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

India

Ankita Budhraja

Rishi Sharma

Balbeer Singh

Medium modifications to jet angularities using SCET with Glauber gluons

<p>Energy correlators have recently come to the forefront of jet substructure studies at colliders due to their remarkable properties: they naturally separate physics at different scales, are robust to contamination from soft radiation, and offer a direct connection with quantum field theory. The current parametrization used for energy correlators, however, is based on redundant pairwise angles with complex phase space restrictions. In this Letter, we introduce a new parametrization of energy correlators that features a simpler phase space structure and preserves information about the orientation of jet constituents. Further, our parametrization drastically reduces the computational cost to compute energy correlators on experimental data; whereas the time to compute a traditional projected <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-point energy correlator scales as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>M</mi><mi>N</mi></msup><mo>/</mo><mi>N</mi><mo>!</mo></math> on a jet with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> particles, our new parametrization achieves a scaling of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>M</mi><mn>2</mn></msup><mi>ln</mi><mi>M</mi></math>, remarkably independently of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>. Even for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>3</mn></math>, this improved scaling is particularly important for studies of heavy ion collisions, and higher values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> will enable new qualitative understanding of gauge theories. Theoretical calculations for our new energy correlators differ from those of traditional parametrizations only at next-to-next-to-leading logarithmic accuracy and beyond, and we expect that our simpler phase space structure will simplify those calculations. We also discuss how to extend our parametrization to resolved <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-point energy correlators that encode angular distances between greater numbers of particles, yielding intuitive visualizations of jet substructure that are qualitatively different for different jet samples. We propose two possible generalizations for probing multiprong jets and testing jet scaling behavior.</p>

United States

Samuel Alipour-fard

Netherlands

Jesse Thaler

Wouter J. Waalewijn

New Angles on Energy Correlators

Energy correlators characterize the asymptotic energy flow in scattering events produced at colliders, from which the microscopic physics of the scattering can be deduced. This view of collisions is akin to analyzes of the Cosmic Microwave Background, and a range of promising phenomenological applications of energy correlators have been identified, including the study of hadronization, the deadcone effect, measuring <math altimg='si1.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>s</mi></mrow></msub></math> and the top quark mass. While <italic>N</italic>-point energy correlators are interesting to study for larger values of <italic>N</italic>, their evaluation is computationally intensive, scaling like <math altimg='si2.svg'><msup><mrow><mi>M</mi></mrow><mrow><mi>N</mi></mrow></msup><mo stretchy='false'>/</mo><mi>N</mi><mo>!</mo></math>, where <italic>M</italic> is the number of particles. In this Letter, we develop a fast, approximate method for their evaluation exploiting that correlations at a given angular scale are insensitive to effects at other (widely-separated) scales. This implies that the energy correlator can be computed on (sub)jets, effectively reducing <italic>M</italic>. Furthermore, we utilize a dynamical (sub)jet radius that allows us to obtain reliable results without restricting the angular scales being probed. For concreteness, we focus on the projected energy correlator which projects onto the largest separation between the <italic>N</italic> directions. E.g. for <math altimg='si3.svg'><mi>N</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>7</mn></math> we find a speed up of up to four orders of magnitude, depending on the desired accuracy. We also consider the possibility of raising the energy to a power higher than one in the energy correlator, which has been proposed to reduce soft sensitivity. These higher-power correlators are not collinear safe, but as a byproduct our approach suggests a natural method to regularize them, such that they can be described using perturbation theory. This Letter is accompanied by a public code that implements our method.

<small-caps>FastEEC</small-caps>: Fast evaluation of <italic>N</italic>-point energy correlators

