M. J. Betancourt

Cruising the simplex: Hamiltonian Monte Carlo and the Dirichlet distribution

Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo. I introduce a series of transformations that reshape the canonical Dirichlet distribution into a form more amenable to efficient MCMC algorithms and demonstrate its utility with a few examples.

Elliptic flow of identified hadrons in Au+Au collisions at √sNN=7.7–62.4 GeV

Measurements of the elliptic flow, upsilon(2), of identified hadrons (pi(+/-), K-+/-, K-s(0), p, (p) over bar, phi, Lambda, (Lambda) over bar, Xi(-), (Xi) over bar (+), Omega(-), (Omega) over bar (+)) in Au + Au collisions at root s(NN) = 7.7, 11.5, 19.6, 27, 39, and 62.4 GeV are presented. The measurements were done at midrapidity using the time-projection chamber and the time-of-flight detectors of the Solenoidal Tracker at RHIC experiment during the beam-energy scan program at Relativistic Heavy Ion Collider. A significant difference in the upsilon(2) values for particles and the corresponding antiparticles was observed at all transverse momenta for the first time. The difference increases with decreasing center-of-mass energy, root s(NN) (or increasing baryon chemical potential, mu(B)), and is larger for the baryons as compared to the mesons. This implies that particles and antiparticles are no longer consistent with the universal number-of-constituent quark (NCQ) scaling of upsilon(2) that was observed at root s(NN) = 200 GeV. However, for the selected group of particles (p(+), K+, K-s(0), p, Lambda, Xi(-), Omega(-)) NCQ scaling at (m(T) - m(0))/n(q) > 0.4 GeV/c(2) is not violated within +/- 10%. The upsilon(2) values for f mesons at 7.7 and 11.5 GeV are approximately two standard deviations from the trend defined by the other hadrons at the highest measured p(T) values.

Jet-Hadron Correlations in sqrt{s_{NN}} = 200 GeV Au+Au and p+p Collisions

Azimuthal angular correlations of charged hadrons with respect to the axis of a reconstructed (trigger) jet in Au+Au and p+p collisions at √[s(NN)]=200  GeV in STAR are presented. The trigger jet population in Au+Au collisions is biased toward jets that have not interacted with the medium, allowing easier matching of jet energies between Au+Au and p+p collisions while enhancing medium effects on the recoil jet. The associated hadron yield of the recoil jet is significantly suppressed at high transverse momentum (pTassoc) and enhanced at low pTassoc in 0%-20% central Au+Au collisions compared to p+p collisions, which is indicative of medium-induced parton energy loss in ultrarelativistic heavy-ion collisions.