Double Type-I Seesaw Mechanism

• Double Type-I seesaw mechanism is a nested neutrino-mass model where light Majorana masses arise after two sequential suppressions by heavy singlet fields.
• It can be realized via a pure singlet framework or a left–right symmetric variant that incorporates an initial Type III step followed by a Type I seesaw.
• The mechanism is embedded in renormalizable models that link neutrino mass generation with collider testability and viable leptogenesis scenarios.

to=arxiv_search ՞նչ query="Double seesaw mechanism neutrino masses left-right symmetric (Chakrabortty, 2010, Grimus et al., 2013)" max_results=10 {"query":"Double seesaw mechanism neutrino masses left-right symmetric (Chakrabortty, 2010, Grimus et al., 2013)","max_results":10} to=arxiv_search to=search_arxiv ￣奇米影视json {"query":"Double seesaw mechanism neutrino masses (Chakrabortty, 2010, Grimus et al., 2013)","max_results":10} to=arxiv_search_tool 天天中彩票网络json {"query":"Double seesaw mechanism neutrino masses","max_results":5} The double Type-I seesaw mechanism is a sequential neutrino-mass construction in which the light Majorana masses arise only after two nested suppressions by heavy neutral fermions. In the fully singlet realization, the Standard Model is extended by ordinary right-handed neutrinos $S_{jR}$ and by extra singlets $N_{jR}$; the only tree-level Majorana mass is assigned to the $N_R$ sector, so integrating out $N_R$ first induces a Majorana mass for $S_R$, and integrating out $S_R$ then yields the light-neutrino mass matrix (Grimus et al., 2013). Closely related literature also uses the label “double” seesaw for a left–right symmetric variant in which a Type III step in the $SU(2)_R$ sector feeds a second, Type I step for the active neutrinos (Chakrabortty, 2010). This usage suggests that the defining feature is the two-stage suppression pattern, rather than a unique choice of heavy fields.

1. Defining structure and nomenclature

In the singlet construction of the double Type-I seesaw, the neutrino sector contains three layers of neutral fields: the active neutrinos $\nu_L$, the ordinary right-handed singlets $S_R$, and the extra singlets $N_R$. The mass matrix is organized so that there is no tree-level Majorana term for the intermediate singlets $N_{jR}$0, while the deepest singlet layer $N_{jR}$1 carries a large Majorana mass $N_{jR}$2 (Grimus et al., 2013). The first seesaw therefore generates an effective Majorana mass for $N_{jR}$3, and the second seesaw uses that induced scale to suppress the active-neutrino masses.

A common source of terminological confusion is that “double seesaw” is not always identical to “double Type-I seesaw.” In the renormalizable singlet framework, both successive reductions are Type I. In the left–right symmetric construction, by contrast, the first reduction is explicitly described as a Type III seesaw in the $N_{jR}$4 sector, followed by a Type I seesaw in the $N_{jR}$5 sector (Chakrabortty, 2010). This distinction matters for field content and phenomenology, but not for the basic nested-seesaw logic.

Realization	Heavy-sector structure	Light-neutrino mass
Double Type-I	$N_{jR}$6 and $N_{jR}$7 singlets	$N_{jR}$8
Left–right “variant double” seesaw	$N_{jR}$9 and $N_R$0	$N_R$1 with $N_R$2

The table isolates the formal similarity: in both cases an intermediate heavy neutral state receives its Majorana mass only after a prior decoupling step. The underlying ultraviolet completions, however, are structurally different.

2. Canonical singlet formulation

The fully singlet construction extends the Standard Model by two layers of right-handed neutrino singlets: ordinary right-handed neutrinos $N_R$3 and extra singlets $N_R$4, with $N_R$5 (Grimus et al., 2013). In the basis

$N_R$6

the neutrino mass terms are

$N_R$7

or, equivalently,

$N_R$8

Here $N_R$9 is the $N_R$0 Dirac mass matrix linking $N_R$1 to $N_R$2, $N_R$3 is a $N_R$4 Dirac mass matrix linking $N_R$5 to $N_R$6, and $N_R$7 is the $N_R$8 Majorana mass matrix for the $N_R$9. The only Majorana mass allowed at tree level is $S_R$0, which softly breaks one of the flavour symmetries (Grimus et al., 2013).

