Cosmological Consequences of a Highly Decoupled Right-handed Neutrino

Author(s)

King, Stephen F., Roshan, Rishav, Show, Sudipta

Abstract

In the minimal type-I seesaw, one right-handed neutrino (RHN) can decouple from neutrino mass generation. Such a state is usually neglected, yet its feeble couplings make it long-lived, and it can dominate the energy density of the Universe before decaying. We study this in a minimal $U(1)_{B-L}$ model, where the RHNs are produced through $B-L$ gauge interactions, for the cases of a decoupled lightest RHN $N_1$ and a decoupled heaviest RHN $N_3$. The resulting early matter-dominated era dilutes the baryon asymmetry, and for decoupled $N_3$ it also delays the equilibration of the charged-lepton Yukawa interactions, allowing a lighter $N_1$ to generate the asymmetry in the unflavoured regime. Breaking $U(1)_{B-L}$ forms cosmic strings whose gravitational-wave background acquires a spectral break from the early matter-dominated era, with a frequency set by the decoupled RHN mass and the lightest neutrino mass, within reach of future detectors such as SKA, THEIA, LISA, $μ$ARES, DECIGO and ET.

Figures

Evolution of the various energy densities, $\rho_R$ (black) and $\rho_{N_1}$ (red) as a function of the temperature $T$.
Caption Evolution of the various energy densities, $\rho_R$ (black) and $\rho_{N_1}$ (red) as a function of the temperature $T$.
Evolution of the baryon asymmetry with the expansion of the Universe for a fixed value of parameters: $M_1=10^{8}~\rm{GeV},~M_2=10^{12}~\rm{GeV},~r=10,~a=0.48,~b=-0.9$ for three different values of $m_{l}$.
Caption Evolution of the baryon asymmetry with the expansion of the Universe for a fixed value of parameters: $M_1=10^{8}~\rm{GeV},~M_2=10^{12}~\rm{GeV},~r=10,~a=0.48,~b=-0.9$ for three different values of $m_{l}$.
Evolution of the various energy densities,$\rho_R$ (black) and $\rho_{N_3}$ (red), as a function of the temperature $T$.
Caption Evolution of the various energy densities,$\rho_R$ (black) and $\rho_{N_3}$ (red), as a function of the temperature $T$.
Variation of $\langle \Gamma_\alpha \rangle/\mathcal{H}$ vs. $T$ for standard (solid lines) and modified (dot-dashed and dashed) scenarios.
Caption Variation of $\langle \Gamma_\alpha \rangle/\mathcal{H}$ vs. $T$ for standard (solid lines) and modified (dot-dashed and dashed) scenarios.
Variation of $\langle \Gamma_\tau \rangle/\mathcal{H}$ vs. $T$ for standard (solid lines) and modified (dot-dashed and dashed) scenarios.
Caption Variation of $\langle \Gamma_\tau \rangle/\mathcal{H}$ vs. $T$ for standard (solid lines) and modified (dot-dashed and dashed) scenarios.
Evolution of the baryon asymmetry with the expansion of the Universe for a fixed value of parameters: $M_3=10^{14}~\rm{GeV},~M_1=5\times10^{11}~\rm{GeV},~r=10,~a=0.12,~b=-0.1$ for three different values of $m_{l}$.
Caption Evolution of the baryon asymmetry with the expansion of the Universe for a fixed value of parameters: $M_3=10^{14}~\rm{GeV},~M_1=5\times10^{11}~\rm{GeV},~r=10,~a=0.12,~b=-0.1$ for three different values of $m_{l}$.
The GW spectral shapes for local strings are shown with a period of eMD for a fixed value of parameters: $M_1=10^{8}~{\rm{GeV}},~v_{\rm BL}=10^{13}{\rm{GeV}}$ for three different values of $m_{l}$.
Caption The GW spectral shapes for local strings are shown with a period of eMD for a fixed value of parameters: $M_1=10^{8}~{\rm{GeV}},~v_{\rm BL}=10^{13}{\rm{GeV}}$ for three different values of $m_{l}$.
