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By E. A. Paschos
Concise creation to electroweak thought for graduate scholars and researchers in straight forward particle physics.
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31) Taking the limit q 2 → 0 with m 2π = 0 in the last two equations, we obtain √ 2MgA = gπNN f π. 32) This is the Goldberger–Treiman relation. For the experimental values of the coupling constants it holds at the 10% level. It is a remarkable relation, relating the pion–nucleon coupling constant to two couplings of weak interactions. There is a second way of looking at partially conserved axial current (PCAC). The meaning of PCAC is that the actual world is not far from the limit in which the axial currents are conserved at the expense of having zero-mass pions (m π = 0, f π = 0).
G. (1958), Phys. Rev. 109, 1860 For PCAC: Adler, S. , and Dashen, R. F. (1968), Current Algebras (New York, W. A. ) Cabibbo, N. (1963), Phys. Rev. Lett. 10, 531 Cheng, T. , and Li, L. F. (1984), Gauge Theory of Elementary Particle Physics (Oxford, Clarendon Press) Goldberger, M. , and Treiman, S. B. (1958), Phys. Rev. 1 Introduction The quark model arose from the analysis of symmetry patterns observed when particles were grouped together according to their spin and parity. When the eight mesons with J p = 0− are displayed in a strangeness (S) versus isospin (I3 ) plane, they form the octet of Fig.
It must be Lorentz-invariant and invariant under ˆ It must also contain the kinetic term of the Bμ fields. In analogy to the B → B. procedure of obtaining gauge-invariant field strengths in electrodynamics, we define μν Fi μ μ = ∂ ν Bi − ∂ μ Biν + e f i jk B j Bkν . 14) If we introduce the vector notation μ μ μ B μ = B1 , B2 , . 14) as F μν = ∂ ν B μ − ∂ μ B ν + e B μ × B ν . 17) does not occur in electrodynamics and is introduced to assure that F μν transforms as a vector under gauge transformations.