Calculations at the Amplitude Level - Using a helicity amplitude formalism Tim Coughlin – Christmas meeting Jan 2006

Why do calculations at the amplitude level? –The diffractive production process with forward Protons. Helicity amplitude formalism –The Weyl - van der Waerden formalism. The calculation of gluino production. Plans for this coming year. Overview

Diffractive production with forward tagged protons Production of a central system via scattering of Protons through very small angles. This is the process the FP420 collaboration is hoping to observe. I am trying to understand the ‘Durham model’ of this process. V.A. Khoze, A.D. Martin, M.G. Ryskin, hep-ph/

Cross-section factorises into two parts: The ‘Durham model’ Only transversely polarised gluons, with equal helicities, contribute to the sub-process amplitude. Average over two possible helicity configurations. ‘Effective luminosity’ Sub-process cross-section

Weyl - van der Waerden formalism - S. Dittmaier, hep-ph/ Rewrite amplitude in 2-spinor notation. i.e. Construct spinors which are helicity eigenstates. Represent gauge Boson polarisation vectors in terms of 2-spinors. Choose gauge to simplify expression for the amplitude.

Construct spinors using eigenvectors of the matrix: These satisfy the Dirac equation and are helicity eigenstates. Choice of spinors

Choice of polarisation vectors for massless spin-1 particles Polarisation vectors can be represented using 2-spinors:

Example calculation: Gluino production ‘Spilt Super Symmetry’ model. – W. Kilian et. al, hep-ph/ Gluino mass can be below TeV scale. Can also be long lived enough to form ‘R-hadrons’ – Distinct signature! Calculated the ‘sub-process cross-section’ at lowest order.

Gluino production continued M (λλ'→σσ') = - p σ p' σ' k λ k' λ' k λ k' λ' p σ p' σ'

Applying Weyl-van-der-Waerden formalism: Differential cross-section (summed over gluino helicities): For 200 GeV gluinos, total diffractive production cross-section: Gluino production: The result

This Year Calculate differential cross-section for production of gluino- gluino bound-states. Turn my attention to the ‘effective luminosity’ part of the process. –Specifically, how infrared divergences in the quark level amplitude are regulated when the quarks are bound into a colour singlet state.