arXiv subjects

W. A. Horowitz

Publications and source records attributed to W. A. Horowitz.

At least 37 records · Page 2Linked to original sources

arXiv2023

Inconsistencies in, and short pathlength correction to, $R_{AA}(p_T)$ in $\mathrm{A}+\mathrm{A}$ and $\mathrm{p} + \mathrm{A}$ collisions

We present the first leading hadron suppression predictions in $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{p}+\mathrm{Pb}$ collisions from a convolved radiative and collisional energy loss model in which partons propagate through a realistic background and in which the inelastic energy loss receives a short pathlength correction. We find that the short pathlength correction is small for $D$ and $B$ meson $R_{AA}(p_T)$ in both $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{p}+\mathrm{Pb}$ collisions. However the short pathlength correction leads to a surprisingly large reduction in suppression for $π$ mesons in $\mathrm{p}+\mathrm{Pb}$ and even $\mathrm{Pb}+\mathrm{Pb}$ collisions. We systematically check the consistency of the assumptions used in the radiative energy loss derivation - such as collinearity, softness, and large formation time - with the final numerical model. While collinearity and softness are self-consistently satisfied in the final numerics, we find that the large formation time approximation breaks down at modest to high momenta $p_T \gtrsim 30$ GeV. We find that both the size of the small pathlength correction to $R_{AA}(p_T)$ and the $p_T$ at which the large formation time assumption breaks down are acutely sensitive to the chosen distribution of scattering centers in the plasma.

hep-ph↗

arXiv2023

Assumption Breakdown in Radiative Energy Loss

We show that an integral assumption in DGLV radiative energy loss - the large formation time assumption - is violated at high-$p_T$ for phenomenologically relevant parameters. We further investigate the phenomenological impact of placing a new kinematic bound on the radiated gluon transverse momentum, which ensures that there are no contributions to the energy loss from regions of parameter space that violate the large formation time assumption. We find that this places a large sensitivity on the exact kinematic cutoff used, similar to the known collinear cutoff sensitivity, indicating the theoretical need for a rederivation of DGLV radiative energy with the large formation time assumption relaxed in order to make rigorous predictions. We additionally find that this large formation time cutoff dramatically reduces the size of a short pathlength correction to the DGLV radiative energy loss, which is of phenomenological interest in predicting suppression in small $p +A$ systems. We compute the phenomenological predictions utilizing this large formation time cutoff in both $p+A$ and $A+A$ collisions at the LHC, in a convolved radiative and elastic energy loss model.

hep-ph↗

arXiv2023

Finite System Size Correction to the Effective Coupling in $ϕ^4$ Scattering

We compute and explore numerically the finite system size correction to NLO $2\to2$ scattering in massive scalar $ϕ^4$ theory. The derivation uses "denominator regularization" (instead of the usual dimensional regularization) on a spacetime with spatial directions compactified to a torus, with characteristic lengths not necessarily of equal size. We determine a useful analytic continuation of the generalized Epstein zeta function to isolate the usual UV divergence. Self-consistently, the renormalized finite system size correction reduces to zero as the system size goes to infinity and, further, satisfies the optical theorem. One of our checks of unitarity leads to a generalization of a number theoretic result from Hardy and Ramanujan. Precise numerical exploration of the finite system size correction to the amplitude and coupling when two spatial dimensions are finite requires the exploitation of the analytic structure of the finite system size result via a dispersion relation. We find that the finite system size scattering amplitude exhibits "geometric" bound states. Even away from these bound states, the finite system size correction to the effective coupling can be large.

hep-th↗

arXiv2023

Energy Loss in Small Collision Systems

We present leading hadron suppression predictions in $Pb+Pb$ and $p+Pb$ collisions from a convolved radiative and collisional energy loss model in which partons propagate through a realistic background, and in which the radiative energy loss receives a short pathlength correction. We find that the short pathlength correction is small for $D$ meson $R_{AA}(p_T)$ in both $Pb+Pb$ and $p+Pb$ collisions. However the short pathlength correction leads to a surprisingly large reduction in suppression for $π$ mesons in $p+Pb$ and even $Pb+Pb$ collisions, providing a qualitative explanation for the rapid rise in $π$ meson $R_{AA}(p_T)$ at the LHC. We find that the size of the short pathlength correction to $R_{AA}(p_T)$ is acutely sensitive to the chosen distribution of scattering centers in the plasma. Furthermore we find that conventional elastic energy loss models, which apply the central limit theorem to the number of scatterings, dramatically overpredict suppression in $\mathrm{p}+\mathrm{A}$ collisions, calling for short pathlength corrections to elastic energy loss.

