Yukawa coupling

Yukawa coupling
Name	Yukawa coupling
Field	Theoretical physics
Introduced by	Hideki Yukawa
Year	1935

Yukawa coupling The Yukawa coupling is a fundamental parameter in particle physics that quantifies the strength of a scalar–fermion interaction first proposed by Hideki Yukawa; it appears in relativistic quantum field theories, the Standard Model, and many extensions such as Supersymmetry, grand unified theories, and String theory. It plays a central role in the generation of fermion masses after Higgs mechanism driven spontaneous symmetry breaking, and in radiative corrections studied via renormalization group methods and precision tests at colliders like the Large Hadron Collider.

Definition and physical significance

A Yukawa coupling denotes the coefficient multiplying a gauge-invariant local operator coupling a scalar field to a fermion bilinear in a Lagrangian introduced by Hideki Yukawa; in phenomenology it is associated with interactions between the Higgs boson and matter fields such as the electron, muon, tau lepton, up quark, down quark, top quark, and bottom quark. The parameter directly influences decay widths measured at the ATLAS experiment and CMS experiment and affects processes constrained by experiments at facilities like LEP and Tevatron. Yukawa couplings also enter calculations of flavor observables probed by collaborations including Belle (experiment) and LHCb and are central to patterns studied in proposals from Pati–Salam model to SO(10) unified frameworks.

Mathematical formulation

In four-dimensional relativistic quantum field theory the Yukawa term in the Lagrangian is typically written as y ψ̄ φ ψ for a Dirac fermion ψ and scalar φ, where y is the Yukawa coupling. For chiral theories one writes distinct couplings y_L and y_R coupling left-handed and right-handed Weyl spinors; such terms must respect gauge symmetries of groups like SU(2) and U(1) in the Standard Model. In matrix notation for N generations the Yukawa sector uses matrices Y_u, Y_d, Y_e connecting flavor eigenstates; diagonalization involves biunitary transformations related to the Cabibbo–Kobayashi–Maskawa matrix and the Pontecorvo–Maki–Nakagawa–Sakata matrix in the quark and lepton sectors respectively.

Yukawa interactions in the Standard Model

The Standard Model includes Yukawa interactions between the Higgs field doublet and the fermion multiplets: Q, u_R, d_R for quarks and L, e_R for leptons. The Yukawa matrices Y_u, Y_d, Y_e are complex matrices that break global flavor symmetries such as SU(3)_flavor and lead to physical observables like quark mixing encoded in the CKM matrix. Top-quark Yukawa interactions are particularly significant due to the large mass of the top quark, influencing Higgs boson production via gluon fusion and decay channels studied by ATLAS experiment and CMS experiment.

Role in mass generation and symmetry breaking

After the Higgs mechanism the scalar acquires a vacuum expectation value (vev) v, converting Yukawa couplings y into fermion masses m = y v/√2 for Dirac fermions in the Standard Model. This mechanism ties mass hierarchies among particles like the electron, muon, tau lepton, up quark, charm quark, and top quark to hierarchies in Yukawa parameters and raises questions addressed by flavor models such as Froggatt–Nielsen mechanism and texture proposals in flavor symmetry studies. Yukawa interactions also affect electroweak precision observables measured at LEP and global fits performed by collaborations including Particle Data Group.

Renormalization and running of Yukawa couplings

Yukawa couplings are scale-dependent and obey renormalization group equations derived from perturbative calculations in frameworks like Quantum Chromodynamics and Electroweak theory. The running of Yukawa couplings, particularly the top Yukawa, contributes to the stability analysis of the Higgs potential and the question of vacuum meta-stability studied in the context of the Planck scale and scenarios motivated by GUT boundary conditions in groups such as SU(5) and SO(10). Higher-order corrections involve computations by collaborations and groups using techniques from Dimensional regularization and tools employed by projects like MadGraph and FeynArts.

Experimental measurements and constraints

Direct measurements of Yukawa couplings come from Higgs production and decay rates measured at the Large Hadron Collider by ATLAS experiment and CMS experiment, while indirect constraints also arise from flavor-changing processes measured by LHCb, Belle II, and earlier by BaBar (experiment). The top Yukawa is probed via tt̄H associated production and loop-induced processes such as Higgs to gluon–gluon, while bottom and tau Yukawas are constrained through H→bb and H→ττ channels; muon Yukawa evidence has been reported in H→μμ searches. Beyond collider bounds, cosmological constraints from Big Bang nucleosynthesis and baryogenesis scenarios in models like Electroweak baryogenesis can restrict Yukawa structures.

Extensions and Yukawa textures in beyond-Standard-Model theories

Beyond the Standard Model, Yukawa sectors are extended in theories including Supersymmetry, two-Higgs-doublet models studied in 2HDM contexts, and Seesaw mechanism frameworks for neutrino mass, often invoking texture zeros, flavor symmetries such as U(1)_FN, or horizontal groups like A4 to explain hierarchies. Grand unified proposals in SO(10) or SU(5) aim to relate Yukawa matrices across fermion sectors, while string-inspired constructions attempt to derive Yukawa coefficients from compactification data in Calabi–Yau manifold models and D-brane setups. Experimental programs at High-Luminosity Large Hadron Collider and proposed facilities like the International Linear Collider aim to further probe these textures and discriminate models.

Category:Particle physics