Factorization formulas for exclusive multijet cross sections

What the study found: The paper derives factorization formulas for exclusive n-jet limits, where one or more jets are unresolved. It shows that the leading-power phase space separates into hard, radiation, and soft parts, and that generic resolution variables can be described using fully differential beam, jet, and soft functions.
Why the authors say this matters: The authors conclude that their framework can be simplified for specific resolution variables, and they present it as a way to handle rapidity divergences and numerical evaluation of subtracted soft functions. They also state that the method can be used for both SCET II- and SCET I-type resolution variables.
What the researchers tested: The study uses an asymptotic expansion of the multijet cross section and the method of regions to identify relevant phase-space regions. It applies infrared factorization properties of squared matrix elements at leading power to derive the factorization formula, and it regularizes rapidity divergences with a time-like reference vector in a method called the z_N-prescription.
What worked and what didn't: The leading-power phase space factorized into a hard phase space and separate radiation phase spaces for collinear sectors and the soft sector. The zero-bin contributions were shown to combine with the soft function to define a subtracted soft function free of rapidity divergences and suitable for numerical evaluation. As an application, the authors derived factorization formulas for several transverse-momentum-like variables and identified one variable that factorizes into simple cumulant functions to all orders in perturbation theory.
What to keep in mind: The abstract does not describe experimental data or numerical results beyond the stated factorization results. It also does not give detailed limitations, so the scope is limited to the kinematic limit and variables discussed in the paper.

Key points

• The paper derives factorization formulas for exclusive n-jet cross sections when one or more jets are unresolved.
• The leading-power phase space is shown to split into hard, radiation, and soft parts.
• A time-like reference vector is used in the z_N-prescription to regularize rapidity divergences.
• Zero-bin contributions combine with the soft function to form a subtracted soft function suitable for numerical evaluation.
• The authors derive formulas for several transverse-momentum-like variables and identify one variable with all-orders cumulant factorization.