Order In Opacity Research Articles

Understanding parton evolution in matter from renormalization group analysis

We perform a renormalization group (RG) analysis of collinear hadron production in deep inelastic scattering on nuclei. We consider the limit where the parent parton energy E is large, while the medium opacity L/λg remains small. We identify the fixed order and leading ln⁡(E/ξ2L) enhanced medium contributions to the semi-inclusive cross sections and derive RG equations that resum multiple emissions near the endpoints of the splitting functions at first order in opacity. These evolution equations treat the same type of radiation enhancement in matter as the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi approach, but differ in the way one regulates the collinear divergences. They provide a unique analytic insight into the problem of resummation and a faster and more efficient path to phenomenology. The new RG evolution framework is applied to study fragmentation in eA reactions.

Medium-induced photon bremsstrahlung in neutrino-nucleus, antineutrino-nucleus, and electron-nucleus scattering from multiple QED interactions

Interactions of charged leptons with nuclei and the naive tree-level kinematics of these processes are affected by radiation of photons induced by the QED nuclear medium. We evaluate cross section modifications at leading orders of the number of correlated interactions inside the nucleus, known as the opacity expansion. We derive results for soft and collinear types of the bremsstrahlung at the first three orders in opacity and generalize them to higher orders. We present the leading in opacity energy spectra of soft and collinear photons and radiative energy loss inside the nucleus for experiments with lepton kinematics in the GeV energy range. At leading power of the Glauber soft-collinear effective field theory, the soft radiation is further resummed to all orders both in opacity and in the electromagnetic coupling constant. We find that the soft and collinear medium-induced radiation is vacuumlike, and additional corrections are power suppressed. Despite the negligible modification to the induced photon spectra, the nuclear medium-induced radiation sizably affects the broadening of charged leptons in the direction orthogonal to their propagation. Published by the American Physical Society 2024

Jet quenching in anisotropic flowing matter

We study the interplay between the flow and hydrodynamic gradients in jet quenching at first order in opacity. We find that the mixed flow-gradient contributions in jet quenching are enhanced by the medium length and survive in the eikonal limit, dominating over other medium evolution effects. The resulting modification to the jet quenching parameter and energy loss rate can be substantial, leading to ample phenomenological implications. We also compute the leading corrections to the jet broadening due to the flow velocity gradients and consider the leading gradient effects in the medium-induced branching for general kinematics, extending the recent considerations of jets in inhomogeneous media. These results can be straightforwardly coupled to matter simulations, providing new opportunities for jet tomography in heavy-ion collisions. Published by the American Physical Society 2024

Importance of higher orders in opacity in quark-gluon plasma tomography

Importance of higher orders in opacity in quark-gluon plasma tomography

Jet broadening in flowing matter: Resummation

In this work, we obtain the leading corrections to the jet momentum broadening distribution in a QCD medium arising from the transverse flow of the matter. We first derive the single-particle propagator of a highly energetic parton resumming its multiple interactions with the homogeneous flowing matter, explicitly keeping the leading subeikonal flow terms. Then, we use this propagator to obtain the jet broadening distribution and its leading moments. We show that this distribution becomes anisotropic in the presence of transverse flow, since its odd moments are generally non-zero and proportional to the transverse velocity of the medium. Finally, we evaluate several odd moments, which we compare to the corresponding results at first order in opacity, showing that accounting for multiple in-medium scatterings is essential to describe some observables in dense nuclear matter.

Ab initio coupling of jets to collective flow in the opacity expansion approach

We calculate the leading corrections to jet momentum broadening and medium-induced branching that arise from the velocity of the moving medium at first order in opacity. These results advance our knowledge of jet quenching and demonstrate how it couples to collective flow of the quark-gluon plasma in heavy-ion collisions and to the orbital motion of partons in cold nuclear matter in deep inelastic scattering at the electron-ion collider. We also compute the leading corrections to jet momentum broadening due to transverse gradients of temperature and density. We find that these effects lead to both anisotropic transverse momentum diffusion proportional to the medium velocity and anisotropic medium-induced radiation emitted preferentially in the direction of the flow. We isolate the relevant sub-eikonal corrections by working with jets composed of scalar particles with arbitrary color factors interacting with the medium by scalar QCD. Appropriate substitution of the color factors and light-front wave functions allow us to immediately apply the results to a range of processes including $q \rightarrow q g$ branching in real QCD. The resulting general expressions can be directly coupled to hydrodynamic simulations on an event-by-event basis to study the correlations between jet quenching and the dynamics of various forms of nuclear matter.

