Using the functional method, one-loop matching of the type-I, -II and -III seesaw models are investigated and the results are presented in both the Green's and the Warsaw bases. Although these models generate the same dimension-5 Weinberg operator, they could induce quite different types of dimension-6 effective operators that can be utilized for model discrimination. We also find the threshold effects from one-loop matching could be significant, which turn out to allow triggering electroweak symmetry breaking radiatively in type-II seesaw while forbid that in type-I/-III models. An analytical criterion for such radiative symmetry breaking is also derived in type-II seesaw. Finally, we investigate the indirect signatures from different types of dimension-6 operators at high-energy colliders, low-energy precision experiments and forward physics facilities for model discrimination.
In this paper, we continue to construct the low-energy effective field theories (EFTs) of the canonical seesaw models, which are natural extensions of the Standard Model (SM) to accommodate tiny but nonzero neutrino masses. Different from three right-handed neutrino singlets in the type-I seesaw model, the Higgs triplet in the type-II seesaw model participates directly in the electroweak gauge interactions, rendering the EFT construction more challenging. By integrating out the heavy Higgs triplet in the functional-integral formalism, we carry out a complete one-loop matching of the type-II se…
The canonical type-I seesaw model with three heavy Majorana neutrinos is one of the most natural extensions of the standard model (SM) to accommodate tiny Majorana masses of three ordinary neutrinos. At low-energy scales, Majorana neutrino masses and unitarity violation of lepton flavor mixing have been extensively discussed in the literature, which are respectively generated by the unique dimension-five Weinberg operator and one dimension-six operator in the seesaw effective field theory (SEFT) with the tree-level matching. In this work, we clarify that a self-consistent calculation of radiat…
The renormalization group (RG) running of the neutrino mass operator is required for comparing the predictions of neutrino models at high energy with the experimental data at low energies. In the type I seesaw scenario with n_G right-handed neutrinos, the RG running is also performed in the effective theories above and between the thresholds given by the masses of the right-handed neutrinos. At these thresholds, the effective theories are matched. When calculating the two-loop RG running, the matching has to be performed at the one-loop level. In this work, we calculate the one-loop matching f…
In this talk, we present the results of the complete one-loop matching of the seesaw model onto its low-energy effective theory by integrating out three right-handed neutrinos at the one-loop level. We find that there are 31 independent dimension-6 (dim-6) operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis, and the standard-model couplings and the Wilson coefficient of the Weinberg operator acquire threshold corrections at the one-loop level. The complete Lagrangian up to dim-6 at the one-loop level is derived, which is indispensable for consistent explorations …
In this paper, we accomplish the complete one-loop matching of the type-I seesaw model onto the Standard Model Effective Field Theory (SMEFT), by integrating out three heavy Majorana neutrinos with the functional approach. It turns out that only 31 dimension-six operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, and most of them appear at the one-loop level. The Wilson coefficients of these 31 dimension-six operators are computed up to $\mathcal{O}\left( M^{-2}\right)$ with $M$ being the mass scale of heavy Majorana neutrinos. As th…
Motivated by the ATLAS and CMS discovery of a Higgs-like boson with a mass around 125 GeV, and by the need of explaining neutrino masses, we analyse the three canonical SUSY versions of the seesaw mechanism (type I, II and III) with CMSSM boundary conditions. In type II and III cases, SUSY particles are lighter than in the CMSSM (or the constrained type I seesaw), for the same set of input parameters at the universality scale. Thus, to explain $m_{h^0} \simeq 125 GeV$ at low energies, one is forced into regions of parameter space with very large values of $m_0$, $M_{1/2}$ or $A_0$. We compare …
