Resonant Higgs pair production as a probe of stop at the LHC
Received: June
Resonant Higgs pair production as a probe of stop at
Guang Hua Duan 0 1 2 3 6 8 9 10
Lei Wu 0 1 3 5 7 8 9 10
Rui Zheng 0 1 3 4 8 9 10
0 Davis , CA, 95616 U.S.A
1 Beijing , 100049 China
2 School of Physical Sciences, University of Chinese Academy of Sciences
3 Beijing , 100190 China
4 Department of Physics, University of California , USA
5 ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics
6 Institute of Theoretical Physics, Chinese Academy of Sciences
7 Department of Physics and Institute of Theoretical Physics, Nanjing Normal University
8 nal states. In the region of stop
9 The University of Sydney , New South Wales, 2006 Australia
10 Nanjing , Jiangsu, 210023 China
Searching for top squark (stop) is a crucial task of the LHC. When the avor conserving two body decays of the stop are kinematically forbidden, the stops produced near the threshold will live long enough to form bound states which subsequently decay through annihilation into the Standard Model (SM) mixing angle t~ ! 0 or =2, we note that the LHC13 TeV diphoton resonance data can give a strong bound on the spin0 stoponium ( t~) and exclude the constituent stop mass m~ t up to about 290 GeV. While in the large stop mixing region, the stoponium will dominantly signi cance level at the LHC with the luminosity L = 3000 fb 1. decay to the Higgs pair. By analyzing the process pp ! t~ ! h(! bb)h(! that a large portion of the parameter space on the mt~1 { t~ plane can be probed at 2
Supersymmetry Phenomenology

ArXiv ePrint: 1706.07562
1 Introduction
2 Diphoton resonance constraint on the stoponium
3 DiHiggs decay of stoponium with bb +
nal states at the LHC
4 Conclusions
1
Introduction
mass splitting which leads to di erent decay modes. For instance, when mt~1 > mt + m~01
and t~1 mainly decays to t ~01, the top quark from stop decay can be quite energetic and
a stop mass up to 940 GeV for a massless lightest neutralino has been excluded by the
very recent LHC run2 data [17]. When the
avorconserving two body decays channels
the light stop would be the threebody decay t~1 ! W +b ~01, the twobody
like t~1 ! t ~01 and t~1 ! b ~1+ are kinematically forbidden, the primary decay channels of
avorchanging
decay t~1 ! c ~01 or the fourbody decay t~1 ! bf 0f ~01 [18{25]. The current null results of
LHC searches for these decay channels have correspondingly excluded the stop mass up
to
500 GeV, 310 GeV and 370 GeV for certain mass splitting between the stop and the
LSP [17].
It should be mentioned that such a light stop usually has very small decay width [26]
compared to the typical binding energy of t~1t~1 bound state (stoponium). In this case,
two stops produced nearthreshold could live long enough to form a stoponium due to the
Coulomblike attraction via the QCD interaction. In contrast to the existing direct stop
pair searches, stoponium if formed, will resonantly decay to a pair of the SM particles and
can be independent of the assumptions of the LSP mass and the branching ratios of the
{ 1 {
stop. Therefore, it is expected that the search of stoponium can provide a complementary
probe to the direct stop pair production at the LHC.
The phenomenologies of the stoponium have been studied at colliders [26{34]. In
particular, the diphoton channel was studied and found to be a promising way to observe
stoponium at the LHC in refs. [26{28]. The diboson decay of stoponium with W W and ZZ
nal states were also examined in [32, 33]. In [35], the authors investigated the diHiggs
decay of stoponium with bb
nal states and found it to be a viable channel at the LHC.
But the loop induced diphoton decay of the Higgs boson can be sizably a ected by other
sparticles, such as the light stau in the MSSM [36].
high mass resonances at 13 TeV LHC. Then we explore the potential of probing the stop
in Higgs pair production with bb +
nal states at highluminosity LHC (HLLHC).
As a comparison with bb
channel, although the bb +
channel su ers from relatively
complicated backgrounds, it has a larger branching ratio. Besides, it is expected that the
reconstruction e ciency of
can reach
80% with the likelihood
taggers in the future
LHC experiment [
37, 38
]. This will make bb +
channel become another promising way of
discovering, or con rming the stoponium at the LHC. The paper is organized as follows. In
section 2, we introduce productions and decays of the stoponium and display the limits on
stoponium mass from the LHC13 TeV data. In section 3, we investigate the observability
of the diHiggs decay of the stoponium with bb
nal states at the LHC. Finally, we
draw our conclusions in section 4.