nucl-th↗

arXiv2022

Jet Broadening in the Opacity and Twist Expansions

We compute the in-medium jet broadening $\langle p_\perp^2\rangle$ to leading order in energy in the opacity expansion. At leading order in $α_s$ the elastic energy loss gives a jet broadening that grows with $\ln E$. The next-to-leading order in $α_s$ result is a jet narrowing, due to destructive LPM interference effects, that grows with $\ln^2 E$. We find that in the opacity expansion the jet broadening asymptotics are -- unlike for the mean energy loss -- extremely sensitive to the correct treatment of the finite kinematics of the problem; integrating over all emitted gluon transverse momenta leads to a prediction of jet broadening rather than narrowing. We compare the asymptotics from the opacity expansion to a recent twist-4 derivation of $\langle p_\perp^2\rangle$ and find a qualitative disagreement: the twist-4 derivation predicts a jet broadening rather than a narrowing. Comparison with current jet measurements cannot distinguish between the broadening or narrowing predictions. We comment on the origin of the difference between the opacity expansion and twist-4 results.

hep-ph↗

arXiv2022

NLO finite system size corrections to $2\to2$ scattering in $ϕ^4$ theory using newly derived sum of sinc functions

Previously an equation of state for the relativistic hydrodynamics encountered in heavy-ion collisions at the LHC and RHIC has been calculated using lattice gauge theory methods. This leads to a prediction of very low viscosity, due to the calculated trace anomaly. Finite system corrections to this trace anomaly could challenge this calculation, since the lattice calculation was done in an effectively infinite system. In order to verify this trace anomaly it is sensible to add phenomenologically relevant finite system corrections. We investigate massive $ϕ^4$ theory with periodic boundary conditions on $n$ of the 3 spatial dimensions. $2\to2$ NLO scattering is then computed. Using a newly derived formula for an arbitrary dimensional sum of sinc functions, we show that the NLO finite size corrections preserve unitarity.

hep-th↗

arXiv2022

Denominator Regularization in Quantum Field Theory

We propose a novel regularization scheme in quantum field theory, denominator regularization (den reg). As simple to apply as dimensional regularization, and similarly compatible with a minimal subtraction renormalization scheme, den reg manifestly 1) maintains Lorentz invariance, 2) maintains gauge invariance, 3) maintains supersymmetry, 4) correctly predicts the axial anomaly, and 5) yields Green functions that satisfy the Callan-Symanzik equation. Den reg also naturally enables regularization in asymmetric spacetimes, finite spacetimes, curved spacetimes, and in thermal field theory.

hep-th↗

arXiv2022

Finite System Size Correction to NLO Scattering in $ϕ^4$ Theory

We compute $2\rightarrow2$ scattering in massive $ϕ^4$ theory on $\mathbb R^{1,m}\times T^n$ to NLO. We perform the calculations using "denominator regularization" instead of the usual dimensional regularization, which allows for asymmetric configurations of the $T^n$. We give a transparent derivation of and equation for the analytic continuation of the generalized Epstein zeta function. We show that the Optical Theorem is satisfied and generalize a conjecture by Hardy on square counting functions. We comment on the implications.

hep-th↗

arXiv2022

The QCD Equation of State in Small Systems

We present first results on finite system size corrections to the equation of state, trace anomaly, and speed of sound for two model systems: 1) free, massless scalar theory and 2) quenched QCD with periodic boundary conditions (PBC). We further present work-in-progress results for quenched QCD with Dirichlet boundary conditions.

hep-ph↗

arXiv2021

Strongly Coupled Heavy and Light Quark Thermal Motion from AdS/CFT

We give a pedagogical presentation of heavy and light probe quarks in a thermal plasma using the AdS/CFT correspondence. Three cases are considered: external heavy and light quarks undergoing Brownian motion in the plasma, and an external heavy quark moving through the plasma with a constant velocity. For the first two cases we compute the mean-squared transverse displacement of the string's boundary endpoint. At early times the behaviour is ballistic, while the late time dynamics are diffusive. We extract the diffusion coefficient for both heavy and light quarks in an arbitrary number of dimensions and comment on the relevance for relativistic heavy ion phenomenology.