We investigate the LHC discovery potential for electroweak scale heavy neutrino singlets (seesaw I), scalar triplets (seesaw II) and fermion triplets (seesaw III). For seesaw I we consider a heavy Majorana neutrino coupling to the electron or muon. For seesaw II we concentrate on the likely scenario where the new scalars decay to two leptons. For seesaw III we restrict ourselves to heavy Majorana fermion triplets decaying to light leptons plus gauge or Higgs bosons, which are dominant except for unnaturally small mixings. The possible signals are classified in terms of the charged lepton multi…
Seesaw Models under the Lens of Angular Distributions at $μ^+μ^-,\, μ^+ μ^+, \, μ^+ γ$ and $μ^+ e^-$ Colliders
Indian Institute of Technology Hyderabad（印度理工学院海德拉巴分校）；INFN, Gruppo Collegato di Cosenz & Dipartimento di Fisica, Università della Calabria（意大利国家核物理研究所科森扎合作组与卡塔尼亚大学物理系）；Theoretical Physics Division, Physical Research Laboratory（物理研究实验室理论物理部）
In terms of flavor invariants, we establish the intimate connection between leptonic CP 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 ${\cal O}^{αβ}_5 = \overline{\ell^{}_{α\rm L}} \widetilde{H} \widetilde{H}^{\rm T} \ell^{\rm C}_{β\rm L}$ and the dimension-six operator ${\cal O}^{αβ}_6 = \overline{\ell^{}_{α\rm L}} \widetilde{H} {\rm i} \not\!\partial \…
As is well known, the smallest neutrino mass turns out to be vanishing in the minimal seesaw model, since the effective neutrino mass matrix $M^{}_ν$ is of rank two due to the fact that only two heavy right-handed neutrinos are introduced. In this paper, we point out that the one-loop matching condition for the effective dimension-five neutrino mass operator can make an important contribution to the smallest neutrino mass. By using the available one-loop matching condition and two-loop renormalization group equations in the supersymmetric version of the minimal seesaw model, we explicitly calc…
The neutrino option is a scenario where the electroweak scale, and thereby the Higgs mass, is generated simultaneously with neutrino masses in the seesaw model. This occurs via the leading one loop and tree level diagrams matching the seesaw model onto the Standard Model Effective Field Theory. We advance the study of this scenario by determining one loop corrections to the leading order matching results systematically, performing a detailed numerical analysis of the consistency of this approach with Neutrino data and the Standard Model particle masses, and by examining the embedding of this s…
The canonical seesaw models are one of the simplest and most natural scenarios that can account simultaneously for neutrino masses and matter-antimatter asymmetry in our universe. Below the seesaw scale, one can integrate out the heavy degrees of freedom to construct the seesaw effective field theory (SEFT). In this talk, we investigate the connection between the full seesaw model and the low-energy SEFT from a brand-new perspective: the invariant theory. Using the powerful tool of Hilbert series, we demonstrate the intimate relation between the flavor space of the SEFT and that of its ultravi…
We investigate matching conditions and threshold corrections between full and effective theories based on the type I seesaw mechanism. In general, using an intuitive Feynman diagrammatical approach, we compute the amplitudes before and after integrating out heavy right-handed neutrinos at the matching scale. In particular, we derive the one-loop matching conditions between the full and the effective theories. The matching conditions of the parameters are influenced by one-loop corrections to the corresponding vertices as well as wave function corrections for the Higgs and the lepton fields. Ou…
A HEFT Perspective on the Type-II Seesaw Model and the Complete Basis of Lepton-Number-Violating Operators
School of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理与信息技术学院）；Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS)（基础科学研究院宇宙理论物理中心）
In this paper, we systematically study the algebraic structure of the ring of the flavor invariants and the sources of CP violation in the seesaw effective field theory (SEFT), which is obtained by integrating out heavy Majorana neutrinos in the type-I seesaw model at the tree level and thus includes the dimension-five Weinberg operator and one dimension-six operator. For the first time, we calculate the Hilbert series and explicitly construct all the primary flavor invariants in the SEFT. We show that all the physical parameters can be extracted using the primary invariants and any CP-violati…
