arXiv:hep-ph/0305116v1 12 May 2003
February 1, 2008
Sliding Singlet Mechanism Revisited
Nobuhiro Maekawaaand Toshifumi Yamashitab
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
We show that the unification of the doublet Higgs in the standard model (SM)
and the Higgs to break the grand unified theory (GUT) group stabilizes the sliding
singlet mechanism which can solve the doublet-triplet (DT) splitting problem. And
we generalize this attractive mechanism to apply it to many unified scenarios. In this
paper, we try to build various concrete E6unified models by using the generalized
sliding singlet mechanism.
The well-known success of the gauge coupling unification in the minimal supersymmetric
standard model (MSSM) likely supports the attractive idea of supersymmetric grand
unified theory (SUSY-GUT). On the other hand, we know there are some obstacles in
constructing a realistic SUSY-GUT. One of the biggest problems is the so-called DT
splitting problem. Generically in SUSY-GUTs, there are color triplet partners of the
MSSM Higgs, and the nucleon decay via dimension five operators becomes too rapid.
In order to suppress this proton decay, the color triplet partners must have very large
mass (≫ MGUT ∼ 1016GeV), in contrast to the doublet Higgs whose mass has to be
of order the weak scale MW ∼ 102GeV. Some ideas to solve this problem have been
proposed : the sliding-singlet mechanism[1, 2, 3, 4], the missing partner mechanism[5, 6],
the Dimopoulos-Wilczek (DW) mechanism, the GIFT mechanism, and via orbifold
Among these ideas, the first mechanism is the smartest solution which realizes the
DT splitting dynamically. Although it was shown that the originally proposed SU(5)
model cannot act effectively if SUSY breaking effect is considered, some authors have
proposed SU(6) extensions in which this mechanism acts without destabilization due to
SUSY breaking[2, 3, 4]. In this paper, we abstract the essence of this sliding singlet
mechanism in SU(6) models and generalize it to apply to many other unified theories.
Actually in E6unification it is found that for many directions of VEV of the adjoint Higgs
this mechanism may act. Corresponding to these breaking patterns, we construct some
E6Higgs sectors in which the DT splitting problem is indeed solved through this mecha-
nism. Several concrete models are propose in the context of the SUSY-GUT in which an
anomalous U(1)Agauge symmetry, whose anomaly is cancelled by the Green-Schwarz
mechanism, plays an important role[13, 14, 15, 16, 17, 18, 20] in solving various prob-
lems in SUSY scenario. And we examine whether the already proposed realistic quark and
lepton sector is compatible with such a Higgs sector or not. Note that this E6group is
interesting as a unified group, in the sense that the SUSY flavor problem can be solved in
E6SUSY-GUT with anomalous U(1)Aand non-abelian horizontal gauge symmetry.
In section 2, we briefly review the sliding singlet mechanism in the context of SU(5)
and SU(6). In section 3, we generalize this mechanism to the general gauge group. In
section 4, we construct some concrete Higgs sectors.
2 The Sliding Singlet Mechanism
In this section, We review the present status of the sliding singlet mechanism. For this
purpose, we sometimes omit details, which are described in each references.
The sliding singlet mechanism was originally proposed in the context of SU(5), in which
the following terms are allowed in the superpotential;
Wss=¯H(A + Z)H.
in E6group there are three U(1) which commute with the SM gauge group, we can select
two of three doublets in the fundamental representation 27 to become massless by the
sliding singlet mechanism, though one of the three is enough to realize the DT splitting.
Among the various GUTs we examined in this paper, it is the most promising model in
which the L and¯L components in 10 of SO(10) in 27 of E6become massless by the sliding
singlet mechanism. This vacuum is nothing but the Dimopoulos-Wilczek type vacuum.
To make the¯L component in 27 massless by the sliding singlet mechanism is important
to realize large top Yukawa coupling. For this purpose, it is enough that¯L in 27 becomes
massless by the sliding singlet mechanism, namely, the charge of¯L is taken to be the same
as that of the SM singlet in 27. The concrete condition is that (a,b,c) = (1
the notation in Table 2. Because L component in 16 is absorbed by the Higgs mechanism,
it is better that the other L component in 10 becomes massless independently by some
mechanism. Of course, to realize DT splitting, it is enough that¯L component Higgs is
guaranteed to be massless, because there must be its massless partner L. However, in
that case, the main component of the partner L tends to come from positively anomalous
U(1)Acharged field (primed field), because positively charged fields have smaller masses
than negatively charged fields. And positively charged Higgs L leads to small down-type
quark Yukawa couplings and therefore too small tanβ.
