IPMU12-0200

Top Polarization and Stop Mixing from Boosted Jet
Substructure

Biplob Bhattacherjee1 , Sourav K. Mandal1 and Mihoko Nojiri1,2,3
1Kavli IPMU (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan
2
3

Theory Group, KEK, Tsukuba, Ibaraki 305-0801, JapanThe Graduate University for Advanced Studies (SOKENDAI)
Tsukuba, Ibaraki 305-0801, Japan

Abstract
Top polarization is an important probe of new physics that couples to the top
sector, and which may be discovered at the 14 TeV LHC. Taking the example ofthe MSSM, we argue that top polarization measurements can put a constraint on
the soft supersymmetry breaking parameter At . In light of the recent discovery ofa Higgs-like boson of mass ∼ 125 GeV, a large At is a prediction of many supersymmetric models. To this end, we develop a detector level analysis methodology
for extracting polarization information from hadronic tops using boosted jet substructure. We show that with 100 fb−1 of data, left and right 600 GeV stops canbe distinguished to 4σ, and 800 GeV stops can be distinguished to 3σ.

Contents
1 Introduction2

1.1

Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

Top polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.3

Stop mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

2 Simulation and analysis

6

2.1

Event generation and detector simulation . . . . . . . . . . . . . . . . . .

6

2.2

Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.3

Top jet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.3.1

Jet clustering and grooming . . . . . . . . . . . . . . . . . . . . .

9

2.3.2

Reconstruction and tagging . . . . . . . . . . . . . . . . . . . . .

10

2.3.3

b-tagging subjets . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

3 Results

12

3.1

Reconstruction quality . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

3.2

tt̄ + jets control region . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

3.3

Sensitivity to stop mixing . . . . . . . . . . . . . . . . . . . . . . . . . .

14

4 Conclusion and outlook

1

Introduction

1.1

Motivation

19

Top physics is an important probe of theories of new physics at the TeV scale, as manyof these theories posit TeV-scale partners to the top quark in order to resolve the Higgs
hierarchy problem. These theories in general have chiral structure, thus a measurementof the top polarization from the decays of top partners can establish useful constraints
on them.
In the case of supersymmetry with R-parity, the composition of the scalar top partner“stop” t̃ in terms of the weak eigenstates t̃R and t̃L can be constrained by observing
the polarization of tops in the decay t̃ → tχ̃01 . The fermionic top partners in extradimensions theories with KK parity and little Higgs theories with T-parity have theanalogous decays t(1) → tB (1) and T 0 → tBH . As discrete parities are desirable because2they limit dangerous contributions to electroweak precision variables [1] and admit WIMP
6 T collider signature provides
dark matter candidates (such as χ̃01 , B (1) and BH ), the t + E
a useful handle on a broad class of well-motivated TeV-scale theories.
There are also numerous theories with and without top partners containing extra
massive gauge bosons Z 0 with decays such as Z 0 → tt̄. Top polarization measurements
can constrain the chiral structure of their couplings to the top quark. In general, tt̄ may
be produced in new heavy resonances.
To date there have been a number of studies on measuring top polarization at theLarge Hadron Collider (LHC). Ref. [2] performed a signal-only Monte Carlo-level analysis in the context of gluino decay, and Ref. [3] performed a Monte Carlo-level analysis
for KK gluons. For the t + E
6 T class, Ref. [4] performed a signal-only parton-level formal calculation, followed by Refs. [5] and [6] performing a Monte Carlo-level analysis
with backgrounds, acceptance cuts and smearing effects. For heavy resonances, Ref. [7]considered the W +jets background and smearing effects, and later Ref. [8] performed asignal-only Monte Carlo-level analysis. Ref. [10] elucidated the benefit of jet substructure for measuring the polarization of boosted hadronic tops for both classes of theories,
although without backgrounds and at Monte Carlo-level.
In this paper we study top polarization for the t + E
6 T class of theories at detector
level including all contamination sources (e.g., ISR/FSR and MPI), relevant detector
effects (e.g., magnetic field) and backgrounds. To this end we focus on pair productionof 600 GeV and 800 GeV t̃1 at the 14 TeV LHC under the simplified model in which
they decay entirely to tχ01 , where χ01 ' B̃ and mχ01 = 100 GeV. We choose to focus onsupersymmetry also because it may be the most well-motivated of this class of theories,
solving the hierarchy problem up to Planck scale as well as enhancing gauge coupling
unification at high scale.
First we will briefly review the kinematics of top polarization and the phenomenologyof t̃L -t̃R mixing. Then we will describe our simulation and analysis methodology, andpresent our results for the expected sensitivity to the stop mixing angle. Finally, we will
look ahead to possibilities for improving and ramifying our methodology.

