arXiv subjects

Matthew D. Sievert

Publications and source records attributed to Matthew D. Sievert.

At least 37 records · Page 2Linked to original sources

arXiv2019

Initial state fluctuations of QCD conserved charges in heavy-ion collisions

We initialize the Quantum Chromodynamic conserved charges of baryon number, strangeness, and electric charge arising from gluon splitting into quark-antiquark pairs for the initial conditions of relativistic heavy-ion collisions. A new Monte Carlo procedure that can sample from a generic energy density profile is presented, called Initial Conserved Charges in Nuclear Geometry (ICCING), based on quark and gluon multiplicities derived within the color glass condensate (CGC) effective theory. We find that while baryon number and electric charge have nearly identical geometries to the energy density profile, the initial strangeness distribution is considerable more eccentric and is produced primarily at the hot spots corresponding to temperatures of $T\gtrsim 400$ MeV for PbPb collisions at $\sqrt{s_{NN}}=5.02$ TeV.

nucl-th↗

arXiv2019

Ultracentral Collisions of Small and Deformed Systems at RHIC: ${U} {U}$, ${d} {Au}$, ${}^{9}{Be} {Au}$, ${}^{9}{Be} {}^{9}{Be}$, ${}^{3}{He} {}^{3}{He}$, and ${}^{3}{He} {Au}$ Collisions

In this paper, we study a range of collision systems involving deformed ions and compare the elliptic and triangular flow harmonics produced in a hydrodynamics scenario versus a color glass condensate (CGC) scenario. For the hydrodynamics scenario, we generate initial conditions using TRENTO and work within a linear response approximation to obtain the final flow harmonics. For the CGC scenario, we use the explicit calculation of two-gluon correlations taken in the high-$p_T$ ``(semi)dilute-(semi)dilute'' regime to express the flow harmonics in terms of the density profile of the collision. We consider ultracentral collisions of deformed ions as a testbed for these comparisons because the difference between tip-on-tip and side-on-side collisions modifies the multiplicity dependence in both scenarios, even at zero impact parameter. We find significant qualitative differences in the multiplicity dependence obtained in the initial conditions+hydrodynamics scenario and the CGC scenario, allowing these collisions of deformed ions to be used as a powerful discriminator between models. We also find that sub-nucleonic fluctuations have a systematic effect on the elliptic and triangular flow harmonics which are most discriminating in $0-1\%$ ultracentral symmetric collisions of small deformed ions and in $0-10\%$ $\mathrm{d} {}^{197}\mathrm{Au}$ collisions. The collision systems we consider are ${}^{238}\mathrm{U} {}^{238}\mathrm{U}$, $\mathrm{d} {}^{197}\mathrm{Au}$, ${}^{9}\mathrm{Be} {}^{197}\mathrm{Au}$, ${}^{9}\mathrm{Be} {}^{9}\mathrm{Be}$, ${}^{3}\mathrm{He} {}^{3}\mathrm{He}$, and ${}^{3}\mathrm{He} {}^{197}\mathrm{Au}$.

hep-ph↗

arXiv2019

A complete set of in-medium splitting functions to any order in opacity

In this Letter we report the first calculation of all ${\cal O}(α_s)$ medium-induced branching processes to any order in opacity. Our splitting functions results are presented as iterative solutions to matrix equations with initial conditions set by the leading order branchings in the vacuum. The flavor and quark mass dependence of the in-medium $q \rightarrow qg$, $g\rightarrow gg$, $q \rightarrow g q$, $g \rightarrow q\bar{q}$ processes is fully captured by the light-front wavefunction formalism and the color representation of the parent and daughter partons. We include the explicit solutions to second order in opacity as supplementary material and present numerical results in a realistic strongly-interacting medium produced in high center-of-mass energy heavy ion collisions at the Large Hadron Collider. Our numerical simulations show that the second order in opacity corrections can change the energy dependence of the in-medium shower intensity. We further find corrections to the longitudinal and angular distributions of the in-medium splitting kernels that may have important implications for jet substructure phenomenology.

hep-ph↗

arXiv2019

One-Loop Fluctuation Entropy of Charge Inversion in DNA

Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. This paper presents calculations of a lattice-gas model of charge inversion for the adsorption of charged dimers on DNA. Each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. The entropy and charge distributions of these three species are calculated including the lowest order fluctuation corrections to mean-field theory. We find that the inclusion of the fluctuation terms has a significant effect on the entropy, primarily in the regime where the dimers are repelled from the DNA molecule and compete with the chemical potential in solution.

