The DOI matches its Crossref record; 62 of the 62 references it cites were found in a registry or an index.
Towards a precision calculation of the effective number of neutrinos Neff in the Standard Model. Part II. Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED
Open accessAbstract
We present in this work a new calculation of the standard-model benchmark value for the effective number of neutrinos, N eff SM, that quantifies the cosmological neutrino-to-photon energy densities. The calculation takes into account neutrino flavour oscillations, finite-temperature effects in the quantum electrodynamics plasma to O(e 3), where e is the elementary electric charge, and a full evaluation of the neutrino-neutrino collision integral. We provide furthermore a detailed assessment of the uncertainties in the benchmark N eff SM value, through testing the value's dependence on (i) optional approximate modelling of the weak collision integrals, (ii) measurement errors in the physical parameters of the weak sector, and (iii) numerical convergence, particularly in relation to momentum discretisation. Our new, recommended standard-model benchmark is N eff SM 3.0440 ±0.0002, where the nominal uncertainty is attributed predominantly to errors incurred in the numerical solution procedure (|δ N eff| ∼10-4), augmented by measurement errors in the solar mixing angle sin 2θ 12 (|δ N eff| ∼10-4).
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Planck 2018 results: VI. Cosmological parameters
Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., et al. (2020) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201833910 · Cited by 14,258
Olive, K. A. (2016) · Chinese Physics C · doi:10.1088/1674-1137/40/10/100001 · Cited by 7,334
Particle Data Group, Zyla, P. A., Barnett, R. M., Beringer, J., Dahl, O., Dwyer, D. A., Groom, D. E., Lin, C. J., Lugovsky, K. S., Pianori, E., et al. (2020) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptaa104 · Cited by 5,180
Dark Matter as a Topological Vacuum Condensate
Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., et al. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1807.06209 · Cited by 3,403
CODATA recommended values of the fundamental physical constants: 2010
Mohr, P. J., Taylor, B. N., & Newell, D. B. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1527 · Cited by 2,441
Finite-Temperature Field Theory: Principles and Applications
Kapusta, J. I., & Gale, C. (2006) · Cambridge University Press eBooks · doi:10.1017/cbo9780511535130 · Cited by 1,935
An, F., An, G., An, Q., Antonelli, V., Baussan, E., Beacom, J., Bezrukov, L., Blyth, S., Brugnera, R., Avanzini, M. B., et al. (2016) · Journal of Physics G: Nuclear and Particle Physics · doi:10.1088/0954-3899/43/3/030401 · Cited by 1,184
The fate of hints: updated global analysis of three-flavor neutrino oscillations
Esteban, I., Gonzalez-Garcia, M. C., Maltoni, M., Schwetz, T., & Zhou, A. (2020) · Journal of High Energy Physics · doi:10.1007/jhep09(2020)178 · Cited by 1,177
The fate of hints: updated global analysis of three-flavor neutrino oscillations
Esteban, I., González-García, M. C., Maltoni, M., Schwetz, T., & Zhou, A. (2020) · Repository KITopen (Karlsruhe Institute of Technology) · doi:10.5445/ir/1000124126 · Cited by 1,097
CODATA recommended values of the fundamental physical constants: 2018
Tiesinga, E., Mohr, P. J., Newell, D. B., & Taylor, B. N. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.025010 · Cited by 908
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Schöneberg, N., Abellán, G. F., Sánchez, A. P., Witte, S. J., Poulin, V., & Lesgourgues, J. (2021) · arXiv · doi:10.48550/arxiv.2107.10291 · Cited by 463
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Di Valentino, E., Said, J. L., Riess, A., Pollo, A., Poulin, V., Gómez-Valent, A., Weltman, A., Palmese, A., Huang, C. D., Bruck, C. V. D., et al. (2025) · Physics of the Dark Universe · doi:10.1016/j.dark.2025.101965 · Cited by 319
Self-citation
Metadata
- Authors
- Bennett, J. J., Buldgen, G., de Salas, P. F., Drewes, M., Gariazzo, S., Pastor, S., & Wong, Y. Y. Y.
- Venue
- Journal of Cosmology and Astroparticle Physics
- Publisher
- IOP Publishing
- Published
- 2021-04-01
- Volume
- 2021
- Issue
- 04
- Pages
- 073
- ISSN
- 1475-7508 (ISSN-L)
- 1475-7516
- OpenAlex
- W3111524432
- Cited by
- 299
- References
- 62
- FWCI
- 11.93
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Bennett, J. J., Buldgen, G., de Salas, P. F., Drewes, M., Gariazzo, S., Pastor, S., & Wong, Y. Y. Y. (2021). Towards a precision calculation of the effective number of neutrinos Neff in the Standard Model. Part II. Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED. Journal of Cosmology and Astroparticle Physics. https://doi.org/10.1088/1475-7516/2021/04/073
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