Light Stop in Precision Top Sample

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Light Stop in Precision Top Sample
Xue-Qian Li a , Zong-Guo Si b , Kai Wang c ,
Liucheng Wang
a
b
c,d ∗
, Liangliang Zhang
a,c
, and Guohuai Zhu
c
School of Physics, Nankai University, Tianjin 300071, China
Department of Physics, Shandong University, Jinan, Shandong 250100, China
c
Zhejiang Institute of Modern Physics, Department of Physics,
Zhejiang University, Hangzhou, Zhejiang 310027, China
d
Bartol Research Institute, Department of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA
Abstract
The uncertainty of tt̄ production cross section measurement at LHC is at a-few-percent level which still allows the
stop pair production t̃t̃∗ with identical visible final states 2b + ` + nj + E T . In this paper, we attempt to use the
existing measurement of W polarization in top quark decay to improve the distinction between stop and top quark
states. We apply the ATLAS method of W -polarization measurement in semi-leptonic tt̄ final state to semi-leptonic
stop pair samples and study its prediction. We find that the faked top events from stop mostly contribute to the lefthanded polarized W due to reconstruction and may enhance the FL . The benchmark point with maximal contribution
to top events only changes FL by 1%. After comparing with the current experiments, we conclude that the current
measurement of W -polarization in t decay cannot exclude the light stop scenario with stop mass around top quark
mass.
∗
Electronic address: [email protected]; (Corresponding Author)
I.
INTRODUCTION
The Higgs boson has been discovered by both ATLAS and CMS Collaborations at the Large Hadron
Collider (LHC). The data on the angular correlation in four-lepton channel prefers the boson to be identified
as a CP-even spin zero J = 0+ state [1]. The over-5σ evidence in the four-lepton channel shows that the
boson has a significant coupling to ZZ [1] and is indeed the Higgs boson which is responsible for electroweak
symmetry breaking (EWSB). The combined analysis in the diphoton and four-lepton channels determines the
reconstructed mass to be around 125 GeV [2].
If the Higgs boson is the fundamental scalar, quadratic divergence of the quantum correction to its mass
is a major concern from the theoretical perspective. The low energy supersymmetry (SUSY) provides an
elegant solution to this problem. Therefore it is generally believed that the SUSY theory should be a natural
extension of the Standard Model (SM). But so far, the direct search for SUSY particles is not successful,
one may wonder if the SUSY particles really exist, but hide themselves in some processes or have been
misidentified. In fact, exploring low energy supersymmetric effects is also one of the leading tasks at the
LHC. With the data of 30 fb−1 integrated luminosity, LHC has pushed the limit for the new physics models,
in particular, the models which predict new strongly interacting particles due to their large production rate.
Squarks and gluino of the low energy supersymmetric model suffer from severe constraints of direct searches
at LHC through various processes, for instance, jets plus missing transverse energy nj + E T or jets plus E T
with leptons and etc. In some models the first two generation squark and gluino masses have been pushed as
[3]
Mg̃ > 1.4 TeV, Mq̃ > 1 TeV .
(1)
For the third generation squark, assuming Br(t̃1 → t + χ̃01 ) = 100%, the stop mass between 200 and 610
GeV has been excluded at 95% confidence level for massless χ̃01 , and the stop mass around 500 GeV is
excluded for χ̃01 masses up to 250GeV [4]. If the mass difference between stop and top quark is less than or
comparable with χ̃01 , such a scenario has not yet been excluded by experimental data. Stop in such a mass
range dominantly decays into bottom quark and the lightest chargino χ̃±
1 . Thus a stop pair production may
be misidentified as a SM tt̄ event. The exclusion limit on the stop mass depends on an assumptions about the
0
mass hierarchy of stop, χ̃±
1 and χ̃1 [4, 5].
Actually, due to enormous background from strong interacting quark-gluon scattering at this proton-proton
collider, only final state with certain distinguishable features can be triggered. Typical trigger requires the
final states combined with hard jet possessing a transverse momentum pJT > 120 GeV, isolated leptons (e± ,
µ± ) or photon (γ) passing basic cuts, large missing transverse energy (E T ) or object with secondary vertex
(b-tag). A good example is the leptonic decay of a top quark which consists of a b-tagged jet, isolated
e± or µ± and E T . The trigger requirement also implies that the scenarios with a compressed spectrum
are less constrained. Final states with hard jets and large missing transverse energy correspond to large
mass difference in strongly interacting resonance with certain kinematics. Due to limited phase space in the
compressed spectrum, the multi-body final state decays are typically suppressed while the loop-induced twobody decays often dominate in such cases, for instance, g̃ → g χ̃01 in gluino-bino co-annihilation scenario and
t̃1 → cχ̃01 in stop-bino co-annihilation scenario. These signals with soft jet final states can easily be buried
under the tremendous jet background. Back-to-back kinematics for the pair production of such gluinos or
stops also reduces the missing transverse energy in the final states. Such final states can only be constrained by
requiring additional initial state radiation (ISR) or final state radiation (FSR) jet via mono-jet plus E T search.
