588
Ö. Özdal
scale g L = g R , but below that, the couplings g L and g R could evolve differently,
and would be different at low energy scales.
Bounds on extra particle masses depend strongly on the above assumptions, in
particular on the size of the right-handed gauge coupling and/or the right-handed
CKM matrix elements, and none more so than the charged gauge boson W R .
This boson is interesting for several reasons. First, regardless of the other details
of the spectrum of left-right models, discovery of a charged gauge boson will
be an indication of the presence of an additional SU (2) symmetry group, and if
testing its decay products would indicate that it is right-handed, this will be an
unambiguous signal for left-right symmetry. 1 Second, the LHC has significantly
improved searches for W R bosons, and the limits on their masses are becoming
more stringent.
Both left- and right-handed fermions are doublets under the extended SU (3) c ⊗
SU (2) L ⊗ SU (2) R ⊗ U(1) B−L gauge group. The electroweak symmetry is broken
by the bi-doublet Higgs field. In addition, to break the SU (2) R ⊗ U(1) B−L gauge
symmetry and to provide Majorana mass terms for neutrinos (the right-handed
neutrino is automatically included in the right-handed lepton doublet), we introduce
the Higgs triplets under SU (2) L ⊗ SU (2) R ⊗ U(1) B−L :
Δ L ≡
δ
+
L /
√
2 δ
++
L
δ 0
L
−δ
+
L /
√
2
∼ (3, 1, 2) , Δ R ≡
δ
+
R /
√
2 δ
++
R
δ 0
R
−δ
+
R /
√
2
∼ (1, 3, 2) .
(1)
While only Δ R is needed for symmetry breaking, Δ L is included to preserve leftright symmetry. After symmetry breaking, the most general vacuum is
=
κ 1 /
√
2
0
0 κ 2 e iα /
√
2
, L =
0
0
v L e iθ L /
√
2 0
, R =
0
0
v R /
√
2 0
.
(2)
For the LRSM model to break down to the SM, the hierarchy of the vacuum
expectation values (VEVs) must be, v R (κ 1 , κ 2 ) v L , and
κ 2
1 + κ 2
2 = v =
246 GeV. Here the presence of non-zero VEV of Δ R , v R breaks the SU (2) R ⊗
U(1) B−L to U(1) Y , while the presence of bi-doublet VEVs κ 1 and κ 2 break the
electroweak symmetry, at the same time inducing a VEV for Δ L denoted by v L .
In the charged sector, the left and right gauge bosons mix to give the mass
eigenstates, W 1 and W 2 ;
W 1
W 2
=
cos ξ − sin ξ
sin ξ cos ξ
W L
W R
,
(3)
1 Unlike the discovery of a Z which can indicate the presence of any variety of additional U(1)
groups.
Ö. Özdal
scale g L = g R , but below that, the couplings g L and g R could evolve differently,
and would be different at low energy scales.
Bounds on extra particle masses depend strongly on the above assumptions, in
particular on the size of the right-handed gauge coupling and/or the right-handed
CKM matrix elements, and none more so than the charged gauge boson W R .
This boson is interesting for several reasons. First, regardless of the other details
of the spectrum of left-right models, discovery of a charged gauge boson will
be an indication of the presence of an additional SU (2) symmetry group, and if
testing its decay products would indicate that it is right-handed, this will be an
unambiguous signal for left-right symmetry. 1 Second, the LHC has significantly
improved searches for W R bosons, and the limits on their masses are becoming
more stringent.
Both left- and right-handed fermions are doublets under the extended SU (3) c ⊗
SU (2) L ⊗ SU (2) R ⊗ U(1) B−L gauge group. The electroweak symmetry is broken
by the bi-doublet Higgs field. In addition, to break the SU (2) R ⊗ U(1) B−L gauge
symmetry and to provide Majorana mass terms for neutrinos (the right-handed
neutrino is automatically included in the right-handed lepton doublet), we introduce
the Higgs triplets under SU (2) L ⊗ SU (2) R ⊗ U(1) B−L :
Δ L ≡
δ
+
L /
√
2 δ
++
L
δ 0
L
−δ
+
L /
√
2
∼ (3, 1, 2) , Δ R ≡
δ
+
R /
√
2 δ
++
R
δ 0
R
−δ
+
R /
√
2
∼ (1, 3, 2) .
(1)
While only Δ R is needed for symmetry breaking, Δ L is included to preserve leftright symmetry. After symmetry breaking, the most general vacuum is
=
κ 1 /
√
2
0
0 κ 2 e iα /
√
2
, L =
0
0
v L e iθ L /
√
2 0
, R =
0
0
v R /
√
2 0
.
(2)
For the LRSM model to break down to the SM, the hierarchy of the vacuum
expectation values (VEVs) must be, v R (κ 1 , κ 2 ) v L , and
κ 2
1 + κ 2
2 = v =
246 GeV. Here the presence of non-zero VEV of Δ R , v R breaks the SU (2) R ⊗
U(1) B−L to U(1) Y , while the presence of bi-doublet VEVs κ 1 and κ 2 break the
electroweak symmetry, at the same time inducing a VEV for Δ L denoted by v L .
In the charged sector, the left and right gauge bosons mix to give the mass
eigenstates, W 1 and W 2 ;
W 1
W 2
=
cos ξ − sin ξ
sin ξ cos ξ
W L
W R
,
(3)
1 Unlike the discovery of a Z which can indicate the presence of any variety of additional U(1)
groups.