1.2

Top polarization

Measurement of top polarization is possible because top quarks undergo weak decay
prior to hadronization, so the top decay products carry information on the polarization3

of the parent quark undisturbed by the hadronization process. The kinematics of top
polarization is presented in Refs. [2, 4, 5, 8, 9]. The decay products of the top quark havethe angular distributions1dΓ∝ 1 + Pt kf cos θtf
Γ d(cos θtf )(1)

where cos θtf is the angle between the daughter momentum and the top spin axis in the
top rest frame; we can take the latter as the direction of top momentum in the lab frame.
Pt = ±1 is the polarization of the top quark, and kf is the “spin analyzing power” of thedaughter flavor. For the b-quark,m2t − m2W
' −0.4(2)
m2t + m2W
whereas for the lepton daughter of a leptonic top decay one finds kl = 1. Consequently
kb = −

we can measure Pt by observing the distribution of cos θtf . For the case of hadronic tops,
this can be done directly by reconstructing the top and resolving the b-quark daughter.
However, for leptonic tops, one cannot fully reconstruct the top momentum due to theneutrino from the W decay. It has been proposed to define cos θtl in an “approximate
rest frame” in semileptonic events with reconstruction of the accompanying hadronic
top [5], or require the leptonic top in a semileptonic event to be highly boosted suchthat one can use alternative measurables which are insensitive to top momentum in thelimit β → 1 [4, 6]. Yet another proposal is to use judicious cuts to preserve polarization
information in the lab frame despite the boost of the leptonic top [8].
In our analysis we measure the polarization of hadronic tops, which has not only theadvantage of being more simple than leptonic methods, but also that of greater statistics,
as 89% of top pairs have one hadronic top whereas only 44% of top pairs are semileptonic [11]. Moreover, leptonic top analysis entails all the difficulties of identifying isolated
leptons in a real hadron collider environment. Standard cone-based lepton isolation lose
efficiency with increasing boost, hampering polarization measurements for heavy parent
states. However, this may be ameliorated by narrowing the isolation cone size as lepton
pT increases [7, 12].

1.3

Stop mixing

As written in the review [13], the stop mass matrix in the weak basis under the minimal
supersymmetric standard model (MSSM) is
Lmt̃ = −

t̃∗L

t̃∗R
4



m2t̃



t̃L
t̃R


(3)

m2t̃ =



m2Q3 + m2t + ∆ũLv(a∗t sin β − µyt cos β)∗v(at sin β − µ yt cos β)m2ū3 + m2t + ∆ũR
∆ũL =∆ũR =

1 2 2− sin θW
2 3

cos(2β)m2Z2 2sin θW cos(2β)m2Z3.

