One-loop mass corrections of interacting string states
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910083726704640 |
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| author | Grimaldi, Lorenzo Bianchi, Massimo Firrotta, Maurizio |
| author_facet | Grimaldi, Lorenzo Bianchi, Massimo Firrotta, Maurizio |
| contents | The free string spectrum is highly degenerate, with a degeneracy that grows exponentially with the mass. Turning on a non-vanishing string coupling $g_s$ introduces interactions, rendering massive string states unstable and allowing them to decay into lower-mass states, with mixing constrained by Lorentz invariance. This behavior is expected already at one-loop level. The imaginary part of the one-loop mass correction is related to the width of the decay into two lower-mass states at tree level, whereas the real part is generally IR-divergent and needs regularization and renormalization. The analysis simplifies for states in the first Regge trajectory. In particular, we consider the one-loop mass corrections for these states in the NS-NS sector of Type-II string theories. We explicitly construct the related vertex operators and exploit the properties of elliptic functions in order to obtain a closed form expression for the integral over the insertion point. We further regularize the divergences of the integral over the modular parameter of the torus by means of the $i\varepsilon$-prescription in string theory. Finally we extract numerical results for the mass correction up to level $N=4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09935 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One-loop mass corrections of interacting string states Grimaldi, Lorenzo Bianchi, Massimo Firrotta, Maurizio High Energy Physics - Theory General Relativity and Quantum Cosmology The free string spectrum is highly degenerate, with a degeneracy that grows exponentially with the mass. Turning on a non-vanishing string coupling $g_s$ introduces interactions, rendering massive string states unstable and allowing them to decay into lower-mass states, with mixing constrained by Lorentz invariance. This behavior is expected already at one-loop level. The imaginary part of the one-loop mass correction is related to the width of the decay into two lower-mass states at tree level, whereas the real part is generally IR-divergent and needs regularization and renormalization. The analysis simplifies for states in the first Regge trajectory. In particular, we consider the one-loop mass corrections for these states in the NS-NS sector of Type-II string theories. We explicitly construct the related vertex operators and exploit the properties of elliptic functions in order to obtain a closed form expression for the integral over the insertion point. We further regularize the divergences of the integral over the modular parameter of the torus by means of the $i\varepsilon$-prescription in string theory. Finally we extract numerical results for the mass correction up to level $N=4$. |
| title | One-loop mass corrections of interacting string states |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.09935 |