Assuming the hierarchy

$S_R$1

one first integrates out the heaviest fields $S_R$2. At tree level this gives an effective Majorana mass for $S_R$3,

$S_R$4

The residual $S_R$5 neutrino mass matrix becomes

$S_R$6

which is a standard Type-I seesaw between $S_R$7 and $S_R$8. Integrating out $S_R$9 then yields

$S_R$0

The same result can be viewed as two successive Type-I seesaws. The first seesaw, with heavy scale $S_R$1, gives an $S_R$2 Majorana mass to the intermediate singlets $S_R$3. The second seesaw, with heavy scale $S_R$4, then generates the final light mass matrix (Grimus et al., 2013).

3. Hierarchy of scales, symmetry protection, and renormalizability

The explicit models realize

$S_R$5

with $S_R$6 at the Fermi scale and $S_R$7 seesaw scale (Grimus et al., 2013). In the TM$S_R$8 model discussed there, the symmetries enforce

$S_R$9

with $SU(2)_R$0 at the high scale, while $SU(2)_R$1 is a bare Majorana term.

The vanishing of any $SU(2)_R$2–$SU(2)_R$3 Majorana term is enforced by an exact $SU(2)_R$4, called $SU(2)_R$5 in the paper. The texture of $SU(2)_R$6 is controlled by two further $SU(2)_R$7-type factors, $SU(2)_R$8 and $SU(2)_R$9, which are softly broken only by the dimension-3 Majorana Lagrangian. In a convenient weak basis one finds

$\nu_L$0

up to small splittings from soft breakings at $\nu_L$1 (Grimus et al., 2013).

The renormalizable character of the construction is explicit. All mass terms and Yukawa couplings in $\nu_L$2 are of dimension $\nu_L$3; the only explicit breaking of the full flavour group happens softly via dimension-2 terms in the scalar potential or dimension-3 terms in $\nu_L$4; no non-renormalizable operators or extra dimensions are invoked; and the field content beyond the Standard Model consists of four Higgs doublets, three scalar singlets, and the six singlet fermions $\nu_L$5 (Grimus et al., 2013). The soft scale $\nu_L$6 is technically natural, being protected by a lepton-number symmetry when $\nu_L$7. This suggests that the hierarchy $\nu_L$8 is not merely an algebraic assumption but part of the symmetry design of the model.

4. Flavour structure and lepton mixing

The double Type-I seesaw can be embedded in a flavour construction in which the lepton mixing matrix is the product of the maximal mixing matrix $\nu_L$9 times a matrix constrained by a well-defined $S_R$0 symmetry (Grimus et al., 2013). In the weak basis chosen there, the charged-lepton mass matrix is diagonalized by the “magic” matrix $S_R$1,

$S_R$2

so that all lepton mixing beyond $S_R$3 comes from diagonalizing the double-seesaw neutrino mass matrix. One then has

$S_R$4

where $S_R$5 diagonalizes $S_R$6.

In the simplest TM$S_R$7 model, $S_R$8 is constrained by a single residual $S_R$9 symmetry under which

$N_R$0

leading to the eigenvector

$N_R$1

and hence to one column of $N_R$2 of the form

$N_R$3

described as “first-column TM$N_R$4” (Grimus et al., 2013).

The more general one-parameter variant preserves a $N_R$5 depending on an angle $N_R$6, and yields

$N_R$7

with $N_R$8 chosen to reproduce the observed $N_R$9 and yielding sharp relations among $N_{jR}$00, $N_{jR}$01, and the CP-phase (Grimus et al., 2013). Within this framework, the double seesaw is not only a mass-suppression mechanism but also the carrier of flavour information, because the symmetries controlling $N_{jR}$02 propagate directly into the structure of $N_{jR}$03.

