Boosted bosons and wavelets

For the LHC Run 2 and beyond, experiments are pushing both the energy and the intensity frontier so the need for robust and efficient pile-up mitigation tools becomes ever more pressing. Several methods exist, relying on uniformity of pile-up, local correlations of charged to neutral particles, and parton shower shapes, all in $y − \phi$ space. Wavelets are presented as tools for pile-up removal, utilising their ability to encode position and frequency information simultaneously. This allows for the separation of individual hadron collision events by angular scale and thus for subtracting of soft, diffuse/wide-angle contributions while retaining the hard, small-angle components from the hard event. Wavelet methods may utilise the same assumptions as existing methods, the difference being the underlying, novel representation. Several wavelet methods are proposed and their effect studied in simple toy simulation under conditions relevant for the LHC Run 2. One full pile-up mitigation tool (‘wavelet analysis’) is optimised and its impact on a few jet kinematic variables assessed in both toy and official 13 ATLAS MC. Finally, a mock search for new resonances in the semi-leptonic WW channel is presented, focusing on the sensitivity improvements achievable using the wavelet analysis. It is found that jet energy bias may be removed and resolution im- proved by O(50%) for $p_{⊥}$ = 300 GeV jets at $\langle \mu \rangle$ = 40. Similarly, jet mass sensitivity for boosted boson jets may be improved by O(100%) under similar conditions. The latter has the effect of increasing the semi-leptonic diboson search sensitivity at $\langle \mu \rangle \approx$ 25 by upwards of 10% for resonance masses relevant for Run 2. Therefore, analyses at ATLAS—as well as e.g. CMS and ALICE—may immediately benefit from employing wavelet-based methods, both for searches and for other specialised tasks. The impact of using wavelet analyses only increases with $\langle \mu \rangle$, underlining their promise at current and future hadron collider experiments.