Non-perturbative determination of the sphaleron rate for first-order phase transitions
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| Format: | Preprint |
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2025
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| _version_ | 1866917204500414464 |
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| author | Annala, Jaakko Rummukainen, Kari Tenkanen, Tuomas V. I. |
| author_facet | Annala, Jaakko Rummukainen, Kari Tenkanen, Tuomas V. I. |
| contents | In many extensions of the Standard Model electroweak phase transitions at high temperatures can be described in a minimal dimensionally reduced effective theory with SU(2) gauge field and fundamental Higgs scalar. In this effective theory, all thermodynamic information is governed by two dimensionless ratios $x \equiv λ_3/g^2_3$ and $y\equiv m^2_3/g^4_3$, where $λ_3$, $m^2_3$ and $g_3$ are the effective thermal scalar self-interaction coupling, the thermal mass and the effective gauge-coupling, respectively. By using non-perturbative lattice simulations to determine the rate of sphaleron transitions in the entire $(x,y)$-plane corresponding to the Higgs phase, and by applying previous lattice results for the bubble nucleation, we find a condition $x(T_c) \lesssim 0.025$ to guarantee preservation of the baryon asymmetry, which translates to $v/T_c \equiv \sqrt{2 Δ\langle ϕ^\dagger ϕ\rangle}/T_c \gtrsim 1.33$ for the (gauge-invariant) discontinuity in Higgs condensate. This indicates that viability of the electroweak baryogenesis requires the phase transition to be slightly stronger than previously anticipated. Finally, we present a general template for analysing such viability in a wide class of beyond the Standard Model theories, in which new fields are heavy enough to be integrated out at high temperature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_04939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-perturbative determination of the sphaleron rate for first-order phase transitions Annala, Jaakko Rummukainen, Kari Tenkanen, Tuomas V. I. High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Lattice In many extensions of the Standard Model electroweak phase transitions at high temperatures can be described in a minimal dimensionally reduced effective theory with SU(2) gauge field and fundamental Higgs scalar. In this effective theory, all thermodynamic information is governed by two dimensionless ratios $x \equiv λ_3/g^2_3$ and $y\equiv m^2_3/g^4_3$, where $λ_3$, $m^2_3$ and $g_3$ are the effective thermal scalar self-interaction coupling, the thermal mass and the effective gauge-coupling, respectively. By using non-perturbative lattice simulations to determine the rate of sphaleron transitions in the entire $(x,y)$-plane corresponding to the Higgs phase, and by applying previous lattice results for the bubble nucleation, we find a condition $x(T_c) \lesssim 0.025$ to guarantee preservation of the baryon asymmetry, which translates to $v/T_c \equiv \sqrt{2 Δ\langle ϕ^\dagger ϕ\rangle}/T_c \gtrsim 1.33$ for the (gauge-invariant) discontinuity in Higgs condensate. This indicates that viability of the electroweak baryogenesis requires the phase transition to be slightly stronger than previously anticipated. Finally, we present a general template for analysing such viability in a wide class of beyond the Standard Model theories, in which new fields are heavy enough to be integrated out at high temperature. |
| title | Non-perturbative determination of the sphaleron rate for first-order phase transitions |
| topic | High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2506.04939 |