In this paper, we rst confront the stoponium with the recent data of searching for
mtXty 1
A
mt2~L = m2Q~3L
+ mt2 + m2Z
sin2
W
cos 2 ;
mt2~R = m2U~3R
Xt = At
cot ;
2
3
+ mt2 +
m2Z sin2
W cos 2 ;
1
2
+
tR
2
3
(2.1)
(2.2)
(2.3)
(2.4)
(2.5)
where mQ~3L
and mU~3R denote the softbreaking mass parameters of the third generation
lefthanded squark doublet Q~3L and the righthanded stop U~3R, respectively. At is the
softbreaking trilinear parameter. We neglect the generation mixing in our study. The
hermitian matrix eq. (2.1) can be diagonalized by a unitary transformation:
t~1 !
~
t2
=
cos t~ sin t~
sin t~ cos t~
!
tL
~ !
~
tR
;
{ 2 {
where t~ 2 [0; ) is the mixing angle between lefthanded (t~L) and righthanded (t~R) stops.
A very narrow decay width of stop1 can naturally appear in the compressed region, in
which the decay width of stop is suppressed either by phase space or loop factor. If the
t~1 is much smaller than binding energy, stop pair produced near the threshold could form
a bound state due to the strong attractive force mediated by gluons. Then, these bound
states will proceed annihilation decay rather than the prompt decay of the constituent stop.
The production of stoponium is mainly from the gluon fusion at the LHC. In
narrowwidth approximation, the leading order (LO) cross section of stoponium is be given by [26]
(gg ! t~) =
2
8m3~
t
s^ Z 1 d x
t~!gg s s^ x
s
fg(x)fg
s^
xs
(2.6)
where s^ is squared centerofmass energy at the parton level and is taken as s^ = m2~ in
t
our calculation.
~t~!gg is the width of stoponium decay to digluon. The nexttoleading
order QCD radiative corrections to stoponium production have been calculated in [40]. We
include these e ects by using the values of Kfactor given in [41].
It should be noted that there are two main uncertainties in the computation of
stoponium production rate. One of them lies in the parametrization of the wavefunction, which
depends on the choice of QCD scale parameter
[42]. Larger value of
leads to greater
coupling and hence stronger binding between the constituent stops. We adopt
= 300 MeV
by following [41]. The other uncertainty comes from the contributions of excited bound
states, such as nS(n
2) and 1P states. In particular, the e ects of higher Swave states
are compared in [41]. The excited states can contribute by either rst decaying into the
lowest stoponium state (1S) or decaying directly into SM
nal states. For instance, the
nonannihilation decay of the 2S state could go entirely to the 1S state and the signal
could be merged with that of the ground state due to the detector energy resolution [26].
In general, states with di erent angular momentum could have very distinct decay modes.
Without thorough knowledge of the decay modes, we will take a conservative approach and
focus on the 1S state.
The main decay channels of the stoponium include t~ !
The LO partial decay widths into transverse gauge bosons are [26]
; Z; ZZ; W W; gg; hh; tt.
( t~ ! gg) ' 3 S
4 2 jR(0)j2 ;
m2~
t
( t~ !
) ' 27
32 2 jR(0)j2
m2~
t
where R(0) = p
4
(0) is the radial wavefunction at the origin. In the nonrelativistic limit
(v ! 0), only fourpoint interaction contributes to the stoponium decays t~ ! gg;
other decay widths can be found in [27, 33]. Radiative corrections to stoponium annihilation
decays to hadrons, photons, and Higgs bosons were calculated in ref. [43].
In
gure 1, we display the decay branching ratios of the stoponium with respect to
the mixing angle t~, where we assume tan
= 10, mt~1 = 0:2 TeV and mt~2 = 2 TeV. It can
be seen that the stoponium dominantly decays to digluon when the mixing angle t~
approaches 0 or =2. While if t~L and t~R have a sizable mixing, the stoponium will dominantly
1If the stop has a large decay width, it could in general produce a wide resonance signal and will be
hardly observed on top of the continuum background [39].
