Standard Model and Beyond · Problem 6.5

The Weak Interactions

Physics — Particle Physics · spin-0-resonance-production

Problem

Suppose there exists a spin-0 resonance

R

with mass

M_R = 1

TeV and width

\Gamma_R \ll M_R

, which couples to gluons, photons,

u\bar{u}

, and

d\bar{d}

, with partial (spin and color summed) decay widths

\bar{\Gamma}_{GG}

\bar{\Gamma}_{\gamma\gamma}

\bar{\Gamma}_{u\bar{u}}

, and

\bar{\Gamma}_{d\bar{d}}

, respectively. Show that the cross section for

pp \to R \to \gamma\gamma

in the narrow width approximation (Appendix F) is of the form

\sigma = [\lambda_{GG}B_{GG} + \lambda_{u\bar{u}}B_{u\bar{u}} + \lambda_{d\bar{d}}B_{d\bar{d}}]\, B_{\gamma\gamma},

where

B_{ij} \equiv \bar{\Gamma}_{ij}/\Gamma_R

is the branching ratio into

ij

. Ignore any contribution of

\gamma\gamma

to the production. Give explicit expressions for the

\lambda_{ij}

in terms of the parton luminosities,

M_R

, and

\Gamma_R

, and calculate their numerical values in fb at LO for the (14 TeV) LHC, assuming

\Gamma_R = 10^{-4}M_R

. Be careful of the color and identical particle factors.