Medium-induced radiative kernel with the Improved Opacity Expansion

We calculate the fully differential medium-induced radiative spectrum at next-to-leading order (NLO) accuracy within the Improved Opacity Expansion (IOE) framework. This scheme allows us to gain analytical control of the radiative spectrum at low and high gluon frequencies simultaneously. The high frequency regime can be obtained in the standard opacity expansion framework in which the resulting power series diverges at the characteristic frequency ωc ∼ hat{q} L2. In the IOE, all orders in opacity are resumed systematically below ωc yielding an asymptotic series controlled by logarithmically suppressed remainders down to the thermal scale T « ωc, while matching the opacity expansion at high frequency. Furthermore, we demonstrate that the IOE at NLO accuracy reproduces the characteristic Coulomb tail of the single hard scattering contribution as well as the Gaussian distribution resulting from multiple soft momentum exchanges. Finally, we compare our analytic scheme with a recent numerical solution, that includes a full resummation of multiple scatterings, for LHC-inspired medium parameters. We find a very good agreement both at low and high frequencies showcasing the performance of the IOE which provides for the first time accurate analytic formulas for radiative energy loss in the relevant perturbative kinematic regimes for dense media.

Gluon emission from heavy quarks in dense nuclear matter

We study the medium-induced gluon emission process experienced by a hard jet parton propagating through the dense nuclear matter in the framework of deep inelastic scattering off a large nucleus. We work beyond the collinear rescattering expansion and the soft gluon emission limit, and derive a closed formula for the medium-induced single gluon emission spectrum from a heavy or light quark jet interacting with the dense nuclear medium via transverse and longitudinal scatterings. Without performing the collinear rescattering expansion, the medium-induced gluon emission spectrum is controlled by the full distribution of the differential elastic scattering rates between the propagating partons and the medium constituents. We further show that if one utilizes heavy static scattering centers for the traversed nuclear matter and takes the soft gluon emission limit, our result can reduce to the first order in opacity Djordjevic-Gyulassy-Levai-Vitev formula.

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.

Inclusive heavy flavor jet production with semi-inclusive jet functions: from proton to heavy-ion collisions

The past several years have witnessed important developments in the QCD theory of jet production and jet substructure in hadronic collisions. In the framework of soft-collinear effective theory, semi-inclusive jet functions and semi-inclusive fragmenting jet functions have allowed us to combine higher order calculations with resummation of potentially large logarithms of the jet radius, ln R. Very recently, the semi-inclusive jet functions for partons fragmenting into heavy flavor jets were computed by Dai, Kim and Leibovich. In this paper we show how the formalism can be extended to c-jet and b-jet production in heavy ion collisions. The semi-inclusive jet functions for heavy flavor jets in a QCD medium are evaluated up to the next-to-leading order in αs and first order in opacity. For phenomenological applications, we also consider the inclusion of the cold nuclear matter effects and the jet energy dissipation due to collisional interactions in matter. We present the numerical predictions for the cross sections and the corresponding nuclear modification factors in proton-nucleus and nucleus-nucleus collisions and compare our results to data from the Large Hadron Collider.

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

In this Letter we report the first calculation of all O(αs) 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→qg, g→gg, q→gq, g→qq¯ 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.

Gluon Spectrum to Any Order in Opacity for Jets at the EIC

Jets produced at a future electron-ion collider (EIC) are predominantly initiated by energetic quarks, and the subsequent branching of these quarks into systems of quarks and gluons is heavily modified by multiple scattering in the nuclear medium. In cold nuclear matter and in the quark-gluon plasma, this feature allows jet cross sections and jet substructure to be used as a probe of the medium's properties. Here we present a formalism for computing the gluon substructure of a quark jet to an arbitrary order in opacity, the average number of scatterings in the medium, while maintaining the exact kinematics of the splitting. We present explicit results at second order in opacity for the first time, along with a recursion relation which can be used to construct the solution for arbitrarily high orders in opacity. The theoretical framework demonstrated here applies equally well to light and heavy quark branching, and is easily generalizable to other systems.

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.

Radiative heavy quark energy loss in an expanding viscous QCD plasma

We study viscous effects on heavy quark radiative energy loss in a dynamically screened medium with boost-invariant longitudinal expansion. We calculate, to first order in opacity, the energy loss by incorporating viscous corrections in the single-particle phase-space distribution function within relativistic dissipative hydrodynamics. We consider the Grad's 14-moment and the Chapman-Enskog-like methods for the nonequilibrium distribution functions. Our numerical results for the charm quark radiative energy loss show that, as compared to static fluid, an expanding ideal (nonviscous) fluid causes a much smaller energy loss. Viscosity in the evolution lead to somewhat enhanced energy loss which is insensitive to the underlying viscous hydrodynamic models used. Further inclusion of viscous correction induces larger energy loss, the magnitude and pattern of this enhancement crucially depend on the form of viscous corrections used.

Kinematics of Heavy Quark Radiative Energy Loss in Viscous QCD Plasma

We present effects of longitudinal expansion of QCD medium on radiative energy loss suffered by heavy quark in a dynamically screened medium. The energy loss expression to the first order in opacity is obtained by incorporating viscous corrections to the equilibrium phase-space distribution function as well as expansion of the medium. Theoretical formalism accounts for medium modified polarization tensor and time dependent cooling because of rapid longitudinal expansion of the QCD medium in relativistic heavy ion collision experiments along with modified phase space. For manifestation we have used distribution function obtained from Grad’s 14-moment expansion in relativistic viscous hydrodynamic evolution. Viscous correction is shown to enhance the radiative energy loss and the result is time dependent. We have also shown $$\eta /s$$ dependence of radiative energy loss for the Grad’s 14-moment distribution function. Our results for energy loss lie within the static plasma results and results obtained considering only ideal Bjorken expansion.