If at and µ are real, the mixing can be represented by the rotation

 


t̃1
cos θ − sin θt̃L=
sin θ cos θ
t̃2
t̃R


(4)

(5)
(6)

(7)

where
tan 2θ =2mt (At − µ/ tan β)2mQ3 − m2ū3 + ∆ũL − ∆ũR

(8)

and in which mt = yt v sin β and At = at /yt have been substituted.
Let us consider the case that tan β  1 and µ, mQ3 and mū3 are of the same order at
low scale; we also assume mQ3 > mū3 at low scale due to renormalization. Then if At = 0
we see that t̃1 ' t̃R (θ ' π/2); conversely, if At >∼ µ then t̃1 will have a significant t̃Lcomponent (θ ∼ π/4). If indeed the mixing angle θ can be measured, then under theseassumptions At may be strongly constrained.
These assumptions can be eased by incorporating other measurables. For example,
knowledge of the t̃1 mass (e.g., from production rates or kinematic constraints) and the
Higgs mass, which takes large corrections at one-loop that depend on At , µ, tan β, mt̃1 andmt̃2 [14], would leave only the relationship between mQ3 and mū3 as a model-dependent
quantity. The recent discovery of a Higgs-like boson [15, 16] with a mass suggesting alarge value of At for TeV-scale supersymmetric scalars [17] may already be hinting at
such a correction.
It has also been proposed to consider the ratios of the branching fractions of stops
decaying to neutralinos and charginos in order to constrain stop mixing parameters.
However, it may require input from both a hadron collider and a linear collider to havesufficient information [18]. In either case, this may be another set of observables which
may be useful in tandem with direct polarization measurements.
To connect the stop mixing angle with top polarization, we consider the interaction

5

term for the decay in our simplified model1 in which χ01 ' B̃,
 
 

1 ∗ 0
2 ∗ 0
0
∆L = gt̃ χ̃ tL + −t̃ χ̃ tR
6 L 1
3 R 1

 
  
1
2
0 ∗ 0
= g t̃1 χ̃1 cos θtL + sin θ
tR
6
3

 
  
1
2
0 ∗ 0
− g t̃2 χ̃1 sin θ
tL + cos θ
tR
6
3

(9)

where the quantities in the parentheses are the hypercharges. Then the observed “effective” mixing angle from the decay t̃1 → tχ̃01 istan θobs = 4 tan θ

.

(10)

Thus for or simplified model the stop mixing angle is amplified in the top polarization
mixing angle, increasing the sensitivity to t̃R and reducing the sensitivity to small t̃Ladmixtures. Under the assumptions given before, this therefore reduces the sensitivity tosmall values of At .
Putting together the Higgs mass correction and top polarization arising from stop
mixing, we can see the theoretical sensitivity of At to the measured top polarization in
Figure 1. Here, the top polarization is defined as (c2L − c2R )/(c2L + c2R ), where cL and cR
are the coupling strengths (1/6) cos θ and (2/3) sin θ to the left-handed and right-handed
tops, respectively. Indeed, sensitivity improves as the tops become more left-handed.2

2

Simulation and analysis

The goal of our analysis is to show that top polarization information can be obtained byreconstructing boosted tops in a realistic hadron collider environment. First we describe
the Monte Carlo generation of our data, then the detector simulation, and finally thereconstruction of top jets using the physics objects from the simulation.

2.1

Event generation and detector simulation

Using Herwig++ 2.5.0 [19] with all physics effects (hadronization, ISR/FSR, MPI) included, we generated left (sin θ = 0), mixed (tan θ = 0.25) and right (sin θ = 1) t̃1 t̃∗1
samples with masses 600 GeV and 800 GeV for the 14 TeV LHC under our simplified
1

For a discussion with completely general χ̃01 , see e.g. Ref. [5].
For this parameter scan, tan β = 10, µ = 1692 GeV and mA = 1791 GeV, consistent with theassumptions in our discussion.
2

6

At [GeV]

3000

2500

2000

1500

1000
-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4
0.6
0.8
1
Average top polarization

