Vacuum energy density from the form factor bootstrap

The form-factor bootstrap is incomplete until one normalizes the zero-particle form factor. For the stress energy tensor we describe how to obtain the vacuum energy density ρ_vac, defined as 〈0|T_μν|0〉 = ρ_vac g_μν, from the form-factor bootstrap. Even for integrable QFT’s in D=2 spacetime dimensions, this prescription is new, although it reproduces previously known results obtained in a different and more difficult thermodynamic Bethe ansatz computation. We propose a version of this prescription in D=4 dimensions. For these even dimensions, the vacuum energy density has the universal form ${\rho }_{\mathrm{vac}}\propto m^D/\mathfrak{g}$ \( {\rho}_{\textrm{vac}}\propto {m}^D/\mathfrak{g} \) where $\mathfrak{g}$ \( \mathfrak{g} \) is a dimensionless interaction coupling constant which can be determined from the high energy behavior of the S-matrix. In the limit $\mathfrak{g}\to 0$ \( \mathfrak{g}\to 0 \) , ρ_vac diverges due to well understood UV divergences in free quantum field theories. If we assume the observed Cosmological Constant originates from the vacuum energy density ρ_vac computed as proposed here, then this suggests there must exist a particle which does not obtain its mass from spontaneous symmetry breaking in the electro-weak sector, which we designate as the “zeron”. A strong candidate for the zeron is a massive Majorana neutrino.