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This paper extends classical results by Langer and Kramers [1-3] and combines them with modern methods from high-temperature field theory [4-8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9-11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4-7, 12-14], all results only hold within this framework.

This paper presents updated Monte Carlo configurations used to model the production of single electroweak vector bosons (W, Z/gamma*) in association with jets in proton-proton collisions for the ATLAS experiment at the Large Hadron Collider. Improvements pertaining to the electroweak input scheme, parton-shower splitting kernels and scale-setting scheme are shown for multi-jet merged configurations accurate to next-to-leading order in the strong and electroweak couplings. The computational resources required for these set-ups are assessed, and approximations are introduced resulting in a factor three reduction of the per-event CPU time without affecting the physics modelling performance. Continuous statistical enhancement techniques are introduced by ATLAS in order to populate low cross-section regions of phase space and are shown to match or exceed the generated effective luminosity. This, together with the lower per-event CPU time, results in a 50% reduction in the required computing resources compared to a legacy set-up previously used by the ATLAS collaboration. The set-ups described in this paper will be used for future ATLAS analyses and lay the foundation for the next generation of Monte Carlo predictions for single vector-boson plus jets production., For complete list of authors see http://dx.doi.org/10.1007/JHEP08(2022)089

This paper presents updated Monte Carlo configurations used to model the production of single electroweak vector bosons (W, Z/gamma*) in association with jets in proton-proton collisions for the ATLAS experiment at the Large Hadron Collider. Improvements pertaining to the electroweak input scheme, parton-shower splitting kernels and scale-setting scheme are shown for multi-jet merged configurations accurate to next-to-leading order in the strong and electroweak couplings. The computational resources required for these set-ups are assessed, and approximations are introduced resulting in a factor three reduction of the per-event CPU time without affecting the physics modelling performance. Continuous statistical enhancement techniques are introduced by ATLAS in order to populate low cross-section regions of phase space and are shown to match or exceed the generated effective luminosity. This, together with the lower per-event CPU time, results in a 50% reduction in the required computing resources compared to a legacy set-up previously used by the ATLAS collaboration. The set-ups described in this paper will be used for future ATLAS analyses and lay the foundation for the next generation of Monte Carlo predictions for single vector-boson plus jets production., For complete list of authors see http://dx.doi.org/10.1007/JHEP08(2022)089

This paper extends classical results by Langer and Kramers [1-3] and combines them with modern methods from high-temperature field theory [4-8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9-11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4-7, 12-14], all results only hold within this framework.

This paper presents updated Monte Carlo configurations used to model the production of single electroweak vector bosons (W, Z/gamma*) in association with jets in proton-proton collisions for the ATLAS experiment at the Large Hadron Collider. Improvements pertaining to the electroweak input scheme, parton-shower splitting kernels and scale-setting scheme are shown for multi-jet merged configurations accurate to next-to-leading order in the strong and electroweak couplings. The computational resources required for these set-ups are assessed, and approximations are introduced resulting in a factor three reduction of the per-event CPU time without affecting the physics modelling performance. Continuous statistical enhancement techniques are introduced by ATLAS in order to populate low cross-section regions of phase space and are shown to match or exceed the generated effective luminosity. This, together with the lower per-event CPU time, results in a 50% reduction in the required computing resources compared to a legacy set-up previously used by the ATLAS collaboration. The set-ups described in this paper will be used for future ATLAS analyses and lay the foundation for the next generation of Monte Carlo predictions for single vector-boson plus jets production., For complete list of authors see http://dx.doi.org/10.1007/JHEP08(2022)089

This paper extends classical results by Langer and Kramers [1-3] and combines them with modern methods from high-temperature field theory [4-8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9-11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4-7, 12-14], all results only hold within this framework.

In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for gravitational-wave calculations. To be specific, the region of applicability and accuracy of the derivative expansion is discussed. The derivative expansion is then compared to a numerical implementation of the Gelfand-Yaglom theorem. Both methods are applied to popular first-order phase transition models, like a loop-induced barrier and a SM-EFT tree-level barrier. The results of these calculations are presented in easy-to-use parametrizations that can directly be used in gravitational-wave calculations. In addition, higher-order corrections for models with multiple scalar fields, such as singlet/triplet extensions, are studied. Lastly, the main goal of this paper is to investigate the convergence and uncertainty of all calculation. Doing so I argue that current calculations for the Standard Model with a tree-level barrier are inaccurate.