The GW spectral shapes for local strings are shown with a period of eMD for a fixed value of parameters:$M_3=10^{14}~{\rm{GeV}},~v_{\rm BL}=10^{14}{\rm{GeV}}$ for three different values of $m_{l}$.
Caption The GW spectral shapes for local strings are shown with a period of eMD for a fixed value of parameters:$M_3=10^{14}~{\rm{GeV}},~v_{\rm BL}=10^{14}{\rm{GeV}}$ for three different values of $m_{l}$.
Variation of $\langle \Gamma_\alpha \rangle/\mathcal{H}$ vs. $T$ for standard (solid lines) and modified (dot-dashed and dashed) scenarios.
Caption Variation of $\langle \Gamma_\alpha \rangle/\mathcal{H}$ vs. $T$ for standard (solid lines) and modified (dot-dashed and dashed) scenarios.
References
  • [1] P. Minkowski, µ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67, 421 (1977).
  • [2] T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  • [3] T. Yanagida, Horizontal Symmetry and Mass of the Top Quark, Phys. Rev. D 20, 2986 (1979).
  • [4] M. Gell-Mann, P. Ramond, and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927, 315 (1979), arXiv:1306.4669 [hep-th].
  • [5] R. N. Mohapatra and G. Senjanovic, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  • [6] J. Schechter and J. W. F. Valle, Neutrino Masses in SU(2) x U(1) Theories, Phys. Rev. D 22, 2227 (1980).
  • [7] J. Schechter and J. W. F. Valle, Neutrino Decay and Spontaneous Violation of Lepton Number, Phys. Rev. D 25, 774 (1982).
  • [8] M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174, 45 (1986).
  • [9] W. Buchmuller, R. Peccei, and T. Yanagida, Leptogenesis as the origin of matter, Ann. Rev. Nucl. Part. Sci. 55, 311 (2005), arXiv:hep-ph/0502169.
  • [10] S. Davidson, E. Nardi, and Y. Nir, Leptogenesis, Phys. Rept. 466, 105 (2008), arXiv:0802.2962 [hep-ph].
  • [11] S. F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576, 85 (2000), arXiv:hep-ph/9912492.
  • [12] S. Antusch, P. Di Bari, D. A. Jones, and S. F. King, Leptogenesis in the Two Right-Handed Neutrino Model Revisited, Phys. Rev. D 86, 023516 (2012), arXiv:1107.6002 [hep-ph].
  • [13] C.-C. Li and G.-J. Ding, Implications of residual CP symmetry for leptogenesis in a model with two righthanded neutrinos, Phys. Rev. D 96, 075005 (2017), arXiv:1701.08508 [hep-ph].
  • [14] A. Datta, R. Roshan, and A. Sil, Imprint of the Seesaw Mechanism on Feebly Interacting Dark Matter and the Baryon Asymmetry, Phys. Rev. Lett. 127, 231801 (2021), arXiv:2104.02030 [hep-ph].
  • [15] S. F. King, Right-handed neutrinos: seesaw models and signatures (2025) arXiv:2502.07877 [hep-ph].
  • [16] P. Konar and S. Show, Unveiling a Hidden Epoch: Impact of Mediator Induced Matter Domination in Freezein Dark Matter, (2025), arXiv:2512.13799 [hep-ph].
  • [17] R. Roshan and S. Show, Delayed Charged Lepton Yukawa Equilibration in Minimal Seesaw, Phys. Rev. Lett. 137, 111802 (2026), arXiv:2510.23712 [hep-ph].
  • [18] J. A. Casas and A. Ibarra, Oscillating neutrinos and muon —¿ e, gamma, Nucl. Phys. B618, 171 (2001), arXiv:hep-ph/0103065 [hep-ph].
  • [19] T. W. B. Kibble, Topology of Cosmic Domains and Strings, J. Phys. A 9, 1387 (1976).
  • [20] H. B. Nielsen and P. Olesen, Vortex Line Models for Dual Strings, Nucl. Phys. B 61, 45 (1973).
