Assuming the lightest supersymmetric particle is the gluino, we treat the
decays gluino->quark-antiquark-neutrino and gluino->gluon-neutrino. Such
couplings can be induced by the R parity violating quark-squark-lepton
interaction which can also be responsible for neutrino masses and mixings.
These R parity violating gluino decays have the same final state structure
(jets plus missing energy) as previously considered decays into
quark-antiquark-photino and gluon-gravitino but with significantly different
gluino lifetimes.Comment: 8 pages, 4 figures, published version plus new referenc

Clavelli, L.

Stremnitzer, H.

Physics Letters B

English

arXiv

AbstractAssuming the lightest supersymmetric particle is the gluino, we treat the decays g̃→qq̄ν and g̃→gν. Such couplings can be induced by the R-parity violating quark–squark–lepton interaction which can also be responsible for neutrino masses and mixings. These R-parity violating gluino decays have the same final state structure (jets plus missing energy) as previously considered decays into quark–antiquark–photino and gluon–gravitino but with significantly different gluino lifetimes

Elsevier - Publisher Connector 

Physics Letters B 576 (2003) 184–188
www.elsevier.com/locate/physletb
R-parity violating decays of the gluino
L. Clavelli a, H. Stremnitzer b
a Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA
b Institut für Theoretische Physik, Universität Wien, A-1090 Vienna, Austria
Received 8 September 2003; accepted 4 October 2003
Editor: H. Georgi
Abstract
Assuming the lightest supersymmetric particle is the gluino, we treat the decays g˜→ qq¯ν and g˜→ gν. Such couplings can
be induced by the R-parity violating quark–squark–lepton interaction which can also be responsible for neutrino masses and
mixings. These R-parity violating gluino decays have the same final state structure (jets plus missing energy) as previously
considered decays into quark–antiquark–photino and gluon–gravitino but with significantly different gluino lifetimes.
 2003 Elsevier B.V.
PACS: 11.30.Pb; 12.60.J; 13.85.-t
Open access under CC BY license.1. Introduction
The possibility of the lightest supersymmetric par-
ticle (LSP) decaying through R-parity violation has
been discussed since the early days of supersymmetry
[1], many studies have been made (e.g. [2]), and many
experimental searches have been undertaken (e.g. [3]).
There seem, however, to have been no investigations
up to now of the possibility considered here of R-
parity violating decays of the gluino. Although these
would be most relevant if the recent theme of a light or
relatively light gluino were to be experimentally con-
firmed they could also be important in the case of a
heavy gluino LSP. In some cases [4,5] the phenom-
enological advantages of a light gluino have as much
to do with a large hierarchy between gluino and squark
masses as with a light gluino mass per se. Most recent
E-mail addresses: lclavell@bama.ua.edu (L. Clavelli),
hanns.stremnitzer@univie.ac.at (H. Stremnitzer).0370-2693 2003 Elsevier B.V.
doi:10.1016/j.physletb.2003.10.009
Open access under CC BY license.light gluino investigations have concentrated on the
mass region around 12 GeV possibly accompanied by
a b squark near 4 GeV [6,7]. Alternative possibilities
have also been noted [8]. In the minimal supersym-
metric standard model (MSSM), a light gluino is typi-
cally accompanied by an even lighter photino allowing
the decay g˜→ qq¯γ˜ . In gauge mediated SUSY break-
ing models, there is often an ultra-light gravitino be-
low the gluino in mass leading to the decay g˜→ gG˜.
In some models these channels are closed leading to
an absolutely stable gluino or to one decaying through
R-parity violating processes. In this article we assume
the gluino is the lightest supersymmetric particle and
we consider lepton number violating gluino decays. In
Section 2 we treat the decays g˜→ qq¯ν. The fact that
the third generation seems, in some respects, special
compared to the first two suggests models in which
the R-parity violation is tied to the third generation.
If the R-parity violation is entirely in the third
generation and the gluino lies below the bb threshold,
L. Clavelli, H. Stremnitzer / Physics Letters B 576 (2003) 184–188 185there will be the loop induced decay g˜ → gν. This