Figure 1: Constraint on trilinear coupling At vs. top polarization measurement from the
MSSM Higgs mass correction for 800 GeV light stop and 123.8 < mh < 126.2.
model. We calculated NLO production cross sections using Prospino2.1 [20], shown in
Table 1.
We consider the backgrounds tt̄+jets, Z+jets, W +jets and tt̄+Z, which we generatedusing MadEvent/MadGraph 5.1.3 [21, 22] + PYTHIA 6.4.25 [23] (also with all physics
effects), taking their leading order cross sections which are also shown in Table 1. All
extra jets are five-flavor (g + u, d, c, s, b).
Processt̃1 t̃∗1 , m = 600 GeVt̃1 t̃∗1 , m = 800 GeV
tt̄+ ≤ 2 jets
(Z → ν ν̄)+ ≤ 3 jets
(W → [l, τ ]ν)+ ≤ 3 jetstt̄ + (Z → ν ν̄)Generator-level cut——
pT,j1 > 300 GeV
pT,j1 , E
6 T > 250 GeV
pT,j1 , E
6 T > 300 GeV—

Cross section
218 fb36.8 fb
40.6 pb
7.8 pb
4.57 pb
0.11 pb

Table 1: Signal and background cross-sections at 14 TeV LHC.
For our detector simulation we used Delphes 2.0.2 [24]. We modified the Delphes
codebase to use FastJet 3.0.3 [25] instead of the bundled version, as the newer version
has an interface to manipulate subjets at specific clustering scales or steps. This allows us
to “prune” the clustering tree to remove contamination, then store the resulting subjets,
all within the Delphes analysis pipeline.
7

The Delphes detector settings are tuned to ATLAS, with the hadronic calorimeter
grid set to match that in the ATLAS TDR [26]. The magnetic field is turned on in thesimulation.

2.2

Cuts

√
We implement the following event cuts, designed to increase the significance S/ S + B
for our characteristic t + E
6 T signature:
1. E
6 T >300 GeV.
2. Leading fat jet pT >400 GeV.
3. If there are no leptons w/ pT > 5 GeV, require subleading fat jet pT >100 GeV.
This cut suppresses processes like W/Z+jets in which the second fat jet is from
QCD, as these jets are likely to be soft. Since the majority of signal events have
leptons due to W → lν and the decay of b-flavored mesons, we require that there
are no leptons for this cut. Thus, this cut is most effective against Z+jets.
4. Lepton is not collimated with E
6 T . For every lepton with pT > 5 GeV, requirecos(φE6 T − φl )< 0.4 .
(6ET + pT,l )/(350 GeV)

(11)

This selects against high E
6 T arising from boosted leptonic W decays in tt̄+jets
and W +jets, as the opening angle between the lepton and E
6 ~T is likely to be muchsmaller in these processes than from a top partner decay.
5. Hard subjet is not collimated with E
6 T . For every subjet with pT > 50 GeV, require
the same as above. This works against hadronic τ from W decays in tt̄+jets andW +jets, as well as highly collimated b-subjets from top decays in tt̄+jets.
6. Require at least one top tagged jet, using the procedure described in the next section.
7. 225 < MT 2 < 650 for 600 GeV stops, and 325 < MT 2 < 850 for 800 GeV stops.
MT 2 is calculated for the leading and subleading jet, with mχ = 0. For the leading
jet we used the reconstructed top jet if top tagged, otherwise we used the trimmed
jet; similarly for the subleading jet. We employed the MT 2 code of Ref. [37].
The resulting cut flow for signal events is shown in Table 2, and for background eventsin Table 3 for 14 TeV LHC @ 100 fb−1 . The cuts reveal some preference for right stops,
which is noted in Ref. [5].
8

Cut
#
Pre-cut
1E
6 T > 300 GeV
2
pT,j1 > 400 GeV
3 If nl = 0, pT,j2 > 100 GeV
4lepton/6ET collimation
5
subjet/6ET collimation
6# top tag ≥ 1
7a
225 < MT 2 < 650
7b
325 < MT 2 < 850

Stop 600 GeV
Left Mixed Right
21900 21900 21900
9513
9739
9857
5415
5496
5472
5150
5220
5192
4155
4315
4394
2914
3046
3084
1014
1065
1082
908
954
969
—
—
—

