Wing Sheung Chan

Object reconstruction and identification 51 The algorithm is capable of classifying a τ had - vis into one of the five modes: 1p0n, 1p1n, 1pXn, 3p0n and 3pXn, where the number before ‘p’ represents the number of h ± ’s and the number before ‘n’ represents the number of π 0 ’s, with ‘X’ denoting > 1 in 1pXn and ≥ 1 in 3pXn. This opens up the possibility to perform decay-mode-specific calibrations and measurements. 3.2.3. Energy calibration The calorimeters and the inner detector trackers measure energy/momentum by very different means, which lead to very different performance. The calorimeters measure energy by absorption. They have a principal energy resolution ( σ E ) that is independent of the direction and improves with the energy of the initial particle: σ E E ∝ 1 √ E . (3.3) On the contrary, the inner detector trackers measure momentum by the curvature of magnetically bent track. The momentum resolution ( σ p ) of a tracker is at its best when measuring low-energy particles that travel in the transverse direction: σ p p ∝ p T . (3.4) These differences imply that the calo TES and pantau TES have very different resolution performance. Alone, neither of the calo TES and pantau TES is optimal for the vast range of physics analyses performed in ATLAS. In this regard, an advanced energy calibration that combines the merits of both the calo TES and pantau TES has been developed. The calibration relies on BDT regression algorithm (also known as boosted regression trees, or BRT) [76, 80] and is referred to as the MVA TES [81] . As an intermediate starting point for the machine learning, the calo TES and pantau TES are first combined using a simpler algorithm. A “combined TES” is defined by the inverse-resolution-weighted average of the calo TES and pantau TES. The transverse momentum in the combined TES is calculated as p comb T = σ 2 p − ρ c,p σ c σ p p calo T + ( σ 2 c − ρ c,p σ c σ p ) p pantau T σ 2 c + σ 2 p − 2 ρ c,p σ c σ p , (3.5) where σ c and σ p are the resolutions of the calo TES and pantau TES respectively, and ρ c,p is the correlation coefficient of the two TESs. The resolutions and correlations are estimated as functions of p T , | η | and reconstructed decay modes based on simulations. The combined TES is then further calibrated by a BDT regression algorithm. The major inputs to the BDT are the transverse momenta at different scales, p LC T , p calo T and p comb T . Additionally, the energy-weighted averages of some cluster moments are also fed into the BDT. These variables are found to be correlated with the residues of the calo TES (defined as p calo T − p truth T , where p truth T is the true p T of the τ had - vis ) according to simulations.