Inside a medium, showers originating from a very high energy particle develop via medium-induced splitting processes such as bremsstrahlung and pair production. During shower development, two consecutive splittings sometimes overlap quantum mechanically, so that they cannot be treated independently. Some of these effects can be absorbed into an effective value of a medium parameter known as $$ \hat{q} $$ . Previous calculations (with certain simplifying assumptions) have found that, after adjusting the value of $$ \hat{q} $$ , the leftover effect of overlapping splittings is quite small for purely gluonic large- showers but is very much larger for large- QED showers, at comparable values of . Here, by investigating the same problem for QCD in the large- limit of many quark flavors, we make a first study of whether the small effect in purely gluonic showers (i) was merely an accident or (ii) is more broadly characteristic of such overlap effects in QCD. We also offer a qualitative explanation for the large size of the effect in QED vs. QCD.

United States

Peter Arnold

China

Omar Elgedawy

Pakistan

Switzerland

Shahin Iqbal

Are in-medium quark-gluon showers strongly coupled? results in the large-

Erratum to: In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers

Inside a medium, showers originating from a very high-energy particle may develop via medium-induced splitting processes such as hard bremsstrahlung or pair production. During shower development, two consecutive splittings sometimes overlap quantum mechanically, so that they cannot be treated independently. Some of these effects can be absorbed into an effective value of a medium parameter known as   <math> <mover> <mi>q</mi> <mo>̂</mo> </mover> </math>  $$ \hat{q} $$ . Previous calculations (with certain simplifying assumptions) have found that, after adjusting the value of   <math> <mover> <mi>q</mi> <mo>̂</mo> </mover> </math>  $$ \hat{q} $$ , the leftover effect of overlapping splittings is quite small for purely gluonic large-N c showers but is very much larger for large-N f QED showers, at comparable values of Nα. Those works did not quite make for apples-to-apples comparisons: the gluon shower work investigated energy deposition from a gluon-initiated shower, whereas the QED work investigated charge-deposition from an electron-initiated shower. As a first step to tighten up the comparison, this paper investigates energy deposition in the QED case. Along the way, we develop a framework that should be useful in the future to explore whether the very small effect of overlapping splitting in purely gluonic showers is an artifact of having ignored quarks.

CERN

Strongly vs. weakly coupled in-medium showers: energy stopping in large-N f QED

We study whether in-medium showers of high-energy gluons can be treated as a sequence of individual splitting processes <math><mrow><mi>g</mi><mo>→</mo><mi>g</mi><mi>g</mi></mrow></math>, or whether there is significant quantum overlap between where one splitting ends and the next begins. Accounting for the Landau-Pomeranchuk-Migdal (LPM) effect, we calculate such overlap effects to leading order in high-energy <math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></math> for the simplest theoretical situation. We investigate a measure of overlap effects that is independent of physics that can be absorbed into an effective value <math><msub><mover><mi>q</mi><mo>^</mo></mover><mi>eff</mi></msub></math> of the jet-quenching parameter <math><mover><mi>q</mi><mo>^</mo></mover></math>.

Are Gluon Showers inside a Quark-Gluon Plasma Strongly Coupled? A Theorist’s Test

We give details of our study as to whether high-energy gluon showers inside a QCD medium can be treated as a sequence of individual splitting processes <math><mi>g</mi><mo>→</mo><mi>g</mi><mi>g</mi></math>, or whether there is significant quantum overlap between where one splitting ends and the next begins (neglecting effects that can be absorbed into an effective value of the jet-quenching parameter <math><mover><mi>q</mi><mo>^</mo></mover></math> that characterizes the medium). The study is carried out by imagining in-medium gluon-shower development in the simplest theoretical situation, which includes imagining a very large, static, homogeneous medium and taking the large <math><msub><mi>N</mi><mi>c</mi></msub></math> limit. Along the way, we also show how in-medium shower evolution can be written in terms of a “net” splitting rate <math><mo>[</mo><mi>d</mi><mi>Γ</mi><mo>/</mo><mi>d</mi><mi>x</mi><msub><mo>]</mo><mrow><mi>net</mi></mrow></msub></math>, and we provide a moderately simple analytic fit to our numerical results for the overlap effects included in that rate, which we hope may be of use to others wishing to study possible consequences of overlapping splittings.

Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: Gluon shower development

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths (formation lengths) of two consecutive splitting processes overlap, avoiding soft-emission approximations. Previous work made a “nearly-complete” calculation of the effect of overlapping formation times on gluonic splittings such as g → gg → ggg (with simplifying assumptions such as an infinite QCD medium and the large-N c limit). In this paper, we extend those previous rate calculations from nearly-complete to complete by including processes involving the exchange of longitudinally-polarized gluons. In the context of Lightcone Pertubation Theory, used earlier for the “nearly-complete” calculation, such exchanges are instantaneous in lightcone time and have their own diagrammatic representation.

Germany

Tyler Gorda

The LPM effect in sequential bremsstrahlung: incorporation of “instantaneous” interactions for QCD

An important question concerning in-medium high-energy parton showers in a quark-gluon plasma or other QCD medium is whether consecutive splittings of the partons in a given shower can be treated as quantum mechanically independent, or whether the formation times for two consecutive splittings instead have significant overlap. Various previous calculations of the effect of overlapping formation times have either (i) restricted attention to a soft bremsstrahlung limit, or else (ii) used the large-N c limit (where N c = 3 is the number of quark colors). In this paper, we make a first study of the accuracy of the large-N c limit used by those calculations of overlap effects that avoid a soft bremsstrahlung approximation. Specifically, we calculate the 1/   <math> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </math>  $$ {N}_{\mathrm{c}}^2 $$  correction to previous N c = ∞ results for overlap g → gg → ggg of two consecutive gluon splittings g → gg. At order 1/   <math> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </math>  $$ {N}_{\mathrm{c}}^2 $$ , there is interesting and non-trivial color dynamics that must be accounted for during the overlap of the formation times.

The LPM effect in sequential bremsstrahlung: 1/   <math> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </math>  $$ {\mathrm{N}}_{\mathrm{c}}^2 $$  corrections

Erratum to: The LPM effect in sequential bremsstrahlung: nearly complete results for QCD

Consider the in-medium splitting g → gg of a very high-energy gluon traversing a QCD medium, accounting for the Landau-Pomeranchuk-Migdal (LPM) effect. It has been known for some time that soft radiative corrections to that splitting generate a double-log correction to the splitting rate, whose effects can be absorbed into running of the medium parameter   <math> <mover> <mi>q</mi> <mo>̂</mo> </mover> </math>  $$ \hat{q} $$  describing the rate of transverse momentum kicks to high-energy particles due to small-angle scattering from the medium. Less has been known about sub-leading, single logarithms in this context. In this paper, we find analytic formulas for those single logs (with various caveats and clarifications).