hep-th↗

arXiv2021

Geometrically confined thermal field theory: Finite size corrections and phase transitions

Motivated by the recent shocking results from RHIC and LHC that show quark-gluon plasma signatures in small systems, we study a simple model of a massless, noninteracting scalar field confined with Dirichlet boundary conditions. We use this system to investigate the finite size corrections to thermal field theoretically derived quantities compared to the usual Stefan-Boltzmann limit of an ideal gas not confined in any direction. Two equivalent expressions with different numerical convergence properties are found for the free energy in $D$ rectilinear spacetime dimensions with $c\le D-1$ spatial dimensions of finite extent. We find that the First Law of Thermodynamics generalizes such that the pressure depends on direction but that the Third Law is respected. For systems with finite dimension(s) but infinite volumes, such as a field constrained between two parallel plates or a rectangular tube, the relative fluctuations in energy are zero, and hence the canonical and microcanonical ensembles are equivalent. We present precise numerical results for the free energy, total internal energy, pressure, entropy, and heat capacity of our field between parallel plates, in a tube, and in finite volume boxes of various sizes in 4 spacetime dimensions. For temperatures and system sizes relevant for heavy ion phenomenology, we find large deviations from the Stefan-Boltzmann limit for these quantities, especially for the pressure. Further investigation of an isolated system of fields constrained between parallel plates reveals a divergent isoenergetic compressibility at a critical length $L_c\sim1/T$. We have thus discovered a new second order phase transition via a first principles calculation, a transition that is driven by the size of the system.

hep-th↗

arXiv2020

B-meson Nuclear Modification Factor and $\mathbf{v_2(p_T)}$ in a Strongly Coupled Plasma in $\mathbf{Pb+Pb}$ Collisions at $\mathbf{\sqrt{s_{NN}}=2.76}$ TeV and $\mathbf{\sqrt{s_{NN}}=5.5}$ TeV

We present predictions for the suppression of B-mesons using AdS/CFT techniques assuming a strongly coupled quark-gluon plasma at $\sqrt{s_{NN}}=2.76$ TeV for central collisions and $\sqrt{s_{NN}}=5.5$ TeV for various centrality classes. We provide estimates of the systematic theoretical uncertainties due to 1) the mapping of QCD parameters to those in $\mathcal N = 4$ SYM and 2) the exact form of the momentum dependence of the diffusion coefficient predicted by AdS/CFT. We show that coupling energy loss to flow increases $v_2$ substantially out to surprisingly large momenta, on the order of $\sim 25$ GeV/c, thus pointing to a possible resolution of the $R_{AA}$ and $v_2$ puzzle for light hadrons.

hep-ph↗

arXiv2019

Short path length corrections to Djordjevic-Gyulassy-Levai-Vitev energy loss

We compute the correction to the energy loss of a hard parton due to short separation distances between the creation of the particle and the in-medium scattering center that stimulates bremsstrahlung radiation, to first order in opacity. In deriving the result we make full use of the large formation time assumption, which results in a significant reduction of the number of diagrams contributing to the small separation distance correction. An asymptotic analysis of our small separation distance correction term finds that the correction dominates at large $\sim 100$ GeV parent parton energies; scales like $L$ with the size of the system for small $L$, but like $L^0$ at larger $L$; and breaks color triviality. An extensive numerical investigation of the correction term confirms the aforementioned analytic findings, reveals that the correction term does not go to zero for large $L$, finds that the correction is sensitive to the mass of the parent parton, and shows a crucial dependence of the energy loss on a proper treatment of the physics of separation distances on the order of the Debye screening length. However, an examination of the large formation time approximation shows that it is violated for much of the phase space of the emitted radiation, implying a need to investigate the sensitivity of jet quenching results from relaxing this approximation. Our result constitutes an important step toward understanding partonic energy loss in small colliding systems.

