Scattering amplitudes

Scattering amplitudes
Name	Scattering amplitudes
Field	Quantum field theory
Introduced	20th century
Notable people	Richard Feynman, Freeman Dyson, Murray Gell-Mann, Steven Weinberg, Roger Penrose

Contents

Scattering amplitudes Scattering amplitudes are quantities that encode probabilities for transitions between asymptotic states in high-energy processes and appear across particle physics, quantum field theory, and string theory. They connect calculational frameworks developed by figures associated with CERN, Princeton University, Institute for Advanced Study, Harvard University, and Stanford University and provide the basis for phenomenology used by experiments at Large Hadron Collider, SLAC National Accelerator Laboratory, Fermilab, DESY, and KEK. Modern research unites techniques from communities around Perimeter Institute, Simons Foundation, Institute for Advanced Study, Caltech, and Max Planck Society.

Introduction

Scattering amplitudes arise when evaluating S-matrix elements associated with processes studied at Large Hadron Collider, Stanford Linear Accelerator Center, Brookhaven National Laboratory, CERN, and Fermilab. They are computed using frameworks developed by Richard Feynman, Freeman Dyson, Murray Gell-Mann, Steven Weinberg, and Gerard 't Hooft and are essential for predictions compared against data from collaborations such as ATLAS, CMS, LHCb, ALICE, and Belle II. Research on analytic structure and symmetries has involved institutions like Perimeter Institute, Institute for Advanced Study, Princeton University, Harvard University, and Caltech.

The formal definition employs the S-matrix formalism introduced by John von Neumann-era developments and refined by Paul Dirac, Richard Feynman, and Freeman Dyson in perturbative Quantum Electrodynamics contexts. Amplitudes are functions on spaces of kinematic invariants such as Mandelstam variables introduced in work connected to Satyendra Nath Bose-era scattering analyses and later formalized by researchers at CERN and SLAC National Accelerator Laboratory. Analyticity, crossing symmetry, and unitarity—principles examined in studies affiliated with Princeton University, Institute for Advanced Study, Caltech, and Yale University—constrain their singularity structure. Representation theory tools from École Normale Supérieure and Institute for Advanced Study relate amplitudes to spinor-helicity variables associated with work by Roger Penrose and later formalists at Harvard University and Stanford University.

Traditional methods use Feynman diagrams developed by Richard Feynman and resummation techniques refined by Freeman Dyson and Gerard 't Hooft at CERN and Utrecht University. Modern numerical and algebraic approaches leverage spinor-helicity formalisms influenced by Roger Penrose, unitarity methods popularized by groups at Princeton University and Stanford University, and recursion relations introduced in collaborations linked to Cambridge University and Imperial College London. Tools and software packages from teams at SLAC National Accelerator Laboratory, DESY, Fermilab, CERN, and University of Durham implement Monte Carlo and on-shell reduction techniques used by ATLAS and CMS analysis groups. Loop integrals are evaluated using methods developed at Max Planck Society, University of Edinburgh, Yale University, and Columbia University, often employing algebraic geometry perspectives from IHES and Mathematical Sciences Research Institute.

Amplitudes underpin predictions for collider processes at Large Hadron Collider, Tevatron, HERA, and LEP and inform precision measurements pursued by collaborations at Brookhaven National Laboratory and KEK. They are crucial for tests of the Standard Model developed by CERN-linked theorists and for searches for beyond-Standard-Model signatures considered by research groups at Fermilab, SLAC National Accelerator Laboratory, and Lawrence Berkeley National Laboratory. In theoretical physics, amplitudes connect to string-theory constructs from Institute for Advanced Study and Princeton University, to holographic dualities explored at Perimeter Institute and Harvard University, and to effective field theories developed at Caltech and Stanford University.

On-shell techniques, championed by researchers associated with Princeton University, Perimeter Institute, Institute for Advanced Study, Stanford University, and Cambridge University, bypass off-shell Lagrangian machinery used in earlier work by Steven Weinberg and Gerard 't Hooft. The spinor-helicity formalism and Britto–Cachazo–Feng–Witten recursion (BCFW) emerged from collaborations involving groups at Caltech, Harvard University, Imperial College London, and Cambridge University. Research into the amplituhedron and geometric formulations was advanced by teams at Institute for Advanced Study, Princeton University, and Perimeter Institute, while connections to twistor theory trace to Roger Penrose and developments at Oxford University and Cambridge University. Recent progress includes contributions from scientists at Simons Foundation, Max Planck Society, SLAC National Accelerator Laboratory, CERN, and Harvard University.

Seminal results include analytic formulae for tree-level gluon amplitudes by groups at Princeton University and Cambridge University, Parke–Taylor formula connections discovered in collaborations involving University of Manchester and Imperial College London, and one-loop unitarity methods refined at SLAC National Accelerator Laboratory and DESY. The discovery of surprising cancellations in gravity amplitudes involved work at Institute for Advanced Study, Princeton University, and Perimeter Institute. Precision multi-loop computations relevant for Large Hadron Collider phenomenology were carried out by teams at CERN, Max Planck Society, Lawrence Berkeley National Laboratory, and Yale University.