Breakdown of the Narrow Width Approximation for New Physics

The narrow-width approximation is used in high-energy physics to reduce the complexity of scattering calculations. It is a fortunate accident that it works so well for the standard model, but in general it will fail in the context of new physics. We find numerous examples of significant corrections when the calculation is performed fully off shell including a finite width, notably from effects from the decay matrix elements, not just phase space. If not taken into account, attempts to reconstruct the Lagrangian of a new physics discovery from data would result in considerable inaccuracies and likely inconsistencies.

Figure 1

Feynman diagrams for various example processes discussed in the text: (a) scalar field theory toy model, (b) gluino resonance in supersymmetry, (c) VSS, and (d) SFF momentum-dependent renormalizable interaction vertices.

Figure 2

Ratio of effective to naïve BRs (left axis) and off shell to NWA cross sections (right axis) for the MSSM process $u\overline{d}\to {\tilde{\chi }}_1^{+}\overline{s}{\tilde{s}}_L$ at the LHC [cf. Fig. 1b]. The resonant gluino has an additional partial width of 0.5%, 1%, 2%, 5% of its mass (solid curve, dashed curve, dash- dotted curve, and dotted curve) due to decays to stops and sbottoms. The first- and second-generation squarks lie in the shaded band for all SPS benchmark points with a heavier gluino.

Figure 3

MSSM gluino decay asymmetry to degenerate-mass left-chiral versus right-chiral squarks as a function of the squark to gluino mass ratio, in ${\tilde{\chi }}_1^{+}\tilde{g}$ production at the LHC, as discussed in the text. The NWA predicts exactly zero for all masses. The downward-sloping (yellow) [upward-sloping (blue)] curves are for multimode [single-mode] decays; line types and shaded band as in Fig. 2.