cond-mat.soft↗

arXiv2019

Shrinking the Quark Gluon Plasma

In recent years the understanding on the limits of the smallest possible droplet of the Quark Gluon Plasma has been called into question. Experimental results from both the Large Hadron Collider and the Relativistic Heavy Ion Collider have provided hints that the Quark Gluon Plasma may be produced in systems as small as that formed in pPb or dAu collisions. Yet alternative explanations still exist from correlations arising from quarks and gluons in a color glass condensate picture. In order to resolve these two scenarios, a system size scan has been proposed at the Large Hadron Collider for collisions of ArAr and OO. Here we make predictions for a possible future run of ArAr and OO collisions at the Large Hadron Collider and study the system size dependence of a variety of flow observables. We find that linear response (from the initial conditions to the final flow harmonics) becomes more dominant in smaller systems whereas linear+cubic response can accurately predict multi-particle cumulants for a wide range of centralities in large systems.

nucl-th↗

arXiv2018

Quark branching in QCD matter to any order in opacity beyond the soft gluon emission limit

Cold nuclear matter effects in reactions with nuclei at a future electron-ion collider (EIC) lead to a modification of semi-inclusive hadron production, jet cross sections, and jet substructure when compared to the vacuum. At leading order in the strong coupling, a jet produced at an EIC is initiated as an energetic quark, and the process of this quark splitting into a quark-gluon system underlies experimental observables. The spectrum of gluons associated with the branching of this quark jet is heavily modified by multiple scattering in a medium, allowing jet cross sections and jet substructure to be used as a probe of the medium's properties. We present a formalism that allows us to compute the gluon spectrum of a quark jet to an arbitrary order in opacity, the average number of scatterings in the medium. This calculation goes beyond the simplifying limit in which the gluon radiation is soft and can be interpreted as energy loss of the quark, and it significantly extends previous work which computes the full gluon spectrum only to first order in opacity. The theoretical framework demonstrated here applies equally well to light parton and heavy quark branching, and is easily generalizable to all in-medium splitting processes.

hep-ph↗

arXiv2018

Valence Quark Transversity at Small $x$

In our previous work we established a formalism which allows one to determine the small-$x$ asymptotics of any transverse momentum-dependent parton distribution function (TMD PDF) of the proton at small values of strong coupling. In this paper we apply this formalism to the valence quark transversity TMD. We relate the valence quark transversity to the transversely polarized dipole scattering amplitude, written in terms of the fundamental transversely-polarized "Wilson line" operator, an expression for which we derive explicitly as well. We then write down the evolution equation for the transversely polarized dipole amplitude. Solving that equation we arrive at the following small-$x$ asymptotics of the valence quark transversity in the large-$N_c$ limit: \begin{align} h_{1T}^v (x, k_T^2) \sim h_{1T}^{\perp \, v} (x, k_T^2) \sim \left( \frac{1}{x} \right)^{-1 + 2 \, \sqrt{\frac{α_s \, N_c}{2 \, π}} } . \notag \end{align} This result is in agreement with one of the two possible small-$x$ asymptotics for the transverse structure function found previously by Kirschner, Mankiewicz, Schäfer, and Szymanowski.

hep-ph↗

arXiv2018

Small-$x$ Asymptotics of the Gluon Helicity Distribution

We determine the small-$x$ asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large $N_c$. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small $x$. In the process we obtain an interesting new result: in contrast to the unpolarized dipole gluon TMD case, the operator governing the small-$x$ behavior of the dipole gluon helicity TMD is different from the operator corresponding to the polarized dipole scattering amplitude (used in our previous work to determine the small-$x$ asymptotics of the quark helicity distribution). We then construct and solve novel small-$x$ large-$N_c$ evolution equations for the operator related to the dipole gluon helicity TMD. Our main result is the small-$x$ asymptotics for the gluon helicity distribution: $ΔG \sim \left( \tfrac{1}{x} \right)^{α_h^G}$ with $α_h^G = \tfrac{13}{4 \sqrt{3}} \, \sqrt{\tfrac{α_s \, N_c}{2 π}} \approx 1.88 \, \sqrt{\tfrac{α_s \, N_c}{2 π}}$. We note that the power $α_h^G$ is approximately 20$\%$ lower than the corresponding power $α_h^q$ for the small-$x$ asymptotics of the quark helicity distribution defined by $Δq \sim \left( \tfrac{1}{x} \right)^{α_h^q}$ with $α_h^q = \tfrac{4}{\sqrt{3}} \, \sqrt{\tfrac{α_s \, N_c}{2 π}} \approx 2.31 \, \sqrt{\tfrac{α_s \, N_c}{2 π}}$ found in our earlier work.