Relaxing real-time order in opacity and linearizability

In this paper we introduce two families of safety properties: ♢-opacity and ♢-linearizability. The new properties relax (to a various degree) the real-time order requirement on transaction execution in opacity and, analogically, the real-time order requirement on operation execution in linearizability. This way we can formalize the guarantees provided by a wide class of strongly consistent replicated systems for which opacity and linearizability are too strong. We show the formal relationship between ♢-opacity and ♢-linearizability which allows us to directly compare semantics of transactional and non-transactional systems and, in particular, opacity and linearizability in their original definitions. We also illustrate how the new properties can be used by proving correctness of Deferred Update Replication, a well known optimistic concurrency control scheme. We show that it satisfies update-real-time opacity, a member of the ♢-opacity family, which allows read-only and aborted transactions to operate on stale (but still consistent) data.

Resummation of Jet Shapes and Extracting Properties of the Quark-Gluon Plasma

Understanding the properties of the quark-gluon plasma (QGP) that is produced in ultra-relativistic nucleus-nucleus collisions has been one of the top priorities of the heavy ion program at the LHC. Energetic jets are produced and subsequently quenched in the collisions. Such jet quenching phenomena provide promising tools to probe the medium properties by studying the modification of jets due to the medium interactions. Significant modifications of jet shapes have been measured. In this talk we focus on the calculation of jet shapes in both proton-proton and lead-lead collisions using soft-collinear effective theory (SCET), with Glauber gluon interactions in the medium. Large logarithms in jet shapes are resummed at next-to-leading logarithmic (NLL) accuracy by the renormalization-group evolution between hierarchical jet scales. The medium interactions contribute as power corrections, and we calculate the modification of jet shapes at leading order in opacity with the static QGP model. Preliminary results are presented with good agreement with the recent CMS jet shape measurements.

Coherence phenomena between initial and final state radiation in a dense QCD medium

Abstract In this work we investigate medium modifications to the interference pattern between initial and final state radiation. We compute single gluon production off a highly energetic parton that undergoes a hard scattering and subsequently crosses a dense QCD medium of finite size. We extend our previous studies obtained at first order in opacity by providing general results for multiple soft scatterings and their specific formulation within the harmonic oscillator approximation. We show that there is a gradual onset of decoherence between the initial and final state radiation due to multiple scatterings, that opens the phase space for large angle emissions. By examining the multiplicity of produced gluons, we observe a potentially large double logarithmic enhancement for dense media and small opening angles. This result points to a possible modification of the evolution equations due to a QCD medium of finite size. We briefly comment on the phenomenological consequences of this setup in high-energy nuclear collisions.

The contribution of medium-modified color flow to jet quenching

Abstract Multiple interactions between parton showers and the surrounding QCD matter are expected to underlie the strong medium-modifications of jet observables in ultra- relativistic heavy ion collisions at RHIC and at the LHC. Here, we note that such jet- medium interactions alter generically and characteristically the color correlations in the parton shower. We characterize these effects in a color-differential calculation of the medium-induced gluon radiation spectrum to first and second order in opacity. By interfacing simple branching histories of medium-modified color flow with the Lund hadronization model, we analyze how the medium modification of color correlations can affect the distribution of hadronic fragments in jets. Importantly, we observe that jet-medium interactions give rise to the medium-induced color decoherence of gluons from the parton shower. Since hadronization respects color flow and since each color singlet in a parton shower is hadronized separately, this medium-induced color decoherence leaves characteristic signatures in the jet fragmentation pattern. In particular, it can contribute to the quenching of leading hadron spectra. Moreover, it can increase strongly the yield of soft hadronic fragments from a jet, while the distribution of more energetic hadrons follows naturally the shape of a vacuum-like fragmentation pattern of lower total energy.

Dynamical magnetic enhancement of light and heavy quark jet quenching at RHIC

A new Monte Carlo implementation of Djordjevicʼs dynamical scattering generalization of the DGLV radiative energy loss opacity series is used with a hybrid interpolation scheme to compute both light and heavy quark jet quenching up to third order in opacity. The enhancement of the ratio of bottom to charm quark energy loss due to perturbative long range color magnetic effects in nonuniform Bjorken expanding geometries is found to reduce the significance of the heavy quark jet puzzle posed by the observed near equality (within sizeable errors) of pion and nonphotonic electron nuclear modification at RHIC. Jet Flavor Spectroscopy discussed below will be a powerful tool to differentiate competing dynamical models of the QGP produced in ultra-relativistic nuclear collisions.