Hard isolated leptons require large chargino-neutralino mass difference ∆M = Mχ̃±1 − Mχ̃01 . Although the
masses of Mχ̃±1 and Mχ̃02 have been pushed up to 315 GeV if they decay through gauge bosons to a massless
χ̃01 via direct search of tri-lepton plus E T , the latest bound indeed leaves a corner of Mχ̃±1 ' 150 GeV with
Mχ̃01 ' 100 GeV [6] 1 . On such a mass assumption, a light stop with mass around 190 GeV decaying with
100% branching ratio (BR) to a bottom quark and a chargino survives existing tests [5]. The assumption on
a light stop and decoupled other sfermions seems to be plausible, because the Yukawa coupling of stop is
much larger than other Yukawa couplings, which may affect drastically the renormalization group equations
for the squark masses even if soft masses are the same at some high energy scale. For light stops, it is difficult
to distinguish the events involving them from the enormous top-quark background. At LHC with the central
1
Search of charginos from squark or gluino cascade decay in jets with lepton nj + E T + `± puts stronger bounds on chargino
masses but it’s also model-dependent so we didn’t take it account. Instead, we only take the direct search bounds which is more
independent of model assumptions.
energy 8 TeV, the tt̄ production is
√
σtt̄
s=8 TeV
= 241 ± 2(stat.) ± 31(syst.) ± 9(lumi.) pb,
(2)
which is consistent with the theoretical prediction σttht̄ = 238+22
−24 pb. For 200 GeV stop, its pair production is
only 6 pb at LHC with the central energy 8 TeV. Even for 180 GeV stop, its pair production is around 20 pb,
which is still within the error bar of tt̄ events.
On the other hand, the prompt decay of top quark before hadronization provides an opportunity to explore
its various properties like charge and mass. This feature also makes the precision measurement of top quark
possible. As a consequence of its huge mass mt = 173.2 GeV, precision measurement of top quark plays
an important role in testing the SM dynamics, for instance, the studies on the top-quark forward-backward
asymmetry at Tevatron [7–10]. The precision measurement of weak decay of top quark is also a test of the
Higgs mechanism. Both top quark and weak gauge boson W ± acquire masses from spontaneously EWSB.
In so-called Higgs mechanism, the Goldstone degree of freedom becomes the longitudinal polarization of
W boson, 0 . Since top quark is the heaviest particle from EWSB, top quark couples to the Goldstone
µ
boson more strongly which results in a mt /mW enhancement as 0∗
µ ūb PL γ ut ∝ mt /mW . The W bosons
from top-quark decay can be produced either longitudinal, left-handed or right-handed, with the helicity
fractions F0 , FL and FR respectively. Due to the mt /mW enhancement, one has F0 =
FL =
2
(mt /mW )2 +2
(mt /mW )2
(mt /mW )2 +2
' 70%,
' 30% and FR = 0 in the limit mb = 0. Theoretically, the precision predictions of helicity
fractions are obtained by next-to-next-to-leading order (NNLO) perturbative QCD (pQCD) calculations.
Because of the angular momentum conservation and neutrino being only left-handed, the helicity fractions
F0 , FL and FR can be measured by detecting the moving direction of the lepton from W -boson decay [11–
15]. Experimentally, such precision measurements of helicity fractions require a full reconstruction of W
boson and top quark. Thus only tt̄ events with semileptonic decays are taken into account. The precision
measurement of F0 , FL and FR can test the V−A structure of the W tb vertex, the Higgs mechanism as
well as the NNLO pQCD calculation. If events of light stop pairs exist, they can also contribute to those
measurements, since they can fake the semileptonic tt̄ events. In this paper, we study whether the precision
measurement of W -polarization in top sample can help to distinguish the light stop events, if they do exist,
from the SM tt̄ background.
In our studies, we employ the basic cuts described in [13]. We require the final states of semileptonic tt̄
events to contain an isolated lepton (electron or muon), missing transverse momentum E T and four jets with
following pT requirements:
• pT > 20 GeV for an isolated electron or muon;
• pT > 25 GeV and |η| < 2.5 for every jet.
Stop pair events and tt̄ pairs have very different kinematic features and the events probabilities that pass the
selection cuts are also different. Here, we use the survival probability after cuts to quantize the bounds.
The cut survival probability depends on various factors, for instance, mass difference and polarization of
gauginos. The pT of b-jet or lepton significantly depends on the mass differences Mt̃ − Mχ±1 or Mχ±1 − Mχ01 .
