PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

ight handed neutrino N R can be exactly fitted to the spinorial 16 F representation of
SO(10) [26]. The direct product of two 16 F field gives [27]
16×16 = 10+120+126 (2.28)
The Pati-Salam gauge group SU(4) C
×SU(2) L
×SU(2) R
is a subgroup of the gauge group
SO(10). The left-right symmetric gauge group SU(3) C
×SU(2) L
×SU(2) R
×U(1) B−L is
a subgroup of the Pati-Salam gauge group and hence is also a subgroup of the SO(10).
One can understand the interactions between different representations of the SO(10) in
terms of the Pati-Salam of left-right decomposition [28,29]. The 16, 10, 120 and 126
fields of the SO(10) have these following decompositions under the Pati-Salam subgroup
SU(4) C
×SU(2) L
×SU(2) R
10 = (1,2,2)+(6,1,1)
and
16 = (4,2,1)+(4,1,2)
120 = (1,2,2)+(10,1,1)+(10,1,1)+(6,3,1)+(6,1,3)+(15,2,2)
126 = (6,1,1)+(10,3,1)+(10,1,3)+(15,2,2)
The SU(3) C
×U(1) B−L
is a subgroup of SU(4) C
. The representations ¯4, 6, 10 and
15 hence can be further subdivided under the SU(3) C
× U(1) B−L
gauge group [28,29].
With 16 F , 10, 126 field contents of SO(10), one could realize type-I and type-II seesaw as
follows,
• The Dirac mass term N ˜H† R L of Eq. (2.14) is generated from the interaction
16 F 16( F 10 H ). The 10 H has ( a ) bi-doublet Φ H = (1,2,2,0). The lepton doublet
νL NR
L = and L
e R = are components of 16
L e F fields and transforms as
R
(1,2,1,-1) and (1,1,2,-1) under the left-right symmetry gauge ( group. ) The interaction ( )
νL NR
of the bi-doublet Φ H field with the SU(2) doublets L = and L
e R =
L e R
generates the Dirac mass term, after the electroweak symmetry is broken.
• The Majorana mass term M ¯N R NR C of Eq: (2.14) is generated from the Yukawa
interaction Y 126 16 F 16 F 126 H of SO(10). The 126 in the above contains a Higgs field
∆ R which transforms as a triplet under the SU(2) R
gauge group and is singlet under
SU(2) L
. The direct product of the multiplet L R of 16 F with the Higgs triplet ∆ R of
126 generates the Majorana mass term of the right handed neutrino after the Higgs
triplet ∆ R gets vacuum expectation value [30,31]. Hence, the Majorana mass term
of the right handed neutrino is M ∼ Y 126 〈∆ R 〉.
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