  • [21] P. Auclair et al., Probing the gravitational wave background from cosmic strings with LISA, JCAP 04, 034, arXiv:1909.00819 [astro-ph.CO].
  • [22] B. Goncharov et al., On the Evidence for a Commonspectrum Process in the Search for the Nanohertz Gravitational-wave Background with the Parkes Pulsar Timing Array, Astrophys. J. Lett. 917, L19 (2021), arXiv:2107.12112 [astro-ph.HE].
  • [23] J. Ellis and M. Lewicki, Cosmic String Interpretation of NANOGrav Pulsar Timing Data, Phys. Rev. Lett. 126, 041304 (2021), arXiv:2009.06555 [astro-ph.CO].
  • [24] S. Blasi, V. Brdar, and K. Schmitz, Has NANOGrav found first evidence for cosmic strings?, Phys. Rev. Lett. 126, 041305 (2021), arXiv:2009.06607 [astro-ph.CO].
  • [25] R. Samanta and S. Datta, Gravitational wave complementarity and impact of NANOGrav data on gravitational leptogenesis, JHEP 05, 211, arXiv:2009.13452 [hep-ph].
  • [26] G. Lazarides, R. Maji, R. Roshan, and Q. Shafi, Heavier W-boson, dark matter and gravitational waves from strings in an SO(10) axion model, (2022), arXiv:2205.04824 [hep-ph].
  • [27] G. Lazarides, R. Maji, R. Roshan, and Q. Shafi, A predictive SO(10) model, JCAP 12, 009, arXiv:2210.03710 [hep-ph].
  • [28] R. Roshan and G. White, Using gravitational waves to see the first second of the Universe, Rev. Mod. Phys. 97, 015001 (2025), arXiv:2401.04388 [hep-ph].
  • [29] K. Schmitz and T. Schroeder, Gravitational waves from cosmic strings for pedestrians, JCAP 01, 025, arXiv:2412.20907 [astro-ph.CO].
  • [30] Y. Cui, M. Lewicki, D. E. Morrissey, and J. D. Wells, Cosmic Archaeology with Gravitational Waves from Cosmic Strings, Phys. Rev. D 97, 123505 (2018), arXiv:1711.03104 [hep-ph].
  • [31] Y. Cui, M. Lewicki, D. E. Morrissey, and J. D. Wells, Probing the pre-BBN universe with gravitational waves from cosmic strings, JHEP 01, 081, arXiv:1808.08968 [hep-ph].
  • [32] Y. Gouttenoire, G. Servant, and P. Simakachorn, Beyond the Standard Models with Cosmic Strings, JCAP 07, 032, arXiv:1912.02569 [hep-ph].
  • [33] S. Blasi, V. Brdar, and K. Schmitz, Fingerprint of low-scale leptogenesis in the primordial gravitationalwave spectrum, Phys. Rev. Res. 2, 043321 (2020), arXiv:2004.02889 [hep-ph].
  • [34] D. Borah, S. Jyoti Das, A. K. Saha, and R. Samanta, Probing WIMP dark matter via gravitational waves’ spectral shapes, Phys. Rev. D 106, L011701 (2022), arXiv:2202.10474 [hep-ph].
  • [35] D. Borah, S. Jyoti Das, and R. Roshan, Probing high scale seesaw and PBH generated dark matter via gravitational waves with multiple tilts, Nucl. Phys. B 1002, 116528 (2024), arXiv:2208.04965 [hep-ph].
  • [36] S. Datta, A. Ghoshal, A. Spalding, and G. White, Gravitational wave spectral shapes as a probe of long lived right-handed neutrinos, leptogenesis and dark matter. Global versus local B − L cosmic strings, JHEP 03, 245, arXiv:2511.01779 [astro-ph.CO].
  • [37] J. A. Dror, T. Hiramatsu, K. Kohri, H. Murayama, and G. White, Testing the Seesaw Mechanism and Leptogenesis with Gravitational Waves, Phys. Rev. Lett. 124, 041804 (2020), arXiv:1908.03227 [hep-ph].