±
Whether lepton is boosted or anti-boosted in the χ±
1 rest frame then depends on the polarization of χ1 which
is determined by the mixing of wino and higgsino as well as the b-Yukawa coupling. However, if the chargino
is produced nearly at rest, which is the case for the scenario we are focusing on, the boost or anti-boost effect
of lepton is minor. In Table I, we list survival probabilities of a few benchmark points 2 . We also simulate the
2
We assume the sleptons are much heavier than chargino to minimize the flavor violation. Therefore, the chargino decay branching
fraction is similar to the BR of the W boson.
Mt̃ (GeV) Mχ± (GeV) Mχ01 (GeV) σt̃t̃∗ · BR (pb)
1
· σt̃t̃∗ · BR · K (pb)
A
150
110
80
8.205
0.06%
0.082
B
160
115
85
5.758
0.82%
0.08
C
170
130
90
4.222
1.35%
0.097
D
180
130
90
3.067
1.76%
0.092
E
190
140
95
2.27
2.49%
0.096
F
200
150
100
1.742
3.13%
0.0927
TABLE I: Survival probabilities after cuts for stop events and cross sections are shown for [email protected] NLO QCD
K-factor is taken to be 1.7.
survival probability for semi-leptonic tt̄ in SM at 8 TeV LHC.
SM
tt̄ = 14.42%
(3)
The benchmark point C with maximal final rate in Table I only corresponds to the effective tt̄ cross section
as
0.097/SM
tt̄ /BR = 2.33 pb,
which is within the uncertainty of cross section measurement.
(4)
W0+
l+
WL+
WR+
ν
l+
ν
ν
l+
FIG. 1: The spin correlations between lepton l+ and W -boson are shown for the left-handed polarized WL+ (left), the
longitudinal polarized W0+ (center) and the right-handed polarized WR+ (right).
This paper is organized as follow. In Section II, we discuss in detail how to measure W -polarization in the
semi-leptonic tt̄ events. Section III is devoted to the light stop scenario with Higgs mass 125GeV. We show
our results and analysis in Section IV and finally conclude with a summary in section V.
II.
MEASUREMENTS OF W POLARIZATION IN THE SEMILEPTONIC tt̄ EVENTS
The W boson from top-quark decay can be produced either longitudinal, left-handed or right-handed, with
the helicity fractions F0 , FL and FR respectively. The sum of the helicity fractions satisfies FL +FR +F0 = 1.
Measurements of these helicity fractions are very important to test the V -A structure of the SM, the Higgs
mechanism, and the NNLO pQCD calculation. Experimentally, helicity fractions are firstly measured by the
CDF and D0 experiments at Fermilab [11]. In the early 7 TeV-8 TeV running of the LHC, precision studies
of W -boson polarization from top-quark decay have also been performed by both the ATLAS and CMS
Collaborations [12–15]. All experiments require to detect the moving direction of the lepton from W -boson
decay [16]. For the ATLAS Collaboration, they define the angle θ∗ between the momentum direction of the
lepton from the W -boson decay and the reversed momentum direction of the bottom quark from top-quark
decay, both boosted into the W -boson rest frame [12–14]. For the CMS Collaboration, they use an equivalent
definition as the angle θ∗ between the three momentum of charged lepton in the W rest frame and the W
momentum in the top rest frame [15]. Because the W boson must be fully reconstructed for each event, only
semi-leptonic tt̄ final state can be taken into account. The spin correlations of the process W + → l+ ν are
shown in Fig. (1) for different polarized W -boson. Because of the angular momentum conservation and
neutrino being only left-handed, the lepton l+ is boosted in the opposite moving direction of left-handed
polarized WL+ . Namely, M(WL+ → l+ ν) ∝ (1 − cos θ∗ )2 . By that analogy, l+ is boosted in the same
moving direction of right-handed polarized WR+ with M(WR+ → l+ ν) ∝ (1 + cos θ∗ )2 . For the longitudinal
polarized W0+ , the lepton l+ is generally moving in the vertical direction with M(W0+ → l+ ν) ∝ sin2 θ∗ .
The normalized decay rate of the process t → W + b, W + → l+ ν can be given as
3
3
3
1 dΓ
= (1 − cos θ∗ )2 FL + (1 + cos θ∗ )2 FR + sin2 θ∗ F0 .
∗
Γ d cos θ
8
8
4
(5)
In SM, the V −A structure of the W tb vertex contributes to the left-handed helicity fraction. The longitudinal
helicity comes from the Goldstone boson component of W boson after EWSB while the right-handed helicity
fraction is suppressed by the mass of bottom-quark mb . In the limit mb = 0 as the leading order, FR is
vanishing with FL =
2
(mt /mW )2 +2
and F0 =
(mt /mW )2
.
(mt /mW )2 +2
So the helicity fractions are approximately 30%
left-handed and 70% longitudinal. Including the finite bottom-quark mass and electroweak effects, NNLO
pQCD predictions for the W-boson helicity fractions are FL = 0.311, FR = 0.0017 and F0 = 0.687 [17].