nucl-th↗

arXiv2018

Small-$x$ Helicity Evolution: an Operator Treatment

We rederive the small-$x$ evolution equations governing quark helicity distribution in a proton using solely an operator-based approach. In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic and operator-based methods. In this work, we re-derive the double-logarithmic small-$x$ evolution equations for quark helicity in terms of the "polarized Wilson lines", the operators consisting of light-cone Wilson lines with one or two non-eikonal local operator insertions which bring in helicity dependence. For the first time we give explicit and complete expressions for the quark and gluon polarized Wilson line operators, including insertions of both the gluon and quark sub-eikonal operators. We show that the double-logarithmic small-$x$ evolution of the "polarized dipole amplitude" operators, made out of regular light-cone Wilson lines along with the polarized ones constructed here, reproduces the equations derived in our earlier works. The method we present here can be used as a template for determining the small-$x$ asymptotics of any transverse momentum-dependent (TMD) quark (or gluon) parton distribution functions (PDFs), and is not limited to helicity.

hep-ph↗

arXiv2018

Multiparticle Production at Mid-Rapidity in the Color-Glass Condensate

In this paper, we compute a number of cross sections for the production of multiple particles at mid-rapidity in the semi-dilute / dense regime of the color-glass condensate (CGC) effective field theory. In particular, we present new results for the production of two quark-antiquark pairs (whether the same or different flavors) and for the production of one quark-antiquark pair and a gluon. We also demonstrate the existence of a simple mapping which transforms the cross section to produce a quark-antiquark pair into the corresponding cross section to produce a gluon, which we use to obtain various results and to cross-check them against the literature. We also discuss hadronization effects in the heavy flavor sector, writing explicit expressions for the production of various combinations of $D$ and $\bar D$ mesons, $J/ψ$ mesons, and light hadrons. The various multiparticle cross sections presented here contain a wealth of information and can be used to study heavy flavor production, charge-dependent correlations, and "collective" flow phenomena arising from initial-state dynamics.

hep-ph↗

arXiv2018

Toward Initial Conditions of Conserved Charges Part I: Spatial Correlations of Quarks and Antiquarks

In this paper, we study the spatial correlations among quarks and antiquarks produced at mid-rapidity by gluon pair production in the color glass condensate framework. This paper is the first part of a series in which we calculate a complete set of quark/quark, quark/antiquark, and antiquark/antiquark spatial correlation functions in heavy-light ion collisions, with the goal of incorporating their conserved charges into the initial conditions of hydrodynamics. The physical mechanisms captured in this calculation include geometric, entanglement, and interaction-mediated correlations. In this first paper, we construct the building blocks for the correlations arising from single- and double-pair production, studying in detail the single-pair case and the general features of the double-pair case. We find a rich correlation structure in transverse coordinate space, with different mechanisms dominating over different length scales, and we present explicit results for the quark-antiquark correlations in the single-pair production regime. We reserve a detailed discussion of the double-pair production regime for the next paper in this sequence.

hep-ph↗

arXiv2017

Small-$x$ Asymptotics of the Quark Helicity Distribution: Analytic Results

In this Letter, we analytically solve the evolution equations for the small-$x$ asymptotic behavior of the (flavor singlet) quark helicity distribution in the large-$N_c$ limit. These evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-$x$ asymptotics, which we exploit here to obtain an analytic solution. We find that the small-$x$ power-law tail of the quark helicity distribution scales as $Δq^S (x, Q^2) \sim \left(\tfrac{1}{x} \right)^{α_h}$ with $α_h = \tfrac{4}{\sqrt{3}} \sqrt{\tfrac{α_s N_c}{2π}}$, in excellent agreement with the numerical estimate $α_h \approx 2.31\sqrt{\tfrac{α_s N_c}{2π}}$ obtained previously. We then verify this solution by cross-checking the predicted scaling behavior of the auxiliary "neighbor dipole amplitude" against the numerics, again finding excellent agreement.

