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Universal seesaw mechanism?

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Aharon Davidson at Ben-Gurion University of the Negev
Aharon Davidson
Kameshwar C. Wali at Syracuse University
Kameshwar C. Wali
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Abstract

The idea that fermions acquire their masses via a universal seesaw mechanism can provide a plausible explanation for the mass hier- archy me{\mathrm{m}}_{\mathrm{e}},u,d≃\simeq{}{10}^{\mathrm{-{}}4}MW{\mathrm{M}}_{\mathrm{W}}. A minimal SU(3)C{)}_{\mathrm{C}}⨂\bigotimes{}SU(2)L{)}_{\mathrm{L}} ⨂\bigotimes{}SU(2)R{)}_{\mathrm{R}}⨂\bigotimes{}U(1{)}_{\mathrm{B}\mathrm{-{}}\mathrm{L}} grand unifiable realization is presented. Whereas the fermionic representation is enlarged to include SU(2)L{)}_{\mathrm{L}}⨂\bigotimes{}SU(2)R{)}_{\mathrm{R}} singlets, the Higgs system contains none of the conventional scalars of left-right-symmetric models. An alternative way to account for the superlightness of neutrinos emerges.
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VOLUME 59, NUMBER 4PHYSICAL REVIEW LETTERS 27 Jvr v1987
Universal Seesaw Mechanism?
Aharon Davidson 'and Kameshwar C. Wali
Physics Department, Syracuse University, Syracuse, New York 13244
(Received 15 April 1987)
The idea that fermions acquire their masses via auniversal seesaw mechanism can provide aplausible
explanation for the mass hierarchy m, „d=10 M~. Aminimal SU (3)cI3 SU(2)zSSU(2)Q
SU(1)s zgrand-unifiable realization is presented. Whereas the fermionic representation is enlarged to
include SU(2)z SSU(2)z singlets, the Higgs system contains none of the conventional scalars of left-
right-symmetric models. An alternative way to account for the superlightness of neutrinos emerges.
PACS numbers: 12.15.Ff, 12.10.Dm
Aremarkable, yet still somewhat mysterious, feature
of the Glashow-Weinberg-Salam electroweak scheme' is
that spontaneous symmetry breaking and fermion masses
are both triggered by one and the same Higgs scalar.
On the one hand, it is useful to have some guidance as to
how to choose the otherwise arbitrary Higgs system. On
the other hand, it seems as if naturalness is lost in the
following sense. If the electron and the 8' bosons ac-
quire mass via acommon vacuum expectation value, why
is it that
qz(3, 2, 1)(l3, q~(3, 1,2))l3,
lz(1,2, 1) ), l~(1, 1,2) (4)
ther input. The scheme lends itself to SU(5)z SSU(5)g
grand unification.
Consider an SU(3)CSSU(2)zSU(2)~SU(I)g
electronuclear model, and allow for the following fer-
mionic content. In addition to the standard complex
representation
m, =10 M~?
Further, this mass hierarchy is numerically not so
diA'erent from
let there be an exotic real representation
uz g(3, I, 1)4,
l3dz ~(3,1, I)2/3,
vz ~(I, 1, 1)p, ez ~(1, 1,1)(5)
m, ~10 'm„ (2)
but somehow it has not received due attention. The
latter hierarchy is not confronted in the minimal elec-
troweak model.
Whereas the difhculty associated with m, «M~ per-
sists when SU(2)z SU(1)„ is enlarged to SU(2)z
SSU(2)~SU(1)g z, the m„&&m, problem can be ad-
dressed by invoking the so-called seesaw mechanism.
The higher the mass scale of the now mandatory vz
(which is not the case in the standard electroweak mod-
el), the lighter is vz. The price, however, is aricher
Higgs system which necessarily includes
P(2, 2)p+ P(3, 1)—
z+ P(1,3) (3)
What physics gives rise to m, /Mn «1? Is there an al-
ternative way to account for m, /m, «1'? Are these two
hierarchies correlated?
In an attempt to deal with the above questions, we
have adopted an unorthodox approach. Rather than
sticking to afixed fermionic set while complicating the
Higgs system, we hereby enlarge the fermionic represen-
tation but simplify the Higgs system to its limits. In par-
ticular, none of the conventional scalars specified by Eq.
(3) are present! Yet, the electron does acquire mass, via
auniversal seesaw mechanism, and at the same time the
superlightness of the neutrinos follows without any fur- yz(1, 2, 1) )+y~(1,1, 2) (7)
The various (B L) charges hav—
ebeen carefully adjust-
ed such that each ordinary fermion fhas its own nonmir-
ror f" companion with matching SU(3)cSU(I)g as-
signments [g =T3z+ T3++ 2(B—
L)]. By such assign-
ments, we have unfortunately ruined the ingenious inter-
pretation of B—
Las the fourth color.