  • [38] M. Chianese, S. Datta, G. Miele, R. Samanta, and N. Saviano, Probing flavored regimes of leptogenesis with gravitational waves from cosmic strings, Phys. Rev. D 111, L041305 (2025), arXiv:2406.01231 [hep-ph].
  • [39] A. Datta and A. Sil, Probing Leptogenesis through Gravitational Waves, (2024), arXiv:2410.01900 [hepph].
  • [40] H. Murayama, B. Noether, and J. Schütte-Engel, Observing Leptogenesis in Action with Gravitational Waves, (2025), arXiv:2506.15772 [hep-ph].
  • [41] L. Covi, E. Roulet, and F. Vissani, CP violating decays in leptogenesis scenarios, Phys. Lett. B 384, 169 (1996), arXiv:hep-ph/9605319.
  • [42] N. Aghanim et al. (Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO].
  • [42] N. Aghanim et al. (Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO].
  • [43] A. Datta, R. Roshan, and A. Sil, Effects of Reheating on Charged Lepton Yukawa Equilibration and Leptogenesis, Phys. Rev. Lett. 132, 061802 (2024), arXiv:2206.10650 [hep-ph].
  • [44] A. Datta, R. Roshan, and A. Sil, Flavor leptogenesis during the reheating era, Phys. Rev. D 108, 035029 (2023), arXiv:2301.10791 [hep-ph].
  • [45] R. Barbieri, P. Creminelli, A. Strumia, and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys. B 575, 61 (2000), arXiv:hep-ph/9911315.
  • [46] E. Nardi, Y. Nir, J. Racker, and E. Roulet, On Higgs and sphaleron effects during the leptogenesis era, JHEP 01, 068, arXiv:hep-ph/0512052.
  • [47] A. Abada, S. Davidson, F.-X. Josse-Michaux, M. Losada, and A. Riotto, Flavor issues in leptogenesis, JCAP 04, 004, arXiv:hep-ph/0601083.
  • [48] E. Nardi, Y. Nir, E. Roulet, and J. Racker, The Importance of flavor in leptogenesis, JHEP 01, 164, arXiv:hepph/0601084.
  • [49] S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP 03, 018, arXiv:hep-ph/0607330.
  • [50] P. S. B. Dev, P. Di Bari, B. Garbrecht, S. Lavignac, P. Millington, and D. Teresi, Flavor effects in leptogenesis, Int. J. Mod. Phys. A 33, 1842001 (2018), arXiv:1711.02861 [hep-ph].
  • [51] A. Datta, R. Roshan, and A. Sil, Scalar triplet flavor leptogenesis with dark matter, Phys. Rev. D 105, 095032 (2022), arXiv:2110.03914 [hep-ph].
  • [52] J. M. Cline, K. Kainulainen, and K. A. Olive, On the erasure and regeneration of the primordial baryon asymmetry by sphalerons, Phys. Rev. Lett. 71, 2372 (1993), arXiv:hep-ph/9304321.
  • [53] J. M. Cline, K. Kainulainen, and K. A. Olive, Protecting the primordial baryon asymmetry from erasure by sphalerons, Phys. Rev. D 49, 6394 (1994), arXiv:hepph/9401208.
  • [54] H. A. Weldon, Effective Fermion Masses of Order gT in High Temperature Gauge Theories with Exact Chiral Invariance, Phys. Rev. D 26, 2789 (1982).
  • [55] M. Quiros, Finite temperature field theory and phase transitions, in ICTP Summer School in High-Energy Physics and Cosmology (1999) pp. 187–259, arXiv:hep-ph/9901312.
  • [56] E. Senaha, Symmetry Restoration and Breaking at Finite Temperature: An Introductory Review, Symmetry 12, 733 (2020).
  • [57] M. A. Luty, Baryogenesis via leptogenesis, Phys. Rev. D 45, 455 (1992).
  • [58] A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56, 5431 (1997), arXiv:hep-ph/9707235.
  • [59] P. Konar, A. Mukherjee, A. K. Saha, and S. Show, A dark clue to seesaw and leptogenesis in a pseudo-Dirac singlet doublet scenario with (non)standard cosmology, JHEP 03, 044, arXiv:2007.15608 [hep-ph].