In order to obtain the distribution of cos θ∗ , we need to reconstruct W boson and top quark in each semileptonic tt̄ event. Four-momentum information of lepton or jet final state is experimentally available. For the
neutrino final state, its px and py component can be fixed by the measured missing transverse momentum in
each semi-leptonic tt̄ event. For the pz component of neutrino, we fix it by using the χ2 method given by the
ATLAS Collaboration [13]. Here the χ2 is defined as
χ2 =
(mlνja − mt )2 (mjb jc jd − mt )2 (mlν − mW )2 (mjc jd − mW )2
+
+
+
,
2
2
σt2
σt2
σW
σW
(6)
with the top-quark mass mt = 172.5 GeV, the W -boson mass mW = 80.4 GeV, the expected top-quark
mass resolution σt = 14 GeV and the expected W -boson mass resolution σW = 10 GeV. Here l denotes the
isolated lepton and ν denotes the neutrino. ja,b,c,d are four different jets in each event. In this paper, we don’t
use any b-tagging information of each jet. mlvja is the invariant mass of the lepton l, the neutrino ν and the
jet ja . By that analogy, mjb jc jd , mlv and mjc jd are all invariant masses. For each semi-leptonic tt̄ event, we
scan the pz of neutrino from -3.5 TeV to 3.5 TeV and make ja,b,c,d correspond to all possible combinations
of four jets. By minimizing the χ2 , we obtain the correct pz component of neutrino [13]. Moreover, we can
distinguish one b-jet, which accompanies with a leptonic W -boson, from other jets. So each semi-leptonic tt̄
event can be fully reconstructed via this best pairing. No event is rejected according to this χ2 method. cos θ∗
can be analyzed event by event.
Then the exact values of FL , FR and F0 are determined with angular asymmetries. By counting events,
one can always define an angular asymmetry as
AZ =
N (cos θ∗ > z) − N (cos θ∗ < z)
N (cos θ∗ > z) + N (cos θ∗ < z)
(7)
with −1 ≤ z ≤ 1. The most obvious choice is z = 0, which leads to the well-known forward-backward
(FB) asymmetry AFB . When we integrate cos θ∗ out in Eq. (5), AFB depends only on FL and FR as AFB =
3
(FR
4
− FL ). Two additional choices of angular asymmetries can be conveniently defined by choosing z+ =
−(22/3 − 1) and z− = 22/3 − 1. Integrated cos θ∗ out in Eq. (5), one has A+ = 3β[F0 + (1 + β)FR ] and
A− = −3β[F0 + (1 + β)FL ] with β = 21/3 − 1. Using AFB , A+ and A− as input under the constraint
FL + FR + F0 = 1, the helicity fractions of W -boson from top-quark decay can be obtained as


1
+ −βA−

FL = 1−β
−A
,

3β(1−β 2 )


1
− −βA+
FR = 1−β
+A
,
3β(1−β 2 )




F = − 1+β + A+ −A− .
0
1−β
3β(1−β)
III.
(8)
LIGHT STOP AND 125 GEV HIGGS BOSON
In the decoupling MSSM limit, the 125 GeV new particle can be identified as the lightest CP-even Higgs
boson h. At tree level, the Higgs mass of h is determined as m2h = m2Z cos2 2β. The dominating loop
contribution comes from the top/stop sector. If the splitting of the stop masses is relatively small, the mass of
h up to 1-loop precision is [18]
"
4
3m
M2
Ã2t
m2h ' m2Z cos2 2β + 2 t 2 log SUSY
+
2
4π v
m2t
MSUSY
Ã2t
1−
2
12MSUSY
!#
,
(9)
2
with EWSB vacuum expectation values (VEV) v = 174 GeV, the averaged stop mass square MSUSY
=
mt̃1 mt̃2 . Here Ãt = At − µ cot β with tan β the ratio of the VEVs of the two Higgs fields which lead
to EWSB, At the trilinear squark coupling which breaks the R-symmetry, and µ Higgsino mass parameter,
respectively. The term
Ã2t
2
MSUSY
1−
Ã2t
2
12MSUSY
2
reaches its maximum when Ã2t /MSUSY
= 6 , which corresponds
to the maximal Higgs mass scenario. In order to predict mh =125 GeV in the MSSM, a large Ãt is necessary
for moderate light stops [19–27]. In the meantime, the stop mass matrix is


2
2
t
m + mt + DL
mt Ãt
.
