Energy loss improvements

1. Energy loss improvements Niels van Eldik, Peter Kluit, Alan Poppleton, Andi Salzburger, Sharka Todorova MCP in Physics and Performance Week 6 February 2013

2. Introduction • Currently the Energy loss description for muons passing the calorimeter has a precision of about Et 100 MeV. • For mass measurements using the combined and or muon (standalone) measurements it is important to improve significantly the precision of the E loss description. • The target that we want to put here is a description that is accurate at e.g. the 10 MeV level. • This we want to achieve on a track-track basis. • This project will need improvements in several areas: • the Tracking Calorimeter description: E loss MOP and sigma modeling • 2) (analytic) computing and reconstruction

3. Introduction: Physics • Concerning physics: • Firstly one can get rid of part of the Landau tail. In particular for isolated muons. This is done by the Muid Combined algorithm. • Secondly, we cannot fully get rid of the Landau tails; but we can give the right (well-centered) MOP value. This means that the MOP of di-muon resonances like Jpsi and Z will be (about) well centered.

4. Calorimeter Tracking geometry • The current situation is the following. • There is a layer based description of the calorimeter to describe the E loss and its error. • This description is not used in Muid because it is not precise enough. The Muid description is basically an eta-phi-p map that gives MOP Eloss and its error. • There are two roads that might improve the situation: • Improve the E loss description of the Calorimeter • Improve the precision of the Muid Eloss map • It is hard to conceive that a map with a precision of 10 MeV can be made. We think however it is possible to achieve a very precise description of the E loss in the calorimeter. • This would require a volume based TG description of the calorimeter.

5. Calorimeter Tracking geometry In the Muon system a volume based TG description gives a very accurate description of the material traversed. For the Muon system this is the best we can achieve. A similar description of the calorimeter would give on a track-by-track basis the E loss. And this is - in my opinion - the ultimate description one wants to have. Both Sharka and Andi are willing to work on this topic. Requirements Eloss: for a given track one wants to know the MOP Eloss value and its error. Secondly one needs the track length in the Calorimeter and its error. Identification: crossed cells and the MOP E loss per cell and its error (for use in Muon Calorimeter Identification algorithms)

6. Energy loss modeling Energy loss modeling is described by a Landau distribution that is characterized by a MOP value and a width or sigma value. The mean MOP energy and the sigma depend on the momentum of the muon and consists of a linear and a logarithmic term. The tracking geometry takes uses dependencies. To obtain a precise description Geant4 simulations and TG should agree on these underlying parametrisations and the material characteristics (such as X0). A study of the Eloss shape in the MC in different regions of the detector was performed. It was found out that the Eloss shape in the Barrel does NOT have a Landau shape. In the Endcap it can be described by a Landau distribution.

7. Energy loss modeling Fit: frac*Landau + (1-frac) Gaussian Puzzle Barrel has 83% Gaussian! Endcap only 4%

8. Barrel: Energy loss modeling Barrel has more Gaussian shape. Why is this? First observed by Alan and Kostas. Their explanation: The distribution has two components: one of Landau component and another track length component. If the track length varies due to multiple scattering the mean of the Landau will be smeared with a Gaussian. Here a model that indeed does the job for 10% track length smearing

9. Energy loss modeling Conclude: Energy loss modeling is described by a Landau distribution that is characterized by a MOP value and a width or sigma value. Need also to know the track length variations dL/L in the Calorimeter to account for the effect observed in the Barrel. That is why on slide this is added as a requirement to the TG description. Reconstruction and computing issues: Back tracking and the impact of the Landau tail. Numerical precision and the Landau distribution, convolutions. Approximation to the Landau distribution.

10. Back tracking and the impact of the Landau Suppose we have a track measured in the MS its q/p distribution will be rather Gaussian. The momentum resolution dp/p in the Muon System is given below:

11. Back tracking and the impact of the Landau If one has a Landau distribution for the Eloss one can calculate the distribution at the IP – so after backtracking- by the following convolution: N(p’) = Integral Landau(E,EMOP,σL)*Gaus(p’-E, σp) dE Note that also the impact of the track variation in the Barrel calorimeter can be written in this form where σp = EMOPdL/L. The point is that the MOP value of the distribution N(p’) is not EMOP anymore. If σL is very small the shift will be very small. However for larger values of σL the shift will depend on σp . This means that in the backtracking the new EMOP value after the convolution should be used. The proposal is to calculate the correction analytically using per track the σp rvalue as shown on slide 9.

12. Numerical issues with the Landau distribution The first approach was to use the formula on slide 10 and compute it. This turns out to be not that trivial: the Landau distribution itself using e.g. the root implementation has a problem. The MOP value you put in is not the maximum of the distribution… It is shifted by about 40 MeV. MOP value of 3 GeV input The maximum of the curve is shifted by 40 MeV The point is that we need a precision of << 10 MeV on the MOP value

13. Numerical issues with the Landau distribution and convolutions The second issue is that one has to use numerical integration and FFT to get the Landau convoluted with a Gaussian distribution. It is far from easy to reach the required numerical precision. To circumvent these problems I decided to move to a set of analytical functions that allow convolution and fast robust fitting. The Landau will be approximated by the x/(a2+x2) 2 for x>0 x = E + E0 a = 3.59524 σL EMOP = E0 + a/√3 and the Gaussian by a 1/(b2+x2) 2 . These functions can be convoluted analytically and fitted to the data.

14. Approximation to the Landau distribution In red the chosen approximation to the Landau function from root (correcting for the problem from slide 11)

15. Next steps • First test version of the volume based Calorimeter Tracking Geometry • Validation of the TG using G4 simulations • Improve the test version etc. • The numerical analytical functions are in place. They should be further validated and tested. • Work them out to give corrections to EMOP • Calculate σ+ and σ – that is used in the CB track fit • Calculate the correction to EMOP if a calorimeter measurement has been obtained below the EMOP+2*σMOP • The test version of TG can already be used to test the importance of the track length variations in the Barrel calorimeter