90 likes | 172 Views
Study of Convergence in Proton Reconstruction Algorithm for TOTEM. Ayah Massoud Penn State University. Outline. Introduction Purpose of TOTEM Minimization Algorithms What I’ve done and future work. TOTEM ( TOT al E lastic M easurement). Purpose:
E N D
Study of Convergence in Proton Reconstruction Algorithm for TOTEM Ayah Massoud Penn State University
Outline • Introduction • Purpose of TOTEM • Minimization Algorithms • What I’ve done and future work
TOTEM(TOTalElastic Measurement) Purpose: • Measure total p-p cross section to an accuracy of 1% based on Optical Theorem • Measure elastic scattering in the range 10-3<|t|<8 GeV2 where and • Deeper understanding of proton structure by studying elastic scattering with large momentum transfers
Total pp cross sections as function of √s • Current models predictions: 90-130 mb • Aim of TOTEM: • ~1% accuracy • Normalize s for another particle from stotal • Calculate probability of interaction 14 TeV
Proton Reconstruction • Complicated software simulates pp and detectors and reconstructs the proton kinematics based on optical models • Since L is measured and need to find G, a minimization algorithm is implemented • My task is to figure out what conditions lead to these divergences and minimize error Fractional momentum change Initial position Horizontal and vertical scattering angles
Minimization Algorithms • 1)Newton’s Method: • For minimum to exist: • G and V=G-1 have to be positively defined • All eigenvalues are positive
Cont’ 2) c2 Minimization: non-linear least squares • Less no. of iterations • Sometimes the covariance matrix does not converge to the true covariance matrix
What I’ve been doing so far: • More ROOT • CMSSW and CVS framework • Minimization package MINUIT Future work • Apply minimization to actual data • Error measurements