It is true that postulating the extra fermionic structure
seems, at first glance, superfluous and quite unnatural.
Do we have acompelling theoretical reason for doing it?
The positive answer is provided by arecently proposed
left-right- symmetric, yet flavor-chiral Georgi-Glashow-
type, SU(5)z SSU(5)~ grand-unification scheme.
While SU(3)c=SU(3)z+z and U(1)a—
z:U(1)z+R
SU(2)z zare contained in SU(5)z ~, respectively. It is
straightforward to verify that the above fermionic repre-
sentation is in fact
yz(1065*61;I)+Vr~(1;10&5*$1).
vz ~(1;1)are optional here, but mandatory in the
SO(10)z SSO(10)~ generalization. The underlying
unification is, however, beyond the scope of the present
paper.
The associated Higgs system is minimal. It consists of
two complex doublets
393
VOLUME 59, NUMBER 4PHYSICAL REVIEW LETTERS 27 JUL+ 1987
V= gg i,,(rt,ty;)(yjty, )—gny,'y;.
i=L,R
i,j=L,R
We cannot think of any simpler left-right-symmetric
generalization of the standard steinberg-Salam doublet.
In particular, note that the only Higgs scalar appearing
in all conventional SU(2)z SSU(2)~ SU(1)~ zmodels,
namely p(1,2, 2)o, the standard source of quark and/or
lepton masses, is absent. Also missing are p(1,3, 1)
+p(1, 1,3) 2, the conventional sources for inducing neu-
trino Majorana masses. The simplicity of the Higgs sys-
tem has an immediate low-energy consequence. Since
the charged scalar degrees of freedom are incorporated
to make Wz—
gmassive, the two (real) remnant physical
scalars are necessarily electrically neutral.
The most general renormalizable Higgs potentiaj in-
volving pz ~is given by
The above potential, however, is too constrained, so that
the imposition of the discrete left-right symmetry implies
either t. L=t. Ror alternatively t. z=0, where I.zR
=(pz ~). To gain atree-level hierarchy rz &&r~, we
heave to assume that left-right symmetry is explicitly
broken, thus allowing for
gz +gR.
This should be regarded, however, as an eA'ective conse-
quence of physics beyond SU(3)z @SU(2)z SSU(2)~
SUz —
I, where left-right symmetry is only spontaneous-
ly broken. Invoking SU(5)z SSU(5)~ unification ideas,
we do anticipate in fact that SU(2)z and SU(2)~ would
not share acommon evolution (that is if only 3,4genera-
tions exist).
Let us examine now the quark sector. On top of the
oA'-diagonal Yukawa couplings
+Y k(Y zqzdz&P+ YdzqzhldI+ YR&z Pique+ Ydzdz p~q~)+H. c.,(io)
there are the SU(3)cSU(2)zSU(2)~SU(1)~
invariant mass terms
(xg Rz ikey +xddz dR )+H~c
M„= uRt-R Xu (i2a)
Md= YdR t-'R Xd (i21 )
Once the gauge symmetry is spontaneously broken down
to SU(3)z. SU(1)g, the tree-level mass matrices
0Yuz I'z
!there is no group-theoretical reason why x„and the ad-
ditional bare Majorana mass term, should be quite
diferent from x, „d. Still, with vz «vR «x already es-
tablished, we now proceed to show how the neutrino su-
perlightness follows naturally, with no further assump-
tions.
Taking into account the fact that both vz and
transform trivially under SU(3)z SSU(2)z SSU(2)~
SU(1)~ z, the emerging neutrino mass matrix, in the
(vz, vz, vz, vz )space, reads
Yz gvz g-m(Wz ~), (i 3)
make their appearance. It is convenient to extract the
eigenmasses and the fz gfz gmixing ang—
les by di-
agonalizing MM~ and MM, respectively. By natural-
ness, we expect Yvz" L
Yvz t-'L YvR &'R XX2
Yvz "'L Yvz t- L
YvR ~'R YvR I-'R
YL,R~'L, R«
With this in mind, the quark eigenmasses become
(i4)
whereas the so-called "survival hypothesis" suggests (but
does not imply) The lowest eigenmasses are
m(v, )-vz/x,
phy
m(vg )-vR/x,
phy
m„d —
vz vg/x &m(Wz ), (is) establishing the original seesaw result
and the fz ~fz pmixing angles—are of order
m(Wz ~)/x, respectively. This is the essence of our
model. The mass hierarchy m„d =10 m(Wz )may
signify physics beyond the SU(2)R breaking scale. The
fact that our model is SU(5)z SSU(5)~ embeddable
suggests that xpresumably marks the mass scale associ-
ated with SU(3)z SU(3)~ SU(3)z. or U(I)z
eU(I), —
U(i), ,
As far as the leptons are concerned, the discussion
goes along the same lines, up to the neutrino puzzle, of
course. Naturalness means Y„z ~vz ~—
m(Wz ~), and
m(vz"")m(v~ )=m, .(18)
Note that both m(v~ ~) are lighter by afactor of
m(W~)/x than the corresponding masses predicted by
left-right-symmetric models. If v~/x =vz/v~, for in-
stance, vR may be as light as the WL bosons. It should
also be noted that had we introduced just asingle vz, we
would have faced m(vz ")=0. Such astrict massless-
phy
ness is kinematical (detM, =0), as in the standard mod-
el.The low-energy eN'ects can be described by an eAective
Lagrangean. Such aLagrangean includes dimension-Ave
394
VOLUME 59, NUMBER 4PHYSICAL REVIEW LETTERS 27 JULY 1987
terms of the generic form —
(I/x)p ff. With the usual
symmetry breaking, the various fermionic masses are
recovered. This establishes an interesting link with the
conventional left-right- symmetric scheme: The conven-
tional scalars are bilinears of the new scalars, namely
p(2, 2)o —
p3pR, p(3, 1) q-Pt, and p(1,3) —
2—
hatt.
