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Constraining the Space of Standard Model Effective Field Theory Using Geometric Methods

POSTER

Abstract

Standard Model Effective Field Theory(SMEFT) is an approach to search for Physics beyond the Standard Model. This project focuses on constraining the parameter space of dimension-8 operator coefficients in SMEFT, since their experimental effects are important in determining UV-completeness. The parameter space of the dim-8 operator is a convex cone dual to a spectrahedron. Finding the boundaries of this convex cone is equivalent to finding the extremal ray(ER) of its dual spectrahedron. Previous research has found the analytic solution to the ER of this spectrahedron for small degrees of freedom (n$=$2, 3). The present work aims to find the analytic solution for larger degrees of freedom. Numerical methods were developed to find ER for larger n. From the numerical solutions, we proposed conjectures for general analytic solutions. The conjectures for n$=$4 and rank $=$ 2 have been proved thoroughly, and several other cases, such as n$=$5, 6 and rank $=$ 3 have been understood by extending the ideas from the proofs. Present analysis suggests that a general analytic solution for all n is not promising. Current and future work consists in investigating special cases with more physical relevance.

Authors

  • Valerie Wu

    Reed College

  • Kristin Rabosky

    Middle Tennessee State University, University of Alabama Tuscaloosa, Swarthmore College, CT Clinical Innovation Center, Department of Radiology, Mayo Clinic, Rochester, MN, Bard College, Wright State University, University of Michigan, University of Hawai'i-Manoa, Rice University, University of Alaska Fairbanks, University of Utah, South Dakota School of Mines and Technology, Furman University, University of Notre Dame, Theoretical Physics Division, Institute of High Energy Physics, the Chinese Academy of Sciences, Peng Huanwu Center for Fundamental Theory, University of Science and Technology China, University of Cambridge, University of Kansas, SLAC National Accelerator Laboratory, Planetary Science Institute, Iowa State University, College of Idaho, University of Washington, Bothell, Ottawa Hills High School, Case Western Reserve University, Yale University and Strasbourg Astronomical Observatory, Yale University, Korea Astronomy and Space Science Institute, NOIRLab, Purdue University, Korea Instotute for Advanced Study, Perimeter Institute, Rutgers University, University of Maryland, Juniata College, Columbia University, City University of New York / American Museum of Natural History, Columbia University / American Museum of Natural History, Morehead State University, Hofstra University, Occidental College, Georgia Institute of Technology, School of Physics and Astronomy, University of Minnesota, The Oskar Klein Centre, Department of Astronomy, University of Mississippi, Stanford/KIPAC/SLAC, University of Connecticut, Kansas State University, Vassar College, Penn State, Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Department of Physics, Worcester Polytechnic Institute, Clark University, University of Illinois at Urbana-Champaign, Rhodes College, Rensselaer Polytechnic Institute, Harvard University, Cornell University, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433 & UES, Inc., 4401 Dayton-Xenia Rd, Dayton, OH 45432, Department of Physics, University of Dayton, Dayton Ohio & Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Los Alamos National Laboratory, Utah State University, Ramapo College of NJ, Brookhaven National Laboratory, Research Center of Topological Functional Materials and Henan Key Laboratory of Photovoltaic Materials, Henan Univers., Brookhaven National Laboratory, Montclair State University, Weber State University

  • Kristin Rabosky

    Middle Tennessee State University, University of Alabama Tuscaloosa, Swarthmore College, CT Clinical Innovation Center, Department of Radiology, Mayo Clinic, Rochester, MN, Bard College, Wright State University, University of Michigan, University of Hawai'i-Manoa, Rice University, University of Alaska Fairbanks, University of Utah, South Dakota School of Mines and Technology, Furman University, University of Notre Dame, Theoretical Physics Division, Institute of High Energy Physics, the Chinese Academy of Sciences, Peng Huanwu Center for Fundamental Theory, University of Science and Technology China, University of Cambridge, University of Kansas, SLAC National Accelerator Laboratory, Planetary Science Institute, Iowa State University, College of Idaho, University of Washington, Bothell, Ottawa Hills High School, Case Western Reserve University, Yale University and Strasbourg Astronomical Observatory, Yale University, Korea Astronomy and Space Science Institute, NOIRLab, Purdue University, Korea Instotute for Advanced Study, Perimeter Institute, Rutgers University, University of Maryland, Juniata College, Columbia University, City University of New York / American Museum of Natural History, Columbia University / American Museum of Natural History, Morehead State University, Hofstra University, Occidental College, Georgia Institute of Technology, School of Physics and Astronomy, University of Minnesota, The Oskar Klein Centre, Department of Astronomy, University of Mississippi, Stanford/KIPAC/SLAC, University of Connecticut, Kansas State University, Vassar College, Penn State, Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Department of Physics, Worcester Polytechnic Institute, Clark University, University of Illinois at Urbana-Champaign, Rhodes College, Rensselaer Polytechnic Institute, Harvard University, Cornell University, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433 & UES, Inc., 4401 Dayton-Xenia Rd, Dayton, OH 45432, Department of Physics, University of Dayton, Dayton Ohio & Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Los Alamos National Laboratory, Utah State University, Ramapo College of NJ, Brookhaven National Laboratory, Research Center of Topological Functional Materials and Henan Key Laboratory of Photovoltaic Materials, Henan Univers., Brookhaven National Laboratory, Montclair State University, Weber State University

  • Kristin Rabosky

    Middle Tennessee State University, University of Alabama Tuscaloosa, Swarthmore College, CT Clinical Innovation Center, Department of Radiology, Mayo Clinic, Rochester, MN, Bard College, Wright State University, University of Michigan, University of Hawai'i-Manoa, Rice University, University of Alaska Fairbanks, University of Utah, South Dakota School of Mines and Technology, Furman University, University of Notre Dame, Theoretical Physics Division, Institute of High Energy Physics, the Chinese Academy of Sciences, Peng Huanwu Center for Fundamental Theory, University of Science and Technology China, University of Cambridge, University of Kansas, SLAC National Accelerator Laboratory, Planetary Science Institute, Iowa State University, College of Idaho, University of Washington, Bothell, Ottawa Hills High School, Case Western Reserve University, Yale University and Strasbourg Astronomical Observatory, Yale University, Korea Astronomy and Space Science Institute, NOIRLab, Purdue University, Korea Instotute for Advanced Study, Perimeter Institute, Rutgers University, University of Maryland, Juniata College, Columbia University, City University of New York / American Museum of Natural History, Columbia University / American Museum of Natural History, Morehead State University, Hofstra University, Occidental College, Georgia Institute of Technology, School of Physics and Astronomy, University of Minnesota, The Oskar Klein Centre, Department of Astronomy, University of Mississippi, Stanford/KIPAC/SLAC, University of Connecticut, Kansas State University, Vassar College, Penn State, Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Department of Physics, Worcester Polytechnic Institute, Clark University, University of Illinois at Urbana-Champaign, Rhodes College, Rensselaer Polytechnic Institute, Harvard University, Cornell University, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Air Force Research Lab, Wright-Patterson AFB, Ohio 45433 & UES, Inc., 4401 Dayton-Xenia Rd, Dayton, OH 45432, Department of Physics, University of Dayton, Dayton Ohio & Air Force Research Lab, Wright-Patterson AFB, Ohio 45433, Los Alamos National Laboratory, Utah State University, Ramapo College of NJ, Brookhaven National Laboratory, Research Center of Topological Functional Materials and Henan Key Laboratory of Photovoltaic Materials, Henan Univers., Brookhaven National Laboratory, Montclair State University, Weber State University