Snowmass accord

The Snowmass Accord is an agreement on the definition of hadronic jets reached by a group of theorists and experimentalists at the 1990 Summer Study on High Energy Physics in Snowmass, Colorado. It was published as "Toward a Standardization of Jet Definitions" by J. E. Huth and ten co-authors. The accord had two parts: a list of general properties that any jet definition should satisfy, and a specific fixed-radius cone algorithm in pseudorapidity–azimuth space intended for use by both hadron collider experiments and theoretical calculations.

The cone specification proved incomplete in practice. Experiments had to add their own procedures for choosing seeds and for splitting and merging overlapping cones, and the resulting algorithms were later shown to be infrared unsafe. The general criteria, by contrast, have remained a standard reference point. They are routinely cited in reviews of jet algorithms, and the sequential-recombination algorithms used at the Large Hadron Collider are often presented as the first practical algorithms to satisfy them fully.

Background

In hadron collisions, quarks and gluons produced in a hard scattering appear in detectors as collimated sprays of hadrons. Turning those hadrons, or the calorimeter energy they deposit, into jets requires an explicit algorithm, and the result depends on the algorithm and its parameters. Through the 1980s each hadron-collider experiment used its own cone-type procedure, with many differing implementation choices.

This became a practical problem around 1990, when the first next-to-leading order (NLO) QCD calculations of inclusive jet cross sections at hadron colliders appeared, from S. D. Ellis, Z. Kunszt and D. E. Soper, and from F. Aversa, P. Chiappetta, M. Greco and J. P. Guillet. A meaningful comparison between such calculations and data requires that both use the same jet definition, applicable both to a handful of partons in a calculation and to many particles or calorimeter towers in an experiment.

The 1990 Snowmass Summer Study

The accord came out of the 1990 Summer Study on High Energy Physics, "Research Directions for the Decade", held in Snowmass, Colorado, from 25 June to 13 July 1990. It was written up as a short contribution to the proceedings (pages 134–136) and also circulated as Fermilab report FERMILAB-CONF-90-249-E, dated December 1990.

The eleven authors were J. E. Huth, N. Wainer, K. Meier, N. Hadley, F. Aversa, M. Greco, P. Chiappetta, J. P. Guillet, S. Ellis, Z. Kunszt and D. E. Soper. The group combined experimentalists with the members of both theory groups then computing NLO jet cross sections. Later reviews describe the authors as an influential group of theorists and Tevatron experimentalists.

Content

General criteria

The best-known part of the accord is a list of properties that a jet definition should have. In paraphrase, a jet definition should be:

1. straightforward to implement in an experimental analysis;
2. straightforward to implement in a theoretical calculation;
3. defined at any order of perturbation theory;
4. such that it yields finite cross sections at any order of perturbation theory;
5. such that its cross sections are relatively insensitive to hadronization.

The first two requirements mean the same algorithm must accept partons as input in a calculation and particles, tracks or calorimeter towers as input in an experiment. The fourth is in effect a requirement of infrared and collinear safety. The fifth asks that jet observables depend as little as possible on non-perturbative effects such as hadronization and the underlying event.

Cone definition

The accord also specified a cone algorithm. A jet is a direction in pseudorapidity ($\eta$) and azimuth ($\phi$) that maximizes the transverse energy flowing through a cone of fixed radius $R$ around it. A particle or calorimeter cell $i$ belongs to the cone if its distance from the jet axis satisfies

${\sqrt {(\eta _{i}-\eta _{J})^{2}+(\phi _{i}-\phi _{J})^{2}}}\leq R.$

The jet is treated as massless. Its transverse energy is the scalar sum of the constituents' transverse energies, and its direction is the transverse-energy-weighted centroid:

$E_{T}=\sum _{i\in \mathrm {cone} }E_{T,i},\qquad \eta _{J}={\frac {1}{E_{T}}}\sum _{i\in \mathrm {cone} }E_{T,i}\,\eta _{i},\qquad \phi _{J}={\frac {1}{E_{T}}}\sum _{i\in \mathrm {cone} }E_{T,i}\,\phi _{i}.$

A jet is a "stable" cone: one whose centroid, computed from its contents, coincides with the axis used to draw it.

Implementation and limitations

The CDF experiment at the Tevatron was the first to implement the accord and found that it was not a complete definition. The accord did not say how to locate stable cones, nor what to do when stable cones overlapped. CDF's resulting iterative cone algorithm, JetClu, started from seed towers above an energy threshold and added a split–merge step for overlapping cones. Other experiments made different choices, so in practice "Snowmass cone" jets were not identical from one analysis to another.

These additions also broke the accord's own requirements. Because the jet-finding started from seeds, the result could depend on soft radiation, appearing as a logarithmic dependence of calculated cross sections on the seed threshold. At parton level, theorists approximated the experimental behavior with an extra parameter, $R_{\mathrm {sep} }$, controlling when two partons were merged into one jet. For Tevatron Run II the midpoint cone algorithm added extra seeds between pairs of jets to reduce the problem. Later analysis showed that seeded cone algorithms, including the midpoint variant, remained infrared unsafe at higher orders. The seedless SISCone algorithm, published in 2007, was the first cone algorithm shown to satisfy infrared and collinear safety.

Legacy

The accord is widely regarded as the first serious attempt to standardize jet definitions across experiments and between theory and experiment. Its title, "toward" a standardization, has been read as a sign that the authors did not yet know what the standard definition should be, nor how to meet their own criteria at a hadron collider.

Sequential-recombination algorithms offered an alternative without the split–merge ambiguities of cones. The k_T algorithm was adapted to hadron collisions in 1993. The Cambridge–Aachen (C/A) algorithm, developed in 1997–1999, clusters particles purely by angular distance. Its angular ordering makes it the standard choice for reclustering the constituents of large-radius jets and declustering them in substructure studies, as in the mass-drop and soft-drop taggers. The anti-k_T algorithm, introduced in 2008, produces regular, cone-like jets while remaining infrared and collinear safe. It became the default jet algorithm of the ATLAS and CMS experiments at the LHC.

The Snowmass criteria remain the standard checklist against which jet algorithms are judged and are reproduced in textbooks and lecture notes on jet physics.

See also

• Jet (particle physics)
• Hadronization
• Quantum chromodynamics
• Snowmass Process