Tracking resolution 9th December 2016 1
Material for tracking seminar intrinsic pt resolution for equidistant measurement resolution in case of correlated errors N ef vs Np e.g Space charge distortion, Time response function ● requirement for the precision of calibration ● approximate formulas - intrinsic p t resolution in case of combined (non equidistant) p t measurement consideration for the TPC+ITS+TRD diferent fmuctuation scenarios ● 9th December 2016 2
q/p t resolution. T rack-let update In the case of N equidistant measurement q/pt resolution Gluckstern [NIM 24 (1963) 381] (for N>10) Track-let position resolution for N cl independent clusters Alice TPC - Numerical simulation Curvature resolution at limit of high N eff N tr track-lets (15 in example) N cl space points per tracklet (8 in example) Global fjt with the N tr track-lets and global fjt with the N tr x N cl space points - similar performance In T oy Simulation example space points assumed to be independent ● → N efallf =N tr x N cl 9th December 2016 3
TPC q/p t resolution. Track-let update In the case of N equidistant measurement q/pt resolution Gluckstern [NIM 24 (1963) 381] (for N>10) Track-let position resolution for N cl independent clusters Alice TPC - Numerical simulation Curvature resolution at limit of high N eff Number of efective point N ef reduced by correlation between measurement ( N ef !=N points ) T rack-let consideration Speed-up track fjt (e.g 6 Kalman propagate and Update instead of 159) ● Possibility to account for correlation. ● track-let length longer than correlation length ● Approximation of analytical formulas for non equidistant measurement ● 9th December 2016 4
N ef in case of correlated measurement. Examples. Distortion due space charge Time response function (TRF) correlating p 3 - scale parameter 3.7 cm (ALICE TRD) ∆ (cm) pad-row Helix fjt for correlated measurement TPC Space charge distortion example ● N ef ~N all /N corr =159/20~8 ALICE TRD TRF example ● N ef= N all /N corr =20/6 ~ 3. 9th December 2016 5
Space charge fmuctuation Run2 scenario Small ion hotspot Ion integration time ~ 0.1 s S ~ 3x3 cm R in ~83 cm R out ~245cm Volume fraction F = 0.00017 Expected relative fluctuation of space charge originating at volume Signifjcant relative fmuctuation of the space charge Limit cases: big volume limit 1/(F µ track )<<2 → σ/µ ~sqrt(1/N Events ● small volume limit 1/(F µ track )>>2 → σ/µ ~1/s*sqrt(1/N track ● Run 2 O(20-30%) for pp and Pb (small volume limit) - consistent with measurement Run3 Pb-Pb O(2-5%) 9th December 2016 6
Space charge fmuctuation Expected relative fluctuation of space charge Signifjcant relative fmuctuation of the space charge Limit cases: big volume limit 1/(F µ track )<<2 → σ/µ ~sqrt(1/N Events) ● small volume limit 1/(F µ track )>>2 → σ/µ ~sqrt(1/N track ● Run 2 O(20-30%) for pp and Pb (small volume limit) - consistent with measurement Run3 Pb-Pb O(2-5%) 9th December 2016 7
Combined p t resolution. T oy MC Toy MC setup ITS TPC TRD ITS N tr 6 layers σ r φ ef ~ 0.01 cm TPC N tr - 159 layers TRD N tref 6 layers σ r φ ef ~ 0.05 cm Hight SC distortion Small TPC σ r φ Nominal TPC σ r φ σ r φ limit limit resolution Combined pt resolution signifjcantly better than TPC only High distortion limit - q/p t resolution fully determined by ITS and TRD ● Close to TPC nominal resolution - linear scaling of q/p t resolution as ● function of TPC σ r φ 9th December 2016 8
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