{ 3 {
(2.7)
. All
0.100
∼ t
gg
γγ
Zγ
WW
ZZ
hh
tt
HJEP09(217)3
0.0
0.1
0.4
0.5
0.2
0.3
=2, we plot only the region t~ 2 [0; =2] here and also in gure 5.
decay to a pair of Higgs bosons because of the enhancement induced by the Higgsstop
coupling
ht~1t~1 .2 We also checked and found that branching ratios of the stoponium have a
weak dependence of tan . So we will assume tan
= 10 in our following calculations. Due
to the distinctive signature of two photon
nal states, the stoponium decay to diphoton
o ers a very sensitive way to observing stoponium at hadron colliders.
The bound on stoponium from 8 TeV run at the LHC is given in [44]. In gure 2, we
update the result with the LHC13 TeV diphoton resonance data [45]. We can see that
the stoponium mass can be excluded up to about 580 GeV for the mixing angles t~ =
=2,
which is stronger than that from LHC13 TeV direct searches for the fourbody decay
~
t1 ! bf 0f ~01 with pure bino LSP in the region of mt~1
m ~01 < 15 GeV [17]. However, due
to the branching ratio suppression e ect, there is still no constraint on the stoponium from
the diphoton data for the mixing angles t~ =
=8; =4. We also checked the bounds on the
stoponium from current null results of LHC searches for Z
and diboson resonances and
found that they can not give stronger limits than the diphoton data.
3
DiHiggs decay of stoponium with bb +
nal states at the LHC
Given that the stoponium can have a large branching fraction into the two Higgs bosons, we
will investigate its observability through the resonant Higgs pair production with bb +
nal states at the 14 TeV LHC,
pp ! t~ ! hh ! bb +
;
(3.1)
mv2t2 + m2Zc2 ct2 12
v2
23 s2W + st2 23 s2W
+ st2ct2 m2~
t1
v2
mt2~2 .
2The trilinear coupling between the SM Higgs and stop quark t~1 takes the form [44]: ht~1t~1 = p2v
{ 4 {
0.01
ATLAS, s =13 TeV, 36.9 fb1
θ∼t=0
mη∼t [GeV]
2 experimental upper limit (yellow band) is taken from [45]. Here we also assumed tan
where one tau lepton decays hadronically ( had) and the other decays leptonically. had is
reconstructed using clusters in the electromagnetic and hadronic calorimeters with medium
We generate partonlevel events of the stoponium production and subsequent
decay into Higgs pair using the code for resonant Higgs pair production [47] within
lepton decays are modeled by TAUOLA [49]. Then we
perform parton shower and hadronization with PYTHIA [50]. The fast detector simulation
is implemented with Delphes [51]. We use the bjet tagging e ciency parametrization as
80% [52] and set the misidenti cation 10% and 1% for cjets and light jets, respectively.
We also assume the
tagging e ciency is 40%. We set the renormalization scale
R and
factorization scale F as the default eventbyevent value. We cluster the jets by choosing
the antikt algorithm with a cone radius
R = 0:4 [53]. The major backgrounds come
from events with a jet misidenti ed as had, including tt, Z(!
+
)bb and Z(!
+
)jj
processes.
In gure 3, we present distributions of the ditau invariant mass m , two bjets
invaristruct m
from the observed lepton, had and Emiss. One can see that m
T
ant mass mbb, the transverse mass of the lepton plus missing energy system m`T and the
ditau transverse momentum pT . The simple transverse mass method is used to
recondistribution
shows a relatively broad peak around the Higgs boson mass with a long tail,3 as a
comparison with mbb distribution. Another variable m`T can e ectively reduce tt background
since the lepton in signal is not from W boson decay. The variable pT is used to select the
events with the boosted Higgs boson candidate on the transverse plane. For such events,
m
resolution is improved and a better separation between the signal t~ !
and the
3This can be improved by using the advanced experimental MMC reconstruction technique [54].
{ 5 {
HJEP09(217)3
transverse mass of the lepton plus missing energy system m`T and the ditau transverse momentum
pT . The stoponium mass is taken as m t~ = 500 GeV.
background Z !
