Light stops in the MSSM parameter space
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Modern Physics Letters A
c© World Scientific Publishing Company
LIGHT STOPS IN THE MSSM PARAMETER SPACE
A.V.GLADYSHEV1,2, D.I.KAZAKOV1,2, M.G.PAUCAR1
1 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,
141980, 6 Joliot-Curie, Dubna, Moscow Region, Russian Federation
gladysh@theor.jinr.ru, kazakovd@theor.jinr.ru, manuel@theor.jinr.ru
2Institute of Theoretical and Experimental Physics,
117218, 25 Bolshaya Cheremushkinskaya, Moscow, Russian Federation
Received (Day Month Year)
Revised (Day Month Year)
We consider the regions of the MSSM parameter space where the top squarks become
light and even may be the LSP. This happens when the triple scalar coupling A becomes
very big compared to m0. We show that in this case the requirement that the LSP
is neutral imposes noticeable constraint on the parameter space excluding low m0 and
m1/2 similar to constraint from the Higgs mass limit. In some cases these constraints
overlap. This picture takes place in a wide region of tanβ. In a narrow band close to
the border line the stops are long-lived particles and decay into quarks and neutralino
(chargino). The cross-section of their production at LHC via gluon fusion mechanism in
this region may reach a few pb.
Keywords: Supersymmetry; long-lived particles.
PACS Nos.: 12.60.Jv, 14.80.Ly
1. Introduction
Preparing for SUSY discovery at LHC one faces the problem of well defined predic-
tions since the variety of models and scenarios open up a wide range of possibili-
ties 1,2,3,4,5,6. Due to the absence of a SUSY golden mode, one has to explore the
parameter space looking for high cross-sections, low background processes, typical
missing energy events, etc. All these possibilities are realized within some mechanism
of SUSY breaking (mSUGRA and gauge mediation are the most popular) and de-
pend on particular choice of a region in SUSY parameter space 7,8,9,10,11,12,13,14.
Besides commonly accepted benchmark points which are widely discussed in the
literature 15,16,17,18 there still exist some exotic regions in parameter space where
unusual relations hold and one can expect interesting phenomena. In particular, in
Ref. 19 we considered the so-called coannihilation region in mSUGRA parameter
space where one can have long-lived staus which can decay at some distance from
the collision point or even fly through detector. This region of m0 − m1/2 plane
http://arxiv.org/abs/0704.1429v1
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2 A.V.Gladyshev, D.I.Kazakov, M.G.Paucar
exists for all values of tanβ and moves towards higher values of m0 and m1/2 with
increase of the latter. However, the area where one can have long-lived particles is
very narrow (for each tanβ) and needs severe fine-tuning.
Here we explore another region of parameter space which appears only for large
negative scalar triple coupling A0 and is distinguished by the light stops. On the
border of this region, in full analogy with the stau coannihilation region, the top
squark becomes the LSP and near this border one might get the long-lived stops.
Below we discuss this possibility in detail and consider also its phenomenological
consequences for the LHC.
2. Constraints on the MSSM Parameter Space for Large Negative
Values of A
In what follows we consider the MSSM with gravity mediated supersymmetry break-
ing and the universal soft terms. We thus have the parameter space defined by
m0,m1/2, A, tanβ and we take the sign of µ to be positive motivated by contribu-
tion to the anomalous magnetic moment of muon 20,21,22,23,24,25,26,27. Imposing
the constraints like: i) the gauge couplings unification 28,29,30, ii) neutrality of the
LSP 31,32, iii) the Higgs boson and SUSY mass experimental limits 33,34,35, iv)
radiative electroweak symmetry breaking, we get the allowed region of parameter
space. Projected to the m0 −m1/2 plane this region depends on the values of tanβ
and A. In case when A is large enough the squarks of the third generation, and first
of all stop, become relatively light. This happens via the see-saw mechanism while
diagonalizing the stop mass matrix
m̃2tL mt(At − µ cotβ)
mt(At − µ cotβ) m̃
where
tL = m̃
(4M2W −M
Z) cos 2β,
tR = m̃
(M2W −M
Z) cos 2β.
