Spelling out leptonic <math display="inline"><mi>C</mi><mi>P</mi></math> violation in the language of invariant theory

Yu, Bingrong; Zhou, Shun

doi:10.1103/PhysRevD.106.L051701

Spelling out leptonic $C P$ violation in the language of invariant theory

Bingrong Yu
(
- Beijing, Inst. High Energy Phys. and
- Beijing, GUCAS
)
,
Shun Zhou
(
- Beijing, Inst. High Energy Phys. and
- Beijing, GUCAS
)

Mar 1, 2022

12 pages

Published in:

Phys.Rev.D 106 (2022) 5, L051701

Published: Sep 1, 2022

e-Print:

2203.00574 [hep-ph]

DOI:

10.1103/PhysRevD.106.L051701 (publication)

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Abstract: (APS)

In terms of flavor invariants, we establish the intimate connection between leptonic

C P

violation in the canonical seesaw model for neutrino masses and that in the seesaw effective field theory (SEFT). For the first time, we calculate the Hilbert series and explicitly construct the primary flavor invariants in the SEFT by considering both the dimension-five Weinberg operator

O_{5}^{α β} = \bar{ℓ_{α L}} \tilde{H} {\tilde{H}}^{T} ℓ_{β L}^{C}

and the dimension-six operator

O_{6}^{α β} = (\bar{ℓ_{α L}} \tilde{H}) i \partial ({\tilde{H}}^{†} ℓ_{β L})

at the tree-level matching. The inclusion of only the Wilson coefficients

C_{5}^{α β}

and

C_{6}^{α β}

already enables the SEFT to incorporate all physical information about the full seesaw model. Moreover, the minimal sufficient and necessary conditions for

C P

conservation both in the SEFT and in the full theory are clarified, and the matching between the flavor invariants in both theories is accomplished. Through the matching of flavor invariants, the

C P

asymmetries necessary for successful leptogenesis are directly linked to those in neutrino-neutrino and neutrino-antineutrino oscillations at low energies. Surprisingly, it is revealed that the precise measurements of

C_{5}^{α β}

and

C_{6}^{α β}

in low-energy experiments are powerful enough to probe the full seesaw model, including

C P

violation for cosmological matter-antimatter asymmetry.

Note:

7+5 pages, 2 tables, more discussions added, accepted for publication as a Letter in Phys. Rev. D

new physics
lepton: flavor
lepton: coupling
invariance: flavor
effective field theory
operator: Weinberg
operator: dimension: 6
seesaw model
leptogenesis
matter: asymmetry

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Spelling out leptonic CP violation in the language of invariant theory

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Spelling out leptonic $C P$ violation in the language of invariant theory