M2t̃ =  t̃L
t
2
2
mt Ãt
mt̃R + mt + DR
(10)
Here mt̃L and mt̃R are the left-handed and right-handed soft SUSY breaking stop masses. The D terms,
in units of MZ2 cos 2β, are given in terms of the weak isospin and electric charge of the stop by: DLt =
t
It3 − et sin2 θW and DR
= et sin2 θW . This stop mass matrix can be diagonalized by a unitary matrix to give
mass eigenstates t̃1 and t̃2 . For moderate mt̃L and mt̃R , Ãt ought to be large to predict mh =125 GeV. Such a
large off-diagonal term mt Ãt would lead to a big splitting of stop masses. So the scenario with a light t̃1 is
possible and t̃1 should be around 50% of t̃L and 50% of t̃R . These features are maintained in NMSSM with a
small λ but changed in NMSSM with a large λ. This is because m2h = m2Z cos2 2β + λ2 v 2 sin 2β at tree-level
in NMSSM. Here the second term λ2 v 2 sin 2β originates from the interaction λHu Hd S in the superpotential,
where S is the singlet in NMSSM. Due to the extra contribution λ2 v 2 sin 2β to Higgs mass at tree level, it
would be easier to realize a 125 GeV Higgs boson in NMSSM [28, 29]. A large Ãt may not be necessary.
The light mass eigenstate t̃1 may be pure t̃L or pure t̃R in NMSSM.
0
As argued in the previous section, the scenario with mt̃1 = 200 GeV, χ̃±
1 = 150 GeV and χ̃1 = 100 GeV
has not yet been excluded by existing experimental data. In this case, t̃1 decays totally into bottom-quark and
chargino. The polarization of chargino from stop decay has been recently discussed in [30]. In the MSSM,
the relevant Lagrangians involving t̃1 → bχ̃+
1 are following [31]
Lbt̃χ̃+1 = {[−gV11 t̃L + yt V12 t̃R ]b̄PR + yb U12 t̃L b̄PL }χ̃+c
1 .
(11)
Here Uij (Vij ) are the neutralino (chargino) mixing matrices and yt (yb ) is the top (bottom) Yukawa coupling.
The mass eigenstate χ̃+
1 is combined by wino and higgsino, which is determined by the wino parameter M2
and the higgsino parameter µ. In Eq. (11), the wino component of χ̃+
1 contributes to the first term while the
higgsino component contributes to two other terms. In the rest frame of stop, χ̃+
1 and the bottom-quark are
produced back to back. If the chargino is pure wino-like, the t̃L component of t̃1 decays into χ̃+
1 via the first
term of Eq. (11). In this case χ̃+
1 is always in the left-handed helicity eigenstate since this wino-stop-bottom
vertex is corresponding to the weak interaction. Left-hand χ̃+
1 means that the spin is opposite to the direction
of its motion. If chargino has a siginificant higgsino component, the t̃R component of t̃1 may decay into
+
left-handed χ̃+
1 via the second term of Eq. (11). χ̃1 from stop decay can be right-handed via the third term of
Eq. (11), which can be significantly enhanced by a large bottom Yukawa coupling yb . Comparing to the top
Yukawa coupling yt , yb can be significantly enhanced by a large tan β as
yb
yt
=
√mb / √mt
2vd
2vu
=
mb
mt
tan β
Similar to the process t → W + b, W + → l+ ν, there exists some spin correlation between lepton and
+
0 +
chargino for the cascade decay t̃1 → bχ̃+
1 , χ̃1 → χ̃1 l ν. But for this case, the correlation is more complex due
to chargino three-body decay mediated by slepton exchange and W-boson exchange. The angular distribution
M2 >> µ
number of events
number of events
M2 << µ
3500
3000
2500
2500
2000
1500
2000
1500
1000
1000
500
500
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
cosθ*
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
cosθ*
FIG. 2: At parton level, the chargino χ̃+
1 can be fully reconstructed since all information of neutralino, lepton and
neutrino is known. We show the cos θ∗ distribution in the χ̃+
1 rest frame. Left: Assuming M2 µ, the chargino is
wino-like. The cos θ∗ distribution peaks at θ = π since the chargino from stop decay is mainly left-handed. Right:
Assuming µ M2 with a large tan β, the chargino is higgsino-like as well as a large bottom Yukawa coupling yb . So
the right-handed helicity of the chargino is significant.
of the lepton from chargino decay can be used to partially probe the chargino polarization [32]. We can define
the angle θ∗ between the momentum direction of the lepton from chargino decay and the reversed momentum
direction of bottom quark from stop decay, both boosted into the chargino rest frame. Because of angular
momentum conservation, the distribution of cos θ∗ would in general peak at θ∗ = π for left-handed χ̃+
1 [32].
∗
∗
If χ̃+
1 is totally in the right-handed helicity eigenstate, the distribution of cos θ should peak at θ = 0. To
illustrate this feature, we consider two extreme cases in this paper. One is under the assumption M2 µ,
+
which leads to a nearly wino-like χ̃+
1 . In this case χ̃1 from stop decay is always in the left-handed helicity.