Stop 800 GeV
Left Mixed Right
3680 3680
3680
2394 2411
2433
1816 1835
1825
1756 1773
1764
1515 1555
1559
1171 1209
1208
450
456
463
—
—
—
364
369
374

Table 2: Cut flow for signal events at 14 TeV LHC @ 100 fb−1 .
Cut#Generator-level
1E
6 T > 300 GeV
2
pT,j1 > 400 GeV
3 If nl = 0, pT,j2 > 100 GeV
4lepton/6ET collimation
5
subjet/6ET collimation
6# top tag ≥ 1
7a
225 < MT 2 < 650
7b
325 < MT 2 < 850tt̄+jets
4.06 × 106
1.30 × 105
90503
88133
21518
4412
1140
554
275

Z+jets
7.8 × 105
4.96 × 105
2.28 × 105
1.01 × 105
98441
60860
305
222
141

W +jets
4.57 × 105
4.36 × 105
3.20 × 105
2.68 × 105
69865
37852
99
56
45

tt̄ + Z
11000
815
351
326
237
149
52
43
30

Table 3: Cut flow for background events at 14 TeV LHC @ 100 fb−1 .

2.3

Top jet reconstruction

Many aspects of this analysis are well-reviewed in Ref. [27].
2.3.1

Jet clustering and grooming

Hadrons are clustered as fat jets using the Cambridge/Aachen algorithm [28] with cone
size R = 1.2 and subjet cone size ∆R = 0.2. These numbers are chosen such that the
distribution in the number of subjets per fat jet peaks at ∼ 3 in our signal samples after
the following grooming procedures:
1. The jet clustering trees are “pruned” [29] using the mass-drop condition [30]mjn−1 < 0.8 × mjn(12)where mjn−1 is the invariant mass of the hardest parent jet, and mjn is the invariant
mass of the child jet at clustering step n. We also require the subjet separation
9

conditiondkT (jn−1,1 , jn−1,2 ) > (∆R)2 · m2jn

(13)

where dkT is the kT distance between the two parents jets. This removes contamination from MPI and ISR, improving top reconstruction quality. We take the fatjet (and its subjets) at the clustering step where both conditions are satisfied.
2. This jet is then “trimmed” [31], removing subjets with pT < 10 GeV. This further
reduces contamination.
The trimmed jet is then fed to our top reconstruction algorithm.
2.3.2

Reconstruction and tagging

The following algorithm is attempted for every fat jet:
1. Require pT > 400 GeV for the untrimmed jet.
2. Require at least three subjets.
3. Require that one b-subjet jb is reconstructed in the jet.
4. Find the subjet combination j1 j2 jb , of which no pair of subjets are within ∆R ofeach other, and which gives the closest invariant mass to mt . Require also that thisinvariant mass be in the window (150, 200) GeV.
5. If there is no successful tag, require at least four subjets and retry the step above
with four-subjet combinations j1 j2 j3 jb .
6. Optionally require one two-subjet combination to have an invariant mass in theloose W mass window (50, 110) GeV. We present our main results both with andwithout this requirement.
This algorithm differs from the Johns Hopkins top tagger [32] by declustering more than
two steps in the pruning stage if necessary, using a mass drop condition rather than a pTdrop condition, having an absolute rather than fractional trimming threshold, requiring
a b-tag instead of imposing a W mass condition, and not imposing a top helicity angle
condition (as this is our observable). The algorithm also differs from the CMS tagger [33]by not requiring a minimum two-subjet invariant mass.

