Densities Of Heavy Quarks Research Articles

Heavy quarkonium suppression in a fireball

We perform a comprehensive study of the time evolution of heavy-quarkonium states in an expanding hot QCD medium by implementing effective field theory techniques in the framework of open quantum systems. The formalism incorporates quarkonium production and its subsequent evolution in the fireball including quarkonium dissociation and recombination. We consider a fireball with a local temperature that is much smaller than the inverse size of the quarkonium and much larger than its binding energy. The calculation is performed at an accuracy that is leading-order in the heavy-quark density expansion and next-to-leading order in the multipole expansion. Within this accuracy, for a smooth variation of the temperature and large times, the evolution equation can be written as a Lindblad equation. We solve the Lindblad equation numerically both for a weakly-coupled quark-gluon plasma and a strongly-coupled medium. As an application, we compute the nuclear modification factor for the $\Upsilon(1S)$ and $\Upsilon(2S)$ states. We also consider the case of static quarks, which can be solved analytically. Our study fulfils three essential conditions: it conserves the total number of heavy quarks, it accounts for the non-Abelian nature of QCD and it avoids classical approximations.

Quarkonium suppression in heavy-ion collisions: An open quantum system approach

We address the evolution of heavy-quarkonium states in an expanding quark-gluon plasma by implementing effective field theory techniques in the framework of open quantum systems. In this setting we compute the nuclear modification factors for quarkonia that are $S$-wave Coulombic bound states in a strongly-coupled quark-gluon plasma. The calculation is performed at an accuracy that is leading-order in the heavy-quark density expansion and next-to-leading order in the multipole expansion. The quarkonium density-matrix evolution equations can be written in the Lindblad form, and, hence, they account for both dissociation and recombination. Thermal mass shifts, thermal widths and the Lindblad equation itself depend on only two non-perturbative parameters: the heavy-quark momentum diffusion coefficient and its dispersive counterpart. Finally, by numerically solving the Lindblad equation, we provide results for the $\Upsilon(1S)$ and $\Upsilon(2S)$ suppression.

Controlling the sign problem in finite-density quantum field theory

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the “telegraphic” approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.

Quarkonium Suppression in a Strongly-Coupled Quark–Gluon Plasma

We compute the quarkonium nuclear modification factor in a strongly coupled quark–gluon plasma for quarkonia that are S-wave Coulombic bound states. We perform the analysis in a non-relativistic effective field theory framework that is accurate at leading-order in the heavy-quark density expansion and at next-to-leading order in the multipole expansion. We write and solve the Lindblad equation for the heavy quark–antiquark density. Thermal mass shift, width and the Lindblad equation depend on only two non-perturbative parameters: the heavy-quark momentum diffusion coefficient and its dispersive counterpart. Finally, we provide preliminary numerical results for the nuclear modification factors of the 1S and 2S bottomonium states.

Emergent Lifshitz scaling from N = 4 $$ \mathcal{N}=4 $$ SYM with supersymmetric heavy-quark density

We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z = 7. The equations also admit an asymptotically AdS5 × S5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in $$ \mathcal{N}=4 $$ SYM.

(Super)Yang-Mills at finite heavy-quark density

We study the gravitational duals of $d$-dimensional Yang-Mills theories with $d\leq 6$ in the presence of an ${\cal O} (N^2)$ density of heavy quarks, with $N$ the number of colors. For concreteness we focus on maximally supersymmetric Yang-Mills, but our results apply to a larger class of theories with or without supersymmetry. The gravitational solutions describe renormalization group flows towards infrared scaling geometries characterized by fixed dynamical and hyperscaling-violating exponents. The special case $d=5$ yields an $AdS_3 \times \mathbb{R}^4 \times S^4$ geometry upon uplifting to M-theory. We discuss the multitude of physical scales that separate different dynamical regimes along the flows, as well as the validity of the supergravity description. We also present exact black brane solutions that encode the low-temperature thermodynamics.

How to measure the charm density in the proton

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio R(x, Q 2) = F L /F T and/or the azimuthal cos(2φ) asymmetry in DIS. Our approach is based on the following observations. First, the ratio R(x, Q 2) = F L /F T and azimuthal cos(2φ) asymmetry in heavy-quark leptoproduction are stable, both parametrically and perturbatively, within pQCD. Second, both these quantities are sensitive to resummation of the mass logarithms of the type αsln(Q 2/m 2). We conclude that the heavy-quark densities in the nucleon can, in principle, be determined from high-Q 2 data on the Callan-Gross ratio and/or the azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.

Measurements of vector bosons plus jets production with the ATLAS detector at the LHC

The production of jets in association with a W or Z boson in proton-proton collisions at √s = 7 TeV is measured with the ATLAS detector at the LHC. The cross sections, differential in several kinematic variables, have been measured up to high jet multiplicities and are compared to new higher-order QCD calculations. Measurements of vector bosons in association with heavy flavor, such as W+c and W+b production, have unique sensitivity to the heavy quark density of the proton. Differential cross sections are presented and compared to QCD predictions at NLO.

Heavy quark density in $ \mathcal{N} $ = 4 SYM: from hedgehog to Lifshitz spacetimes

We study the effect of an O(N 2) density of heavy quarks in strongly coupled $ \mathcal{N} $ = 4 SUSY Yang-Mills theory in the large N limit. This is achieved in the type IIB supergravity dual by introducing a uniformly smeared density of macroscopic string sources stretching to the boundary of AdS 5 × S 5. The backreacted system exhibits a flow from an AdS 5 “hedgehog” geometry to a scaling Lifshitz-like solution Lif5 × S 5 with dynamical critical exponent z = 7, wherein the scaling symmetry is broken by a logarithmic running dilaton. We find an exact black brane solution within the scaling regime which describes the low temperature thermodynamics of the system.

Azimuthal asymmetry and ratio R = F L /F T as probes of the charm content of the proton

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and/or azimuthal $\cos(2\varphi)$ asymmetry in deep inelastic lepton-nucleon scattering. Our approach is based on the perturbative stability of the QCD predictions for these two quantities. We resume the mass logarithms of the type $\alpha_{s}\ln\left( Q^{2}/m^{2}\right)$ and conclude that heavy-quark densities in the nucleon can, in principle, be determined from data on the Callan-Gross ratio and/or azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.