hep-ph↗

arXiv2019

Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory

We study the pressure anisotropy in anisotropic finite-size systems in SU(3) Yang-Mills theory at nonzero temperature. Lattice simulations are performed on lattices with anisotropic spatial volumes with periodic boundary conditions. The energy-momentum tensor defined through the gradient flow is used for the analysis of the stress tensor on the lattice. We find that a clear finite-size effect in the pressure anisotropy is observed only at a significantly shorter spatial extent compared with the free scalar theory, even when accounting for a rather large mass in the latter.

hep-lat↗

arXiv2018

From Heavy-Ion Collisions to Compact Stars: Equation of State and Relevance of the System Size

In this article, we start by presenting state-of-the-art methods allowing us to compute moments related to the globally conserved baryon number, by means of first principle resummed perturbative frameworks. We focus on such quantities for they convey important properties of the finite temperature and density equation of state, being particularly sensitive to changes in the degrees of freedom across the quark-hadron phase transition. We thus present various number susceptibilities along with the corresponding results as obtained by lattice quantum chromodynamics collaborations, and comment on their comparison. Next, omitting the importance of coupling corrections and considering a zero-density toy model for the sake of argument, we focus on corrections due to the small size of heavy-ion collision systems, by means of spatial compactifications. Briefly motivating the relevance of finite size effects in heavy-ion physics, in opposition to the compact star physics, we present a few preliminary thermodynamic results together with the speed of sound for certain finite size relativistic quantum systems at very high temperature.

hep-ph↗

arXiv2017

Two Gluon Emission from MHV: Two Particle Correlations and the Deviation from Poisson

We derive the momentum distribution for two soft and collinear gluons emitted from an off-shell quark, modeled by a $qγ\rightarrow qgg$ scattering process and computed using the maximal helicity violating (MHV) technique. We find the explicit non-Abelian corrections to the independent emission Poisson distribution in QED and demonstrate the efficiency of the MHV technique in perturbative QCD calculations. The gluonic two particle correlation function is highly suggestive of that measured in high-multiplicity $pp$ and $pA$ collisions, with a tight correlation in angle but broad correlation in rapidity. Further, the autocorrelation generated by the non-Abelian correlation can provide a significant non-hydrodynamical source of $v_2$ in these high multiplicity $pp$ and $pA$ collisions. Finally, these two gluon correlations can be used to calibrate Monte Carlo shower codes for a more accurate description of QCD processes in $pp$ collisions.

hep-ph↗

arXiv2017

Bottomonia Suppression in Heavy Ion Collisions from AdS/CFT

We compute for the first time the suppression of bottomonia in a strongly coupled QGP and compare the results to those from a weakly coupled QGP. Using imaginary time techniques we numerically determine the real and imaginary parts of the ground state binding energy of the bottomonia in one potential computed from AdS/CFT and another computed from pQCD. We then use these binding energies in a suppression model to determine the $Υ$(1S) nuclear modification factor in $\sqrt{s}_{NN}=2.76$ TeV Pb+Pb collisions. AdS/CFT significantly overpredicts the suppression compared to data, although the predictive power of our calculation is limited by its significant sensitivity to the exact details of the suppression model.

hep-ph↗

arXiv2017

AdS/CFT predictions for azimuthal and momentum correlations of $b\bar{b}$ pairs in heavy ion collisions

We use an energy loss model sensitive to thermal fluctuations to compute the azimuthal and momentum correlations of $b\bar{b}$ pairs traversing a strongly coupled plasma from Pb+Pb collisions at LHC ($\sqrt{s}=2.76\text{TeV}$). The azimuthal correlations are compared with those from perturbative QCD based simulations. When restricted to leading order production processes, we find that the strongly coupled correlations of high transverse momentum pairs ($>4\text{GeV}$) are broadened less efficiently than the corresponding weak coupling based correlations, while low transverse momentum pairs (1-4GeV) are broadened with similar efficiency, but with an order of magnitude more particles ending up in this momentum class. The strong coupling momentum correlations we compute account for initial correlations and reveal that the particle pairs suppressed from initially high momenta to the low momentum domain do not suffice to explain the stark difference to the weak coupling results in momentum correlations for 1-4GeV. From this, we conclude that $b\bar{b}$ pairs are more likely to stay correlated in momentum when propagating through a strongly coupled plasma than a weakly coupled one.

hep-ph↗