10

Kinematic region
pT < 30 GeV
30 GeV < pT < 60 GeV
60 GeV < pT < 450 GeV
450 GeV < pT < 1000 GeV
1000 GeV < pT

Efficiency
0%
60%
70%
60%
0%

Table 4: Utilized b-tagging efficiencies.
Our algorithm differs also from the HEPTopTagger [34] by not imposing the various
two-subjet mass requirements, having a mandatory b-tag, and also by implementing foursubjet reconstruction.
We make these choices to enhance top tagging efficiency, presuming that the top parent
particle has already been discovered. Nonetheless, top mistagging does not overwhelm
the signal as will be apparent in our results.
2.3.3

b-tagging subjets

We require b-tagging in our top reconstruction algorithm to reconstruct the observablecos θtb with high fidelity, but also to suppress top mistagging from background processes.
Utilizing recent advances in b-tagging by the LHC detector collaborations, we employ theb-tagging efficiencies (shown in Table 4) recently validated at 7 TeV LHC by CMS for
their CSVM tagger [35]. We impose the upper limit pT = 1000 GeV to be conservative,
though it is not indicated by the CMS study. We choose to use the CMS efficiencies since
they are validated up to pT = 670 GeV, though a recent ATLAS study [36] shows similar
efficiencies up to 200 GeV.
However, we do not implement mistagging, as this depends on various factors thatare best implemented by experimenters — mistagging rates vary rapidly with tagging
efficiency and so are sensitive to systematic uncertainties that we cannot model. We
expect charm jets to contribute to most of the mistags. For example, in Ref. [35] a 60%
b-tagging efficiency nominally results in a 10% charm mistagging rate in Monte Carlo,
whereas for 50% b-tagging efficiency this drops to 4%. The mistagging rate for lighter
flavors is ∼ 1%, so this contribution is negligible.
We apply these b-tagging efficiencies at parton level. To reconstruct a b-subjet wesum all the subjets within ∆R = 0.2 of the b-parton, as this captures some hard FSR.
If more than one b-parton yields a matching subjet inside a given fat jet, that fat jet isrejected and is not top tagged.

11

3

Results

3.1

Reconstruction quality

To illustrate the effectiveness of our reconstruction method, we show the jet invariant mass
distribution at different stages in Figure 2. For signal processes and tt̄+jets, few jets arelost in the pruning phase; however, without jet cluster pruning, we find that the cos θtb
distribution loses fidelity compared to the parton-level expectation. The subsequent
trimming step is essential for removing soft contamination, resulting in a shift of theinvariant mass lower towards the correct top mass. Then, requiring at least three subjets
and a b-tag narrows the distribution further. Finally, top reconstruction assembles the
subjets with correct invariant mass. Modulo b-tagging efficiency, the top tagging efficiency
for hadronic tops in our samples which pass the pT cut is ∼ 60%. Conversely, top

2500# of jets# of jets

reconstruction suppresses Z+jets and W +jets by a factor of O(100).
2200
2000
1800

2000

1600
1400

1500

1200
1000
1000

800
600

500

400
200
50

100

150

200

250

300

350

400

0
0

450
500
mj [GeV]200# of jets# of jets

0
0

180

50

100

150

200

250

300

350

400

450
500
mj [GeV]

50

100

150

200

250

300

350

400

450
500
mj [GeV]

8000
7000

160
6000
140
5000

120
100

4000

80

3000

60
2000
40
1000

20
0
0

50

100

150

200

250

300

350

400

0
0

450
500
mj [GeV]Figure 2: Jet invariant mass sequence for 600 GeV mixed stops (upper left), 800 GeV
mixed stops (upper right), tt̄+jets (lower left) and Z+jets (lower right). In each panel,from back to front, shown is the jet mass distribution after pT > 400 GeV cut (blue),
requiring successful pruning (yellow), trimming (gray), requiring three or more subjets(cyan), b-tagging (magenta), and finally top tagging (green).

