William Allan Bardeen (born September 15, 1941, in Washington, Pennsylvania) is an American theoretical physicist who worked at the Fermi National Accelerator Laboratory. He is renowned for his foundational work on the chiral anomaly (the Adler-Bardeen theorem), the Yang-Mills and gravitational anomalies, the development of quantum chromodynamics and the scheme frequently used in perturbative analysis of experimentally observable processes such as deep inelastic scattering, high energy collisions and flavor changing processes.
He also played a major role in developing a theory of dynamical breaking of electroweak symmetry via top quark condensates, leading to the first composite Higgs models. His work on the chiral symmetry breaking dynamics of heavy-light quark bound states correctly predicted abnormally long-lived resonances which are chiral symmetry partners of the ground states, such as the . He also developed an analytic, non-perturbative approach for the calculation of non-leptonic decays of Kaons, known as Dual QCD.
Bardeen is considered one of the world's leading authorities on quantum field theory in its application to real-world physical phenomena.
Bardeen lives in Warrenville, Illinois, with is wife Marge, who was manager of the Education Department at Fermilab.[2] He has two grown children: Charles a retired Project Scientist at the National Center for Atmospheric Research, Boulder, CO, and Karen, who taught chemistry at Oak Park and River Forest High School, Oak Park, Illinois. He is the son of physicist John Bardeen[3] and Jane Maxwell Bardeen.
Scientific Contributions
Bardeen is co-inventor of the theory of the chiral anomaly, which is of foundational importance in modern theoretical physics. He developed with Stephen L. Adler the "non-renormalization theorem" (known as the Adler–Bardeen theorem).[4] This proves that the anomaly coefficient is not subject to renormalization to all orders in perturbation theory and anticipates the fact that it is associated with topological index theorems.
Bardeen, in a tour de force, computed the full, nontrivial structure of the chiral anomaly in non-abelian Yang-Mills gauge theories.[5] This leads to the distinction between the "consistent anomaly" and the "covariant anomaly." The consistent anomaly is a definition of the loop integrals that satisfies "Wess-Zumino consistency conditions"[6] and is symmetric between left- and right-handed chiral fermions in the Feynman loop. The consistent anomaly is generally related to topology, e.g., the structure and coefficient obtained by Bardeen's calculation turns out to be equivalent to that generated by a topological Chern-Simons term built of Yang-Mills fields in 5 dimensions.
In this work he introduced the "Bardeen counter-term" which maintains the conservation of the vector current in the definition of the loop integral, and places the anomaly in the axial current. This is known as the "covariant anomaly," and is relevant to physics where the vector current is conserved (and reverts to the Adler result in QED with coefficient increased by a factor of 3 over that of the consistent anomaly).[7] These distinctions are crucial to the Wess-Zumino-Witten term, which is an essential part of chiral Lagrangians, describing the anomalous physics of pseudoscalars and vector mesons,[8] and topological effects in Yang-Mills gauge theories, such as the instanton physics in QCD. With Bruno Zumino, Bardeen formulated the theory of the gravitational anomaly which is of fundamental importance to string theory.[9]
On sabbatical, working at CERN in 1971, Bardeen collaborated with Murray Gell-Mann, Harald Fritzsch, and Heinrich Leutwyler. They considered a gauge theory of quark interactions, in which each quark comes in one of three varieties called “colors.’’ They wrote down the theory now known as quantum chromodynamics (QCD) and, through the chiral anomaly, established the existence of the three quark colors from the rate of decay.[10]
With his colleagues Andrzej Buras, Dennis Duke and Taizo Muta, Bardeen helped to formulate perturbation theory for quantum chromodynamics, introducing the systematic scheme for loop-level perturbation theory, frequently used in the analysis of QCD processes in high energy experiments.[11] With Buras and Jean-Marc Gerard he developed an analytical, non-perturbative framework for the calculation of non-leptonic decays of K-mesons and mixing. This approach, based on QCD with large led to several results, confirmed by numerical lattice calculation 30 years later. One of these results is the identification of the dominant QCD dynamics responsible for the so-called rule in decays, a long-standing puzzle since 1955.[12] With coauthors Sherwin Love and Chung Ngoc Leung, Bardeen also explored theoretical mechanisms for the origin of scale breaking in quantum field theory in conjunction with chiral symmetry breaking and the role of the dilaton.[13][14]
In the early 1990s it became clear that the top quark was much heavier than originally anticipated, and that top quarks may be strongly coupled at very short distances. This raised the possibility that pairs of top quarks could form a composite Higgs boson, which led to top quark condensates,[15] and novel dynamical approaches to electroweak symmetry breaking. The theory, developed with Christopher T. Hill and Manfred Lindner, predicted a heavy top quark, governed by the infrared fixed point (about 20% heavier than the observed top quark mass of 175 GeV), but it tended to predict too heavy a Higgs boson, almost twice the observed mass of 125 GeV. Nonetheless, this was the first composite Higgs boson model and the general idea remains an intriguing possibility.