The other case bases on the assumption M2 µ as well as a large tan β. So the right-handed helicity of
0
the chargino is significant. In both cases, we assume mt̃1 = 200 GeV, χ̃±
1 = 150 GeV, χ̃1 = 100 GeV and
all masses of sleptons around 1TeV. We use the code Madgraph5 [33] to simulate the whole process. At
parton level, the chargino can be fully reconstructed since all information of neutralino, lepton and neutrino
is known. So the cos θ∗ distribution can be exactly obtained in the chargino rest frame at parton level. In Fig.
(2), we show the cos θ∗ distribution under two different assumptions. We find that the right-handed helicity
of χ̃+
1 can be significant if the lightest chargino is higgsino-like as well as a large tan β. For W -boson from
top-quark decay, the right-hand helicity fraction FR is approximately vanishing and is severely constrained
by experimental data. So in this paper, we would like to study whether such a right-hand helicity structure of
χ̃+
1 from stop decay can help to distinguish the light stop events from the SM top-quark events.
M2 >> µ
number of events
number of events
M2 << µ
10000
8000
6000
9000
8000
7000
6000
5000
4000
4000
3000
2000
2000
1000
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
cosθ*
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
cosθ*
FIG. 3: Left: M2 µ. Right: µ M2 with a large tan β. The cos θ∗ distribution of stop events are given in the fake
W -boson rest frame after χ2 combination. Both figures are shown at the parton level. The results after pythia and pgs
will be similar to the parton level results.
IV.
RESULTS AND ANALYSIS
Experimentally, we don’t even know there exists chargino from stop decay. The final states from a semileptonic decay of t̃1 t̃∗1 are an isolated lepton, missing transverse energy E T , two bottom-quark jets and two
light-quark jets. With identical final states, t̃1 t̃∗1 events will be mis-identified as the SM top events. So the
cos θ∗ distribution in the χ̃+
1 rest frame, as shown in Fig. (2), cannot be experimentally measured. The ATLAS
method of W -polarization measurement in semi-leptonic tt̄ final state will be applied to semi-leptonic stop
pair samples. We would like to study this prediction of t̃1 t̃∗1 . Firstly, the ATLAS χ2 method will lead to
a fake pZ component of neutrino momentum. For each t̃1 t̃∗1 event, the fake pZ may be far from the real
value since the lightest neutralino χ̃01 also contributes to missing transverse energy E T . Secondly, the χ2
method inevitably results in a fake W -boson rest frame for each t̃1 t̃∗1 event. The cos θ∗ distribution can only
be obtained in such a fake W -boson rest frame. Lastly, for some t̃1 t̃∗1 events, a fake leptonic-branch b-jet may
be picked out of the four jets by minimizing the χ2 . If so, the reversed momentum direction of the bottom
quark, which accompanies with a leptonic W boson, is incorrect. This wrong momentum also leads to a
fake cos θ∗ . In fig. (3), we show the cos θ∗ distribution of stop events in fake W -boson rest frame after χ2
method. The left figure is corresponding to the assumption M2 µ while the right figure is corresponding
to the assumption µ M2 with a large tan β. Both cos θ∗ distributions peak at θ∗ = π. These behaviors are
generally corresponding to left-handed helicity states. Since the W boson from top-quark decay is roughly
30% left-handed, it seems to be hard to distinguish the light stop event from SM background by analyzing
the polarization.
But we know that the right-handed helicity of the chargino from stop decay is significant under the assumption µ M2 with a large tan β, as shown in the right of fig. (2). In fig. (2), cos θ∗ is defined in the
chargino rest frame in order to probe the polarization of chargino. Unfortunately, it cannot be experimentally
µ >> M
µ << M
2
number of events
number of events
2
Real mbl
5000
χ2 mbl
4000
5000
Real mbl
4000
χ2 mbl
3000
3000
2000
2000
1000
1000
0
0
50
100
150
200
250
0
0
50
100
150
mbl
200
250
mbl
FIG. 4: Left: M2 µ. Right: µ M2 with a large tan β. The blue line is Mbl in the real combination while the red
line is Mbl after χ2 combination. All results about stop events are shown at the parton level.
measured. When the χ2 method of W -polarization measurement in semi-leptonic tt̄ final state is applied to
semi-leptonic stop pair events, cos θ∗ can only be defined in the W -boson rest frame. In the right of fig. (3),
the right-handed component seems disappeared. To understand the cos θ∗ distribution, we focus on a general
defination of angle θ∗ , which is between the momentum direction of the lepton and the reversed momentum
·~
pb
direction of the bottom quark, both boosted into a specific chosen frame. Thus cos θ∗ = − |~pp~ll||~
, where the
pb |
momentum p~l and p~b depend on the chosen frame. Since the lepton and bottom quark are approximately
massless, we rewrite cos θ∗ as
El · Eb − p~l · p~b − El · Eb
p l · pb
=
−1
|~
pl | |~
pb |
|~
pl | |~
pb |
Mlb2
− 1.
