General positivity bounds for spin observables in particle inclusive production

TL;DR

This paper extends positivity bounds for spin observables in inclusive particle production to include parity violation, providing new constraints applicable to high-energy processes like W/Z production at RHIC.

Contribution

It generalizes existing positivity bounds to parity-violating reactions, offering a systematic method to derive new constraints involving all spin observables.

Findings

Derived non-trivial positivity bounds for parity-violating processes

Identified specific bounds relevant for $pp o W^{\pm}/Z^0+X$ and $pp o \ell^{\pm}+X$

Potentially testable at RHIC's longitudinal spin program

Abstract

Positivity constraints, derived initially assuming parity conservation, for the inclusive reaction of the type $A({spin 1/2})+B({spin 1/2})\to C+X$, where the spins of both initial spin-1/2 particles can be in any possible directions and no polarization is observed in the final state, are generalized to the case of parity violation. By means of a systematic method, we obtain non-trivial bounds involving all the spin observables of the reaction and we discuss some relevant physics processes. Particularly we discover a non-trivial positivity constraint for the processes, $pp\to W^{\pm}/Z^0+X$ or $pp\to \ell^{\pm}+X$ where $\ell^{\pm}$ decayed from $W^{\pm}/Z^0$, which could be checked at the ongoing longitudinal spin program at RHIC.