Medium modifications to jet angularities using SCET with Glauber gluons

We perform a comprehensive analysis of medium modifications on ungroomed jet angularities, $\tau_a$, within the framework of Soft-Collinear Effective Theory with Glauber gluons (SCET$_{\rm G}$). Angularities are a one-parameter family of jet substructure observables with angularity exponent $a < 2$ for infrared safety. Variation of the angularity exponent allows one to modify the relative weighting of the collinear-to-soft radiations in the jet, thereby giving access to different moments of the jet transverse momentum spectrum. In this article, we focus on $a<1$ and provide detailed results for $a=-1, 0$, and $0.5$. Within SCET$_{\rm G}$, the interactions between jet and medium constituents are mediated by off-shell Glauber gluons generated from the color sources in the medium. While medium modifications are incorporated into the jet function via the use of medium-induced splitting functions, the soft function remains unmodified for $a<1$. For all values of $a$, we find that compared to jets in vacuum, the medium-modified distributions are shifted towards smaller values of jet angularity and have a steeper fall. This redistribution of the ungroomed angularity spectrum is more apparent for a jet with a larger cone size and for higher values of $a$. We also present results for the medium sensitivity towards $p_T$ of the jet and for a jet initiated in a less central event ($10-30\%$ centrality). Finally, we provide the ratios of nucleus-nucleus and proton-proton differential angularity distributions for different angularity exponents, and for two values of the jet radius parameter.