  • [60] W. Buchmuller, P. Di Bari, and M. Plumacher, Leptogenesis for pedestrians, Annals Phys. 315, 305 (2005), arXiv:hep-ph/0401240.
  • [61] A. De Simone and A. Riotto, Quantum Boltzmann Equations and Leptogenesis, JCAP 08, 002, arXiv:hepph/0703175.
  • [62] A. Vilenkin, Cosmic Strings and Domain Walls, Phys. Rept. 121, 263 (1985).
  • [63] E. W. Kolb and M. S. Turner, The Early Universe, Vol. 69 (1990).
  • [64] J. Preskill and A. Vilenkin, Decay of metastable topological defects, Phys. Rev. D 47, 2324 (1993), arXiv:hepph/9209210.
  • [65] A. Vilenkin and E. P. S. Shellard, Cosmic strings and other topological defects (1994).
  • [66] G. Agazie et al. (NANOGrav), The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett. 951, L8 (2023), arXiv:2306.16213 [astro-ph.HE].
  • [67] A. Afzal et al. (NANOGrav), The NANOGrav 15 yr Data Set: Search for Signals from New Physics, Astrophys. J. Lett. 951, L11 (2023), arXiv:2306.16219 [astroph.HE].
  • [68] W. Buchmüller, V. Domcke, K. Kamada, and K. Schmitz, The Gravitational Wave Spectrum from Cosmological B − L Breaking, JCAP 10, 003, arXiv:1305.3392 [hep-ph].
  • [69] W. Buchmuller, V. Domcke, H. Murayama, and K. Schmitz, Probing the scale of grand unification with gravitational waves, Phys. Lett. B 809, 135764 (2020), arXiv:1912.03695 [hep-ph].
  • [70] S. F. King, S. Pascoli, J. Turner, and Y.-L. Zhou, Gravitational Waves and Proton Decay: Complementary Windows into Grand Unified Theories, Phys. Rev. Lett. 126, 021802 (2021), arXiv:2005.13549 [hep-ph].
  • [71] B. Fornal and B. Shams Es Haghi, Baryon and Lepton Number Violation from Gravitational Waves, Phys. Rev. D 102, 115037 (2020), arXiv:2008.05111 [hep-ph].
  • [72] W. Buchmuller, V. Domcke, and K. Schmitz, Stochastic gravitational-wave background from metastable cosmic strings, JCAP 12 (12), 006, arXiv:2107.04578 [hep-ph].
  • [73] M. A. Masoud, M. U. Rehman, and Q. Shafi, Sneutrino tribrid inflation, metastable cosmic strings and gravitational waves, JCAP 11, 022, arXiv:2107.09689 [hep-ph].
  • [74] A. Afzal, W. Ahmed, M. U. Rehman, and Q. Shafi, µhybrid Inflation, Gravitino Dark Matter and Stochastic Gravitational Wave Background from Cosmic Strings, (2022), arXiv:2202.07386 [hep-ph].
  • [75] A. Vilenkin, Cosmic string dynamics with friction, Phys. Rev. D 43, 1060 (1991).
  • [76] J. J. Blanco-Pillado, K. D. Olum, and B. Shlaer, Large parallel cosmic string simulations: New results on loop production, Phys. Rev. D 83, 083514 (2011), arXiv:1101.5173 [astro-ph.CO].
  • [77] D. P. Bennett and F. R. Bouchet, Evidence for a Scaling Solution in Cosmic String Evolution, Phys. Rev. Lett. 60, 257 (1988).
  • [78] D. P. Bennett and F. R. Bouchet, Cosmic string evolution, Phys. Rev. Lett. 63, 2776 (1989).
  • [79] A. Vilenkin, Gravitational radiation from cosmic strings, Phys. Lett. B 107, 47 (1981).
  • [80] N. Turok, Grand Unified Strings and Galaxy Formation, Nucl. Phys. B 242, 520 (1984).
