Goldstone Boson Equivalence Theorem

The Goldstone boson equivalence theorem is a theorem in quantum field theory . It says that at high energies, longitudinally polarized gauge bosons can be replaced by the corresponding Goldstone bosons for the calculation of elements of the S matrix . It was proven by Michael Chanowitz and Mary Gaillard in 1985 .

background

In an unbroken quantum field theory, gauge bosons are always massless and can therefore only have transverse spin polarization. Due to the Goldstone theorem , when the symmetry is broken , which leads to the mass of the gauge bosons, a corresponding Goldstone boson is created for each massive gauge boson.

At high energies, the constant rest energy of a particle, i.e. its mass due to the equivalence of mass and energy , is negligible in comparison to the kinetic energy , and all particles can be regarded as approximately massless. The Goldstone-Boson equivalence theorem therefore describes how to proceed with the longitudinal polarization in this case.

Details of the statement

Designates a scattering amplitude with longitudinal gauge bosons and the corresponding scattering amplitude in which the gauge bosons were replaced by Goldstone bosons with identical momentum , then: ${\displaystyle \prod _{i=1}^{n}\epsilon _{\mu _{i}}^{0}(p_{i}){\mathcal {A}}^{\mu _{1}\dots \mu _{n}}(p_{1},\dots ,p_{n})}$ ${\displaystyle n}$
${\displaystyle {\mathcal {A}}_{\phi _{1}\dots \phi _{n}}(p_{1},\dots ,p_{n})}$ ${\displaystyle p_{i}}$

${\displaystyle \prod _{i=1}^{n}\epsilon _{\mu _{i}}^{0}(p_{i}){\mathcal {A}}^{\mu _{1}\dots \mu _{n}}(p_{1},\dots ,p_{n})=\mathrm {i} ^{-n}{\mathcal {A}}_{\phi _{1}\dots \phi _{n}}(p_{1},\dots ,p_{n})+{\mathcal {O}}(m/E)}$

swell

• Michael S. Chanowitz and Mary K. Gaillard: The TeV Physics of Strongly Interacting W's and Z’s . In: Nucl. Phys. B . No. 261 , 1985, pp. 379 ff ., doi : 10.1016 / 0550-3213 (85) 90580-2 .