Lagrangian of standard model
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The Lagrangian of the Standard Model: An Overview
Introduction to the Standard Model Lagrangian
The Standard Model (SM) of particle physics is a theoretical framework that describes the electromagnetic, weak, and strong nuclear interactions. The Lagrangian of the Standard Model is a mathematical function that encapsulates the dynamics of these fundamental forces and the particles that mediate them. It is a cornerstone of modern physics, providing a comprehensive description of particle interactions.
Dimension-Six Terms in the Standard Model Lagrangian
When considering the Standard Model as an effective low-energy theory, higher-dimensional interaction terms appear in the Lagrangian. Dimension-six terms, in particular, have been extensively studied. These terms were initially enumerated by Buchmüller and Wyler, who identified 80 independent operators assuming baryon number conservation. However, recent classifications have refined this number to 59 independent operators, highlighting redundancies in the original list1. This refinement is crucial for accurate theoretical predictions and experimental validations.
Nonminimal Standard-Model Extension (SME) Lagrangians
The Standard-Model Extension (SME) incorporates possible violations of Lorentz invariance, extending the Standard Model to include such effects. The leading-order classical Lagrangian for the nonminimal SME covers all fermion operators and provides a point-particle analog of the effective field theory description of Lorentz violation2. This Lagrangian is essential for studying the phenomenological implications of Lorentz violation in gravitational fields and has connections to Finsler geometry3.
Classical Lagrangians and Hamilton Operators
A significant aspect of the SME involves deriving classical Lagrangians that can be quantized to yield Hamilton operators consistent with the field-theory description. This process has been shown to be feasible for the minimal SME, ensuring that classical Lagrangians can be derived even for complex sets of coefficients5. This consistency is vital for bridging classical and quantum descriptions of particle interactions.
Effective Lagrangians and Symmetry Breaking
Effective Lagrangians play a crucial role in understanding the symmetries and symmetry breaking mechanisms within the Standard Model. These Lagrangians encapsulate the global symmetries of quantum field theory and provide insights into the symmetry breaking sector of the Standard Model, including Quantum Chromodynamics (QCD) and gravity9. This understanding is fundamental for exploring new physics beyond the Standard Model.
Computational Approaches to Standard Model Lagrangians
Recent research has explored computational approaches to derive the fundamental Lagrangians of the Standard Model. By employing variants of Girard's Linear Logic, researchers have shown that certain logical structures can generate the Yang-Mills and Einstein-Hilbert Lagrangian densities. This approach offers a novel perspective on the unification of fundamental forces at the level of underlying logic10.
Conclusion
The Lagrangian of the Standard Model is a complex yet elegant mathematical formulation that describes the fundamental interactions of particles. Advances in understanding higher-dimensional terms, Lorentz-violating extensions, and computational methods continue to refine and expand our knowledge of particle physics. These developments not only enhance our theoretical framework but also pave the way for discovering new physics beyond the Standard Model.
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Most relevant research papers on this topic
Dimension-six terms in the Standard Model Lagrangian
This paper updates the classification of dimension-six terms in the Standard Model Lagrangian, identifying 59 independent operators with 0-5 fermion fields, and 5 new operators in the four-fermion sector.
Highly CitedLeading-order classical Lagrangians for the nonminimal standard-model extension
The paper presents a leading-order classical Lagrangian for the nonminimal Standard-Model Extension, useful for phenomenological studies of classical bodies in gravitational fields and conceptual work on explicit Lorentz violation in gravity.
Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension
This paper identifies classical point-particle equivalents for the fermion sector of the nonminimal Standard-Model Extension, revealing new constraints on coefficients and connections to Finsler geometry.
Standard model at 200 GeV
The paper provides interpolation formulas for the fundamental Lagrangian parameters in the Standard Model at 200 GeV, suitable for matching to candidate new physics models at very high mass scales.
From classical Lagrangians to Hamilton operators in the Standard-Model Extension
Quantization of classical Lagrangians for the minimal Standard-Model Extension can be consistently performed, enabling the derivation of classical Lagrangians for two previously unexplored sectors.
The Standard model in the latticized bulk
Extra dimensions with explicit Higgs do not improve the naturalness problem in the Standard Model in 4+1 dimensions.
Highly CitedThe Lee-Wick standard model
The Lee-Wick standard model stabilizes the Higgs mass against quadratically divergent radiative corrections, making computation and interpretation more transparent, but does not satisfy usual analyticity conditions.
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