hep-ph↗

arXiv2017

Small-$x$ asymptotics of the quark helicity distribution

We construct a numerical solution of the small-$x$ evolution equations recently derived in \cite{Kovchegov:2015pbl} for the (anti)quark helicity TMDs and PDFs as well as the $g_1$ structure function. We focus on the case of large $N_c$ where one finds a closed set of equations. Employing the extracted intercept, we are able to predict directly from theory the behavior of the helicity PDFs at small $x$, which should have important phenomenological consequences. We also give an estimate of how much of the proton's spin may be at small $x$ and what impact this has on the so-called "spin crisis."

hep-ph↗

arXiv2016

Helicity Evolution at Small x: Summary of Recent Developments

We construct small-$x$ evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $α_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $α_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. We construct a numerical solution of the helicity evolution equations in the large-$N_c$ limit. Employing the extracted intercept, we are able to predict directly from theory the behavior of the quark helicity PDFs at small $x$, which should have important phenomenological consequences. We also give an estimate of how much of the proton's spin may be at small $x$ and what impact this has on the so-called "spin crisis." Based on JHEP 1601 (2016) 072 (arXiv:1511.06737), arXiv:1610.06197 and arXiv:1610.06188.

hep-ph↗

arXiv2016

Helicity Evolution at Small $x$: Flavor Singlet and Non-Singlet Observables

We extend our earlier results for the quark helicity evolution at small $x$ to derive the small-$x$ asymptotics of the flavor singlet and flavor non-singlet quark helicity TMDs and PDFs and of the $g_1$ structure function. In the flavor singlet case we re-derive the evolution equations obtained in our previous paper on the subject, performing additional cross-checks of our results. In the flavor non-singlet case we construct new small-$x$ evolution equations by employing the large-$N_c$ limit. All evolution equations resum double-logarithmic powers of $α_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the single-logarithmic powers of $α_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. We solve the linearized flavor non-singlet equation analytically, obtaining an intercept which agrees with the one calculated earlier by Bartels, Ermolaev and Ryskin using the infra-red evolution equations. Our numerical solution of the linearized large-$N_c$ evolution equations for the flavor singlet case is presented in the accompanying Letter and is further discussed here.

hep-ph↗

arXiv2016

Helicity Evolution at Small-x

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $α_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $α_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin.

hep-ph↗

arXiv2015

Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution

We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) using the tools of saturation physics. By generalizing the quasi-classical Glauber-Gribov-Mueller/McLerran-Venugopalan approximation to allow for the possibility of spin-orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large "nucleus." To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer-Mulders distribution. We observe that spin-orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon.

hep-ph↗

arXiv2015

Probing short-range nucleon-nucleon interactions with an Electron-Ion Collider

We derive the cross-section for exclusive vector meson production in high energy deeply inelastic scattering off a deuteron target that disintegrates into a proton and a neutron carrying large relative momentum in the final state. This cross-section can be expressed in terms of a novel gluon Transition Generalized Parton Distribution (T-GPD); the hard scale in the final state makes the T-GPD sensitive to the short distance nucleon-nucleon interaction. We perform a toy model computation of this process in a perturbative framework and discuss the time scales that allow the separation of initial and final state dynamics in the T-GPD. We outline the more general computation based on the factorization suggested by the toy computation: in particular, we discuss the relative role of "point-like" and "geometric" Fock configurations that control the parton dynamics of short range nucleon-nucleon scattering. With the aid of exclusive $J/Ψ$ production data at HERA, as well as elastic nucleon-nucleon cross-sections, we estimate rates for exclusive deuteron photo-disintegration at a future Electron-Ion Collider (EIC). Our results, obtained using conservative estimates of EIC integrated luminosities, suggest that center-of-mass energies $s_{NN}\sim 12$ GeV$^2$ of the neutron-proton subsystem can be accessed. We argue that the high energies of the EIC can address outstanding dynamical questions regarding the short-range quark-gluon structure of nuclear forces by providing clean gluon probes of such "knockout" exclusive reactions in light and heavy nuclei.

nucl-th↗