  • [81] T. Vachaspati and A. Vilenkin, Gravitational Radiation from Cosmic Strings, Phys. Rev. D 31, 3052 (1985).
  • [82] J. J. Blanco-Pillado, K. D. Olum, and B. Shlaer, The number of cosmic string loops, Phys. Rev. D 89, 023512 (2014), arXiv:1309.6637 [astro-ph.CO].
  • [83] C. J. A. P. Martins and E. P. S. Shellard, Quantitative string evolution, Phys. Rev. D 54, 2535 (1996), arXiv:hep-ph/9602271.
  • [84] C. J. A. P. Martins and E. P. S. Shellard, Extending the velocity dependent one scale string evolution model, Phys. Rev. D 65, 043514 (2002), arXiv:hep-ph/0003298.
  • [85] J. J. Blanco-Pillado and K. D. Olum, Stochastic gravitational wave background from smoothed cosmic string loops, Phys. Rev. D 96, 104046 (2017), arXiv:1709.02693 [astro-ph.CO].
  • [86] T. Charnock, A. Avgoustidis, E. J. Copeland, and A. Moss, CMB constraints on cosmic strings and superstrings, Phys. Rev. D 93, 123503 (2016), arXiv:1603.01275 [astro-ph.CO].
  • [87] S. Datta, A. Ghosal, and R. Samanta, Baryogenesis from ultralight primordial black holes and strong gravitational waves from cosmic strings, JCAP 08, 021, arXiv:2012.14981 [hep-ph].
  • [88] Y. Gouttenoire, G. Servant, and P. Simakachorn, BSM with Cosmic Strings: Heavy, up to EeV mass, Unstable Particles, JCAP 07, 016, arXiv:1912.03245 [hep-ph].
  • [89] M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Class. Quant. Grav. 27, 194002 (2010).
  • [90] P. Amaro-Seoane et al. (LISA), Laser Interferometer Space Antenna, (2017), arXiv:1702.00786 [astroph.IM].
  • [91] S. Kawamura et al., Current status of space gravitational wave antenna DECIGO and B-DECIGO, PTEP 2021, 05A105 (2021), arXiv:2006.13545 [gr-qc].
  • [92] A. Sesana et al., Unveiling the gravitational universe at µ-Hz frequencies, Exper. Astron. 51, 1333 (2021), arXiv:1908.11391 [astro-ph.IM].
  • [93] G. Janssen et al., Gravitational wave astronomy with the SKA, PoS AASKA14, 037 (2015), arXiv:1501.00127 [astro-ph.IM].
  • [94] J. Garcia-Bellido, H. Murayama, and G. White, Exploring the Early Universe with Gaia and THEIA, (2021), arXiv:2104.04778 [hep-ph].
  • [95] S. F. King, R. Roshan, X. Wang, G. White, and M. Yamazaki, Quantum gravity effects on dark matter and gravitational waves, Phys. Rev. D 109, 024057 (2024), arXiv:2308.03724 [hep-ph].
  • [96] G. Domènech, C. Lin, and M. Sasaki, Gravitational wave constraints on the primordial black hole dominated early universe, JCAP 04, 062, [Erratum: JCAP 11, E01 (2021)], arXiv:2012.08151 [gr-qc].
  • [97] A. Datta and A. Sil, Probing leptogenesis and the minimal neutrino seesaw mechanism through gravitational waves, Phys. Rev. D 114, 035040 (2026), arXiv:2410.01900 [hep-ph].
  • [98] P. Konar and S. Show, Unraveling Freeze-in Dark matter through the echoes of gravitational waves, (2025), arXiv:2506.08106 [hep-ph].
  • [99] M. Aker et al. (KATRIN), The design, construction, and commissioning of the KATRIN experiment, JINST 16 (08), T08015, arXiv:2103.04755 [physics.ins-det].
  • [100] A. Ashtari Esfahani et al. (Project 8), Determining the neutrino mass with cyclotron radiation emission spectroscopy—Project 8, J. Phys. G 44, 054004 (2017), arXiv:1703.02037 [physics.ins-det].