The infrared-safe Minkowskian Curci-Ferrari model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913743683715072 |
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| author | Oribe, Santiago Peláez, Marcela Reinosa, Urko |
| author_facet | Oribe, Santiago Peláez, Marcela Reinosa, Urko |
| contents | We discuss the existence of Landau-pole-free renormalization group trajectories in the Minkowskian version of the Curci-Ferrari model as a function of a running parameter $q^2$ associated to the four-vector $q$ at which renormalization conditions are imposed, and which can take both space-like ($\smash{q^2<0}$) and time-like ($\smash{q^2>0}$) values. We discuss two possible extensions of the infrared-safe scheme defined in Ref. [Phys. Rev. D, 84, 045018, 2011] for the Euclidean version of the model, which coincide with the latter in the space-like region upon identifying $\smash{Q^2\equiv-q^2}$ with the square of the renormalization scale in that reference. The first extension uses real-valued renormalization factors and leads to a flow in the time-like region with a similar structure as the flow in the space-like region (or in the Euclidean model), including a non-trivial fixed point and a family of trajectories bounded at all scales by the value of the coupling at this fixed point. Interestingly, the fixed point in the time-like region has a much smaller value of $λ\equiv g^2N/16π^2$ than the corresponding one in the space-like region, a value closer to the perturbative boundary $\smash{λ=1}$. However, in this real-valued infrared-safe scheme, the flow cannot connect the time-like and space-like regions. Thus, it is not possible to deduce the relevant time-like flow trajectory from the sole knowledge of a space-like flow trajectory. To try to cure this problem, we investigate a second extension of the Euclidean IR-safe scheme, which allows for complex-valued renormalization factors. We discuss under which conditions these schemes can make sense and study their ability to connect space- and time-like flow trajectories. In particular, we investigate to which types of time-like trajectories the perturbative space-like trajectories are mapped onto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The infrared-safe Minkowskian Curci-Ferrari model Oribe, Santiago Peláez, Marcela Reinosa, Urko High Energy Physics - Phenomenology High Energy Physics - Theory We discuss the existence of Landau-pole-free renormalization group trajectories in the Minkowskian version of the Curci-Ferrari model as a function of a running parameter $q^2$ associated to the four-vector $q$ at which renormalization conditions are imposed, and which can take both space-like ($\smash{q^2<0}$) and time-like ($\smash{q^2>0}$) values. We discuss two possible extensions of the infrared-safe scheme defined in Ref. [Phys. Rev. D, 84, 045018, 2011] for the Euclidean version of the model, which coincide with the latter in the space-like region upon identifying $\smash{Q^2\equiv-q^2}$ with the square of the renormalization scale in that reference. The first extension uses real-valued renormalization factors and leads to a flow in the time-like region with a similar structure as the flow in the space-like region (or in the Euclidean model), including a non-trivial fixed point and a family of trajectories bounded at all scales by the value of the coupling at this fixed point. Interestingly, the fixed point in the time-like region has a much smaller value of $λ\equiv g^2N/16π^2$ than the corresponding one in the space-like region, a value closer to the perturbative boundary $\smash{λ=1}$. However, in this real-valued infrared-safe scheme, the flow cannot connect the time-like and space-like regions. Thus, it is not possible to deduce the relevant time-like flow trajectory from the sole knowledge of a space-like flow trajectory. To try to cure this problem, we investigate a second extension of the Euclidean IR-safe scheme, which allows for complex-valued renormalization factors. We discuss under which conditions these schemes can make sense and study their ability to connect space- and time-like flow trajectories. In particular, we investigate to which types of time-like trajectories the perturbative space-like trajectories are mapped onto. |
| title | The infrared-safe Minkowskian Curci-Ferrari model |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.14291 |