12

The quality of reconstruction is also apparent in the signal-only cos θtb distributions
shown in Figure 3. One sees that the parton-level and reconstructed distributions coincide
up to statistical fluctuations. The distributions at pre-cut/tag parton-level match Ref. [4],except they have a downward tilt due to the b-partons losing energy to FSR. One sees
also that there is less contrast between left and mixed stops with mass 600 GeV thanwith mass 800 GeV. This is due to the W daughter subjets not passing the trimming
threshold.
0.09

0.09

0.09

0.08

0.08

0.08

0.07

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0.07

0.06

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0.01

0.01

0
-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

10-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

10-1 -0.8 -0.6 -0.4 -0.2

0.09

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0.01

0
-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

10-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

10-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

10

0.2 0.4 0.6 0.8

1

Figure 3: cos θtb distributions for stops only, normalized to one. Left to right are left,
mixed, and right stop samples; upper row is for 600 GeV stops, the lower for 800 GeV
stops. Shown in each panel are the reconstructed distribution (black), parton-level distribution (blue), and parton-level distribution before cuts and tagging (green).

3.2

tt̄ + jets control region

As experimenters are likely to rely on data rather than Monte Carlo for the tt̄+jets
background, we demonstrate a control region by inverting cuts #4 and #5, requiringthat there be at least one lepton or hard subjet highly collimated with E
6 ~T . An array ofcos θtb distributions for this region is shown in Figure 4. They evince little contaminationfrom signal and other backgrounds.
13

It may be of concern that the collimation cuts #4 and #5 might introduce distortions
to the cos θtb distributions obtained from top tagging. In Figure 5 we show that the polarization distribution for tt̄+jets is invariant under these cuts up to statistical fluctuations.
We show also in Figure 6 that the MT 2 cut does not distort the polarization distributionof tt̄+jets in the control region. Thus, it is safe to use a data-driven tt̄+jets backgroundfrom this region.
3000

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Figure 4: Event distributions of cos θtb for tt̄+jets in the control region at 14 TeV LHC @100 fb−1 . Left-to-right are left, mixed and right stop samples; upper row is for 600 GeV
stops, the lower row for 800 GeV stops. Shown in each panel top to bottom is signal(red), tt̄+jets (blue), Z+jets (green), W +jets (yellow), and tt̄ + Z (gray; hardly visible).

3.3

Sensitivity to stop mixing

Our measurable is cos θtb , where θtb is the angle between the b daughter and the top spin
axis in the top rest frame. To calculate sensitivity, we sum the cos θtb distributions fromsignal and background processes. For the tt̄+jets contribution, we use the control region
distribution normalized to the total of the signal region distribution. This sum is shownin Figure 7, where we have rebinned the data to use only two bins in order to minimize the14

dNtop/d(cos θtb)

0.09
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Figure 5: Distributions of cos θtb for tt̄+jets, normalized to one. Shown are the distribution without collimation cuts (black), with the lepton collimation cut only (blue), withthe subjet collimation cut only (red), and with both collimation cuts applied (cyan).
trials penalty. The corresponding p-values for distinguishing stop mixing hypotheses areshown in Table 5. For 600 GeV stops at 14 TeV LHC @ 100 fb−1 , left and right mixtures
can be distinguished to better than 4σ, and left/right can be distinguished from themixed state to better than 1.5σ. For 800 GeV stops, left and right can be distinguishedto nearly 3σ.
Truth
left
mixed
right

Hypothesis (mt̃1 =600 GeV)
left
mixed
right
1
0.047 2.6 × 10−6
0.058
1
0.030
−6
8.1 × 100.032
1Hypothesis (mt̃1 =800 GeV)
left
mixed
right
1
0.16
0.00140.17
10.24
0.0018 0.25
1

Table 5: p-values for distinguishing stop mixing hypotheses at 14 TeV LHC @ 100 fb−1 ,with no W mass condition.
Except for tt̄ + Z, most of the tops from the background processes surviving the cutsand reconstruction are due to extra QCD jets carrying b-flavor. The results therefore
are improved somewhat by imposing a loose W mass condition in the top reconstruction
algorithm. If we require the mass of some two-subjet combination (not including theb-subjet) to be in the window (50, 110) GeV, we obtain the sum plot shown in Figure 8
and the corresponding p-values in Table 6. For 600 GeV stops, left and right can now
15

dNtop/d(cos θtb)

