ar X iv : h ep - p h / 04 05 05 2 v 1 6 M ay 2 00 4 Using lepton charge asymmetry to investigate the spin of supersymmetric particles at the LHC

Using lepton charge asymmetry to investigate the spin of supersymmetric particles at the LHC. Abstract If signals suggesting supersymmetry (SUSY) are discovered at the LHC then it will be vital to measure the spin of the new particles to demonstrate that they are indeed the predicted super-partners. A method is discussed by which the spins of some of the SUSY particles can be investigated. Angular distributions in sparticle decays lead to charge asymmetry in lepton-jet invariant mass distributions. The size of the asymmetry is proportional to the primary production asymmetry between squarks and anti-squarks. Monte Carlo simulations are performed for a particular mSUGRA model point at the LHC, demonstrating that the shape of the resultant asymmetry distributions are consistent with a spin-0 slepton and a spin-1 2 ˜ χ 0 2 , but are not consistent with the pure phase-space decays one would obtain from both sparticles being scalars. 1 Spin correlations and charge asymmetry In a paper [1] detailing the method by which spin correlations were added to the HERWIG [2, 3] Monte Carlo event generator, Peter Richardson indicated an example of part of a supersymmetric decay chain, in which spin correlations might have an interesting effect on the kinematics of the emitted particles. When the decay of the slepton is also considered, (fig. 1), the final state consists of two opposite-signed leptons of the same family, a quark jet, and missing energy from the undetected˜χ 0 1. I first consider the distribution of invariant mass of the quark or anti-quark jet from the squark decay, and the lepton or anti-lepton from the˜χ 0 2 decay. Using the terminology of [4], this lepton is known as the 'near' lepton, as opposed to the lepton from the slepton decay, which is called the 'far' lepton. Initially I investigate the parton-level distributions which one would obtain if the sign of the squark and the identity of the lepton were known. The complications arising from our inability to (a) distinguish which lepton came from which decay, and (b) measure the charge of the (s)quark are dealt with in sec. 4. In the approximation in which the quark and lepton are massless, and the SUSY particles are on-mass-shell, then the l near q invariant mass has a simple and direct interpretation in terms of the angle, θ * , between the quark and lepton in the˜χ 0 2 rest frame