The strong coupling constant: state of the art and the decade ahead
D. d’Enterria, S. Kluth, G Zanderighi, César Ayala, Miguel A. Benitez-Rathgeb, J. Blümlein, Diogo Boito, Nora Brambilla, D. Britzger, S. Camarda, A. M. Cooper-Sarkar, Thomas Cridge, Gorazd Cvetič, D. d’Enterria, Mattia Dalla Brida, A. Deur, F. Giuli, Maarten Golterman, André H. Hoang, J. Huston, Matthias Jamin, S. Kluth, A. V. Kotikov, V.G. Krivokhizhin, A S Kronfeld, Viljami Leino, K. Lipka, Tomi P. Mäkelä, B. Malaescu, Kim Maltman, Simone Marzani, Vicent Mateu, S. Moch, Pier Francesco Monni, Pavel Nadolsky, Paolo Nason, A. V. Nesterenko, Redamy Pérez-Ramos, Santiago Peris, Péter Petreczky, Antonio Pich, K. Rabbertz, Alberto Ramos, Daniel Reichelt, Antonio Rodríguez–Sánchez, Juan Rojo, M. Saragnese, L. Sawyer, M Schott, S. Schumann, B. G. Shaikhatdenov, Stefan Sint, Grégory Soyez, Diego Teca, Antonio Vairo, M. Vos, Christopher M. Waits, Johannes Heinrich Weber, M. Wobisch, Kang Xie, G Zanderighi
Abstract
Abstract Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant α S . The current <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>%</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:math> uncertainty of the QCD coupling evaluated at the reference Z boson mass, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0.1179</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0009</mml:mn> </mml:math> , is one of the limiting factors to more precisely describe multiple processes at current and future colliders. A reduction of this uncertainty is thus a prerequisite to perform precision tests of the Standard Model as well as searches for new physics. This report provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling. The current <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> world average is derived from a combination of seven categories of observables: (i) lattice QCD, (ii) hadronic τ decays, (iii) deep-inelastic scattering and parton distribution functions fits, (iv) electroweak boson decays, hadronic final-states in (v) e + e − , (vi) e–p, and (vii) p–p collisions, and (viii) quarkonia decays and masses. We review the current status of each of these seven <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> extraction methods, discuss novel α S determinations, and examine the averaging method used to obtain the world-average value. Each of the methods discussed provides a ‘wish list’ of experimental and theoretical developments required in order to achieve the goal of a per-mille precision on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> within the next decade.