5. Left–right symmetric variant and the role of Type III mediation

A distinct realization embeds the double-seesaw idea in a next to minimal left–right symmetric model with gauge group

$N_{jR}$04

where parity is spontaneously broken (Chakrabortty, 2010). The fermion content includes the usual quark and lepton doublets,

$N_{jR}$05

$N_{jR}$06

together with a bidoublet $N_{jR}$07, $N_{jR}$08 and $N_{jR}$09 doublets $N_{jR}$10, $N_{jR}$11, and new triplet fermions

$N_{jR}$12

each a Majorana multiplet $N_{jR}$13. Additional mixed Higgs multiplets $N_{jR}$14 and $N_{jR}$15 are introduced, with $N_{jR}$16 and $N_{jR}$17 (Chakrabortty, 2010).

The Dirac mass from the bidoublet is

$N_{jR}$18

After $N_{jR}$19 and $N_{jR}$20, and for $N_{jR}$21, $N_{jR}$22, the neutral mass matrix in the basis $N_{jR}$23 is

$N_{jR}$24

In the limit $N_{jR}$25, the $N_{jR}$26 entry $N_{jR}$27 can be dropped at leading order. Writing $N_{jR}$28 and $N_{jR}$29, one obtains

$N_{jR}$30

The first step is to integrate out $N_{jR}$31 at tree level, which induces a Majorana mass for $N_{jR}$32,

$N_{jR}$33

The second step is then an effective $N_{jR}$34 seesaw for $N_{jR}$35,

$N_{jR}$36

which yields

$N_{jR}$37

The paper also gives the compact form

$N_{jR}$38

described there as the textbook “double” seesaw formula (Chakrabortty, 2010). This variant clarifies that the broader double-seesaw idea can interpolate between different ultraviolet mediators.

6. Heavy spectra, collider tests, and leptogenesis

The left–right symmetric realization was constructed so that at least one of the triplet fermions and the right handed neutrinos are at TeV scale and others are heavy (Chakrabortty, 2010). For the triplet fermions, the masses are approximately the bare $N_{jR}$39. In a three-family choice one may take, for example,

$N_{jR}$40

so that $N_{jR}$41 and $N_{jR}$42 lie at the few-hundred-GeV scale. The right-handed neutrino masses satisfy

$N_{jR}$43

and with $N_{jR}$44 GeV and $N_{jR}$45, one finds one eigenvalue at $N_{jR}$46, two others much heavier (Chakrabortty, 2010).

At the LHC, the triplets can be produced through

$N_{jR}$47

Production of $N_{jR}$48 is suppressed by mixing, but possible via

$N_{jR}$49

The triplet decays include

$N_{jR}$50

with partial widths proportional to $N_{jR}$51, and mixing $N_{jR}$52 (Chakrabortty, 2010).

The promising final states are multi-lepton channels such as $N_{jR}$53, $N_{jR}$54, $N_{jR}$55jets, and $N_{jR}$56, as well as same-sign dileptons $N_{jR}$57jets and opposite-sign dileptons + jets. The same-sign dilepton channel is identified as a clean LNV signal, while the opposite-sign dilepton channel has a large rate though larger Standard Model background. If $N_{jR}$58 is at the TeV scale, its decays can proceed through

$N_{jR}$59

or

$N_{jR}$60

when one $N_{jR}$61 (Chakrabortty, 2010).

The same heavy states are also relevant for leptogenesis. Both the heavy $N_{jR}$62’s and the triplets $N_{jR}$63 can decay out of equilibrium and violate CP, generating a lepton asymmetry. The paper gives a CP-asymmetry formula for $N_{jR}$64, a hierarchical-limit expression for $N_{jR}$65, and notes that triplet decays $N_{jR}$66 give a similar asymmetry, smaller by an $N_{jR}$67 factor but partially compensated by the triplet’s three components. Mixed loops, such as $N_{jR}$68 in $N_{jR}$69 decay or vice versa, further enrich the CP sources (Chakrabortty, 2010). In this sense, the double-seesaw setup is not only a mass-generation mechanism but also a framework in which collider-accessible heavy fermions and leptogenesis can be discussed within the same parameterization.