=
2El Eb
cos θ∗ =
(12)
Here Mlb is the invariant mass of the lepton and bottom quark. El (Eb ) is the energy of lepton (bottom quark),
which depends on the chosen frame. For stop events in the chargino rest frame, Eb =
m2t̃ −m2 +
χ̃1
1
2mχ̃+
is fixed due
1
to energy-momentum conservation. In order to understand the fake polarization, we show Mbl , El and Eb of
the stop events in Fig. (4), Fig. (5) and Fig. (6), respectively.
In Fig. (4), the blue line is Mbl in the real combination while the red line is Mbl after χ2 combination. Since
Mbl is Lorentz invariant, it is independent of the chosen frame. The difference between the real combination
and χ2 combination only originates from the wrong combination of lepton and bottom quark after minimizing
the χ2 . For some t̃1 t̃∗1 events, a fake leptonic-branch b-jet may be picked out of the four jets to get Mbl . Since
we do not use the b-tagging information of four jets in our paper, even a light-quark jet might be faked as
the leptonic-branch b-jet. To reduce the events with the wrong combination, we suggest to use b-tagging in
the χ2 reconstruction. However, from Fig. (4) we know that the distributions of real and fake Mbl of stop
events are similar. In Fig. (5), we show the distribution of El from the light stop events. The blue line is
El boosted into the real χ̃+
1 rest frame while the red line is El boosted in the fake W -boson rest frame after
χ2 combination. El in the fake W -boson rest frame are generally larger than one in the real χ̃+
1 rest frame.
µ >> M
µ << M
2
12000
number of events
number of events
2
chargino rest frame
10000
fake W rest frame
8000
12000
chargino rest frame
10000
fake W rest frame
8000
6000
6000
4000
4000
2000
2000
0
0
20
40
60
80
100
120
0
0
140
20
40
60
El
80
100
120
140
El
FIG. 5: Left: M2 µ. Right: µ M2 with a large tan β. The blue line is El boosted into the real χ̃+
1 rest frame
while the red line is El boosted into the fake W -boson rest frame after χ2 combination.
Moreover, El in the fake W -boson rest frame roughly peaks at 40 GeV. For tt̄ events in the W -boson rest
frame, we know that El =
MW
2
=40 GeV due to energy-momentum conservation. So after the χ2 method is
applied to semi-leptonic stop pair events, the distribution of El from stop decay becomes similar to El from
top-quark decay. Eb are shown in Fig. (6). Eb in blue line is in the real χ̃+
1 rest frame and Eb in red line is
in the fake W -boson rest frame after χ2 combination. Because of energy-momentum conservation, Eb in the
µ >> M
µ << M
2
number of events
number of events
2
50000
chargino rest frame
40000
fake W rest frame
50000
30000
20000
20000
10000
10000
50
100
150
200
250
300
fake W rest frame
40000
30000
0
0
chargino rest frame
0
0
50
100
150
Eb
200
250
300
Eb
FIG. 6: Left: M2 µ. Right: µ M2 with a large tan β. The blue line is Eb boosted into the real χ̃+
1 rest frame
while the red line is Eb boosted into the fake W -boson rest frame after χ2 combination.
real
χ̃+
1
rest frame is fixed to Eb =
m2t̃ −m2 +
χ̃1
1
2mχ̃+
1
=
2002 −1502
2×150
GeV = 58 GeV. In general, we can see that Eb in
the fake W -boson rest frame are larger than Eb in the real χ̃+
1 rest frame.
√
Finally, we show the combination Eb El of stop-pair events in Fig. (7). The blue line is corresponding to
√
√
Eb El boosted into the real χ̃+
Eb El boosted into the fake
1 rest frame while the red line is corresponding to
√
W -boson rest frame after χ2 combination. In both the left and the right figure, Eb El in the fake W -boson
µ >> M
µ << M
2
10000
chargino rest frame
fake W rest frame
8000
number of events
number of events
2
10000
chargino rest frame
8000
6000
6000
4000
4000
2000
2000
0
0
20
40
60
80
100
120
140
0
0
fake W rest frame
20
ElEb
40
60
80
100
120
140
ElEb
√
FIG. 7: Left: M2 µ. Right: µ M2 with a large tan β. The blue line is Eb El boosted into the real χ̃+
1 rest frame
√
while the red line is Eb El boosted into the fake W -boson rest frame after χ2 combination.
rest frame is larger than
√
Eb El in the real χ̃+
1 rest frame. According to Eq. (12), this first term in the second
∗
line is suppressed by Eb El . So comparing to cos θ∗ in the real χ̃+
1 rest frame, cos θ in the W -boson rest frame
is consequently approaching to -1. That is why both of fake cos θ∗ distributions in Fig. (3) peak at θ∗ = π.
Correspondingly, cos θ∗ distributions in the chargino rest frame, as shown in Fig. (2), are more even in the
cos θ∗ range [−1, 1].
