Leptophobic Z in Supersymmetry and Where to Find Them
561
handed neutrino and its supersymmetric partner in this framework. The Higgs sector
consists of two charged H ± and four neutral scalar bosons, which are a pseudoscalar
A and three neutral scalars h, H , and H , where h and H are being MSSM-like
Higgs. This spectrum also creates an extended gaugino sector with a total of six
neutralinos where chargino sector remains unchanged.
At tree level, the squared mass of Z boson is given by
M
2
Z = g
(Q
S
2 v
2
S + Q
H u
2 v
2
H u
+ Q
H d
2 v
2
H d
) ,
where g being the coupling constant of the U(1) gauge group, Q
i is corresponding
U(1) charge of singlet s, doublet H u , and doublet H d superfields, and v i being their
respective vacuum expectation values. The existence of the U(1) group leads to
extra D- & F-terms which contributes to the masses of the supersymmetric partners
and Higgses. Large bounds of Z boson requires large v S which further leads to
a heavy particle spectrum especially in the Higgs sector. Thus, requiring massive
Z also causes massive particle spectrum, which can be tuned via corresponding
softmasses.
The interaction Lagrangian of the fields ˆ
B μ and ˆ
Z
μ with the fermions is
suppressed by their corresponding coupling and charge, g 1 Y i and g Q
i , respectively,
where i represents the corresponding fermionic field in the interaction, g 1 and g are
U(1) Y and U(1) couplings, respectively. The typical E 6 -inspired relation between
U(1) Y and U(1) couplings is taken to be g /g 1 =
√
5/3. In [11], it has been shown
that shifting this relation from GUT scale to Z -mass scale, and abandoning grand
unification assumption, and adding the possibility to decay through supersymmetric
particles, can reduce Z mass limit up to 300 GeV depending on θ E 6 angle [12, 13].
Breaking SUSY sector in a higher scale generates enough room for U(1) coupling
to grow via renormalisation group equations which leads to larger g and higher
production amplitudes for Z . Thus, breaking SUSY in a lower energy scale limits
the growth in g and reduces the production cross section, which leads to relatively
less stringent mass bounds for Z . In Fig. 1 we compared high-mass dilepton limit
from ATLAS collaboration [2] to our results, sampling θ E 6 at −0.79π (U(1)
η )
and 0 (U(1)
ψ ), where Z production has been calculated in next-to-leading order
(NLO) precision. In both panels, the y-axis shows the production cross section
with its branching fraction to dilepton final states where Z mass varied between
2 and 5 TeV within the bounds of narrow width approximation. Panels show the
effect of different breaking scales where for the left panel g /g 1 relation is taken
at GUT scale, and in the right panel, it downgraded to Z mass scale. The dashed
line shows the case where Z is only allowed to decay into the SM particles (USM),
and the dotted line shows the case with SUSY particles added (UMSSM). The error
bars represent the theoretical uncertainties, scale and parton distribution function
(PDF) uncertainties added in quadrature. The calculation has been performed via
MADGRAPH [14]. The left panel of Fig. 1 reveals that, when the relation between
couplings are assumed to be taken at GUT scale, the addition of supersymmetric
partners to the possible decay channels improves the mass limits around 20% and
561
handed neutrino and its supersymmetric partner in this framework. The Higgs sector
consists of two charged H ± and four neutral scalar bosons, which are a pseudoscalar
A and three neutral scalars h, H , and H , where h and H are being MSSM-like
Higgs. This spectrum also creates an extended gaugino sector with a total of six
neutralinos where chargino sector remains unchanged.
At tree level, the squared mass of Z boson is given by
M
2
Z = g
(Q
S
2 v
2
S + Q
H u
2 v
2
H u
+ Q
H d
2 v
2
H d
) ,
where g being the coupling constant of the U(1) gauge group, Q
i is corresponding
U(1) charge of singlet s, doublet H u , and doublet H d superfields, and v i being their
respective vacuum expectation values. The existence of the U(1) group leads to
extra D- & F-terms which contributes to the masses of the supersymmetric partners
and Higgses. Large bounds of Z boson requires large v S which further leads to
a heavy particle spectrum especially in the Higgs sector. Thus, requiring massive
Z also causes massive particle spectrum, which can be tuned via corresponding
softmasses.
The interaction Lagrangian of the fields ˆ
B μ and ˆ
Z
μ with the fermions is
suppressed by their corresponding coupling and charge, g 1 Y i and g Q
i , respectively,
where i represents the corresponding fermionic field in the interaction, g 1 and g are
U(1) Y and U(1) couplings, respectively. The typical E 6 -inspired relation between
U(1) Y and U(1) couplings is taken to be g /g 1 =
√
5/3. In [11], it has been shown
that shifting this relation from GUT scale to Z -mass scale, and abandoning grand
unification assumption, and adding the possibility to decay through supersymmetric
particles, can reduce Z mass limit up to 300 GeV depending on θ E 6 angle [12, 13].
Breaking SUSY sector in a higher scale generates enough room for U(1) coupling
to grow via renormalisation group equations which leads to larger g and higher
production amplitudes for Z . Thus, breaking SUSY in a lower energy scale limits
the growth in g and reduces the production cross section, which leads to relatively
less stringent mass bounds for Z . In Fig. 1 we compared high-mass dilepton limit
from ATLAS collaboration [2] to our results, sampling θ E 6 at −0.79π (U(1)
η )
and 0 (U(1)
ψ ), where Z production has been calculated in next-to-leading order
(NLO) precision. In both panels, the y-axis shows the production cross section
with its branching fraction to dilepton final states where Z mass varied between
2 and 5 TeV within the bounds of narrow width approximation. Panels show the
effect of different breaking scales where for the left panel g /g 1 relation is taken
at GUT scale, and in the right panel, it downgraded to Z mass scale. The dashed
line shows the case where Z is only allowed to decay into the SM particles (USM),
and the dotted line shows the case with SUSY particles added (UMSSM). The error
bars represent the theoretical uncertainties, scale and parton distribution function
(PDF) uncertainties added in quadrature. The calculation has been performed via
MADGRAPH [14]. The left panel of Fig. 1 reveals that, when the relation between
couplings are assumed to be taken at GUT scale, the addition of supersymmetric
partners to the possible decay channels improves the mass limits around 20% and