N-Jettiness: An Inclusive Event Shape to Veto Jets

Abstract: Jet vetoes are essential in many Higgs and new-physics analyses at the LHC and Tevatron. The signals are typically characterized by a specific number of hard jets, leptons, or photons, while the backgrounds often have additional jets. In such cases vetoing undesired additional jets is an effective way to discriminate signals and background. Given an inclusive event sample with N or more jets, the veto to have only N energetic jets defines an "exclusive" N-jet cross section. This strongly restricts the phase space of the underlying inclusive N-jet cross section and causes large double logarithms in perturbation theory that must be summed to obtain theory predictions. Jet vetoes are typically implemented using jet algorithms. This yields complicated phase-space restrictions and one often relies on parton-shower Monte Carlos, which are limited to leading-logarithmic accuracy. We introduce a global event shape "N-jettiness", tau_N, which is defined for events with N signal jets and vanishes in the limit of exactly N infinitely narrow jets. Requiring tau_N << 1 constrains radiation between the N signal jets and vetoes additional undesired jets. This provides an inclusive method to veto jets and to define an exclusive N-jet cross section that can be well-controlled theoretically. N-jettiness yields a factorization formula with inclusive jet and beam functions.

• The paper introduces N-jettiness as a novel method to veto extra jets in collider events, enhancing signal isolation.
• It employs a minimization procedure over particle momenta that incorporates soft radiation and beam functions for precise jet definitions.
• The method enables summation of large logarithms to NNLL accuracy, bridging theory and experiment in modern particle physics.

An Analysis of $N$-Jettiness as an Inclusive Event Shape for Jet Vetoes

In collider physics, particularly in the study of processes involving Higgs bosons and potential new physics at the Large Hadron Collider (LHC) and Tevatron, a common issue is distinguishing signal events from backgrounds. The signal events are characterized by a specific number of energetic particles—jets, leptons, or photons—while background events often have additional, unwanted jets. A powerful strategy to distinguish these is to apply a veto on these excess jets. Traditionally, jet algorithms are employed to implement jet vetoes, but they often impose complex phase-space restrictions, making it challenging to achieve precise theoretical predictions beyond leading-logarithmic accuracy. The paper "N-Jettiness: An Inclusive Event Shape to Veto Jets" by Stewart, Tackmann, and Waalewijn addresses these limitations by introducing the concept of $N$-jettiness, $\tau_N$, which serves as an inclusive event shape for imposing jet vetoes.

Definition and Calculation

The $N$-jettiness $\tau_N$ is formulated as an event shape that quantifies how closely the configuration of an event corresponds to exactly $N$ jets. Mathematically, $\tau_N$ is defined to minimize the sum of products between reference momenta and particle momenta over all detectable particles, inclusive of soft radiation effects. It effectively provides a smooth transition between events with $N$ exact narrow jets and those with hard radiation characterized by additional jets.

Implications and Functional Advantages

$N$-jettiness provides an innovative method to define and calculate an exclusive $N$-jet cross-section that is theoretically well-controlled. By offering a global event shape, $\tau_N$ constraint applies inclusively, avoiding the intricate phase-space complexities associated with traditional jet algorithms. Its formulation supports the summation of large phase-space logarithms through a factorization property, crucial for extending precision in theoretical predictions to next-to-next-to-leading logarithmic (NNLL) orders. This makes calculating higher-order corrections feasible, bridging a significant gap in precision towards experimental comparisons in LHC analyses.

Application

The utility of $N$-jettiness spans different collider environments:

1. $e^+e^- \to 2$ Jets: For electron-positron collisions, $\tau_N$ aligns with known observables like thrust, making it readily implementable for jet event analysis.
2. Drell-Yan Production: The use of a modified beam thrust, $\tau_N$, in scenarios devoid of central jet production, exemplifies how the same concept adapts to processes endemic to hadron colliders.
3. $pp$ Collisions Producing Jets and Leptons: In more complex environments like proton-proton collisions, $\tau_N$ simplifies the consideration of initial and final state radiation by appropriately weighing contributions from beam and jet regions.

Technical Contributions

The paper delivers significant methodological advancements by enabling large logarithms to be systematically summed to all orders using the effective field theory framework (Soft-Collinear Effective Theory, SCET). By defining inclusive jet and beam functions, the results offer both conceptual clarity and pragmatic calculations for measuring large event shape parameters, hence facilitating a direct theoretical interpretation against experimental data.

Future Direction

The innovation of $N$-jettiness sets a platform for theoretical studies that might extend to more intricate event shapes capturing a broader class of particle interactions, or redefining backgrounds across different energy scales. Further experimental validation and practical adaptations for real-time data analysis could see $\tau_N$ altering standard practices in collider data analysis, pushing the precision frontier of modern particle physics research.

In conclusion, $N$-jettiness as introduced by Stewart, Tackmann, and Waalewijn represents a vital progression in jet physics, enabling more precise and versatile jet veto strategies crucial for identifying intricate new-physics signals amid Standard Model backgrounds.