Physics Letters B 766 (2017) 149–152
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Generalized gauge U(1) family symmetry for quarks and leptons
Corey Kownacki, Ernest Ma, Nicholas Pollard, Mohammadreza Zakeri
∗
Physics and Astronomy Department, University of California, Riverside, CA 92521, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
24 November 2016
Received
in revised form 8 January 2017
Accepted
9 January 2017
Available
online 11 January 2017
Editor:
A. Ringwald
If the standard model of quarks and leptons is extended to include three singlet right-handed neutrinos,
then the resulting fermion structure admits an infinite number of anomaly-free solutions with just one
simple constraint. Well-known examples satisfying this constraint are B–L, L
μ
–L
τ
, B–3L
τ
, etc. We derive
this simple constraint, and discuss two new examples which offer some insights to the structure of
mixing among quark and lepton families, together with their possible verification at the Large Hadron
Collider.
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
Table 1
Fermion
assignments under U (1)
F
.
Particle SU(3)
C
SU(2)
L
U (1)
Y
U (1)
F
Q
iL
= (u, d)
iL
321/6n
i
u
iR
312/3 n
i
d
iR
31−1/3 n
i
L
iL
= (ν, l)
iL
12−1/2 n
i
l
iR
11−1 n
i
ν
iR
110n
i
1. Introduction
In the standard model of particle interactions, there are three
families of quarks and leptons. Under its SU(3)
C
× SU(2)
L
×U (1)
Y
gauge symmetry, singlet right-handed neutrinos ν
R
do not trans-
form.
They are not included in the minimal standard model which
only has three massless left-handed neutrinos. Since neutrinos are
now known to be massive, ν
R
should be considered as additions to
the standard model. In that case, the model admits a possible new
family gauge symmetry U(1)
F
, with charges n
1,2,3
for the quarks
and n
1,2,3
for the leptons as shown in Table 1.
To
constrain n
1,2,3
and n
1,2,3
, the requirement of gauge anomaly
cancellation is imposed. The contributions of color triplets to the
[SU(3)]
2
U (1)
F
anomaly sum up to
[SU(3)]
2
U (1)
F
:
1
2
3
i=1
(2n
i
−n
i
−n
i
); (1)
*
Corresponding author.
E-mail
address: mzake001@ucr.edu (M. Zakeri).
and the contributions of Q
iL
, u
iR
, d
iR
, L
iL
, l
iR
to the U (1)
Y
[U (1)
F
]
2
anomaly sum up to
U (1)
Y
[U (1)
F
]
2
:
3
i=1
6
1
6
−
3
2
3
−
3
−
1
3
n
2
i
+
2
−
1
2
−(−
1)
n
i
2
. (2)
Both are automatically zero, as well as the [U (1)
F
]
3
anomaly be-
cause
all fermions couple to U (1)
F
vectorially. The contributions of
the SU(2)
L
doublets to the [SU(2)]
2
U (1)
F
anomaly sum up to
[SU(2)]
2
U (1)
F
:
1
2
3
i=1
(3n
i
+n
i
); (3)
and the contributions to the [U (1)
Y
]
2
U (1)
F
anomaly sum up to
[U (1)
Y
]
2
U (1)
F
:
3
i=1
6
1
6
2
−3
2
3
2
−3
−
1
3
2
n
i
+
2
−
1
2
2
−(−1)
2
n
i
=
3
i=1
−
3
2
n
i
−
1
2
n
i
.
(4)
Both are zero if
3
i=1
(3n
i
+n
i
) =0. (5)
http://dx.doi.org/10.1016/j.physletb.2017.01.013
0370-2693/
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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