QCD multijet background. is achieved. This selection also has the advantage of reducing the In our analysis, we select events that satisfy the following criteria:
We require exactly one lepton (e or ) with pT (`) > 26 GeV, j ej < 2:47 or j j < 2:5.
We further require the presence of a hadronically decayed tau h carrying opposite
electric charge with pT ( h) > 20 GeV and j h j < 2:5.
We require at least two jets with pT (j) > 30 GeV and j j j < 2:5 and two of them are
b tagged.
We require 80 GeV < mbb < 150 GeV, 80 GeV < m
p
T > 120 GeV and jmbb
m t~j < 0:08m t~.
< 150 GeV, m`T < 50 GeV,
m`T
can suppress Z(!
In table 1, we present a cut ow of cross sections for the signal and backgrounds
at 14 TeV LHC. After the dib jets and ditau invariant mass cuts, we
nd that the cut
< 50 GeV can reduce the tt background by about half. The cut p
> 120 GeV
T
)bb backgrounds by an extra factor of six. The total
{ 6 {
2 [80; 150] GeV
tt
Z( )bb
Z( )jj
signal(m t~ = 500 GeV)
mbb
< 0:08m t~
0.29
s=14TeV, ∫Ldt=3000 fb1, S/ B=5
400
475
550
700
775
850
625
t
m ~(GeV)
signal signi cance S=p
m t~j < 0:08m t~ can further hurt tt background by about O(102)
)bb by about O(10).
nal states needed for the signal signi cance S=pB = 5
In gure 4, we plot the cross sections of the process pp ! t~ ! hh with bb +
at the HLLHC. It can be
=bb
seen that the cross section of the process pp !
about 800 fb/100 fb to reach 5
t~ ! hh ! bb +
=bb
should be
signi cance at m t~ = 400 GeV. When the stoponium is
heavier than about 700 GeV, the required cross section of bb +
channel for a tau tagging
e ciency
= 40% can be comparable with that of bb
channel studied in [35]. If tagging
e ciency can be improved to
80% estimated in [
37, 38
], the sensitivity of bb +
channel
is expected to become better than that of bb
channel for m t~ & 570 GeV.
hh ! bb +
In gure 5, we show the 2
exclusion limits from the diHiggs decay channel t~ !
and the diphoton decay channel t~ !
for mt~2 = 1 TeV and 2 TeV on the
plane of mt~1 versus stop mixing angle t~ at the HLLHC. We can see that the stop mass
mt~1 can be excluded up to
380 (450) GeV in the large stop mixing region =7 . t~ . =3
{ 7 {
m
m
t∼
t∼
2
2
=
=
2
1
θ∼t /π
0.0
for mt~2 = 1 TeV and 2 TeV on the plane of mt~1 versus stop mixing
angle t~ at the HLLHC. The result of diphoton decay channel is taken from ref. [44].
by the diHiggs decay channel t~ ! hh ! bb +
depends on the Higgsstop coupling
, since the branching ratio of t~ ! hh
ht~1t~1 . For a given mixing angle t~, a larger mt~2 sets a
mixing region, such as t~ .
=7 or t~ &
di erence m2~
t1
m2~ . The diphoton decay channel t~ !
t2
stronger bound on mt~1 because the Higgsstop coupling ht~1t~1 is proportional to the mass
=3, which is complementary to the diHiggs decay
mainly excludes small stop
channel.
4
Conclusions
In this paper, we confront the stoponium with the recent data of searching for high mass
resonances at 13 TeV LHC, and explore the potential of probing the stoponium in resonant
Higgs pair production with bb +
nal states at the LHC. We note that the LHC13 TeV
diphoton resonance data can give a strong bound on the spin0 stoponium ( t~) and exclude
the constituent stop mass mt~1 up to about 290 GeV in the small stop mixing region. While
in the large stop mixing region, the stoponium will dominantly decay to Higgs pair. By
analyzing the process pp ! t~ ! h(! bb)h(!
), we nd that the stop mass mt~1 can
+
be excluded up to
380 (450) GeV at the LHC with the luminosity L = 3000 fb 1
.
Acknowledgments
This work was supported by the Australian Research Council, by the National Natural
Science Foundation of China (NNSFC) under grants No. 11305049.
{ 8 {
Open Access.
This article is distributed under the terms of the Creative Commons
Attribution License (CCBY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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