Vacuum energy density from the form factor bootstrap

A bstract 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 $$ {\rho}_{\textrm{vac}}\propto {m}^D/\mathfrak{g} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>vac</mml:mi> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mi>D</mml:mi> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>g</mml:mi> </mml:math> where $$ \mathfrak{g} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> is a dimensionless interaction coupling constant which can be determined from the high energy behavior of the S-matrix. In the limit $$ \mathfrak{g}\to 0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> <mml:mo>→</mml:mo> <mml:mn>0</mml:mn> </mml:math> , 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.