The off-diagonal terms increase with A, become large for large mq (that is why the
third generation) and give negative contribution to the lightest squark mass defined
by minus sign in eq.(1).
m̃21,2 =
m̃2tL + m̃
(m̃2tL − m̃
2 + 4m2t (At − µ cotβ)
. (1)
Hence, increasing |A| one can make the lightest stop as light as one likes it to
be and even make it the LSP. The situation is similar to that with stau for small
m0 and large m1/2 when stau becomes the LSP. For squarks it takes place for low
m1/2 and low m0. One actually gets the border line where stop becomes the LSP.
The region below this line is forbidden. It exists only for large negative A, for small
A it is completely ruled out by the LEP Higgs limit.
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Light Stops in the MSSM Parameter Space 3
100 200 300 400
  h0,      mass LEP limits
[GeV]
t c1®
~t® c
~t NLSP
LSP ~t
1t® b
= - 800 [GeV]
            mass LEP limits
 mass LEP limits
200 400 600 800
[GeV]
t c1®
1t® b
  h0,      mass LEP limits
= - 1500 [GeV]
             mass LEP limits
~t NLSP
Fig. 1. Allowed region of the mSUGRA parameter space for A0 = −800,−1500 GeV and tan β =
10. At the left from the border stau is an LSP, below the border stop is the LSP. The dotted line is
the LEP Higgs mass limit. Also shown are the contours where various stop decay modes emerge.
It should be noted that in this region one gets not only the light stop, but also
the light Higgs, since the radiative correction to the Higgs mass is proportional to
the log of the stop mass. The stop mass boundary is close to the Higgs mass one
and they may overlap for intermediate values of tanβ. We show the projection of
SUSY parameter space to the m0 −m1/2 plane in Figs. 1 and 2 for different values
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4 A.V.Gladyshev, D.I.Kazakov, M.G.Paucar
200 400 600 800 1000 1200
 m0[GeV]
   h0  mass LEP limits
= - 2500 [GeV]
 t® °
t c1®
~t® c
1t® b
~t NLSP
400 800 1200 1600
[GeV]
~t® c
1t® b
   h0  mass LEP limits
= - 3500 [GeV]
~t NLSP
t c1®
Fig. 2. Allowed region of the mSUGRA parameter space for −2500,−3500 GeV and tan β = 10.
At the left from the border stau is an LSP, below the border stop is the LSP. The dotted line is
the LEP Higgs mass limit. Also shown are the contours where various stop decay modes emerge.
of A and fixed tanβ. To calculate it we use the ISAJET v.7.64 code 36.
One can see that when |A| decreases the border line moves down and finally
disappears. On the contrary, increasing |A| one gets larger forbidden area and the
value of the stop mass at the border increases.
Changing tanβ one does not influence the stop border line, the only effect is the
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Light Stops in the MSSM Parameter Space 5
300 600 900 1200 1500
[GeV]
              m
= 172.7  [GeV]
              A
= -3500  [GeV]
                 Tanb=10  
                 Tanb=20
                 Tanb=30
                 Tanb=40
Fig. 3. Stau and stop constraints in the m0 − m1/2 plane for A0 = −3500 GeV and different
values of tanβ.
shift of stau border line. It moves to the right with increase of tanβ as shown in
Fig.3, so that the whole forbidden area increases and covers the left bottom corner
of the m0 −m1/2 plane.
It should be mentioned that the region near the border line is very sensitive to
the SM parameters, a minor shift in αs or mt and mb leads to noticeable change of
spectrum as can be seen from comparison of different codes at 37,38,39.
The other constraint that is of interest in this region is the relic density one.
Given the amount of the Dark matter from WMAP experiment 40,41 one is left
with a narrow band of allowed region which goes along the stau border line, then
along the Higgs limit line and then along the radiative symmetry breaking line.
