E coeffs 1 Absolute energy calibration V. Morgunov DESY, Hamburg and ITEP, Moscow HCAL main meeting, DESY, January 19, 26 The copy of this talk one can find at the http://www.desy.de/ morgunov Jan 19, 26, DESY
E coeffs 2 Introduction I would like to show the first results for the fresh simulated events by Mokka at the GRID. And a new absolute energy calibration method. Jan 19, 26, DESY
E coeffs 3 How to get calorimeter energy conversion coeffs? Easy: One should run muons in Monte Carlo, take whole energy in absorber and scintillator, and divide it by energy in the scintillator. The reason for this is: if one particle crosses one sampling layer it should deposit the whole energy, but we can measure the scintillator energy only. But: the cascade in matter consists of not only pure particles (track like) but rather dense electromagnetic showers and a mixture of the photoeffect s and compton scattered electrons together with pure track like energy deposition. This leads to the co called e/π ratio for the calorimeter response for different types of particles. The using of the complex calorimeter, which we have in LDC detector, leads to even more tricky procedure for the calibration, because it needs to define the coeffs for each part of the calorimeter with different samplings and then choose the correct ratio between that coeffs to get a correct whole measured energy. So, let us start from the coeffs defined by muon run in the simulation. C = E whole /E visible for each sampling structures, that is in our case three of them. Jan 19, 26, DESY
E coeffs 4 How to get a whole event energy conservation? Hcal energy () 6 5 Old coeffs for t tbar to 6 jets, 5 The simple formula should give us an answer E Ecal + E Hcal = E CM but, we have no this see a picture. 4 So, let us rotate the black line to the position of the red one by rescaling the coefficient of 3 energy conversion (see previous slide). Rotation actually means of the affine trans- 2 formation of this 2 D space. (see next slide) 1 These rotated coeffs consist of all the properties of the whole LDC calorimeters as well as the flavor s containment of the jets! 1 2 3 4 5 6 Ecal energy () Jan 19, 26, DESY
E coeffs 5 The black line equation is: How to rotate? a E Ecal + E Hcal = a (c 1 E vis1 + c 2 E vis2 ) + c 3 H vis = E where: c 1, c 2 and c 3 is an initial energy conversion coeffs, a is the slope which give us the minimal energy width. E is some constant the line should come through the most probable value of the initial energy sum. By the way; if the initial coeffs were bad fitted to the intrinsic mutual calorimeter properties (bad inter calibration), one will never get the sharp top right edge of the energy distribution as well as the most probable line! The red line equation is: E calib ECAL + Ecalib HCAL = E CM energy conservation law. Then we got the new coeffs: where: f = E CM /E ; and Let us require E = E CM and a = 1 exactly. c calib 1 = fa c 1, c calib 2 = fa c 2 and c calib 3 = fc 3 ; c calib 1 E vis1 + c calib 2 E vis2 + c calib 3 H vis = E CM along the most probable line These three coeffs will be applied latter on to each hit in the particular sampling regions of the calorimeter. Jan 19, 26, DESY
