Threshold Effects on the Massless Neutrino in the Canonical Seesaw Mechanism

This poster is based on: D. Zhang, JHEP 10 (2024) 002 III. RGEs and Threshold Effects IV. RG Running of the Determinant VI. Summary V. Two-loop RG Running Effects I. Neutrino Masses ØNeutrino oscillation experiments: at least two neutrinos have non-zero masses Threshold Effects on the Massless Neutrino in the Canonical Seesaw Mechanism Di Zhang ([email protected]) Physik-Department, Technische Universität München James-Franck-Straße, 85748 Garching, Germany NuFIT 6.0 (2024) IC19 without SK atmospheric data Normal Ordering (!ω2=0.6) Inverted Ordering (best fit) bfp ±1ε3εrange bfp ±1ε3εrange sin2ϑ12 0.307+0.012 →0.011 0.275 →0.345 0.308+0.012 →0.011 0.275 →0.345 ϑ12/↑33.68+0.73 →0.70 31.63 →35.95 33.68+0.73 →0.70 31.63 →35.95 sin2ϑ23 0.561+0.012 →0.015 0.430 →0.596 0.562+0.012 →0.015 0.437 →0.597 ϑ23/↑48.5+0.7 →0.941.0→50.548.6+0.7 →0.941.4→50.6 sin2ϑ13 0.02195+0.00054 →0.00058 0.02023 →0.02376 0.02224+0.00056 →0.00057 0.02053 →0.02397 ϑ13/↑8.52+0.11 →0.11 8.18 →8.87 8.58+0.11 →0.11 8.24 →8.91 ϖCP/↑177+19 →20 96 →422 285+25 →28 201 →348 !m2 21 10→5eV27.49+0.19 →0.19 6.92 →8.05 7.49+0.19 →0.19 6.92 →8.05 !m2 3ω 10→3eV2+2.534+0.025 →0.023 +2.463 →+2.606 ↑2.510+0.024 →0.025 ↑2.584 →↑2.438 IC24 with SK atmospheric data Normal Ordering (best fit) Inverted Ordering (!ω2=6.1) bfp ±1ε3εrange bfp ±1ε3εrange sin2ϑ12 0.308+0.012 →0.011 0.275 →0.345 0.308+0.012 →0.011 0.275 →0.345 ϑ12/↑33.68+0.73 →0.70 31.63 →35.95 33.68+0.73 →0.70 31.63 →35.95 sin2ϑ23 0.470+0.017 →0.013 0.435 →0.585 0.550+0.012 →0.015 0.440 →0.584 ϑ23/↑43.3+1.0 →0.841.3→49.947.9+0.7 →0.941.5→49.8 sin2ϑ13 0.02215+0.00056 →0.00058 0.02030 →0.02388 0.02231+0.00056 →0.00056 0.02060 →0.02409 ϑ13/↑8.56+0.11 →0.11 8.19 →8.89 8.59+0.11 →0.11 8.25 →8.93 ϖCP/↑212+26 →41 124 →364 274+22 →25 201 →335 !m2 21 10→5eV27.49+0.19 →0.19 6.92 →8.05 7.49+0.19 →0.19 6.92 →8.05 !m2 3ω 10→3eV2+2.513+0.021 →0.019 +2.451 →+2.578 ↑2.484+0.020 →0.020 ↑2.547 →↑2.421 IC19 without SK atmospheric data Normal Ordering (!ω2=0.6) Inverted Ordering (best fit) bfp ±1ε3εrange bfp ±1ε3εrange sin2ϑ12 0.307+0.012 →0.011 0.275 →0.345 0.308+0.012 →0.011 0.275 →0.345 ϑ12/↑33.68+0.73 →0.70 31.63 →35.95 33.68+0.73 →0.70 31.63 →35.95 sin2ϑ23 0.561+0.012 →0.015 0.430 →0.596 0.562+0.012 →0.015 0.437 →0.597 ϑ23/↑48.5+0.7 →0.941.0→50.548.6+0.7 →0.941.4→50.6 sin2ϑ13 0.02195+0.00054 →0.00058 0.02023 →0.02376 0.02224+0.00056 →0.00057 0.02053 →0.02397 ϑ13/↑8.52+0.11 →0.11 8.18 →8.87 8.58+0.11 →0.11 8.24 →8.91 ϖCP/↑177+19 →20 96 →422 285+25 →28 201 →348 !m2 21 10→5eV27.49+0.19 →0.19 6.92 →8.05 7.49+0.19 →0.19 6.92 →8.05 !m2 3ω 10→3eV2+2.534+0.025 →0.023 +2.463 →+2.606 ↑2.510+0.024 →0.025 ↑2.584 →↑2.438 IC24 with SK atmospheric data Normal Ordering (best fit) Inverted Ordering (!