In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for gravitational-wave calculations. To be specific, the region of applicability and accuracy of the derivative expansion is discussed. The derivative expansion is then compared to a numerical implementation of the Gelfand-Yaglom theorem. Both methods are applied to popular first-order phase transition models, like a loop-induced barrier and a SM-EFT tree-level barrier. The results of these calculations are presented in easy-to-use parametrizations that can directly be used in gravitational-wave calculations. In addition, higher-order corrections for models with multiple scalar fields, such as singlet/triplet extensions, are studied. Lastly, the main goal of this paper is to investigate the convergence and uncertainty of all calculation. Doing so I argue that current calculations for the Standard Model with a tree-level barrier are inaccurate.

In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for gravitational-wave calculations. To be specific, the region of applicability and accuracy of the derivative expansion is discussed. The derivative expansion is then compared to a numerical implementation of the Gelfand-Yaglom theorem. Both methods are applied to popular first-order phase transition models, like a loop-induced barrier and a SM-EFT tree-level barrier. The results of these calculations are presented in easy-to-use parametrizations that can directly be used in gravitational-wave calculations. In addition, higher-order corrections for models with multiple scalar fields, such as singlet/triplet extensions, are studied. Lastly, the main goal of this paper is to investigate the convergence and uncertainty of all calculation. Doing so I argue that current calculations for the Standard Model with a tree-level barrier are inaccurate.

This paper extends classical results by Langer and Kramers [1-3] and combines them with modern methods from high-temperature field theory [4-8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9-11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4-7, 12-14], all results only hold within this framework.

This paper presents updated Monte Carlo configurations used to model the production of single electroweak vector bosons (W, Z/gamma*) in association with jets in proton-proton collisions for the ATLAS experiment at the Large Hadron Collider. Improvements pertaining to the electroweak input scheme, parton-shower splitting kernels and scale-setting scheme are shown for multi-jet merged configurations accurate to next-to-leading order in the strong and electroweak couplings. The computational resources required for these set-ups are assessed, and approximations are introduced resulting in a factor three reduction of the per-event CPU time without affecting the physics modelling performance. Continuous statistical enhancement techniques are introduced by ATLAS in order to populate low cross-section regions of phase space and are shown to match or exceed the generated effective luminosity. This, together with the lower per-event CPU time, results in a 50% reduction in the required computing resources compared to a legacy set-up previously used by the ATLAS collaboration. The set-ups described in this paper will be used for future ATLAS analyses and lay the foundation for the next generation of Monte Carlo predictions for single vector-boson plus jets production., For complete list of authors see http://dx.doi.org/10.1007/JHEP08(2022)089

In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for gravitational-wave calculations. To be specific, the region of applicability and accuracy of the derivative expansion is discussed. The derivative expansion is then compared to a numerical implementation of the Gelfand-Yaglom theorem. Both methods are applied to popular first-order phase transition models, like a loop-induced barrier and a SM-EFT tree-level barrier. The results of these calculations are presented in easy-to-use parametrizations that can directly be used in gravitational-wave calculations. In addition, higher-order corrections for models with multiple scalar fields, such as singlet/triplet extensions, are studied. Lastly, the main goal of this paper is to investigate the convergence and uncertainty of all calculation. Doing so I argue that current calculations for the Standard Model with a tree-level barrier are inaccurate.

This paper extends classical results by Langer and Kramers [1-3] and combines them with modern methods from high-temperature field theory [4-8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9-11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4-7, 12-14], all results only hold within this framework.

This paper presents updated Monte Carlo configurations used to model the production of single electroweak vector bosons (W, Z/gamma*) in association with jets in proton-proton collisions for the ATLAS experiment at the Large Hadron Collider. Improvements pertaining to the electroweak input scheme, parton-shower splitting kernels and scale-setting scheme are shown for multi-jet merged configurations accurate to next-to-leading order in the strong and electroweak couplings. The computational resources required for these set-ups are assessed, and approximations are introduced resulting in a factor three reduction of the per-event CPU time without affecting the physics modelling performance. Continuous statistical enhancement techniques are introduced by ATLAS in order to populate low cross-section regions of phase space and are shown to match or exceed the generated effective luminosity. This, together with the lower per-event CPU time, results in a 50% reduction in the required computing resources compared to a legacy set-up previously used by the ATLAS collaboration. The set-ups described in this paper will be used for future ATLAS analyses and lay the foundation for the next generation of Monte Carlo predictions for single vector-boson plus jets production., For complete list of authors see http://dx.doi.org/10.1007/JHEP08(2022)089

In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for gravitational-wave calculations. To be specific, the region of applicability and accuracy of the derivative expansion is discussed. The derivative expansion is then compared to a numerical implementation of the Gelfand-Yaglom theorem. Both methods are applied to popular first-order phase transition models, like a loop-induced barrier and a SM-EFT tree-level barrier. The results of these calculations are presented in easy-to-use parametrizations that can directly be used in gravitational-wave calculations. In addition, higher-order corrections for models with multiple scalar fields, such as singlet/triplet extensions, are studied. Lastly, the main goal of this paper is to investigate the convergence and uncertainty of all calculation. Doing so I argue that current calculations for the Standard Model with a tree-level barrier are inaccurate.

