Lee, Quigg, and Thacker

Lee, Quigg, and Thacker
Title	Lee, Quigg, and Thacker
Authors	Benjamin W. Lee; C. Quigg; H. B. Thacker
Year	1977
Field	Particle physics; Electroweak interaction
Notable for	Lee–Quigg–Thacker bound on Higgs boson mass; perturbative unitarity constraints

Lee, Quigg, and Thacker Lee, Quigg, and Thacker is a 1977 theoretical paper by Benjamin W. Lee, Chris Quigg, and H. B. Thacker that derived perturbative unitarity constraints on scalar sector scattering amplitudes, producing what is commonly called the Lee–Quigg–Thacker bound on the Higgs boson mass. The work connected calculations in the Standard Model to broader questions in Electroweak interaction phenomenology and influenced searches at facilities such as the CERN Large Electron–Positron Collider and the Large Hadron Collider. The paper sits alongside contemporaneous contributions from figures like Steven Weinberg, Sheldon Glashow, Abdus Salam, and Gerard 't Hooft in shaping modern Particle accelerator program priorities.

Background and Origin of the Paper

The paper arose amid intensive theoretical activity following the formulation of the Standard Model and the renormalization proofs by Gerard 't Hooft and Martinus Veltman, and in the wake of precision work by Glashow, Weinberg, Salam proponents and experimental results from groups at SLAC, Fermilab, and DESY. Lee, Quigg, and Thacker built on earlier studies of symmetry breaking in models advanced by Peter Higgs, François Englert, Robert Brout, and critiques by John Cornwall and Richard Llewellyn Smith on high-energy behavior. The authors aimed to quantify when perturbation theory for weak boson scattering, as developed in treatments by Julian Schwinger, Sergio Fubini, and authors of the Electroweak phase transition literature, would remain valid.

The Lee–Quigg–Thacker Bound and Main Results

Lee, Quigg, and Thacker computed partial-wave amplitudes for longitudinal W boson and Z boson scattering and applied partial-wave unitarity constraints originally formalized by Eugene Wigner and used in analyses by Martin Goldberger and K. M. Watson. They derived an upper limit on the scalar self-coupling and translated it into a numerical bound on the Higgs boson mass, commonly cited near ~1 TeV, by comparing the largest eigenvalue of coupled-channel scattering matrices against the unitarity limit used in studies by Steven Weinberg and Sidney Coleman. The result complemented contemporaneous bounds from triviality studies by Kenneth Wilson and lattice analyses initiated by K. G. Wilson and later pursued at collaborations such as UKQCD and the MILC Collaboration.

Methodology and Theoretical Framework

The authors worked in the spontaneously broken SU(2)×U(1) gauge framework, employing the equivalence theorem connecting longitudinal W boson modes to the would-be Goldstone bosons of the Higgs mechanism as articulated in derivations by John Cornwall, David Politzer, and H. D. Politzer. They evaluated tree-level scattering amplitudes for processes including WLWL → WLWL and WLWL → ZLZL, constructed coupled-channel partial-wave matrices, and imposed unitarity bounds on s-wave eigenvalues following formalism found in texts by Eugene Wigner and reviews by Steven Weinberg. Their approach used perturbative renormalization conditions akin to those developed by Gerard 't Hooft and implemented approximations later refined in analyses by Marciano and Quigg.

Impact on Electroweak Symmetry Breaking and Higgs Physics

The Lee–Quigg–Thacker bound established a concrete target for experiments at CERN, Fermilab, and later the LEP and LHC programs, informing detector designs and search strategies pursued by collaborations such as ATLAS and CMS. It framed theoretical expectations for whether electroweak symmetry breaking would be weakly coupled as in the Minimal Standard Model or strongly coupled as in technicolor proposals by S. Weinberg and L. Susskind, stimulating work on alternatives like composite Higgs boson models from groups including Topcolor researchers and lattice studies led by Michael Creutz. The bound also guided effective field theory formulations used in precision fits by groups centered on LEP Electroweak Working Group and global analyses using techniques from Kenneth Lane and Howard Georgi.

Subsequent Developments and Extensions

Following the discovery of the Higgs boson at the Large Hadron Collider by the ATLAS and CMS collaborations, with mass near 125 GeV, attention shifted to refinements of unitarity arguments in multi-Higgs, singlet-extended, and composite scenarios studied by theorists including Howard Georgi, R. S. Chivukula, Giudice, and Rattazzi. Lattice studies by collaborations such as CLS and ETMC extended triviality and nonperturbative bounds, while unitarization techniques using the K-matrix and dispersion relations invoked methods from S. M. Roy and analyses by Anatoly Vainshtein to explore resonant electroweak scattering. The original Lee–Quigg–Thacker analysis has been generalized to higher representations, multiple scalar fields, and effective-field-theory operators catalogued in bases by Buchmüller–Wyler and later the Warsaw basis.

Reception and Historical Significance

The paper is widely cited in the theoretical particle-physics literature and appears in pedagogical treatments alongside works by Steven Weinberg, Gerard 't Hooft, S. L. Glashow, and Abdus Salam. It served as a benchmark for discussions about the energy scale of new physics, influencing strategy documents by laboratories such as CERN, Fermilab, and advisory panels including the P5. Lee, Quigg, and Thacker’s succinct unitarity argument helped clarify expectations for the Higgs boson well before its experimental observation and remains a canonical example in texts by John Iliopoulos, A. Zee, and Chris Quigg.

Category:Physics papers Category:Particle physics