Finite-width effects on threshold corrections to squark and gluino production

TL;DR

This work assesses how finite decay widths of squarks and gluinos modify threshold-resummed QCD predictions for their LHC production. Using an unstable-particle EFT that combines SCET and pNRQCD, the authors separate resonant and non-resonant contributions and implement soft-gluon and Coulomb resummation with a complex energy to account for width effects. They find that for moderate widths ($\Gamma/\bar{m} \lesssim 5\%$) the zero-width NLL results with bound-state below-threshold contributions provide a reliable description, with residual width-induced uncertainties comparable to inherent resummation ambiguities; for larger widths, non-resonant and higher-order non-relativistic corrections become important and require more complete NLO matching. The study concludes that finite-width effects on total SUSY production are small in practice because the dominant channels involve stable colored sparticles, while narrow-width scenarios may still exhibit bound-state signatures in invariant-mass distributions. Overall, the results support using zero-width threshold resummation augmented by bound-state effects for the relevant MSSM parameter space, and outline the needed steps for extending accuracy to broader width regimes.

Abstract

We study the implication of finite squark and gluino decay widths for threshold resummation of squark and gluino production cross sections at the LHC. We find that for a moderate decay width (Gamma/m < 5%) higher-order soft and Coulomb corrections are appropriately described by NLL calculations in the zero-width limit including the contribution from bound-state resonances below threshold, with the remaining uncertainties due to finite-width effects of a similar order as the ambiguities of threshold-resummed higher-order calculations.

Figures (13)

• Figure 1: Examples of Feynman-diagram topologies contributing to the generic production and decay process \ref{['eq:example-process']}. The second non-resonant diagram contains collinear singularities.
• Figure 2: Diagrammatic representation of the leading resonant and non-resonant contribution to the forward-scattering amplitude in unstable particle effective theory.
• Figure 3: Computation of the matching coefficient of the production operator for squark-antisquark production from the quark-antiquark initial state.
• Figure 4: Computation of the matching coefficient of the four-parton operator for squark-antisquark production and decay. The first diagram is an example of a double-resonant diagram, the second of the interference of a double-resonant and a single-resonant diagram.
• Figure 5: Size of the first Coulomb correction (red, dotted), first and second Coulomb corrections (blue, dashed) and resummed Coulomb corrections (black, solid) relative to the leading cross section in the effective theory as a function of $\bar{\Gamma}$ and for $\bar{m}=1500\, \text{GeV}$. $r$ is defined as $r=m_{\tilde{g}}/m_{\tilde{q}}$. For technical reasons the potential function is set to zero for $E<\Delta E$ as defined in \ref{['eq:DeltaEdef']}.