Operator Identification in Charged Lepton-Flavor Violation: Global EFT Analysis with RG Evolution, Polarization Observables, and Bayesian Model Discrimination at Future Colliders
Universidad Técnica Federico Santa María（弗雷德里克·萨马利亚技术大学）；Millennium Institute for Subatomic Physics at the High-Energy Frontier (SAPHIR)（高能前沿亚原子物理千年研究所（SAPHIR））
We match the seesaw model for generating neutrino masses onto the Standard Model Effective Field Theory (SMEFT). We perform this matching at tree level up to dimension seven in the operator expansion. We explain how some of the perturbations of the neutrino mass matrix due to operators of mass dimension greater than five are tied to integrating out the heavy Majorana mass eigenstates in sequence. We demonstrate that the low energy limit of seesaw models are well described by the SMEFT, particularly when constructed using a flavour space expansion. Flavour space expansions of seesaw models are …
Besides the three canonical seesaw mechanisms, the hybrid scenario, i.e., the so-called type-(I+II) seesaw mechanism containing both the right-handed neutrinos $N^{}_{\rm R}$ and the triplet Higgs $Φ$ is also an appealing extension of the Standard Model (SM) to account for tiny neutrino masses. Recently, the seesaw effective field theories (SEFTs) of the three canonical seesaw mechanisms have already been completely constructed up to one-loop level. In this work, we carry out the one-loop matching of the type-(I+II) seesaw mechanism onto the corresponding type-(I+II) SEFT, which is by no means…
The type-I seesaw model is probably the most straightforward and best studied extension of the Standard Model that can account for the tiny active neutrino masses determined from neutrino oscillation data. In this article, we calculate the complete set of one-loop corrections to charged lepton flavour violating processes within this model. We give the results both using exact diagonalisation of the neutrino mass matrix, and at at leading order in the seesaw expansion (i.e. $\mathcal{O}(v^2/M_R^2)$). Furthermore, we perform the matching onto the $SU(2)_L$ invariant Standard Model Effective Fiel…
If new leptons exist close to the electroweak scale, they can be produced in pairs at LHC through standard or new interactions. We study the production of heavy lepton pairs in SM extensions with: (i) a Majorana or Dirac lepton triplet, as those appearing in type-III seesaw; (ii) a lepton isodoublet (N,E)_{L,R}; (iii) a charged isosinglet E_{L,R}; (iv) a Majorana or Dirac neutrino singlet N and an additional Z' gauge boson. It is shown that the trilepton final state l+-l+-l-+, which has a small SM background, constitutes the golden channel for heavy neutrino searches, being very sensitive to M…
One-loop Renormalization of the Type-I Seesaw Model in the On-shell Scheme
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Center for High Energy Physics, Henan Academy of Sciences（河南省科学院高能物理中心）
The scotogenic neutrino seesaw model is a minimal extension of the standard model with three $\mathbb{Z}_2$-odd right-handed singlet fermions $N$ and one $\mathbb{Z}_2$-odd Higgs doublet $η$ that can accommodate the tiny neutrino mass and provide a dark matter candidate in a unified picture. Due to lack of experimental signatures for electroweak scale new physics, it is appealing to assume these new particles are well above the electroweak scale and take the effective field theory approach to study their effects on low energy observables. In this work we apply the recently developed functional…
Motivated by searches for so-called leptonic scalars at the LHC and the recent measurement of the $W$ boson's mass at the Tevatron, we revisit the phenomenology of the Zee-Babu model for neutrino masses and the ability to differentiate it from the Type II Seesaw model at the LHC. We conclude that this task is much more difficult than previously believed. All inputs equal in the two scenarios, we find that total and differential rates for producing pairs of doubly and singly charged scalars are identical in shape and only differ in normalization. The normalization is given by the ratio of hadro…
We present a renormalization group study of the scalar potential in a minimal $U(1)_{B-L}$ extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kine…
