Publications

Holographic QCD

Chiral transition and meson melting within improved holographic soft wall models

Heat nuclear matter far enough and the particles inside it stop holding together at all. This paper extends the improved holographic soft-wall models to finite temperature by introducing an asymptotically anti-de Sitter black brane. The chiral transition comes out second order in the chiral limit and a crossover at physical quark masses, as expected in two-flavor QCD, and the scalar and vector mesons melt between 90 and 110 MeV, below the chiral transition near 129 MeV. We also predict the hydrodynamic diffusion constant for a flavor current in the deconfined plasma.

Published in Physical Review D, 2025. With Alfonso Ballon-Bayona, Luis A. H. Mamani, and Diego M. Rodrigues.

Chiral phase transition in soft-wall AdS/QCD with scalar-dilaton coupling

The boundary between ordinary nuclear matter and quark-gluon plasma is expected to have a critical point, and holographic models have had a hard time producing one. Coupling the scalar chiral field directly to the dilaton gives the chiral field an effective mass that runs with energy scale. We find that this coupling must be at least 6.0 for spontaneous chiral symmetry breaking to survive in the limit of zero quark mass, and that at that value a critical point appears only when the quark mass is greater than 12.8 MeV.

Published in Physical Review D, 2024. With undergraduate co-authors Robert Meadows and Glenn Brock.

Dynamical AdS/Yang-Mills Model

Glueballs are particles made of pure nuclear force, with no quarks in them at all. Using the superpotential method to build a five-dimensional model that mimics Yang-Mills theory, the scalar glueball spectrum at first contains a tachyon, signaling an instability. Stabilizing the theory with a bulk cosmological constant and a pair of 3-branes, as in the Randall-Sundrum model, gives glueball masses that agree well with lattice gauge theory using very few parameters.

Published in Physical Review D, 2018. With undergraduate co-author Aditya Dhumuntarao and Joseph Kapusta.

Chiral phase transition at finite chemical potential in 2+1-flavor soft-wall AdS/QCD

Whether nuclear matter melts gradually or abruptly depends on how heavy the quarks are. Adding the strange quark and a t’Hooft determinant term to the model reproduces the Columbia plot at zero chemical potential, and extending it to finite quark chemical potential shows that the line dividing first-order transitions from rapid crossovers does not move as the chemical potential grows. This model therefore admits no critical point in the temperature-chemical potential plane, suggesting that a different setup is needed.

Published in Physical Review C, 2018. With undergraduate co-author Theodore Jacobson.

Chiral Phase Transition and Meson Melting from AdS/QCD

As nuclear matter is heated or squeezed, mesons stop existing as bound particles. A quartic term in the scalar potential supplies independent sources of explicit and spontaneous chiral symmetry breaking, giving a second-order chiral transition at 155 MeV in the chiral limit and a crossover at 151 MeV for physical quark mass, both consistent with lattice results. All of the bound states melt at a lower temperature than the chiral transition, so the mass splitting between the vector and axial-vector mesons stays constant right up until the mesons are gone.

With undergraduate co-author Theodore Jacobson.

Three-field potential for soft-wall AdS/QCD

In this paper, we construct a potential for the background fields for the soft-wall model, rather than the previous ad hoc parametrizations. This gives a more consistent foundation for the soft-wall AdS/QCD model and allow for later incorporation of finite temperature effects.

This previous paper showed how to generate potentials for certain simple forms of the background fields.The results diverge greatly from experiment when this technique is applied to the mesons. The mass differences for the excited vector and axial mesons is far too large. We show that this “axial mass gap problem” is unavoidable for potentials that include only two background fields.

One way to resolve this problem is to add a third background field to the model. We construct a potential that has the necessary behavior in both the the large and small limits of the extra dimension, and allows for the tuning of the axial mass splitting.

We numerically calculate the background fields that solve this potential. The meson spectra for the vector, axial-vector, and pseudoscalar mesons calculated from these background fields match well with experimental data.

The scalar mesons require further analysis because their equations of motion mix with the potential directly.

Pseudoscalar Mass Spectrum in a Soft-Wall Model of AdS/QCD

This paper builds on the success of the original modified soft-wall AdS/QCD model by extending it to include the pions. We derived the differential equations that determine the energy levels for the pions, consisting of coupled second-order differential equations.

After analytically solving the system in the high-mass limit, we developed a numerical routine that was used calculate the energy levels. We confirmed a long-known result that relates the pion mass to the mass of the quark, an important check on the validity of the model.

Physics Education and Classical Mechanics

N-body linear force law allowing analytic solutions

The N-body problem is famously unsolvable, but changing the force law slightly makes it solvable exactly, for any number of particles and any masses. If every pair of particles pulls on the other with a force proportional to the product of their masses and to their separation, each particle moves as though it were tied by a single spring to the center of mass of the whole system, with one frequency common to all of them. The analytic trajectories make it cheap to simulate tens of thousands of particles, which we use to calculate pressure and temperature for such a gas in an expanding spherical container.

Published in American Journal of Physics, 2025, and selected for AAPT Journal Highlights. With Joseph West.

Gravity effects in mass-spring-damper models of inelastic collisions

A bouncing ball is usually described by a single number, the coefficient of restitution, treated as a fixed property of the ball. Applying a linear dashpot model to a ball bouncing on a rigid surface, with gravity included, shows that this number is not fixed at all: it depends on impact velocity, most strongly at low speeds and high damping. The paper compares different criteria for deciding when contact ends and proposes a hybrid model that reproduces measurements of a cart bouncing against a spring.

Published in European Journal of Physics, 2023.

Numerical simulation of non-central collisions of spherical magnets

Two magnetic spheres launched past one another snap together and spin rapidly, which makes a memorable classroom demonstration of angular momentum conservation. We model the collision with the exact dipole-dipole force plus a damped-spring contact force, and solve the Newtonian equations of motion. The non-central terms in the dipole force turn out to matter: keeping them reproduces the measured rotation rate of the final barbell shape, while the usual power-law approximation predicts the wrong answer.

Published in European Journal of Physics, 2022. With undergraduate co-author Jacob Shaw.

Delayed rebounds in the two-ball bounce problem

Drop a tennis ball on top of a basketball and it flies off surprisingly high; swap in a ping-pong ball and the big bounce arrives second instead of first. Treating both impacts with a linear dashpot force, rather than as independent instantaneous collisions, and writing the equations of motion in dimensionless form, reduces eight parameters and two initial conditions down to two parameters and one. The delayed rebound shows up in about 12% of the parameter space studied, almost always in cases where the first bounce falls short of what the textbook independent contact model predicts.

Published in European Journal of Physics, 2022.