where ∆m
2
˜ν
R
=
M
N
(A
N
− µ
0
cot β
0
)
and the mass eigenstates ˜ν
∓
are defined in terms of
˜ν
R
, ˜ν
∗
R
as follows:
˜ν
−
=
−i
2
e
iφ/2
˜ν
R
− e
−iφ/2
˜ν
∗
R
, (2.3)
˜ν
+
=
1
2
e
iφ/2
˜ν
R
+ e
−iφ/2
˜ν
∗
R
, (2.4)
where φ is the phase of the off-diagonal element of M
RR
, i.e., φ = arg(M
N
(A
N
−µ
0
cot β
0
)).
In case of real soft SUSY breaking terms, one finds φ = 0 or φ = π, depending on the
relative sign of A
N
and µ
0
. In the former case, we see that ˜ν
−
(φ = 0) = I(˜ν
R
) ≡ ˜ν
I
1
, so the
lightest state is an imaginary sneutrino with m
˜ν
I
1
= m
˜ν
−
and the real type, R(˜ν
R
) ≡ ˜ν
R
1
,
has a larger mass m
˜ν
R
1
= m
˜ν
+
. The other possibility is φ = π, where now ˜ν
−
(φ = π) = ˜ν
R
1
is the lightest state with m
˜ν
R
1
= m
˜ν
−
and ˜ν
I
R
is heavier with m
˜ν
I
R
= m
˜ν
+
.
Before we consider the effect this will have on spectrum points in parameter space,
we must first discuss how we obtain our numerical results. In this work, we have used
the spectra for RH sneutrino LSP candidates in the BLSSM, previously obtained in [38],
where the exact details of the numerical results are discussed in great detail, though we
summarise them here. We have used the SARAH [46] and SPheno [47] programs, consid-
ering a complete universal scenario where the gauge couplings all unify at the GUT scale.
We have scanned over the range [0, 5] TeV in both m
0
and m
1/2
, tan β in [0, 60], A
0
in
[−15, 15] TeV, tan β
0
in the interval [0, 2] with neutrino Yukawa couplings Y
(1,1)
, Y
(2,2)
,
Y
(3,3)
in [0, 1]. Once determined, the boundary conditions are imposed at the GUT scale
and the gauge couplings and gaugino masses are evolved back to the low scale through
two-loop Renormalisation Group Equations (RGEs).
In addition, the masses of the SUSY scalars are determined at low scale where one-
and two-loop corrections are employed for the SM-like Higgs boson mass. In addition, the
masses of the SUSY scalars are determined at low scale where one and two-loop corrections
are employed for the SM-like Higgs boson mass. In this work, we employ an approximate
error in the estimated Higgs boson mass of ±3 GeV [49]. This ban includes only the ex-
perimental error from the uncertainty of the top mass and strong coupling measurements.
There are potentially further errors arising from theoretical uncertainties associated with
the minimisation of the potential at a given loop order. Here we use SPheno, which min-
imises the Higgs potential using the two-loop corrected effective potential. Consequently,
higher loop orders can provide additional contributions to the Higgs mass and can increase
this error in the Higgs mass beyond ±3 GeV. Furthermore, there may be corrections to
the Higgs mass at higher loop orders due to the large Yukawa couplings of the RH neu-
trinos, though they do not directly couple to the Higgs. These issues will likely increase
the uncertainty in the determination of the Higgs mass, but we do not quantify this here.
Nevertheless, since our study concerns mainly the LSP, which will not largely be affected
by the determination of the Higgs mass, the exact level of uncertainty here will not affect
the conclusions of this work.
The M
Z
0
value has been fixed to 4 TeV to comply with dedicated U(1)
B−L
searches,
in particular, the 95% Confidence Level (CL) bound extracted from the di-lepton channel
– 4 –