ω2=6.1) bfp ±1ε3εrange bfp ±1ε3εrange sin2ϑ12 0.308+0.012 →0.011 0.275 →0.345 0.308+0.012 →0.011 0.275 →0.345 ϑ12/↑33.68+0.73 →0.70 31.63 →35.95 33.68+0.73 →0.70 31.63 →35.95 sin2ϑ23 0.470+0.017 →0.013 0.435 →0.585 0.550+0.012 →0.015 0.440 →0.584 ϑ23/↑43.3+1.0 →0.841.3→49.947.9+0.7 →0.941.5→49.8 sin2ϑ13 0.02215+0.00056 →0.00058 0.02030 →0.02388 0.02231+0.00056 →0.00056 0.02060 →0.02409 ϑ13/↑8.56+0.11 →0.11 8.19 →8.89 8.59+0.11 →0.11 8.25 →8.93 ϖCP/↑212+26 →41 124 →364 274+22 →25 201 →335 !m2 21 10→5eV27.49+0.19 →0.19 6.92 →8.05 7.49+0.19 →0.19 6.92 →8.05 !m2 3ω 10→3eV2+2.513+0.021 →0.019 +2.451 →+2.578 ↑2.484+0.020 →0.020 ↑2.547 →↑2.421 ØNon-oscillation experiments: neutrino masses are very tiny No lower limit on the lightest neutrino mass allowing one massless neutrino KATRIN collaboration, 2024 GERDA collaboration, 2020 KAMLAND-ZEN collaboration, 2024 J. Q. Jiang et al., 2024; D. Naredo-Tuero et al., 2024 lCosmological observations: lBeta decay: lNeutrinoless double beta decay: Ivan Esteban et al., 2024 A natural question arises: Can we have an exactly massless neutrino? Is the vanishing neutrino mass stable against quantum corrections if no extra symmetry protects it? If not, it will provide a theoretical lower limit! One-loop RGEs for non-degenerate seesaw scales: The effect neutrino mass matrix: with *Terms in red are overlooked in the previous literatures: S. Antusch et al., 2003; 2005 and Origin of complication lAbove the highest seesaw scale: lBelow the lowest seesaw scale: lAmong seesaw scales: The RGE for the determinant of the neutrino mass matrix: Refer to DZ, 2024 for more details Solution to the RGE: Massless neutrino at the GUT scale Zero determinant at the GUT scale Zero determinant at the EW scale Massless at the EW scale Rank-increase diagram for renormalization of the Weinberg operator: (NMO) (IMO) S. Davidson, G. Isidori, A. Strumia, 2007; Z. Z. Xing, DZ, 2020; A. Ibarra, N. Leister, DZ, 2024 ØWe strictly prove that if the lightest neutrino is initially massless, it remains massless at the one-loop level even if threshold effects are taken into account ØWe revisit the one-loop RGEs in the canonical seesaw mechanism among seesaw scales and obtain the missed terms ØNevertheless, two-loop RG running effects can generate a non-zero mass ~𝑂 10!"#%eV for the initially massless neutrino II. Canonical Seesaw Mechanism ØOne of the simplest and the most natural ways to explain neutrino masses ØAble to elegantly account for the cosmic matter-antimatter asymmetry The (minimal) type-I seesaw mechanism with right-handed neutrinos: One massless neutrino This vanishing neutrino mass is stable against one-loop Renormalization Group (RG) running effects without threshold effects But the case with hierarchical RHN masses is still unclear!!! J. A. Casas, J. R. Espinosa, A. Ibarra, 2000; S. Antusch et al., 2001;2003;2005; J. W. Mei, Z. Z. Xing, 2004; Z. Z. Xing, 2005; J. W. Mei, 2005; T. Ohlsson, H. Zhang, S. Zhou, 2013; T. Ohlsson, S. Zhou, 2014;… S. Antusch et al., 2002; N. J. Benoit et al, 2022 with a) Two right-handed neutrinos (RHNs) b) Three RHNs and Rank-2 neutrino Yukawa matrix III. RGEs and Threshold Effects In a mass-independent renormalization scheme, e.g., the MS/MS scheme: ØDecoupling heavy fields around their mass scales by hand ØPhysics at different scales is linked by the corresponding RG equations (RGEs) Matching conditions at each threshold scale : l : removing the last column of l : removing both the last column and the last row of ldsae Full theory (EFT 3) EFT 2EFT 1EFT 0 𝜇 Λ!" Λ#$% 𝑀& 𝑀' 𝑀( integrate out 𝑁 !" integrate out 𝑁#" integrate out 𝑁$" RGEsRGEsRGEsRGEs The Weinberg Operator The vanishing neutrino mass is stable against one-loop RG running effects EVEN with threshold effects