Transcript ppt
Preliminary study of the LAT towers Response Functions with Cosmic Rays Instrument Analysis Workshop Sara Cutini, G. Tosti, P. Lubrano Instrument Analysis Workshop - Aug 29, SLAC 1 Overview • the analysis of response functions helps to understand the performances of the detector Baseline data taking with Cosmic rays: • Run_135000894 for one tower data • Run_135002052 for two towers data Monte Carlo Data: • Official Surface Muons data for one Tower • New Surface Muons data for one Tower with alignment • study of the PSF only due to the muon behaviour • problem: muons come from all directions Instrument Analysis Workshop - Aug 29, SLAC 2 Method used to derive the “PSF” clusters Development of a procedure to define a “PSF” root variable of the LAT towers •First steps: reconstructed track: reconstructed directions and entry point – Assume track like “true information” – extrapolation of the track in all silicon layers – calculate the difference between the track point and the clusters in every layer separating the X and Y view – create the variable R using the X and Y measurement R X 2 Y 2 Use only the THIN layers Instrument Analysis Workshop - Aug 29, SLAC Y0 X0 X1 Y1 Y2 X2 X3 Y3 Y4 X4 X5 Y5 Y6 . . . . . . . Y17 -Y Z -X 3 Method used to derive the “PSF” • this “variable” contains (i) the information on the reconstruction of the track and (ii) on the geometrical resolution mm mm mm mm mm mm Instrument Analysis Workshop - Aug 29, SLAC 4 Comparison of R for Data and Montecarlo (Tower A). the “PSF” root variable is computed for events satisfying the following muon selection criteria: • 1 and only 1 reconstructed track • energy selection in the calorimeter (consistent with MIP) • geometrical selection on the reconstructed direction • Comparison with official Montecarlo: analyzed with the same algorithm of data •Real Tower A data mm Instrument Analysis Workshop - Aug 29, SLAC 5 Why this difference?? a similar difference in Merit variable: From Analysis Meeting 27th May •Monte Carlo •Real Tower A data Instrument Analysis Workshop - Aug 29, SLAC 6 Issues discussed in Udine Udine: discussion of the problems related to Kalman’s variables: From Analysis Meeting 17th June • Bill and Hiro gave suggestions about the misalignment of the tracker • Tracy and Leon helped to change it in the Monte Carlo • Michael calculated the real “misalignment constants” to be introduced in the new MC. Thanks to all!! Instrument Analysis Workshop - Aug 29, SLAC 7 New Monte Carlo with the (mis)alignment File. new Montecarlo using the alignment file peaks are now shifted to the right position, there are only small differences left in the tails of the distributions Now we find a better agreement between the real and the MC data. Instrument Analysis Workshop - Aug 29, SLAC From Analysis Meeting 17th June 8 New Monte Carlo with the (mis-)alignment file • Better agreement for R (Tower A) when comparing real Cosmic Rays Data to Monte Carlo simulation. •New Monte Carlo simulation •Real Data mm Instrument Analysis Workshop - Aug 29, SLAC 9 Study of PSF R in Z • study of the PSF in R related to the height of the tower: – fit R distribution in each layer: sum of a Gaussian and an exponential to variable power F(x) = The peak is fitted with a Gaussian and the tails by an exponential ! Study the behaviour of R as a function of the “depth” in the Tower. Instrument Analysis Workshop - Aug 29, SLAC 10 Study of PSF R in Z From top of the tracker mm mm mm Instrument Analysis Workshop - Aug 29,mm SLAC mm 11 Study of PSF R in Z mm mm mm mm mm Instrument Analysis Workshop - Aug 29, SLAC 12 Next Steps: 1 - Calculation of the Full Width Half Maximum (FWHM) of the PSF in R using the fit function 2 - Calculation of the RMS Max and Min of the shape of the PSF 3 – Calculation of the value of PSF in R which contains 68% and 95% of the data, respectively Instrument Analysis Workshop - Aug 29, SLAC 13 1a - Analysis of the FWHM vs Z • calculation of FWHM using the fit function and plotted versus Z • errors: analytical calculation with error propagation Linear regression of the Monte Carlo data Instrument Analysis Workshop - Aug 29, SLAC 14 1b - Theta (polar angle) dependance of R Linear Distribution of the FWHM versus Theta. Indeed the dispersion of the PSF in R is related to the length of the track across the detector. Instrument Analysis Workshop - Aug 29, SLAC 15 1c - Phi (Azimuth angle) dependance of R flat distribution within the errors: independence to the Azimuth angle. Instrument Analysis Workshop - Aug 29, SLAC 16 2 - Measure of the RMS max (A) and min (B) with ellipse analysis Description of ellipse method and calculation of the RMS max (A) and min (B) giving the dispersion of the PSF shape: Barycenter: x, y Y expression for the elliptical shape which contains the data: CXX x x CYY y y CXY ( x x )( y y ) R 2 2 2 Theta X Cos 2Theta Sin 2Theta CXX 2 A B2 Sin 2Theta Cos 2Theta CYY A2 B2 1 1 CXY 2CosThetaSin Theta 2 2 A B Instrument Analysis Workshop - Aug 29, SLAC 17 2 - Measure of the RMS max and min with ellipse analysis Plot of A that represent the RMS maximum of ellipse and B the RMS minimum For the Montecarlo data we have still less dispersion. Instrument Analysis Workshop - Aug 29, SLAC 18 3 - Calculation of PSF values at 68% and 95% levels xk 1 F(x) fit function. n: number of bins i Integral( xi ) = k 0 F ( x)dx xk xn F ( x)dx 0 Percent of distribution Sigma 68% Sigma 95% Instrument Analysis Workshop - Aug 29, SLAC PSF R [mm] 19 3 - Calculation of PSF values at 68% and 95% levels • the ratio Sigma 68% over 95% is flat around 0.5 Sigma 95% is twice the Sigma 68% similar to Gaussian distribution. But: the real data show larger dispersion and a different behavior of the tails Instrument Analysis Workshop - Aug 29, SLAC 20 Conclusions • Alignment is a crucial issue when comparing R distributions for real Data and Monìte Carlo simulations. • As expected: The PSF function shows a linear dependence on Z of the tower • As expected: the PSF depends on the polar angle but is independent of the azimuth angle Instrument Analysis Workshop - Aug 29, SLAC 21 Conclusion •The difference which persists between the Monte Carlo and real data could be related to an underestimation of the multiple scattering in the simulation or related to the input flux. A possible solution: Generated New Monte Carlo with a different input flux: Caprice flux Linear Regression of Caprice Monte Carlo data Instrument Analysis Workshop - Aug 29, SLAC 22