Invariant mass distributions in cascade decays

TL;DR

The paper derives analytic, log-based expressions for invariant-mass distributions of massless SM endproducts in cascade decays $D\rightarrow C c\rightarrow B b c\rightarrow A a b c$, with $A$ invisible, and provides region-based formulas for $m_{ca}$, $m_{c2({\rm high})}$, $m_{c2({\rm low})}$, and $m_{cba}$. By expressing kinematics in flat angular variables, the authors obtain tractable, end-point–driven distributions that depend on mass hierarchies through Regions 1–4 and their subregions, facilitating NP parameter extraction at the LHC. They validate and extend the analytic results at the parton level, incorporate effects of widths, cuts, and FSR, and study detector responses with AcerDET, including a consistency-cut method to mitigate combinatorial backgrounds. The work also discusses the occurrence of “feet” in distributions that can bias endpoint determinations and shows how spin configurations can be included in the distributions via simple multiplicative factors, with explicit SUSY examples in the appendix. Overall, the results provide practical, scalable analytic shapes for NP mass reconstruction and diagnostic tools for endpoint reliability in collider analyses.

Abstract

We derive analytical expressions for the shape of the invariant mass distributions of massless Standard Model endproducts in cascade decays involving massive New Physics (NP) particles, D -> Cc -> Bbc -> Aabc, where the final NP particle A in the cascade is unobserved and where two of the particles a, b, c may be indistinguishable. Knowledge of these expressions can improve the determination of NP parameters at the LHC. The shape formulas are composite, but contain nothing more complicated than logarithms of simple expressions. We study the effects of cuts, final state radiation and detector effects on the distributions through Monte Carlo simulations, using a supersymmetric model as an example. We also consider how one can deal with the width of NP particles and with combinatorics from the misidentification of final state particles. The possible mismeasurements of NP masses through `feet' in the distributions are discussed. Finally, we demonstrate how the effects of different spin configurations can be included in the distributions.