In the gauge-boson sector, two characteristic features
are encountered.
(i) It is straightforward to derive
1
M24
0gLgi'L
gz ~'z gag~'~
2 2 —-E2
gtgt'L .gRg~'R g("'L +"'R )
(2O)
primarily because WL—and W~—do not mix. In the ab-
sence of the conventional p(1,2, 2)o, no scalar transforms
nontrivially under both SU(2)L and SU(2)~.
(ii) The neutral (mass) matrix
m(WL R)=gL RVL R, (19)
gives rise to amassless photon
A=sinO WL+ cosO(sing Wtt+ cosg W)-g(gtt Wt +gt Wtt)+gLgtt Wo, (21)
and two heavy Z's (sing tanO in the left-right-
symmetric limit). The standard d,I=—,
'formula
m(Z) cos0=m(WL ), (22)
is accompanied by the less familiar
m(Z')cosg=m(WR). (23)
In conventional left-right-symmetric models for light
neutrinos, SU(2)tt is broken by (p(1, 1,3) 2), so that
m(Z') is heavier by afactor of J2.
To summarize, we have presented asimple alternative
to the conventional SU(3)c SSU(2)L jgl SU(2)~
SU(1)tt Lscenario, with the following distinctive
features: (i) No conventional scalar is introduced. The
complication of the Higgs system has been traded for an
extended fermionic representation, such that each quark
and lepton has an SU(2)L SSU(2)R-singlet companion.
(ii) Whereas vt «v~ assures the emergence of
SU(2)LSU(I)y at low energies, v~ &&x accounts for
v1e „d—
PLt'tt/x (m(WL )via auniversal seesaw mecha-
nism. (iii) With vL «vtt «x established, it follows with
no additional assumptions that m(vL ")—
vt /x and
m(vtt ")—
vtt/x. (iv) The scheme is SU(5)LSSU(5)tt
unifiable. We are aware of the fact that this model is
still not fully realistic. Higher-generational fermions are
much heavier than e,d, u, with the extreme of m, —
M~.
The easy way out is to translate the m, «m„« m,
hierarchy into areversed x, »x„»x, hierarchy. But
what is really needed is amultigenerational generaliza-
tion, with quark and/or lepton masses ranging from
vt. vg/x to vL. Such multigenerational attempts are now
in progress.
This work was supported by the U. S. Department of
Energy under Contract No. DE-F602-85ER40231.
'On leave of absence from Ben-Gurion University of the
Negev, 84105 Beer-Sheva, Israel.
'S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg,
Phys. Rev. Lett. 19, 1264 (1967); A. Salam, in Elementary
Particle Theory, edited by N. Svartholm (Almquist &Wik-
sells, Stockholm, 1969), p. 367.
~J. C. Pati and A. Salam, Phys. Rev. D10, 275 (1974).
M. Gell-Mann, P. Ramond, and R. Slansky, in Supergravi-
ty, edited by P. Van Nienwenhuizen and D. Freedmann
(North-Holland, Amsterdam, 1980); T. Yanagida, in Unified
Theory and Baryon Number in the Uni t.erse, edited by
O. Sawada and A. Sugamoto (KEK, Ibaraki, Japan, 1979).
4R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44,
912 (1980), and Phys. Rev. D23, 165 (1981).
5A. Davidson and K. C. Wali, Syracuse University Report
No. SU-4228-358, 1987 (to be published).
H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438
(1974).
7For arecent review, see, e.g.,H. Harari and Y. Nir, SLAC
Report No. SLAC-PUB-4224, 1987 (to be published).