In the case of light stop when it is almost degenerate with the lightest chargino
and neutralino, when calculating the relic density one has to take into account
not only the annihilation of two stops, but also the coannihilation diagrams. There
are two side processes: stop chargino annihilation and stop neutralino annihilation.
Calculating the relic density with the help of MicrOmegas package 42,43 one finds
that again it is very sensitive to the input parameters, however, since the stop
border line is very close to the Higgs one, the relic density constraint may be met
here fitting A and/or tanβ.
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6 A.V.Gladyshev, D.I.Kazakov, M.G.Paucar
3. Phenomenological Consequences of the Light Stop Scenario
The phenomenology of the discussed scenario is of great interest at the moment
since the first physics results of the coming LHC are expected in the nearest future.
Light stops could be produced already during first months of its operation 44,45.
The main diagrams of pair stop production (as well as other type of squarks) are
presented in Fig. 4. A single stop production via weak interactions is also possible.
Fig. 4. Main stop production diagrams at LHC.
Since stops are relatively light in our scenario, the production cross sections are
quite large and may achieve tens or even hundreds of pb for mt̃ < 150 GeV. The
cross sections and their dependence on the stop mass for different values of |A| are
shown in Fig. 5. As one expects they quickly fall down when the mass of stop is
increased. The range of each curve corresponds to the region in the (m0 − m1/2)
plane where the light stop is the next-to-lightest SUSY particle, and the Higgs
and chargino mass limits are satisfied as well. One may notice, that even for very
large values of |A| when stops become heavier than several hundreds GeV, the cross
sections are of order of few per cent of pb, which is still enough for detection with
the high LHC luminosity.
Being created the stop decay. There are several different decay modes depending
on the stop mass. If stop is heavy enough it decays to the bottom quark and the light-
est chargino (t̃ → bχ̃±
). However, for large values of |A0|, namely A0 < −1500 GeV
the region where this decay takes place is getting smaller and even disappear due
to mass inequality mt̃ < mb + mχ̃±
(see right bottom corner in Fig. 2). In this
case the dominant decay mode is the decay to the top quark and the lightest neu-
tralino (t̃ → tχ̃01). Light stop decays to the charm quark and the lightest neutralino
(t̃ → cχ̃0
) 46. The latter decay, though it is loop-suppressed, has the branching
ratio 100 %.
In Fig. 6 we show different allowed decay modes for different values of |A0| =
800, 1500, 2500, 3500 GeV as functions of the m1/2 parameter. The values of m0
were chosen in the middle of allowed regions in Figs 1 and 2, namely m0 =
250, 450, 650, 1000 GeV. One can see that for small values of m1/2 we are very close
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Light Stops in the MSSM Parameter Space 7
200 400 600 800 1000 1200
[GeV]
                 m>0
=  -800    [GeV]
= -1500   [GeV]
= -2500   [GeV]
= -3500   [GeV]
Fig. 5. Cross sections of the pair stop production as a function of the stop mass. Different curves
correspond to different values of A0 parameter (A0 = −800,−1500,−2500,−3500 GeV).
to the neutralino–stop border line and the only allowed decay mode is t̃ → cχ̃01. With
the increase of the m1/2 the stop mass becomes larger which opens the possibility
of new decay modes (t̃ → bχ̃±
, and later t̃ → tχ̃0
The bottom part of Fig. 6 shows the stop lifetimes for different values of |A0|. The
biggest lifetime corresponds to the t̃ → cχ̃0
decay. Breaks on the curves correspond
to switching on the new decay mode. As one can see the lifetime cold be quite large
in a wide area of the A0−m1/2 parameter space, even for heavy stops if |A0| is very
4. Conclusion
In this letter we have demonstrated that there is a possibility of stop next-to-lightest
supersymmetric particle. For large negative values of the trilinear soft supersym-
metry breaking parameter A0 there exist a narrow band along the line mt̃ = mχ̃0
in the m0 − m1/2 plane where the cross section of stop pair production is quite
large at the LHC energy and stops have relatively large lifetime. This may give
interesting signatures, like secondary vertices inside the detector, or even escaping
the detector. Another interesting possibility is a formation of so-called R-hadrons
(bound states of supersymmetric particles). This may happen if stops live longer
than hadronisation time.
