tions provide connection between Yukawa couplings in the case when LQ interacts with
the SU(2) doublet(s) of the SM fermions. For example, one set of the R
2
Yukawa couplings
that features the CKM matrix V is
L
R
2
Yukawa
⊃ +y
LR
2 ij
¯e
i
R
R
a ∗
2
Q
j,a
L
= +(y
LR
2
V
†
)
ij
¯e
i
R
u
j
L
R
5/3 ∗
2
+ y
LR
2 ij
¯e
i
R
d
j
L
R
2/3 ∗
2
, (2.2)
where y
LR
2
is the 3 ×3 matrix in the flavour space, Q
L
is a left-chiral quark doublet, e
R
is a
right-chiral charged lepton, a = 1, 2 is an SU(2) index, and i, j = 1, 2, 3 are flavour indices.
The couplings of
˜
R
2
, on the other hand, feature the PMNS matrix U since the relevant
lagrangian reads
L
˜
R
2
Yukawa
⊃ −˜y
RL
2 ij
¯
d
i
R
˜
R
a
2
ab
L
j,b
L
= −˜y
RL
2 ij
¯
d
i
R
e
j
L
˜
R
2/3
2
+ (˜y
RL
2
U)
ij
¯
d
i
R
ν
j
L
˜
R
−1/3
2
, (2.3)
where ˜y
RL
2
is the 3 × 3 matrix in the flavour space, L
L
is a left-chiral lepton doublet, d
R
is a right-chiral down-type quark, and
ab
is Levi-Civita symbol. The hermitian conjugate
parts are omitted from eqs. (2.2) and (2.3) for brevity. Note that our convention allows one
to completely neglect the PMNS rotations as the neutrino flavour is not relevant for the
processes we are interested in. In the actual model file implementations the PMNS matrix
is thus set to be an identity matrix whereas the only relevant angle in the CKM matrix
is taken to be the Cabbibo one. These assumptions can be modified using the parameter
restriction files that are provided with each LQ model.
One could also entertain a possibility of introducing one or more right-chiral neutrinos
thus extending the SM fermion sector. This would allow one to study one additional scalar
LQ state —
¯
S
1
≡ (3, 1, −2/3) — and to consider additional sets of Yukawa couplings for
˜
R
2
and S
1
[5]. These three scalar multiplets have the same transformation properties under
the SM gauge group as the squarks, where the role of the right-chiral neutrino(s) could be
played by neutralino(s). The right-chiral neutrino introduction would, in principle, yield
the same phenomenological signatures that one has for those LQs that couple to the left-
chiral neutrinos as long as the right-chiral neutrinos are light enough. This fact and the
close correspondence between the LQ and squark properties is often used to reinterpret
dedicated experimental searches for supersymmetric particles in terms of limits on the
allowed LQ parameter space. See, for example, ref. [8] for a recent recast along these
lines. Be that as it may, the model files we provide can be modified to incorporate these
hypothetical fermionic fields and associated interactions.
We always consider a scenario where the SM is extended with a single scalar LQ
multiplet. From these single LQ model files one can easily generate more complicated
scenarios of new physics (NP) when two or more scalar LQs are simultaneously present at
the energies relevant for collider physics. Since the LQ electric charge eigenstates coincide
with the mass eigenstates in the single LQ extensions we use this property to uniquely
denote a given LQ component. For example, R
5/3
2
(
˜
R
−1/3
2
) is denoted as R2p53 (R2tm13)
in model files. The fact that FeynRules 2.0 [16] does not accommodate antifundamental
representation of SU(3) has prompted us to implement all the LQs as triplets of colour in
model files.
In the MadGraph5 aMC@NLO model parameter card of a given LQ scenario one
can modify the LQ mass m
LQ
and its Yukawa couplings. For example, the 13 element
– 4 –