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Figure 6: Distributions of cos θtb for the tt̄+jets control sample, normalized to one. Shownare the distribution for MT 2 < 225 GeV (black), and for MT 2 > 225 GeV.
be distinguished to better than 4.5σ, and left/right can be distinguished from mixed toroughly 2σ. For 800 GeV stops, left and right can now be distinguished to better than
3σ. However, imposing this W mass condition may increase systematic errors from theW/Z+jets backgrounds due to the greater variation between the negative and positivebins. This occurs because the subjets of the fake W s have lower pT at larger cos θtb , andare less likely to satisfy the W mass condition.
We conclude that stop mixing hypotheses can be distinguished at the 14 TeV LHC
with ∼ 100 fb−1 of data.
Truth
left
mixed
right

Hypothesis (mt̃1 =600 GeV)
left
mixed
right
1
0.018 1.7 × 10−6
0.025
1
0.017
9.0 × 10−7 0.018
1

Hypothesis (mt̃1 =800 GeV)
left
mixed
right
1
0.17 5.6 × 10−4
0.17
1
0.14
7 × 10−4 0.15
1

Table 6: p-values for distinguishing stop mixing hypotheses at 14 TeV LHC @ 100 fb−1 ,with a W mass condition.

16

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Figure 7: Sum of cos θtb distributions from different processes for 14 TeV LHC @ 100 fb−1 ,with no W mass condition. Left to right are left, mixed and right stop samples; upper
row is for 600 GeV stops, and the lower is for 800 GeV stops. Shown are the contributions
from signal (red), tt̄+jets (blue), Z+jets (green), W +jets (yellow), tt̄ + Z (gray).

17

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Figure 8: Sum of cos θtb distributions from different processes for 14 TeV LHC @ 100 fb−1
with a W mass condition. Left to right are left, mixed and right stop samples; upper row
is for 600 GeV stops, and the lower is for 800 GeV stops. Shown are contributions fromsignal (red), tt̄+jets (blue), Z+jets (green), W +jets (yellow), tt̄ + Z (gray).

18

4

Conclusion and outlook

In summary, after reviewing the motivation for top polarization measurement, the kinematics of top polarization, and the phenomenology of stop mixing, we described a simulation and analysis methodology for the t + E
6 T collider signature that can distinguishstop mixing hypotheses at 14 TeV LHC with ∼ 100 fb−1 of data.
There are several possible improvements to the methodology. The first and foremost
is to include polarization information from leptonic decays, perhaps using the techniquesof [7, 12]. Also if, in consultation with experimenters, the trimming threshold of pT =10 GeV or the subjet cone size ∆R = 0.2 can be reduced, this would enhance theperformance of the top reconstruction algorithm. Finally, it may be useful to implement
the top reconstruction technique of Ref. [10] to supplement b-tagging, especially at large
boosts.
Other possible improvements are to:• Implement charm mistagging in the b-tagging algorithm, though this may be nontrivial as discussed in Section 2.3.3.
• Use spin-correlated backgrounds, e.g. from ALPGEN [38]. We did produce a small
sample of tt̄+jets in ALPGEN but found no difference in the cos θtb distribution from
the MadGraph/MadEvent+PYTHIA events used in this analysis.
• Calculate backgrounds at NLO using, e.g., MC@NLO [39] to increase accuracy. However, this is likely beyond our computational capabilities unless it is used only tonormalize the leading-order backgrounds. We estimate that the K-factor for the tt̄
background to be less than 1.2 given our E
6 T cut [40].
In conclusion, the LHC running at 14 TeV may provide new discoveries in the top
sector, in which case top polarization will be an important tool for constraining this new
physics. The methodology in this paper may be useful for this purpose.

Acknowledgments
This work is supported by World Premier International Research Center Initiative (WPI
Initiative), MEXT, Japan. The authors would like to thank T. T. Yanagida and S. Matsumoto for preliminary discussions on this topic.

19

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