-ph↗

arXiv2019

Production of $X(3872)$ Accompanied by a Pion in $B$ Meson Decay

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced by the creation of $D^{*0} \bar{D}^0$ or $D^{0} \bar{D}^{*0}$ at short distances followed by the formation of the bound state from the charm-meson pairs. It can also be produced by the creation of $D^{*} \bar{D}^*$ at short distances followed by the rescattering of the charm mesons into $X π$. We use results of a previous isospin analysis of $B$ meson decays into $K D^{(*)} \bar D^{(*)}$ to estimate the short-distance amplitudes for creating $D^* \bar D^*$. We use an effective field theory for charm mesons and pions called XEFT to calculate the amplitudes for rescattering of $D^{*} \bar{D}^*$ into $X π$ with small relative momentum. The $Xπ$ invariant mass distribution is predicted to have a narrow peak near the $D^{*} \bar{D}^*$ threshold from a charm-meson triangle singularity. We estimate the branching fractions into the peak from the triangle singularity for the decays $B^0 \to K^+ X π^-$ and $B^+ \to K^0 X π^+$.

hep-ph↗