Positivity bounds in scalar-QED EFT at one-loop level
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arXiv
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2025
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| _version_ | 1866914089118203904 |
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| author | Ye, Yunxiao Cao, Xiao Wu, Yu-Hang Gu, Jiayin |
| author_facet | Ye, Yunxiao Cao, Xiao Wu, Yu-Hang Gu, Jiayin |
| contents | Understanding the implication of positivity bounds on loop-generated dim-8 operator coefficients is a nontrivial task, as these bounds only strictly hold when all the contributions are included in the dispersion relation up to a certain loop order in the UV theory. As a step towards more realistic gauge theories such as the Standard Model, in this paper we study the positivity bounds in the Scalar QED Effective Field Theory (EFT) from the scalar-photon scattering ($γϕ\to γϕ$) and the photon-photon scattering ($γγ\to γγ$), derived from the dispersion relation of the full one-loop EFT amplitudes. Assuming the UV theory is weakly coupled and all heavy particles have spin $\leq1$, the leading dim-8 interaction for both amplitudes are generated at the one-loop level in the UV theory. Gauge invariance imposes strong constraints on the loop structures, while potential IR divergences also require careful treatments. Our findings reveal that, for $γϕ\to γϕ$, while the tree-level bound does not necessarily hold, the one-loop $β$-function of the corresponding coefficient always tends to restore the tree-level bound in the IR, unless its actual loop order in the UV theory is further suppressed. For $γγ\to γγ$, on the other hand, the tree-level positivity bound is still robust at the one-loop level in the UV theory. These findings are verified in two example UV models with a heavy scalar extension. Importantly, the bounds on the $β$-functions that we obtain should be considered as an accidental feature at one loop, rather than a fundamental property of the theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_06302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positivity bounds in scalar-QED EFT at one-loop level Ye, Yunxiao Cao, Xiao Wu, Yu-Hang Gu, Jiayin High Energy Physics - Phenomenology High Energy Physics - Theory Understanding the implication of positivity bounds on loop-generated dim-8 operator coefficients is a nontrivial task, as these bounds only strictly hold when all the contributions are included in the dispersion relation up to a certain loop order in the UV theory. As a step towards more realistic gauge theories such as the Standard Model, in this paper we study the positivity bounds in the Scalar QED Effective Field Theory (EFT) from the scalar-photon scattering ($γϕ\to γϕ$) and the photon-photon scattering ($γγ\to γγ$), derived from the dispersion relation of the full one-loop EFT amplitudes. Assuming the UV theory is weakly coupled and all heavy particles have spin $\leq1$, the leading dim-8 interaction for both amplitudes are generated at the one-loop level in the UV theory. Gauge invariance imposes strong constraints on the loop structures, while potential IR divergences also require careful treatments. Our findings reveal that, for $γϕ\to γϕ$, while the tree-level bound does not necessarily hold, the one-loop $β$-function of the corresponding coefficient always tends to restore the tree-level bound in the IR, unless its actual loop order in the UV theory is further suppressed. For $γγ\to γγ$, on the other hand, the tree-level positivity bound is still robust at the one-loop level in the UV theory. These findings are verified in two example UV models with a heavy scalar extension. Importantly, the bounds on the $β$-functions that we obtain should be considered as an accidental feature at one loop, rather than a fundamental property of the theory. |
| title | Positivity bounds in scalar-QED EFT at one-loop level |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.06302 |