E coeffs 6 The results of rotation/rescaling are Hcal energy () 1 8 New coeffs for t tbar to 6 jets, 1 Hcal energy () 5 45 4 New coeffs for t tbar to 6 jets, 5 Hcal energy () 5 45 4 New coeffs for e+ e- to heavy quarks, 5 35 35 6 3 3 25 25 4 2 2 15 15 2 1 1 5 5 2 4 6 8 1 Ecal energy () 5 1 15 2 25 3 35 4 45 5 Ecal energy () 5 1 15 2 25 3 35 4 45 5 Ecal energy () Hcal energy () 1 8 New coeffs for W+ W- to everything, 1 Hcal energy () 5 45 4 New coeffs for W+ W- to everything, 5 Hcal energy () 5 45 4 New coeffs for e+ e- to light quarks, 5 35 35 6 3 3 25 25 4 2 2 15 15 2 1 1 5 5 2 4 6 8 1 Ecal energy () 5 1 15 2 25 3 35 4 45 5 Ecal energy () 5 1 15 2 25 3 35 4 45 5 Ecal energy () Jan 19, 26, DESY
E coeffs 7 Calorimeter energy sum 12 New coeffs for t tbar to 6 jets, 1 Constant 15.8 Mean 982.5 Sigma 24.64 14 New coeffs for t tbar to 6 jets, 5 Constant 111.9 Mean 488.8 Sigma 16.9 14 New coeffs for e+ e- to heavy quarks, 5 Constant 14.5 Mean 495. Sigma 14.78 1 12 12 8 1 1 8 8 6 6 6 4 4 4 2 2 2 2 4 6 8 1 12 1 2 3 4 5 6 7 1 2 3 4 5 6 7 7 New coeffs for W+ W- to everything, 1 Constant 64.38 Mean 992.6 Sigma 25.47 8 New coeffs for W+ W- to everything, 5 Constant 71.89 Mean 496.6 Sigma 14.52 16 New coeffs for e+ e- to light quarks, 5 Constant 139.9 Mean 497.9 Sigma 14.9 6 7 14 5 6 12 4 5 1 4 8 3 3 6 2 2 4 1 1 2 2 4 6 8 1 12 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Jan 19, 26, DESY
E coeffs 8 Check plots 12 1 Check quality, t tbar to 6 jets, 1 Constant 13. Mean.1879 Sigma 18.69 1 Check quality, t tbar to 6 jets, 5 Constant 87.81 Mean 1.22 Sigma 12.62 1 Check quality, e+ e- to heavy quarks, 5 Constant 79.47 Mean -.4959 Sigma 12.84 8 8 8 6 6 6 4 4 4 2 2 2-1 -75-5 -25 25 5 75 1-6 -4-2 2 4 6-6 -4-2 2 4 6 18 16 Check quality, W+ W- to everything, 1 Constant 11.8 Mean 2.684 Sigma 17.37 14 12 Check quality, W+ W- to everything, 5 Constant 98.97 Mean 1.567 Sigma 1.89 9 8 Check quality, e+ e- to light quarks, 5 Constant 72.4 Mean -1.73 Sigma 14.14 14 1 7 12 6 1 8 5 8 6 4 6 4 3 4 2 2 2 1-1 -75-5 -25 25 5 75 1-6 -4-2 2 4 6-6 -4-2 2 4 6 Jan 19, 26, DESY
E coeffs 9 For reference Z pole reaction Hcal energy () 1 8 Z to everything, 91.2 18 16 14 Z to everything, 91.2 Constant 152.3 Mean 9.44 Sigma 4.67 12 6 1 8 4 6 2 4 2 2 4 6 8 1 Ecal energy () 2 4 6 8 1 12 All decay channels are allowed. Jan 19, 26, DESY
E coeffs 1 Let us check the result 12 1 Check quality, Z to everything, 91.2 Constant 99.7 Mean -.5865E-1 Sigma 4.247 Sigma = 44.5 % 8 6 4 2-6 -4-2 2 4 6 Jan 19, 26, DESY
E coeffs 11 Marlin Reco also knows about this LDC (tile HCal), 4T 4 35 3 χ 2 / ndf 139.8 / 63 Prob 1.517e-8 Normalisation 369.5 Mean -.8576 Sigma Central Part 3.399 Sigma Left Tail 9.77 Sigma Right Tail 7.756 Fraction Central Part.7956 25 2 15 1 5-6 -4-2 2 4 6 Jan 19, 26, DESY
E coeffs 12 Conclusion Let us use the energy conservation law with its full power. Jan 19, 26, DESY
E coeffs 13 After the conclusion Picture from ZEUS experiment at HERA. Here is no one line can be used to rotate coeffs. But much more complex method is still available for this case for the absolute energy calibration. Only Linear Collider might give us a possibility to use energy conservation law. Jan 19, 26, DESY