is treated in Section 3 neglecting the possibility of a
right-handed neutrino.
Finally, in the presence of a light right-handed
neutrino, there is the possibility, treated in Section 4,
that the dominant decay could be a two loop process
coupling the gluino to gluon plus νR . It might be
expected that such a dominant decay mechanism
would lead to an ultra-long-lived gluino.
2. The gluino decay to quark–antiquark–neutrino
We assume an R-parity violating and lepton num-
ber violating term in the superpotential of the form
(2.1)W = λ′ijkLiQjDk,
where i, j, k are family indices. Then, if the gluino is
above a quark–antiquark threshold one will have the
gluino decay to qq¯ν corresponding to the graph of
Fig. 1.
The fact that the third generation seems, in some
respects, special compared to the first two suggests
models in which the R-parity violation involves third
generation quarks and squarks only. We, therefore,
take as a working assumption that the non-zero quark
flavor indices in (2.1) are third generation only. In
any case, the experimental limits on R-parity violating
couplings are much less restrictive [2,9] in the third
generation so these could well be dominant. A λ′
involving only third generation quarks could be as
great as 0.1. Then the gluino decay would be into bb¯ν
assuming the gluino mass is above the 2b threshold. In
this case a light gluino pair production could explain
the excess b production seen at Fermilab without
requiring the light b squarks of [6].
The signature of such a decay, hadrons plus missing
energy, would be identical to the conventional qq¯γ˜
decay. The inverse width for this latter decay is
(2.2)τ (g˜→ qq¯γ˜ )≈ m˜4/(m5g˜αsα).
With a light gluino and a squark mass in the 100 GeV
range, this typically results in a gluino lifetime in the
nanosecond range which is counter-indicated by the
KTEV search [10]. If, however, the gluino is the LSP
and decays through the R-parity violating graph of
Fig. 1, the lifetime could easily be much longer so
that the lightest supersymmetric hadron, presumablyFig. 1. Gluino decay into quark–antiquark–neutrino.
the gluino–gluon bound state, would not decay in the
sensitive region of a KTEV type experiment.
(2.3)τ (g˜→ qq¯ν)≈ m˜4/(m5g˜αsλ′2).
The neutrino mass matrix corresponding to the R-
parity violation of (2.1) is [11]
(2.4)Mνii′ ≈
3
8π2
∑
jk
λ′ijkλ′ikjmd(j)md(k)/m˜,
where m˜ is the assumed degenerate squark mass and
md(k) is the down-type quark mass in the kth family.
We have also made the simplification of neglecting
the CKM quark mixing angles and have assumed that
Ad − µ tanβ is of order m˜. If the dominant k, j are
third generation, [11] notes that a 4.5 eV νe mass
would correspond to
(2.5)λ′133 ≈ 7× 10−4
(
m˜
100 GeV
)1/2
although the present indications of a sub-eV neutrino
mass would lead to a λ′ an order of magnitude below
(2.5). Such a relation substituted into (2.3) would lead
to a gluino lifetime depending only on the ratio of
gluino mass to squark mass.
(2.6)
τ (g˜)= 0.013s
(
m˜
1000mg˜
)5(0.1
αs
)(
7× 10−5
λ′i33
)2
.
A gluino–gluon bound state with a lifetime of order
0.013 s might have evaded the current searches since it
would appear as a quasi-stable particle whose ultimate
decay with a missing neutrino could be confused with
a neutron knock-on event.
186 L. Clavelli, H. Stremnitzer / Physics Letters B 576 (2003) 184–1883. The gluino decay to gluon plus neutrino
If the gluino mass is less than twice the mass of the
quarks appearing in the R-parity violating couplings,
one has the hitherto uninvestigated decay
(3.1)g˜→ gν.
A recent analyses of constraints from Z decay sug-
gests at 95% confidence level [12,13]
(3.2)mg˜ > 6.3 GeV/c2.
This limit still allows the possibility that the gluino
mass is below the b quark pair threshold. The matrix
element corresponding to the graph of Fig. 2 plus the
analogous graph where the gluon is emitted from the
squark line is
M= #µ λ
′g32mb
4
u¯(p′)
×
∫
d4k
(2π)4
(
(/p′ + /k)γ µ + γ µ(/p+ /k)
(p+ k)2 −m2b
+ (2k− q)
µ
(k − q)2 − m˜2
)
(3.3)× (1− γ5)u(p) 1
(p′ + k)2 −m2b
1
k2 − m˜2 ,
where p′ = p − q is the final state neutrino momen-
tum.
This amplitude is equivalent to that induced by an
effective magnetic moment coupling
(3.4)L= iµau¯L(ν)σµνqνu(g˜)#µ(g)
with