In recent years, energy correlators have emerged as a powerful tool for studying jet substructure, with promising applications such as probing the hadronization transition, analyzing the quark-gluon plasma, and improving the precision of top quark mass measurements. The projected <italic>N</italic>-point correlator measures correlations between <italic>N</italic> final-state particles by tracking the largest separation between them, showing a scaling behavior related to DGLAP splitting functions. These correlators can be analytically continued in <italic>N</italic>, commonly referred to as <italic>&#957;</italic>-correlators, allowing access to non-integer moments of the splitting functions. Of particular interest is the <math altimg='si1.svg'><mi>&#957;</mi><mo stretchy='false'>&#8594;</mo><mn>0</mn></math> limit, where the small momentum fraction behavior of the splitting functions requires resummation. Originally, the computational complexity of evaluating <italic>&#957;</italic>-correlators for <italic>M</italic> particles scaled as <math altimg='si2.svg'><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn><mi>M</mi></mrow></msup></math>, making it impractical for real-world analyses. However, by using recursion, we reduce this to <math altimg='si3.svg'><mi>M</mi><msup><mrow><mn>2</mn></mrow><mrow><mi>M</mi></mrow></msup></math>, and through the <small-caps>FastEEC</small-caps> method of dynamically resolving subjets, <italic>M</italic> is replaced by the number of subjets. This breakthrough enables, for the first time, the computation of <italic>&#957;</italic>-correlators for LHC data. In practice, limiting the number of subjets to 16 is sufficient to achieve percent-level precision, which we validate using known integer- <italic>&#957;</italic> results and convergence tests for non-integer <italic>&#957;</italic>. We have implemented this in an update to <small-caps>FastEEC</small-caps> and conducted an initial study of power-law scaling in the perturbative regime as a function of <italic>&#957;</italic>, using CMS Open Data on jets. The results agree with DGLAP evolution, except at small <italic>&#957;</italic>, where the anomalous dimension saturates to a value that matches the BFKL anomalous dimension.

Hao Chen

<italic>&#957;</italic>-point energy correletors with <small-caps>FastEEC</small-caps>: Small- <italic>x</italic> physics from LHC jets

We propose a tantalizing possibility that misinterpretation of the reconstructed missing momentum may have yielded the observed discrepancies among measurements of the W-mass in different collider experiments. We introduce a proof-of-principle scenario characterized by a new physics particle, which can be produced associated with the W-boson in hadron collisions and contributes to the net missing momentum observed in a detector. We show that these exotic events pass the selection criteria imposed by various collaborations at reasonably high rates. Consequently, in the presence of even a handful of these events, a fit based on the ansatz that the missing momentum is primarily due to neutrinos (as it happens in the Standard Model), yields a W-boson mass that differs from its true value. Moreover, the best fit mass depends on the nature of the collider and the center-of-mass energy of collisions. We construct a barebones model that demonstrates this possibility quantitatively while satisfying current constraints. Interestingly, we find that the nature of the new physics particle and its interactions appear as a variation of the physics of Axion-like particles after a field redefinition.

Triparno Bandyopadhyay

Samadrita Mukherjee

Tuhin Roy

A twisted tale of the transverse-mass tail

We introduce a new jet observable zest defined on exclusively constructed jets and study its potential to discriminate jets originated from Standard Model heavy particles like <math><mrow><mi>W</mi></mrow></math>, <math><mrow><mi>Z</mi></mrow></math> bosons and top quark from gluon initiated jets. Zest exhibits properties such as boost invariance, stability against global color exchange among partons, and inclusion or exclusion of a few soft particles in the jet. We also observe that for gluon jets, zest distribution is mostly insensitive to the jet mass. These properties make zest a suitable candidate for vetoing gluon jets at the colliders. Zest, when used in conjunction with other substructure observables that are uncorrelated to it, can further improve gluon jet veto. We generalize zest and show that in one limit it is synonymous to particle multiplicity and in the other limit, it projects only the leading particle. Optimization on the parameter of generalized zest further improves the discrimination ability of the observable. We find that for the top quark-initiated jets, the discrimination provided by generalized zest is in close comparison with a class of machine learning-based top taggers. We propose that studying other nonlinear infrared and collinear unsafe observables may help in unveiling the hidden physics of machine learning-based observables.

Ambar Jain

Identifying heavy particle jets with a new nonlinear jet observable

Angularities are event shapes whose sensitivity to the splitting angle of a collinear emission is controlled by a continuous parameter b, with −1 &lt; b &lt; ∞. When measured with respect to the thrust axis, this class of QCD observables includes thrust (b = 1) and jet broadening (b = 0), the former being insensitive to the recoil of soft against collinear radiation, while the latter being maximally sensitive to it. Presently available analytic results for angularity distributions with b ≠ 0 can be applied only close to the thrust limit since recoil effects have so far been neglected. As a first step to establish a comprehensive theoretical framework based on Soft-Collinear Effective Theory valid for all recoil-sensitive angularities, we compute for the first time angularity distributions at one-loop order in α  s  for all values of b taking into account recoil effects. In the differential cross section, these amount to novel sub-leading singular contributions and/or power corrections, where the former are characterized by fractional powers of the angularity and contribute appreciably close to the peak region, also for b ≳ 0.5. Our calculations are checked against various limits known in the literature and agree with the numerical output of the Event2 generator.