Lattice evidence for a large rescaling
of the Higgs condensate.
Maurizio Consoli
Abstract
Recent lattice simulations of
$(\lambda \Phi^4)_4$ theories in the broken phase show that:
a) the bare zero-momentum two-point function
$ \Gamma_2(0)=
\left. \frac{ d^2 V_{\rm eff}}{d \phi^2_B} \right|_{\phi_B= \pm v_B} $ is
related by a non-trivial re-scaling $Z_\varphi$
to the `Higgs mass' $M^2_h$
governing the large-momentum behaviour of the propagator and
b) the
magnitude of $Z_\varphi={{M^2_h}\over{\Gamma_2(0)}}$
increases when approaching the continuum limit. This supports theoretical
expectations where $v_B$ is related by an infinite re-scaling to the
`physical Higgs condensate'
$v_R$ defined through
$\left. \frac{ d^2 V_{\rm eff}}{d \phi^2_R} \right|_{\phi_R= \pm v_R}=M^2_h $.
A finite-temperature analysis supports the same conclusions since the
finite-temperature analog of $Z_\varphi$
is found to diverge when approaching the phase transition.
By denoting
$M_{\rm SSB} \equiv M_h ={\cal O} (v_R)$ the scale
of the broken phase, our results support
the existence of a `hierarchy' of mass scales
$\Gamma_2(0) \ll M^2_{\rm SSB} \ll v^2_B$ that become infinitely far in the
continuum limit.
Elenco dei partecipanti al convegno di Bari.