The generalized sliding singlet mechanism has opened the new possibility to build
various GUT models in which DT splitting is realized. The DW type vacuum is the most
promising vacuum in E6GUTs even in the sense of the sliding singlet mechanism, though
the other possibilities may become also interesting. We hope that such an observation
gives us a key leading to the real GUT which describes our world.
N.M. is supported in part by Grants-in-Aid for Scientific Research from the Ministry of
Education, Culture, Sports, Science and Technology of Japan.
 E. Witten, Phys. Lett. B105 (1981) 267;
D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B113, (1982)151.
 S. Dimopoulos and H. Georgi, Phys. Lett. 117B, (1982) 287;
K. Tabata, I.Umemura and K.Yamamoto, Prog. Theor. Phys. 71 (1984) 615;
A. Sen, Phys. Lett. B148 (1984) 65.
 S.M. Barr, Phys. Rev. D 57 (1998) 190.
 G. Dvali Phys. Lett. B324 (1994) 59.
 H.Georgi, Phys. Lett. B108 (1982)283;
A. Masiero, D.V. Nanopoulos, K. Tamvakis and T.Yanagida, Phys. Lett. 115 (1982)
B. Grinstein, Nucl. Phys. B206 (1982) 387;
 S. M. Barr, Phys. Lett. B112 (1982) 219;
I. Antoniadis, J. Ellis, J. Hagelin and D.V. Nanopoulos, Phys. Lett. B194 (1987)
231. ; ibid. B205, (1988) 459.
 S. Dimopoulos and F. Wilczek, NSF-ITP-82-07;
M. Srednicki, Nucl. Phys. B202 (1982) 327.
 K. Inoue, A. Kakuto and T. Takano, Prog. Theor. Phys. 75 (1986) 664;
A. Anselm and A. Johansen, Phys. Lett. B200, (1988) 331;
A. Anselm, Sov. Phys. JETP 67, (1988) 663;
Z.G. Berezhiani and G. Dvali, Sov. Phys. Lebedev. Inst. Rep. 5, (1989)55;
Z.G. Berezhiani, C. Csaki, and L. Randall, Nucl. Phys. B44, (1995) 61;
M. Bando and T. Kugo, Prog. Theor. Phys. 109,(2003)87.
 Y. Kawamura, Prog. Theor. Phys. 103,(2000)613; ibid. 105 (2001) 691; ibid. 105
 J. Polchinski and L. Susskind, Phys. Rev. D 26, (1982) 3661;
H.P. Nilles, M. Srednicki, and D. Wyler, Phys. Lett. B124, (1982) 237 ;
A.B. Lahanas, Phys. Lett. B124, (1982) 341.
 E. Witten, Phys. Lett. B149 (1984),351;
M. Dine, N. Seiberg and E. Witten, Nucl. Phys. B289 (1987), 589;
J.J. Atick, L.J. Dixon and A. Sen, Nucl. Phys. B292 (1987),109;
M. Dine, I. Ichinose and N. Seiberg, Nucl. Phys. B293 (1987),253.
 M. Green and J. Schwarz, Phys. Lett. B149 (1984),117.
 N. Maekawa, Prog. Theor. Phys. 107, 597 (2002);
N. Maekawa and T. Yamashita, Phys. Rev. Lett. 90 (2003) 121801; Prog. Theor.
Phys. 108, 719 (2002).
 M. Bando and M. Maekawa, Prog. Theor. Phys. 106 (2001) 1255.
 N. Maekawa, To appear in Phys. Lett. B (arXiv:hep-ph/0212141).
 N. Maekawa and T. Yamashita, arXiv:hep-ex/0303207.
 N. Maekawa, Prog. Theor. Phys. 106 (2001)401; arXiv:hep-ph/0110276;
N. Maekawa and T. Yamashita, Prog. Theor. Phys. 107, 1201 (2002).
 N. Maekawa, Phys. Lett. B521 (2001) 42.
 C.D. Froggatt and H.B. Nielsen, Nucl. Phys. B147 (1979) 277.
 N. Maekawa and T. Yamashita, hep-ph/0304293; J. Harada, hep-ph/0305015.
 S.M. Barr and S. Raby, Phys. Rev. Lett. 79 (1997) 4748.