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8 A.V.Gladyshev, D.I.Kazakov, M.G.Paucar
-4000 -3000 -2000 -1000
1/2  [G
 t ~ [1x10-13, 1x10-18, 1x10-25]  [sec]
 t ~ [1x10-18, 1x10-24]               [sec]
 t ~ [1x10-24, 1x10-25]               [sec]
LSP~t
~t® c
t c1®
1t® b
250 500 750 1000 2500
=  -800  [Gev]
= -1500 [Gev]
= -2500 [Gev]
= -3500 [Gev]
 [GeV]
1X10-13
1X10-15
1X10-17
1X10-19
1X10-21
1X10-23
Fig. 6. Different decay modes of stops and corresponding lifetimes.
Experimental Higgs and chargino mass limits as well as WMAP relic density
limit can be easily satisfied in our scenario. However, the strong fine-tuning is re-
quired. Moreover, it is worth mentioning that light stops are favoured by the baryon
asymmetry of the Universe.
October 30, 2018 14:33 WSPC/INSTRUCTION FILE lightstops˙mpla
Light Stops in the MSSM Parameter Space 9
Acknowledgements
Financial support from RFBR grant # 05-02-17603 and grant of the Ministry of
Education and Science of the Russian Federation # 5362.2006.2 is kindly acknowl-
edged.
References
1. H.P. Nilles, Phys. Rept. 110, 1 (1984).
2. H.E. Haber and G.L. Kane, Phys. Rept. 117, 75 (1985).
3. H.E. Haber, Introductory Low-Energy Supersymmetry, Lectures given at TASI 1992,
(SCIPP 92/33, 1993), hep-ph/9306207.
4. D.I. Kazakov, Beyond the Standard Model, Lectures at the European School of High-
Energy Physics 2004, hep-ph/0411064.
5. A.V. Gladyshev and D.I. Kazakov, Yadernaya Fizika 70, No.7, 1 (2007).
6. A.V. Gladyshev and D.I. Kazakov, Supersymmetry and LHC, Lectures given at 9th
International Moscow School of Physics and 34th ITEP Winter School of Physics,
hep-ph/0606288
7. L.E. Ibáñez and G.G. Ross, Nucl. Phys. B 368, 3 (1992).
8. G.G. Ross and R.G. Roberts, Nucl. Phys. B 377, 571 (1992).
9. S. Kelley, J.L. Lopez and D.V. Nanopoulos, Phys. Lett. B 274, 387 (1992).
10. V. Barger, M.S. Berger, P. Ohmann and R. Phillips, Phys. Lett. B 314, 351 (1993).
11. V. Barger, M.S. Berger and P. Ohmann, Phys. Rev. D 49, 4908 (1994).
12. P. Langacker and N. Polonsky, Phys. Rev. D 49, 1454 (1994).
13. W. de Boer, R. Ehret and D.I. Kazakov, Z. Phys. C 67 647 (1995).
14. W. de Boer et al., Z. Phys. C 71, 415 (1996).
15. M. Battaglia et al., Post-LEP CMSSM benchmarks for supersymmetry,
hep-ph/0112013.
16. N. Ghodbane and H.-U. Martyn, Compilation of SUSY particle spectra from Snow-
mass 2001 benchmark models, hep-ph/0201233.
