Vacuum energy density from the form factor bootstrap
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866929736979054592 |
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| author | LeClair, André |
| author_facet | LeClair, André |
| contents | 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 $ρ_{\rm vac}$, defined as $\langle 0| T_{μν} | 0 \rangle = ρ_{\rm vac} \, g_{μν}$, 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 $ρ_{\rm vac} \propto m^D/\mathfrak{g}$ where $\mathfrak{g}$ is a dimensionless interaction coupling constant which can be determined from the high energy behavior of the S-matrix. In the limit $\mathfrak{g} \to 0$, $ρ_{\rm vac} $ diverges due to well understood UV divergences in free quantum field theories. If we assume the the observed Cosmological Constant originates from the vacuum energy density $ρ_{\rm vac}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vacuum energy density from the form factor bootstrap LeClair, André High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics 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 $ρ_{\rm vac}$, defined as $\langle 0| T_{μν} | 0 \rangle = ρ_{\rm vac} \, g_{μν}$, 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 $ρ_{\rm vac} \propto m^D/\mathfrak{g}$ where $\mathfrak{g}$ is a dimensionless interaction coupling constant which can be determined from the high energy behavior of the S-matrix. In the limit $\mathfrak{g} \to 0$, $ρ_{\rm vac} $ diverges due to well understood UV divergences in free quantum field theories. If we assume the the observed Cosmological Constant originates from the vacuum energy density $ρ_{\rm vac}$ 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. |
| title | Vacuum energy density from the form factor bootstrap |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2407.10692 |