RevModPhys.84.1307 - REVIEWS OF MODERN PHYSICS VOLUME 84 JULYSEPTEMBER 2012 From eV to EeV Neutrino cross sections across energy scales J A Formaggio

From eV to EeV: Neutrino cross sections across energy scales J. A. Formaggio * Laboratory for Nuclear Science Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA G. P. Zeller † Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA (published 24 September 2012) Since its original postulation by Wolfgang Pauli in 1930, the neutrino has played a prominent role in our understanding of nuclear and particle physics. In the intervening 80 years, scientists have detected and measured neutrinos from a variety of sources, both man made and natural. Underlying all of these observations, and any inferences we may have made from them, is an understanding of how neutrinos interact with matter. Knowledge of neutrino interaction cross sections is an important and necessary ingredient in any neutrino measurement. With the advent of new precision experi- ments, the demands on our understanding of neutrino interactions is becoming even greater. The purpose of this article is to survey our current knowledge of neutrino cross sections across all known energy scales: from the very lowest energies to the highest that we hope to observe. The article covers a wide range of neutrino interactions including coherent scattering, neutrino capture, inverse beta decay, low-energy nuclear interactions, quasielastic scattering, resonant pion production, kaon production, deep inelastic scattering, and ultrahigh energy interactions. Strong emphasis is placed on experimental data whenever such measurements are available. DOI: 10.1103/RevModPhys.84.1307 PACS numbers: 25.30.Pt, 13.15.+g, 14.60.Lm CONTENTS I. INTRODUCTION 1307 II. A simple case: Neutrino-lepton scattering 1308 A. Formalism: Kinematics 1308 B. Formalism: Matrix elements 1309 C. Experimental tests of electroweak theory 1311 D. Radiative corrections and G F 1312 III. Thresholdless processes: E # ± 0 – 1 MeV 1312 A. Coherent scattering 1312 B. Neutrino capture on radioactive nuclei 1313 IV. Low-energy nuclear processes: E # ± 1 – 100 MeV 1313 A. Inverse beta decay 1314 B. Beta decay and its role in cross section calibration 1314 C. Theoretical calculations of neutrino-deuterium cross sections 1315 D. Other nuclear targets 1316 E. Estimating fermi and Gamow-Teller strengths 1317 F. Experimental tests of low-energy cross sections on nuclei 1318 1. Hydrogen 1318 2. Deuterium 1320 3. Additional nuclear targets 1320 G. Transitioning to higher energy scales 1322 V. Intermediate energy cross sections: E # ± 0 : 1 – 20 GeV 1322 A. Quasielastic scattering 1324 B. NC elastic scattering 1326 C. Resonant single pion production 1327 D. Coherent pion production 1331 E. Multipion production 1331 F. Kaon production 1332 G. Outlook 1333 VI. High-energy cross sections: E # ± 20 – 500 GeV 1333 A. Deep inelastic scattering 1333 VII. Ultra-high-energy neutrinos: 0.5 TeV–1 EeV 1335 A. Uncertainties and projections 1336 VIII. Summary 1337 Acknowledgments 1337 References 1337 I. INTRODUCTION The investigation into the basic properties of the particle known as the neutrino has been a particularly strong and active area of research within nuclear and particle physics.