Bardeen and Hill, in 1994, recognized that heavy-light mesons, which contain a heavy quark and a light anti-quark, provide a unique window on the chiral dynamics of a single light quark. They showed that the (spin)parity ground states are split from the parity partners by a universal mass gap of about due to the light quark chiral symmetry breaking.[16] This correctly predicted an abnormally long-lived resonance ten years before it was discovered by the BABAR collaboration: the . The theory was further developed by Bardeen, Hill and Estia Eichten, and various decay modes were predicted that have been confirmed by experiment.[17] Similar phenomena should be seen in the mesons and (heavy-heavy-light baryons).
Honors
William Bardeen was elected a Fellow of the American Physical Society in 1984. In 1985, Bardeen was awarded a John S. Guggenheim Memorial Foundation Fellowship for research on the application of quantum field theory to elementary particle physics. Previously, he had received the Senior Scientist Award of the Alexander von Humboldt Foundation and an Alfred P. Sloan Foundation Fellowship for research in theoretical physics. Bardeen was awarded the 1996 J.J. Sakurai Prize of the American Physical Society for his work on anomalies and perturbative quantum chromodynamics.[18] He was elected a Fellow of the American Academy of Arts and Sciences in 1998[19] and a member of the National Academy of Sciences in 1999.[20]
↑ Bardeen's calculation was done slightly before, and provided hints to, the non-renormalization at higher orders. The "left-right symmetric anomaly" is not manifestly gauge invariant and a prolonged argument among theorists ensued. The Wess-Zumino consistency conditions appeared afterward and confirmed Bardeen's calculation of the left-right symmetric anomaly as the consistent anomaly. The gauge variation of the D=5 Chern-Simons term produces the consistent anomaly on a D=4 bounding surface.
↑ The Bardeen counter-term is implemented in the Wess-Zumino-Witten term in: Kaymakcalan, O.; Rajeev, S.; Schechter, J. (1984). "Nonabelian Anomaly and Vector Meson Decays". Phys. Rev. D. 30 (3): 594–602. Bibcode:1984PhRvD..30..594K. doi:10.1103/PhysRevD.30.594.; In the Standard Model the gauged electroweak currents must be conserved and the Bardeen counter-term is modified: Harvey, Jeffrey A.; Hill, Christopher T.; Hill, Richard (2007). "Standard Model Gauging of the Wess-Zumino-Witten Term: Anomalies, Global Currents and pseudo-Chern-Simons Interactions". Phys. Rev. D. 30 (8): 085017. arXiv:0712.1230. doi:10.1103/PhysRevD.77.085017. This reproduces B+L violation by the anomaly in the Standard model, and predicts numerous other anomalous processes.
↑ W. A. Bardeen, H. Fritzsch, and M. Gell-Mann, "Light cone current algebra, decay, and annihilation," published in the "Topical Meeting on the Outlook for Broken Conformal Symmetry in Elementary Particle Physics", hep-ph/0211388, "CERN-TH-1538" (July 1972).
↑ Bardeen, William A.; Buras, A.J.; Gerard, J. M. (1987). "A Consistent Analysis of the Rule for K Decays". Phys. Lett. B. 192: 138–144. doi:10.1016/0370-2693(87)91156-7.
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.
The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.
Technicolor theories are models of physics beyond the Standard Model that address electroweak gauge symmetry breaking, the mechanism through which W and Z bosons acquire masses. Early technicolor theories were modelled on quantum chromodynamics (QCD), the "color" theory of the strong nuclear force, which inspired their name.
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