17. M. Battaglia, A. De Roeck, J. Ellis, F. Gianotti, K.A. Olive and L. Pape, Eur. Phys.
J. C 33, 273 (2004).
18. J. Ellis, S. Heinemeyer, K.A. Olive, G. Weiglein, JHEP 0605, 005 (2006).
19. A.V. Gladyshev, D.I. Kazakov and M.G. Paucar, Mod. Phys. Lett. A 20, 3085 (2005).
20. G.W. Bennett et al., Phys. Rev. Lett. 92, 161802 (2004).
21. M. Davier, S. Eidelman, A. Hocker and Z. Zhang, Eur. Phys. J. C 31, 503 (2003).
22. K. Hagiwara, A.D. Martin, D. Nomura and T.Teubner, Phys. Rev. D 69, 093003
(2004).
23. J.F. de Troconiz and F.J. Yndurain, Phys. Rev. D 71, 073008 (2005).
24. K. Melnikov and A. Vainshtein, Phys. Rev. D 70, 113006 (2004).
25. M. Passera, J. Phys. G 31, R75 (2005).
26. W. de Boer, M.Huber, C.Sander and D.I. Kazakov, Phys. Lett. B 515, 283 (2001).
27. W. de Boer, M. Huber, C. Sander, A.V. Gladyshev and D.I. Kazakov, A global
fit to the anomalous magnetic moment, b → Xsγ and Higgs limits in the con-
strained MSSM, in Supersymmetry and unification of fundamental interactions: Pro-
ceedings, eds. D.I. Kazakov and A.V. Gladyshev (World Scientific, 2002), p. 196,
hep-ph/0109131.
28. J.R. Ellis, S. Kelley and D.V. Nanopoulos, Phys. Lett. B 260, 131 (1991).
29. U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B 260, 447 (1991).
30. C. Giunti, C.W. Kim and U.W. Lee, Mod. Phys. Lett. A 6, 1745 (1991).
October 30, 2018 14:33 WSPC/INSTRUCTION FILE lightstops˙mpla
10 A.V.Gladyshev, D.I.Kazakov, M.G.Paucar
31. J.R. Ellis et al., Nucl. Phys. B 238, 453 (1984).
32. G. Jungman, M. Kamionkowski and K. Griest, Phys. Rep. 267, 195 (1996).
33. LEP Higgs Working Group for Higgs boson searches, OPAL Collaboration, ALEPH
Collaboration, DELPHI Collaboration and L3 Collaboration, Search for the Standard
Model Higgs Boson at LEP, CERN-EP/2003-011, hep-ex/0306033.
34. Joint LEP2 SUSY Working Group, Combined LEP Chargino Results up to 208 GeV,
http://lepsusy.web.cern.ch/lepsusy/www/inos_moriond01/charginos_pub.html
35. Combined LEP Selectron/Smuon/Stau Results, 183-208 GeV,
http://lepsusy.web.cern.ch/lepsusy/www/sleptons_summer02/slep_2002.html
36. H. Baer, F. Paige, S.D. Protopescu and X. Tata, ISAJET 7.69. A Monte Carlo Event
Generator for pp, pp̄ and e+, e− reactions, hep-ph/0312045.
37. G. Belanger, S. Kraml, A. Pukhov, hep-ph/0502079.
38. B.C. Allanach, S. Kraml, W. Porod, JHEP 03, 016(2003).
39. http://cern.ch/kraml/comparison/
40. C.L. Bennett et al., Astrophys. J. Suppl. 148, 1 (2003).
41. D.N. Spergel et al., Astrophys. J. Suppl. 148, 175 (2003).
42. G. Belanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs: Version 1.3,
hep-ph/0405253.
43. G. Belanger, F. Boudjema, A. Pukhov and A. Semenov, Comput. Phys. Commun.
149, 103 (2002).
44. B.C. Allanach et al., Les Houches physics at TeV colliders 2005 beyond the standard
model working group: Summary report, hep-ph/0602198.
45. A.M. Abazov et al., Phys. Lett. B 645, 119 (2007). [hep-ex/0611003]
46. K. Hikasa and M. Kobayashi, Phys. Rev. D 36, 724 (1987).
http://arxiv.org/abs/hep-ex/0611003
