Casas-Ibarra

Casas-Ibarra
Name	Casas–Ibarra parametrization
Field	Particle physics, Neutrino oscillation
Introduced	2001
Contributors	Joaquim Casas, Alejandro Ibarra
Related	Seesaw mechanism, PMNS matrix, Majorana neutrino

Casas-Ibarra

The Casas–Ibarra parametrization is a widely used analytical method in Particle physics for expressing Yukawa couplings in models that generate small neutrino masses via the Seesaw mechanism. Developed to translate low-energy information from the Pontecorvo–Maki–Nakagawa–Sakata matrix and neutrino mass measurements into high-energy parameters, the parametrization connects observables from experiments such as Super-Kamiokande, SNO, Daya Bay, KamLAND-Zen, and T2K to model inputs relevant for theories like Grand Unified Theory, Supersymmetry, and leptogenesis scenarios examined at facilities like CERN and Fermilab.

Overview

The parametrization provides an explicit form for the complex Yukawa coupling matrix in Type I Seesaw mechanism models, given the light neutrino mass spectrum and the heavy singlet Majorana masses. It relates the PMNS matrix, low-energy neutrino masses from experiments such as NOvA and JUNO, and an arbitrary complex orthogonal matrix which encodes the unknown high-energy degrees of freedom. The approach has been applied across studies involving Leptogenesis, Flavor symmetry, Left–Right symmetric model, and collider searches at LHC and proposed facilities like ILC.

Casas–Ibarra parametrization

In the standard Type I Seesaw mechanism with three heavy right-handed neutrinos, the Yukawa coupling matrix Y can be written as Y = (1/v) U sqrt(m) R sqrt(M), where U is the PMNS matrix, m is the diagonal matrix of light Majorana neutrino masses measured by Planck (spacecraft) constraints and neutrinoless double beta decay searches at GERDA and EXO-200, M is the diagonal matrix of heavy singlet masses, v is the Higgs boson vacuum expectation value determined at ATLAS and CMS, and R is a complex orthogonal matrix parameterizing the remaining freedom. The parametrization makes explicit the interplay between low-energy CP phases accessible via neutrino oscillation experiments like Hyper-Kamiokande and high-energy CP-violating phases relevant for baryogenesis via Leptogenesis mechanisms studied by groups at IPMU and CERN Theory Department.

Derivation

Starting from the seesaw formula m_nu = - v^2 Y M^{-1} Y^T, diagonalization by the PMNS matrix U yields U^T m_nu U = diag(m1,m2,m3). One can factorize Y as Y = (1/v) U sqrt(diag(m1,m2,m3)) R sqrt(M), where R satisfies R^T R = I. The existence of a complex orthogonal R follows from the singular value decomposition and the freedom to perform basis rotations among right-handed singlets without affecting low-energy observables measured by Super-Kamiokande, SNO, IceCube, or MINOS. The derivation uses methods familiar from studies of mass matrices in Cabibbo–Kobayashi–Maskawa matrix contexts and diagonalization techniques applied in analyses by research groups at Perimeter Institute and CERN.

Applications in neutrino physics

The parametrization is used to explore Leptogenesis models connecting CP violation in the neutrino sector to the Baryon asymmetry of the Universe probed by cosmological observations from WMAP and Planck (spacecraft). It facilitates scans of parameter space to assess constraints from neutrinoless double beta decay searches at KamLAND-Zen, CUORE, and LEGEND, from absolute mass limits set by KATRIN, and from oscillation fits combining results of Daya Bay, RENO, T2K, NOvA, and JUNO. In collider physics, the parametrization informs analyses of heavy neutral lepton production and decay studied at LHCb, ATLAS, CMS, and proposed experiments such as SHiP and FCC. It also aids model building in Grand Unified Theory frameworks like SO(10), and in constructing flavor models by groups at CERN Theory Department and Institute for Advanced Study.

Extensions and generalizations

Beyond the minimal Type I Seesaw mechanism, the Casas–Ibarra technique has been generalized to inverse Seesaw mechanism, linear Seesaw mechanism, and Extended Seesaw frameworks used in Left–Right symmetric model or Inverse Seesaw studies. Extensions incorporate additional sterile states as in models motivated by Short-baseline anomalies and experiments like LSND and MiniBooNE, or embed the parametrization in supersymmetric settings like MSSM and NMSSM where radiative corrections from Renormalization Group running, studied by researchers at IPMU and DESY, modify predictions. Flavor symmetry implementations using groups such as A4, S4, and Delta(27) integrate the R matrix structure into constrained textures explored by collaborations at CERN Theory Department and Perimeter Institute.

Phenomenological implications

Phenomenological studies using the parametrization map viable regions for heavy neutrino masses accessible at LHC, SHiP, or future colliders like FCC while correlating predicted rates for neutrinoless double beta decay at GERDA and CUORE and CP-violating signals measurable by Hyper-Kamiokande and DUNE. The R matrix introduces CP phases that can enhance or suppress the baryon asymmetry produced via Thermal leptogenesis relevant for cosmology constraints from Planck (spacecraft) and large-scale structure surveys by teams at SDSS and DES. Global fits combining data from KATRIN, Planck (spacecraft), Daya Bay, and T2K employ the parametrization to quantify sensitivity to mass ordering, absolute mass scale, and potential signals of heavy neutral leptons sought by ATLAS and CMS.

Category:Neutrino physics