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Evidence for the dead-cone effect in bottom quark initiated jets produced in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS experiment analyzed proton-proton collision data at 13 TeV to provide evidence for the dead-cone effect in bottom quark jets, observing a 4.3 standard deviation preference for a parton shower model that includes this mass-dependent suppression of collinear gluon emissions over one that does not.

Original authors: CMS Collaboration

Published 2026-09-01

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CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the subatomic world, particles do not exist in isolation; they are constantly interacting, colliding, and transforming. When high-energy protons smash together, they often produce sprays of smaller particles called jets. These jets are not random clouds but highly structured streams that follow strict rules dictated by the fundamental forces of nature. One of these forces, known as the strong nuclear force, governs how particles called quarks and gluons behave. A long-standing prediction of the theory describing this force is that heavy particles, such as the bottom quark, behave differently than their lighter cousins when they emit radiation. Specifically, theory suggests that a heavy quark should suppress the emission of particles at very small angles relative to its direction of travel. This creates a quiet zone, or a "dead cone," where radiation is scarce. While this effect has been hinted at in previous studies, observing it directly in the complex environment of a high-energy collision has remained a significant challenge for physicists.

A researcher from the CMS Collaboration at CERN has now provided direct evidence of this phenomenon using data from proton-proton collisions. The researcher analyzed a vast dataset recorded in 2018, corresponding to an integrated luminosity of 59.8 inverse femtobarns, which represents a massive number of collision events. They focused specifically on jets initiated by bottom quarks that originated from the decay of top quark pairs. To understand the internal structure of these jets, the researcher used a technique called iterative declustering. This process involves working backward through the history of a jet, splitting it into smaller and smaller pieces to map out exactly where and when particles were emitted. By plotting these emissions on a specialized map known as the Lund jet plane, they could visualize the density of radiation at different angles and distances from the jet's core.

The analysis required careful selection to ensure the jets being studied were truly from bottom quarks and not from other sources. The researcher employed a "tag-and-probe" strategy, using one jet to confirm the presence of a top quark event and the other as the subject of study. This method avoided the biases that can sometimes be introduced by standard tagging algorithms. Furthermore, because bottom quarks quickly decay into other particles, the researcher used a sophisticated machine learning tool, a transformer encoder, to identify and group the charged particles that came from these decays. This allowed them to reconstruct the original momentum of the bottom quark more accurately, ensuring that the "dead cone" they were looking for was not obscured by the messy aftermath of the decay.

When the researcher compared their measurements to computer simulations, a clear pattern emerged. The data showed a distinct suppression of particle emissions at small angles for the bottom quark jets, exactly as the theory of the dead-cone effect predicts. When they compared the real data to a simulation that included the dead-cone effect, the match was excellent. However, when they compared the data to a simulation where the bottom quark was treated as if it had no mass—effectively removing the dead-cone effect—the model failed to describe the observations. The discrepancy was significant, with the model lacking the effect being disfavored by a statistical significance of 4.3 standard deviations. This level of certainty is strong enough to be considered robust evidence in particle physics, indicating that the suppression is a real physical phenomenon and not a statistical fluke.

The study also highlighted the importance of the mass of the quark in shaping the jet. By comparing the bottom quark jets to jets made of lighter particles, the researcher confirmed that the heavy quarks indeed create a region of suppressed radiation that lighter particles do not. This finding provides a crucial benchmark for refining the computer models that physicists use to simulate particle collisions. These models are essential for interpreting future experiments, including those searching for new physics beyond the current understanding of the universe. By confirming that the dead-cone effect is a real feature of nature, the researcher has helped to solidify the theoretical framework that describes how matter behaves at the smallest scales, turning a long-standing theoretical prediction into a measured reality.

Technical Summary: Evidence for the Dead-Cone Effect in Bottom Quark Initiated Jets

Problem and Motivation
The "dead-cone effect" describes the suppression of collinear gluon emissions from a massive quark, a primary manifestation of quark mass effects in parton showers. In leading-order perturbative Quantum Chromodynamics (QCD), the probability of gluon emission is proportional to $\theta^2 d\theta^2 / [\theta^2 + (m_q/E_q)^2]^2$ , where $\theta$ is the emission angle, $m_q$ is the quark mass, and $E_q$ is the quark energy. This formula predicts a suppression of emissions within an angle $\Delta R_{dead} = m_q/E_q$ along the emitter's direction. While indirect evidence and direct observations in charm quark jets (via $D^0$ mesons) and light-quark comparisons exist, a direct measurement in bottom ( $b$ ) quark jets from top quark pair ( $t\bar{t}$ ) production at the Large Hadron Collider (LHC) remains a critical benchmark for testing parton shower (PS) models and QCD calculations involving heavy flavor.

