http://arxiv.org/abs/1506.05761
The scalar models with exponential interaction, introduced in arXiv:1506.00987, include theories with $\langle \phi(x)\rangle\neq0$. Here, we first consider the theory obtained by normal ordering the exponential of the integrated potential $\int d^Dx\mu^D \exp(-\alpha\phi)$, rather than of $V(\phi)$ itself. This corresponds to fill-in the vacuum of the free scalar theory coupled to the external source with the scalar modes. Next, we show that such a regularization prescription, that we are able to implement in the path-integral formulation, also cures some classical potentials which may be unbounded below. We focus on $V(\phi)=m^4\big(e^{-\phi/m}-e^{\phi/m}\big)$, whose regularized partition function $$ W_R[J]={}_J\langle 0| :e^{-\int d^4xV(\phi)}:|0\rangle_J $$ leads to the exact result $$ \langle\phi(x)\rangle=2m \ , $$ in agreement with the experimental data. Another test is that, while the $(2N+1)$-point function is non-trivial, the full propagator is the free one, so that $m^2$ also corresponds to the pole of the propagator. Such an investigation suggests a natural way to get the lagrangian of the Standard Model, with a different Higgs lagrangian, that may be tested in future experiments at LHC.
M. Matone
Wed, 24 Jun 15
20/54
Comments: 9 pages. Relevant additions. Typos corrected
You must be logged in to post a comment.