In both the left and right figure of Fig. (7), one can see that the
√
Eb El distribution of stop-pair events
in the fake W -boson rest frame roughly peaks at
√
Eb El = 75 GeV. In the meanwhile, because of energy-
m2t −m2W
and El = m2W for tt̄ events in the W -boson rest frame. Thus
q
√
m2t −m2W
for tt̄ events in the W -boson rest frame, Eb El =
= 77 GeV is fixed. So when the χ2 method of
4
√
semi-leptonic tt̄ final state is applied to semi-leptonic stop-pair events, Eb El of stop-pair event in the fake
√
W -boson rest frame is approximately similar to Eb El of top-quark event. That is, if the stop-pair event
momentum conservation, we know Eb =
2mW
is reconstructed by the χ2 method, the cos θ∗ distribution in the fake W -boson rest frame is approximately
governed by the top-pair distribution as
cos θ∗ =
2Mbl2
− 1.
m2t − m2W
(13)
Here the top-quark mass mt = 172.5 GeV and the W -boson mass mW = 80.4 GeV are defined in the χ2
method, as shown in Eq. (6). When the χ2 method of tt̄ final states is applied to stop-pair events, mt and mW
are not physical masses but expected masses. By minimizing the χ2 , the final states of stop-pair events are
expected to have resonances around the mass mt and mW . In order to prove Eq. (13), we would like to vary
mt in the χ2 method. The first term of the right hand of Eq. (13) is suppressed by m2t . If mt becomes larger,
the term
2
2Mbl
2
mt −m2W
becomes small. More stop-pair events will fall into the cos θ∗ range near cos θ∗ = −1. We
vary mt as 200 GeV, 400 GeV and 600 GeV in the χ2 reconstruction and the results are shown in Fig. (8).
As expected, the cos θ∗ distribution is approaching to -1 when mt becomes larger. The cos θ∗ distribution of
stop-pair events in the fake W -boson rest frame is proved to be governed by Eq. (13).
number of events
20000
mt =200 Gev
18000
mt =400 GeV
16000
mt =600 GeV
14000
12000
10000
8000
6000
4000
2000
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
cosθ*
FIG. 8: The cos θ∗ distributions of stop-pair events are given in the W -boson rest frame when the top-quark mass mt in
the χ2 method are varied.
V.
CONCLUSION
The uncertainty of the tt̄ production cross section at LHC is at a-few-percent level. This small range
might accommodate new physics beyond SM, if taking it as a possible signal. The SUSY theory is generally
believed to be a natural extension of the SM. So the gap can be attributed to a stop pair production t̃t̃∗ with
identical final states 2b + ` + nj + E T . Though low energy SUSY is suffering from severe constraints of direct
searches at LHC, a light stop scenario with a compressed spectrum, such as mt̃1 = 200 GeV, χ̃±
1 = 150 GeV
and χ̃01 = 100 GeV, has not yet been excluded. Stop in such a mass range will be mis-identified as a SM
top-quark. In this paper, we attempt to use the precision measurement of W -polarization in top-quark decay
to improve the ability to distinguish the light stop scenario from the SM top-quark background. The prompt
decay of top-quark before hadronization makes the precision measurement of top-quark possible and such a
measurement plays an important role in testing perturbative QCD as well as the Higgs mechanism. When the
ATLAS χ2 method of W -polarization measurement in semi-leptonic tt̄ final state is applied to semi-leptonic
stop-pair events, we find that the cos θ∗ distribution is always approaching to -1. The “faked” top events
from stop mostly contribute to the left-handed polarized W -boson due to the “faked” full reconstruction of
W -boson and top-quark. Since the W -boson from top-quark decay is roughly 30% left-handed, it is hard
to distinguish the light stop event from SM top background by analyzing the polarization. We compute the
FL /FR /F0 contribution from benchmark point C in Table. I, which is of the maximal contribution to tt̄
events. After using Eq. (7) and Eq. (8), the result is listed as following:
SM : FL = 0.303, FR = 0.0493, F0 = 0.647,
SM with stop : FL = 0.313, FR = 0.0497, F0 = 0.638 .
(14)
The benchmark point with maximal contribution to top events only changes FL by 1%, which is far below the
current uncertainty. Thus, we conclude that the current measurement on the W -polarization cannot exclude
the light stop scenario with stop mass around top-quark mass.
Acknowledgement
LW and LZ would like to thank Jiwei Ke for useful discussions about Madgraph5. XL is supported by
the National Science Foundation of China (11075079, 11135009). ZS is supported by the National Science
Foundation of China (11275114). KW is supported in part, by the Zhejiang University Fundamental Research Funds for the Central Universities (2011QNA3017) and the National Science Foundation of China
(11245002,11275168). GZ is supported in part, by the National Science Foundation of China (11075139,
11135006,11375151) and the Program for New Century Excellent Talents in University (Grant No. NCET12-0480).
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