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  • Dec 2024
  • J HIGH ENERGY PHYS
A bstract We propose an extended Left-Right symmetric model with an additional global U(1) X symmetry, which collapses to a residual subgroup ℤ 2 after spontaneous symmetry breaking. In this model, the light active neutrino masses are generated via a double seesaw mechanism with the Dirac submatrix arising at one loop. In addition, the masses of the charged fermions of the Standard Model (SM) that are lighter than the top quark are generated at one loop level and the residual ℤ 2 symmetry ensures the stability of the Dark Matter (DM) candidate of the model. To the best of our knowledge our model has the first implementation of the radiative double seesaw mechanism with the Dirac submatrix generated at one loop level. We show that the model can successfully account for the observed pattern of the SM fermion masses and mixing, and that it is compatible with constraints arising from the muon g-2 anomaly, neutrinoless double beta decay and DM.
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Neutrino Mass and Spontaneous Parity Nonconservation
Article
Full-text available
  • Apr 1980
In weak-interaction models with spontaneous parity nonconservation, based on the gauge group SU(2)/sub L/ x SU(2)/sub R/ x U(1), we obtain the following formula for the neutrino mass: m..nu../sub e/ approx. = m/sub e/ ²/gmW-italic/sub R/, where W/sub R/ is the gauge boson which mediates right-handed weak interactions. This formula, valid for each lepton generation, relates the near maximality of observed parity nonconservation at low energies to the smallness of neutrino masses.
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A Model of Leptons
Article
  • Nov 1967
DOI:https://doi.org/10.1103/PhysRevLett.19.1264
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Unity of All Elementary-Particle Force
Article
  • Feb 1974
Strong, electromagnetic, and weak forces are conjectured to arise from a single fundamental interaction based on the gauge group SU(5).
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Neutrino masses and mixings in gauge models with spontaneous parity violation
Article
  • Jan 1981
Unified electroweak gauge theories based on the gauge group SU(2)L×SU(2)R×U(1)B-L, in which the breakdown of parity invariance is spontaneous, lead most naturally to a massive neutrino. Assuming the neutrino to be a Majorana particle, we show that smallness of its mass can be understood as a result of the observed maximality of parity violation in low-energy weak interactions. This result is shown to be independent of the number of generations and unaffected by renormalization effects. Phenomenological consequences of this model at low energies are studied. Observation of neutrinoless double-β decay will provide a crucial test of this class of models. Implications for rare decays such as μ→eγ, μ→eee̅ , etc. are also noted. It is pointed out that in the realm of neutral-current phenomena, departure from the predictions of the standard model for polarized-electron-hadron scattering, forward-backward asymmetry in e+e-→μ+μ-, and neutrino interactions has a universal character and may be therefore used as a test of the model.
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Erratum: Lepton number as the fourth "color"
Article
  • Jul 1974
Universal strong, weak, and electromagnetic interactions of leptons and hadrons are generated by gauging a non-Abelian renormalizable anomaly-free subgroup of the fundamental symmetry structure SU(4)L×SU(4)R×SU(4′), which unites three quartets of "colored" baryonic quarks and the quartet of known leptons into 16-folds of chiral fermionic multiplets, with lepton number treated as the fourth "color" quantum number. Experimental consequences of this scheme are discussed. These include (1) the emergence and effects of exotic gauge mesons carrying both baryonic as well as leptonic quantum numbers, particularly in semileptonic processes, (2) the manifestation of anomalous strong interactions among leptonic and semileptonic processes at high energies, (3) the independent possibility of baryon-lepton number violation in quark and proton decays, and (4) the occurrence of (V+A) weak-current effects.
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Partial-symmetries of weak interactions
Article
  • Feb 1961
  • Nucl Phys
Weak and electromagnetic interactions of the leptons are examined under the hypothesis that the weak interactions are mediated by vector bosons. With only an isotopic triplet of leptons coupled to a triplet of vector bosons (two charged decay-intermediaries and the photon) the theory possesses no partial-symmetries. Such symmetries may be established if additional vector bosons or additional leptons are introduced. Since the latter possibility yields a theory disagreeing with experiment, the simplest partially-symmetric model reproducing the observed electromagnetic and weak interactions of leptons requires the existence of at least four vector-boson fields (including the photon). Corresponding partially-conserved quantities suggest leptonic analogues to the conserved quantities associated with strong interactions: strangeness and isobaric spin.
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  • Jan 1967
  • 1264-275
  • A Salam
Phys. Rev. Lett. 19, 1264 (1967); A. Salam, in Elementary Particle Theory, edited by N. Svartholm (Almquist & Wiksells, Stockholm, 1969), p. 367. ~J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974).
  • Jan 1969
  • PHYS REV D
  • 275
  • A Salam
A. Salam, in Elementary Particle Theory, edited by N. Svartholm (Almquist & Wiksells, Stockholm, 1969), p. 367. J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974).