Methodology
The analysis utilizes a proton-proton collision dataset recorded by the CMS experiment at $\sqrt{s} = 13$ TeV with an integrated luminosity of 59.8 fb $^{-1}$ (2018 data). The study focuses on $t\bar{t}$ events in the dileptonic ( $e^\pm\mu^\mp$ ) final state.

Event Selection and Jet Identification: To obtain a high-purity sample of $b$ -quark jets without introducing biases from standard flavor-tagging algorithms on the substructure measurement, a "tag-and-probe" (T&P) approach is employed. One leading jet is identified as a $b$ -jet using the DEEPJET algorithm (the "tag"), while the other leading jet (the "probe") is the object of study. The probe is required to contain a secondary vertex (SV) and satisfy kinematic constraints matching it to the lepton from the top decay ( $m_{\ell,j} < 150$ GeV) to suppress background from non-top processes.
Lund Jet Plane (LJP) Construction: The analysis constructs the Lund Jet Plane by reclustering jet constituents using the Cambridge–Aachen (CA) algorithm in ascending angular order. The clustering history is traversed backwards (iterative declustering), splitting jets into subjets. The subjet with higher transverse momentum ( $p_T$ ) is treated as the "emitter," and the lower- $p_T$ subjet as the "emission." The angular separation $\Delta R$ and relative transverse momentum $k_T$ are measured for each step.
Mitigation of Decay Effects: A significant challenge is that $b$ -hadron decays do not follow the approximate angle ordering of QCD radiation, distorting the LJP. To address this, a Transformer Encoder (TFE) algorithm is trained to identify charged decay products of $b$ -hadrons. The four-momenta of these identified constituents are summed to partially reconstruct the charged component of the $b$ -hadron momentum before LJP construction.
Unfolding and Comparison: The measured differential emission density, $\rho(\Delta R) \equiv (1/N_{jet}) dN_{em}/d\ln(R/\Delta R)$ $ρ (Δ R) \equiv (1/ N_{j e t}) d N_{e m} / d ln (R /Δ R)$ , is corrected for detector effects using regularized unfolding (iterative d'Agostini method). The results are compared against generator-level predictions from several Monte Carlo (MC) models:
- Nominal Models: POWHEG+PYTHIA and POWHEG+HERWIG (both including the dead-cone effect).
- Massless Kernel Model: A HERWIG sample where the $b$ -quark mass is set to zero during the parton shower to isolate the dead-cone effect from other mass-dependent hadronization effects.
- Light-Quark Reference: A sample of light-quark jets from hadronic $W$ decays in $tW$ events.

Key Contributions

Novel Selection Strategy: The implementation of a T&P method for $b$ -jet selection avoids the substructure biases inherent in standard $b$ -tagging algorithms, providing a cleaner sample for substructure studies.
Machine Learning for Substructure: The application of a Transformer Encoder to reconstruct $b$ -hadron decay products directly within the jet constituents, successfully recovering the expected smoothly falling emission distribution on the Lund Jet Plane.
Direct Measurement in $t\bar{t}$ : The first direct measurement of the dead-cone effect in $b$ -quark jets originating specifically from top quark decays at $\sqrt{s} = 13$ TeV, covering a $p_T$ range of 40–200 GeV.

Results
The measured emission density distributions show a strong suppression of collinear emissions relative to light-quark jets, consistent with previous observations.

Model Comparison: The data are compared with the nominal models (including the dead-cone effect) and the massless kernel model (excluding the effect).
Statistical Significance: For jets with $40 < p_T < 80$ GeV, the data show a significant deviation from the massless kernel prediction. The $p$ -value for the massless model is $8 \times 10^{-6}$ , corresponding to a significance of 4.3 standard deviations. In contrast, the nominal POWHEG+HERWIG prediction (with the dead-cone effect) agrees well with the data ( $p$ -value of 0.57).
High $p_T$ Sensitivity: For the higher $p_T$ range ( $80 < p_T < 200$ GeV), the sensitivity to the dead-cone effect is limited, as the expected dead-cone angle becomes narrower. Neither model shows a significant deviation from data in this region, though the massless model yields a lower $p$ -value (0.01) compared to the nominal model (0.03).
Uncertainties: Physics modeling uncertainties dominate the systematic errors, particularly in the wide-angle region, while track reconstruction efficiency and background purity corrections contribute smaller uncertainties.

Significance
The paper claims that the measurement provides a new experimental benchmark for the development of parton shower models and QCD calculations that incorporate quark mass effects. The results favor a parton shower model that includes the dead-cone effect over one that does not, with a significance of 4.3 standard deviations in the lower $p_T$ bin. This confirms the theoretical expectation of mass-induced suppression of collinear gluon radiation in heavy-flavor jets. The analysis demonstrates the viability of using advanced machine learning techniques (TFE) to mitigate hadronization effects in jet substructure studies and provides publicly available data (via HEPData) and a RIVET routine to facilitate future theoretical comparisons.

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