Since summer 2021, the Radio Neutrino Observatory in Greenland (RNO-G) is searching for astrophysical neutrinos at energies > 10 PeV by detecting the radio emission from particle showers in the ice around Summit Station, Greenland. We present an extensive simulation study that shows how RNO-G will be able to measure the energy of such particle cascades, which will in turn be used to estimate the energy of the incoming neutrino that caused them. The location of the neutrino interaction is determined using the differences in arrival times between channels and the electric field of the radio signal is reconstructed using a novel approach based on Information Field Theory. Based on these properties, the shower energy can be estimated. We show that this method can achieve an uncertainty of 13% on the logarithm of the shower energy after modest quality cuts and estimate how this can constrain the energy of the neutrino. The method presented in this paper is applicable to all similar radio neutrino detectors, such as the proposed radio array of IceCube-Gen2.

Since summer 2021, the Radio Neutrino Observatory in Greenland (RNO-G) is searching for astrophysical neutrinos at energies > 10 PeV by detecting the radio emission from particle showers in the ice around Summit Station, Greenland. We present an extensive simulation study that shows how RNO-G will be able to measure the energy of such particle cascades, which will in turn be used to estimate the energy of the incoming neutrino that caused them. The location of the neutrino interaction is determined using the differences in arrival times between channels and the electric field of the radio signal is reconstructed using a novel approach based on Information Field Theory. Based on these properties, the shower energy can be estimated. We show that this method can achieve an uncertainty of 13% on the logarithm of the shower energy after modest quality cuts and estimate how this can constrain the energy of the neutrino. The method presented in this paper is applicable to all similar radio neutrino detectors, such as the proposed radio array of IceCube-Gen2.

Since summer 2021, the Radio Neutrino Observatory in Greenland (RNO-G) is searching for astrophysical neutrinos at energies > 10 PeV by detecting the radio emission from particle showers in the ice around Summit Station, Greenland. We present an extensive simulation study that shows how RNO-G will be able to measure the energy of such particle cascades, which will in turn be used to estimate the energy of the incoming neutrino that caused them. The location of the neutrino interaction is determined using the differences in arrival times between channels and the electric field of the radio signal is reconstructed using a novel approach based on Information Field Theory. Based on these properties, the shower energy can be estimated. We show that this method can achieve an uncertainty of 13% on the logarithm of the shower energy after modest quality cuts and estimate how this can constrain the energy of the neutrino. The method presented in this paper is applicable to all similar radio neutrino detectors, such as the proposed radio array of IceCube-Gen2.

Since summer 2021, the Radio Neutrino Observatory in Greenland (RNO-G) is searching for astrophysical neutrinos at energies > 10 PeV by detecting the radio emission from particle showers in the ice around Summit Station, Greenland. We present an extensive simulation study that shows how RNO-G will be able to measure the energy of such particle cascades, which will in turn be used to estimate the energy of the incoming neutrino that caused them. The location of the neutrino interaction is determined using the differences in arrival times between channels and the electric field of the radio signal is reconstructed using a novel approach based on Information Field Theory. Based on these properties, the shower energy can be estimated. We show that this method can achieve an uncertainty of 13% on the logarithm of the shower energy after modest quality cuts and estimate how this can constrain the energy of the neutrino. The method presented in this paper is applicable to all similar radio neutrino detectors, such as the proposed radio array of IceCube-Gen2.

Since summer 2021, the Radio Neutrino Observatory in Greenland (RNO-G) is searching for astrophysical neutrinos at energies > 10 PeV by detecting the radio emission from particle showers in the ice around Summit Station, Greenland. We present an extensive simulation study that shows how RNO-G will be able to measure the energy of such particle cascades, which will in turn be used to estimate the energy of the incoming neutrino that caused them. The location of the neutrino interaction is determined using the differences in arrival times between channels and the electric field of the radio signal is reconstructed using a novel approach based on Information Field Theory. Based on these properties, the shower energy can be estimated. We show that this method can achieve an uncertainty of 13% on the logarithm of the shower energy after modest quality cuts and estimate how this can constrain the energy of the neutrino. The method presented in this paper is applicable to all similar radio neutrino detectors, such as the proposed radio array of IceCube-Gen2.