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| Cabibbo–Kobayashi–Maskawa theory | |
|---|---|
| Name | Cabibbo–Kobayashi–Maskawa theory |
| Field | Particle physics |
| Introduced | 1963, 1973 |
| Key people | Nicola Cabibbo; Makoto Kobayashi; Toshihide Maskawa; Murray Gell-Mann; Richard Feynman |
Cabibbo–Kobayashi–Maskawa theory is the framework in particle physics that describes quark flavor mixing and the origin of CP violation in the Standard Model through a unitary mixing matrix first hinted by Nicola Cabibbo and extended by Makoto Kobayashi and Toshihide Maskawa. It connects weak-interaction eigenstates to mass eigenstates of the up quark and down quark families and underpins phenomena explored at facilities such as CERN, Fermilab, SLAC National Accelerator Laboratory, and KEK. The theory has driven experimental programs involving detectors like LHCb, Belle II, BaBar, and ATLAS and motivated theoretical work by figures including Murray Gell-Mann and Gerard 't Hooft.
The CKM framework formalizes flavor-changing charged-current processes via a unitary 3×3 matrix in the Standard Model of particle physics, explaining transitions among the up quark, charm quark, top quark and the down quark, strange quark, bottom quark. It embeds a complex phase that produces CP violation as observed in decays studied at CERN, Brookhaven National Laboratory, DESY, KEK, and SLAC National Accelerator Laboratory. The formalism is central to interpretations of results from experiments including LHCb, Belle, Belle II, BaBar, and NA62.
The origin traces to Nicola Cabibbo's 1963 proposal for weak strangeness-changing processes and the Cabibbo angle connecting strange quark and down quark transitions, followed by the 1973 extension by Makoto Kobayashi and Toshihide Maskawa who introduced a three-generation unitary matrix to accommodate a single irreducible complex phase for CP violation, motivated by observations at Brookhaven National Laboratory and theoretical needs highlighted by Murray Gell-Mann and Richard Feynman. The empirical confirmation of the charm quark at SLAC National Accelerator Laboratory and Fermilab and the later discovery of the bottom quark and top quark at Fermilab solidified the three-generation picture, which was further tested by CERN programs and flavor factories like Belle and BaBar.
The CKM matrix is a unitary 3×3 matrix V connecting weak eigenstates to mass eigenstates for quark fields; common parametrizations include the original Kobayashi–Maskawa form, the Wolfenstein parametrization introduced by Lincoln Wolfenstein, and the Particle Data Group conventions employed by Particle Data Group compilations. Explicit parametrizations relate matrix elements V_ud, V_us, V_ub, V_cd, V_cs, V_cb, V_td, V_ts, V_tb to mixing angles and a CP-violating phase, enabling comparisons across results from LHCb, Belle II, BaBar, ATLAS, and CMS. Unitarity triangles—derived from orthogonality relations such as the V_ud V_ub* + V_cd V_cb* + V_td V_tb* closure—provide geometric tests used by collaborations at CERN, Fermilab, and KEK.
CKM-driven flavor mixing accounts for processes like kaon mixing and CP violation observed in K meson systems at CERN and Brookhaven National Laboratory, as well as CP asymmetries in B meson decays measured by BaBar, Belle, and LHCb. The single irreducible complex phase in the CKM matrix explains observed direct and indirect CP violation in weak decays, linking to measurements of angles α, β, γ of the unitarity triangle pursued by LHCb and Belle II. Flavor-changing charged currents described by CKM elements determine rates of rare decays studied by NA62, LHCb, and KOTO and affect predictions for processes at ATLAS and CMS.
Determination of CKM elements combines inputs from semileptonic decays of B meson, D meson, and K meson systems measured at Belle II, BaBar, CLEO, LHCb, and BESIII with inputs from lattice calculations and global fits by the CKMfitter Group and UTFit Collaboration. Precision constraints on V_ud derive from nuclear beta decays involving experiments at TRIUMF and Oak Ridge National Laboratory while V_us is constrained by kaon decay studies at NA62 and KLOE. Measurements of V_cb and V_ub from inclusive and exclusive B-decay channels at Belle, BaBar, and LHCb present persistent tensions, and determinations of V_td and V_ts come from neutral meson mixing and rare decay studies at CERN and Fermilab.
Within the Standard Model, CKM mixing arises from Yukawa couplings and electroweak symmetry breaking via the Higgs boson mechanism explored at CERN. Extensions of the CKM picture appear in models with additional quark generations, vector-like quarks, or flavor symmetries studied by theorists at institutions such as Institute for Advanced Study, Perimeter Institute, and CERN Theory Division. Beyond-Standard-Model frameworks like supersymmetry, left–right symmetric models, Grand Unified Theories, and models with extra dimensions can introduce new sources of flavor violation or CP phases probed by experiments at LHCb, ATLAS, CMS, and flavor factories.
Key open issues include the source of the baryon asymmetry of the Universe—for which the CKM CP violation appears insufficient, prompting searches for new CP sources at LHCb, Belle II, ATLAS, and CMS—and the resolution of tensions in V_cb and V_ub determinations scrutinized by Lattice QCD groups at Brookhaven National Laboratory and CERN. Upcoming data from Belle II, the High-Luminosity upgrade at CERN, and future facilities such as proposed Future Circular Collider programs will refine CKM element determinations, test unitarity triangles with greater precision, and probe rare decays measured at NA62 and KOTO to reveal possible physics beyond the Standard Model.