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Study of Convergence in Proton Reconstruction Algorithm for TOTEM

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:

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Study of Convergence in Proton Reconstruction Algorithm for TOTEM

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  1. Study of Convergence in Proton Reconstruction Algorithm for TOTEM Ayah Massoud Penn State University

  2. Outline • Introduction • Purpose of TOTEM • Minimization Algorithms • What I’ve done and future work

  3. 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

  4. 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

  5. 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

  6. Minimization Algorithms • 1)Newton’s Method: • For minimum to exist: • G and V=G-1 have to be positively defined • All eigenvalues are positive

  7. Cont’ 2) c2 Minimization: non-linear least squares • Less no. of iterations • Sometimes the covariance matrix does not converge to the true covariance matrix

  8. 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

  9. Trip to Chamonix

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