Medium modifications to jet angularities using SCET with Glauber gluons

We perform a comprehensive analysis of medium modifications on ungroomed jet angularities, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>τ</a:mi><a:mi>a</a:mi></a:msub></a:math>, within the framework of soft-collinear effective theory with Glauber gluons (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>SCET</c:mi></c:mrow><c:mrow><c:mi mathvariant="normal">G</c:mi></c:mrow></c:msub></c:mrow></c:math>). Angularities are a one-parameter family of jet substructure observables with angularity exponent <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>a</f:mi><f:mo>&lt;</f:mo><f:mn>2</f:mn></f:math> 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 <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>a</h:mi><h:mo>&lt;</h:mo><h:mn>1</h:mn></h:math> and provide detailed results for <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>a</j:mi><j:mo>=</j:mo><j:mo>−</j:mo><j:mn>1</j:mn></j:math>, 0, and 0.5. Within <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mrow><l:mi>SCET</l:mi></l:mrow><l:mi mathvariant="normal">G</l:mi></l:msub></l:math>, 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 <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>a</o:mi><o:mo>&lt;</o:mo><o:mn>1</o:mn></o:math>. For all values of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>a</q:mi></q:math>, 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 <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>a</s:mi></s:math>. We also present results for the medium sensitivity towards <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>p</u:mi><u:mi>T</u:mi></u:msub></u:math> 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.