(3.5)µa ≈ mbαsλ
′
m˜2
.
The corresponding decay rate is
(3.6)Γ (g˜→ gν)= |µa|2m3g˜ ≈
m2bm
3
g˜
α2s λ
′2
m˜4
.
Nominal values of 10 GeV, 10 TeV, 0.1, and 7× 10−5
for mg˜ , m˜, αs , and λ′, would correspond to a gluino
lifetime of 5.2× 10−3 s.
A two loop graph that would lead to a gluino decay
to gluon plus right-handed neutrino is shown in Fig. 3.
To investigate such two loop effects we consider
an extended superpotential containing a right-handedFig. 2. Gluino decay to gluon plus left-handed neutrino.
Fig. 3. Typical Feynman graph for gluino decay to gluon plus
right-handed neutrino.
singlet superfield N .
(3.7)
W =WMSSM + λ′QDL+ #HuHdN + hνLNHu.
Here, lepton number and R-parity violation comes
through a new HuHdN interaction governed by the
coupling constant # in addition to the conventional
λ′ coupling. WMSSM contains the usual Higgs mixing
term µHuHd . The small Yukawa coupling hν is
proportional to the neutrino Dirac mass:
(3.8)hν = m
Dirac
ν
〈Hu〉 .
The effective transition magnetic moment from
Fig. 3 is
(3.9)µa ≈ 1
(4π)3
λ′hνhbαsµBmb
m˜2m2H
.
Here, µB is the off-diagonal entry in the Higgs mass
squared matrix. In the MSSM with electroweak sym-
metry breaking [14], it is given by µB = 12M2A sin(2β)
where MA is the mass of the CP-odd Higgs scalar.
L. Clavelli, H. Stremnitzer / Physics Letters B 576 (2003) 184–188 187This µa , however, would be proportional to the
neutrino mass and would be negligible compared to
the transition magnetic moment of (3.5).
4. A dominant gluino decay to gluon plus
right-handed neutrino
Even in the absence of the R-parity violating
quark–squark–lepton coupling of (2.1), the R-parity
and lepton number violating Higgs–Higgsino–Lepton
coupling in (3.7) could lead to a gluino decay into
gluon plus right-handed neutrino.
The lowest order graph contributing to gluino decay
would be that of Fig. 4 as well as those graphs related
by attaching the gluon to other colored lines or by
changing the flavor of the internal quark (squark)
lines. These amplitudes are proportional to the trilinear
boson coupling parameters A, which are induced in
the softly broken MSSM thru supergravity. We can
entertain the possibility that the λ′ parameters are
negligible and that the dominant trilinear coupling is
that of the top quark. Then the two loop gluino decays
of Fig. 4 could be dominant for a gluino LSP of mass
up to the minimum of twice the top mass or twice the
stop mass:
(4.1)µa ≈ 1
(4π)3
µ cos(2β)mχ0A#αsht
m˜2m2H
,
where mχ0 is the mass of the neutralino. However, if
the top quark is heavier than the neutralino, then mχ0
should be replaced by mt in the estimate here.
Depending on the flavor structure, the # coupling
might be limited only by neutrino mass measurements
and might, therefore, be expected to be extremely
small. It is clear that the corresponding gluino lifetime
could easily be long enough to have cosmological sig-
nificance. There is, for instance, the possibility that the
gluino–gluon bound state could traverse cosmological
distance scales before decaying and, if sufficiently en-
ergetic, could contribute through its decay products to
the ultra-high-energy cosmic rays. We leave delayed
calculation of some of the possible effects discussed
here to future investigations.Fig. 4. Alternative mechanism for gluino decay into gluon plus
right-handed neutrino.
Acknowledgements
This work was supported in part by the US Depart-
ment of Energy under grant DE-FG02-96ER-40967.
One of the authors (L.C.), would like to acknowl-
edge the hospitality of the University of Vienna and
the High Energy Physics Institute of the Austrian
Academy of Sciences where the initial discussion of
the ideas presented here occurred. Discussions with
Alfred Bartl as well as some conversations on the
gluino decay modes of the current Letter with Thomas
Gajdosik are especially acknowledged. It has been
brought to our attention that gluino decays through bi-
linear R-parity violation (as opposed to the trilinear
violation treated here) have also been recently consid-
ered [15].
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R-parity violating decays of the gluino 

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R Parity Violating Decays of the Gluino

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