Parameterization of Parton Distributions Functions Based on Self-Organizing Maps

ORAL

Abstract

Neural network algorithms have been recently applied to construct Parton Distribution Functions (PDFs) parametrizations which provide an alternative to standard global fitting procedures [1]. In this contribution we propose a different technique, namely an interactive neural network algorithm using Self-Organizing Maps (SOMs) [2]. SOMs generate a nonuniform projection from a high dimensional data space onto a low dimensional one (usually 1 or 2 dimensions) by clustering similar PDF representations together. Our SOMs are trained on progressively narrower selections of data samples. The selection criterion is that of convergence towards a neighborhood of the experimental data. Our procedure utilizes all available data on deep inelastic scattering in the kinematical region of 0.001 $\leq x \leq$ 0.75, and 1 $\leq Q^2 \leq$ 100 GeV$^2$, with a cut on the final state invariant mass, W$^2 \geq$ 10 GeV$^2$. Our main goal is to provide a fitting procedure that, at variance with standard neural network approaches, allows for an increased control of the systematic bias. SOMs, in fact, enable the user to directly control the data selection procedure at various stages of the process. \newline \newline [1] L. Del Debbio, S. Forte, J. I. Latorre, A. Piccione and J. Rojo, [NNPDF Collaboration], JHEP \textbf{0503}, 080 (2005). \newline [2] T. Kohonen, ``Self Organizing Maps,'' Springer-Verlag, 1997.

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Authors

  • Y. Loitiere

  • J. Deng

    US Naval Observatory, University of Virginia, Thomas Jefferson National Accelerator Facility, College of William and Mary, US Army Research Office, Brimrose Corporation of America, Hampton University, Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, Department of Physics, Old Dominion University, Norfolk, VA 23529, University of North Carolina at Chapel Hill, Department of Physics, Old Dominion University, Norfolk, Virginia, Department of Physics, Korea University, Seoul, Korea, Department of Physics, University of Virginia, Charlottesville, VA, Department of Physics, Old Dominion University, Norfolk, VA, North Carolina State University and WebAssign, Raleigh, NC, North Carolina State University, Raleigh, NC, Broughton High School, Raleigh, NC, University of Wisconsin at Whitewater, Whitewater, WI, University of North Carolina-Chapel Hill Department of Physics, University of West Virginia - Chemistry Dept., ORNL, Old Dominion University, University of West Virginia Department of Chemistry, Clemson University, South Carolina Governor’s School for Science and Mathematics, College of Charleston, Rice University, Korea Research Institute of Standards and Science, Ohio State University, Wright State University, Yale U, JINR, Dubna, Univ. Fed. do Rio de Janeiro, Vanderbilt Univ./JIHIR(ORNL)/Tsinghua Univ., NSCL(MSU), LLNL, LBNL, Vanderbilt Univ./LBNL/JIHIR(ORNL), Vanderbilt Univ., Jagellonian University, University of Bonn, North Carolina A{\&T} State University, North Carolina Central University, Duke University and TUNL

  • J. Deng

    US Naval Observatory, University of Virginia, Thomas Jefferson National Accelerator Facility, College of William and Mary, US Army Research Office, Brimrose Corporation of America, Hampton University, Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, Department of Physics, Old Dominion University, Norfolk, VA 23529, University of North Carolina at Chapel Hill, Department of Physics, Old Dominion University, Norfolk, Virginia, Department of Physics, Korea University, Seoul, Korea, Department of Physics, University of Virginia, Charlottesville, VA, Department of Physics, Old Dominion University, Norfolk, VA, North Carolina State University and WebAssign, Raleigh, NC, North Carolina State University, Raleigh, NC, Broughton High School, Raleigh, NC, University of Wisconsin at Whitewater, Whitewater, WI, University of North Carolina-Chapel Hill Department of Physics, University of West Virginia - Chemistry Dept., ORNL, Old Dominion University, University of West Virginia Department of Chemistry, Clemson University, South Carolina Governor’s School for Science and Mathematics, College of Charleston, Rice University, Korea Research Institute of Standards and Science, Ohio State University, Wright State University, Yale U, JINR, Dubna, Univ. Fed. do Rio de Janeiro, Vanderbilt Univ./JIHIR(ORNL)/Tsinghua Univ., NSCL(MSU), LLNL, LBNL, Vanderbilt Univ./LBNL/JIHIR(ORNL), Vanderbilt Univ., Jagellonian University, University of Bonn, North Carolina A{\&T} State University, North Carolina Central University, Duke University and TUNL