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| Quark mixing | |
|---|---|
| Name | Quark mixing |
| Field | Particle physics |
| Discovered | 1963 (Cabibbo angle), 1973 (CKM matrix) |
| Discoverers | Nicola Cabibbo, Makoto Kobayashi, Toshihide Maskawa |
Quark mixing Quark mixing describes how the weak interaction eigenstates of up quarks and down quarks are related to their mass eigenstates via a unitary transformation. It is parametrized by the Cabibbo–Kobayashi–Maskawa matrix and underlies processes observed in experiments at facilities such as CERN, Fermilab, KEK, SLAC National Accelerator Laboratory and Brookhaven National Laboratory. The phenomenon connects measurements from collaborations including ATLAS, CMS, LHCb, Belle II, BaBar, CDF, and DØ to theoretical frameworks developed by physicists at institutions like Princeton University, University of Tokyo, Yale University, and CERN Theory Department.
Quark mixing was first conceptualized to explain flavor-changing weak decays of mesons such as K mesons and π mesons and later extended to three generations by Kobayashi and Maskawa. The mixing is encoded in a 3×3 unitary matrix that relates charged-current weak interactions measured in beta decay, kaon decay, and B meson decays to quark mass parameters appearing in models by groups at Harvard University, University of Cambridge, and University of California, Berkeley. Precision determinations involve global fits by collaborations including the CKMfitter Group and the UTfit collaboration using inputs from detectors at LEP, KEKB, RHIC, and Tevatron.
The Cabibbo–Kobayashi–Maskawa matrix (CKM matrix) is a unitary matrix introduced by Nicola Cabibbo, Makoto Kobayashi, and Toshihide Maskawa to describe transitions among up quark, charm quark, top quark and down quark, strange quark, bottom quark. It generalizes the Cabibbo angle first employed to account for strangeness-changing decays observed in experiments at CERN and Brookhaven National Laboratory. The CKM matrix elements V_ud, V_us, V_ub, V_cd, V_cs, V_cb, V_td, V_ts, V_tb are constrained by measurements from KLOE, NA62, LHCb, Belle, BaBar, and CLEO. Parametrizations include the Wolfenstein parametrization introduced by Lincoln Wolfenstein and the original standard parametrization advocated by the Particle Data Group and researchers at CERN and Fermilab.
Derivations of quark mixing arise in the electroweak sector formulated by Sheldon Glashow, Abdus Salam, and Steven Weinberg, where Yukawa couplings to the Higgs boson generate quark mass matrices. Diagonalization of complex mass matrices by unitary transformations at institutes like Institut des Hautes Études Scientifiques and Max Planck Institute for Physics yields the CKM matrix in the charged-current interaction terms developed in textbooks by authors at Oxford University Press and Cambridge University Press. Theoretical approaches incorporate concepts from Quantum Chromodynamics studies at CERN and renormalization group analyses performed by teams at MIT, Caltech, Stanford University, and University of Chicago. Flavor symmetries and texture models have been proposed by groups at Scuola Normale Superiore, Perimeter Institute, and CEA Saclay to explain hierarchies in eigenvalues and mixing angles.
Phenomenology connects CKM elements to observables in decays and oscillations measured by collaborations including LHCb, ATLAS, CMS, Belle II, BaBar, CLEO, CDF, and DØ. Determinations use processes such as semileptonic decays of B mesons at KEKB and SLAC, rare decays studied at NA62 and KOTO, and neutral meson mixing in systems like K0, D0, B0_d and B0_s measured at Tevatron and LHC. Lattice QCD calculations from groups at Brookhaven National Laboratory, Fermilab, Riken, and RIKEN-BNL Research Center supply hadronic matrix elements, while global fits by the CKMfitter Group and UTfit collaboration combine inputs from experiments at LEP and Belle to constrain the unitarity triangle and test consistency with results from NA48 and KTeV.
CP violation in the quark sector is a direct consequence of a nonzero complex phase in the CKM matrix, first connected to observations of indirect CP violation in kaon decays at CERN SPS and experiments by James Cronin and Val Fitch. Direct CP violation was later observed in B meson decays by BaBar and Belle, establishing the CKM mechanism proposed by Kobayashi and Maskawa as the dominant source in the Standard Model. Implications span cosmology and baryogenesis discussions influenced by work from Andrei Sakharov and data from Planck and WMAP as well as searches for electric dipole moments at PSI and TRIUMF. Tests of CP-violating phases continue at LHCb, Belle II, and proposed facilities such as the International Linear Collider and Future Circular Collider.
Beyond-Standard-Model scenarios propose additional sources of flavor mixing and CP violation in frameworks developed at CERN Theory Department, Perimeter Institute, Institute for Advanced Study, and research groups at DESY and SLAC. Models include minimal flavor violation studied by teams at University of Oxford and Universität Hamburg, supersymmetric flavor models from collaborations at Imperial College London and University of Durham, extra-dimension proposals by researchers at Caltech and Princeton University, and theories with vector-like quarks explored at SNS Pisa and Institut de Physique Théorique. Experimental searches for deviations involve data from ATLAS, CMS, LHCb, and flavor factories as well as precision electroweak tests at LEP and proposed measurements at CEPC.
The chronology begins with Cabibbo’s 1963 proposal to explain strangeness-changing weak decays investigated at Brookhaven National Laboratory and CERN, followed by the 1973 Kobayashi–Maskawa paper motivated by discoveries of the charm quark at SLAC and Brookhaven and later the bottom quark at Fermilab and the top quark at Fermilab. Landmark experiments include kaon CP violation studies by Cronin and Fitch leading to Nobel recognition, neutral B meson mixing measurements at ARGUS and CLEO, and CP violation observations by BaBar at SLAC and Belle at KEK. Modern precision era results come from LHCb at CERN, Belle II at KEK, and lattice collaborations worldwide, with theoretical advances by researchers at Harvard, MIT, Stanford, and University of Chicago shaping current understanding.