Top Polarization from Boosted Jet Substructure

. 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 of the MSSM, 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 can be distinguished to 4 . 5 σ , and 800 GeV stops can be distinguished to 3 σ .


Motivation
Top physics is an important probe of theories of new physics at the TeV scale, as many of these theories posit TeV-scale partners to the top quark in order to resolve the Higgs hierarchy problem.
In the case of supersymmetry with R-parity, the composition of the stopt in terms of the weak eigenstatest R andt L can be constrained by observing the polarization of tops in the decayt → tχ 0 1 . In the MSSM, the stop mixing matrix is The fermionic top partners in extra-dimensions theories with KK parity and little Higgs theories with T-parity have the analogous decays t (1) → tB (1) and T → tB H . There are also numerous theories with and without top partners containing extra massive gauge bosons Z with decays such as Z → tt. Top polarization measurements can constrain the chiral structure of their couplings to the top quark.
In this proceeding (based on Ref. [1]) we study top polarization at detector level including all contamination sources (e.g., ISR/FSR and MPI), relevant detector effects (e.g., magnetic field) and backgrounds. We focus on pair production of 600 GeV and 800 GeVt 1 at the 14 TeV LHC under the simplified model in which they decay entirely to tχ 0 1 , where χ 0 1 B and m χ 0 1 = 100 GeV. We choose to focus on supersymmetry also because it may be the most wellmotivated of this class of theories, solving the hierarchy problem up to Planck scale as well as enhancing gauge coupling unification at high scale. We employ the techniques of boosted jet substructure to access the jet clustering information, allowing us to reduce the effects of contamination while also avoiding the combinatoric problem posed by having numerous monolithic jets.

Top polarization
The decay products of the top quark have the angular distributions where cos θ t f 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. P t = ±1 is the polarization of the top quark, and k f is the "spin analyzing power" of the daughter flavor. For the b-quark k b = −0.4 whereas for the lepton daughter k l = 1. Consequently we can measure P t by observing the distribution of cos θ t f . 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 the neutrino from the W decay. It has been proposed to define cos θ tl in an "approximate rest frame" in semileptonic events with reconstruction of the accompanying hadronic top [2], or require the leptonic top in a semileptonic event to be highly boosted such that one can use alternative measurables which are insensitive to top momentum in the limit β → 1 [3,4]. In our analysis we measure the polarization of hadronic tops, which has not only the advantage of being more simple than leptonic methods, but also that of greater statistics. Moreover, leptonic top analysis entails all the difficulties of identifying isolated leptons in a real hadron collider environment.
We consider the backgrounds tt+jets, Z+jets, W+jets and tt + Z, which we generated using MadEvent/MadGraph 5.1.3 and PYTHIA 6.4.25 (also with all physics effects), taking their leading order cross sections. All extra jets are five-flavor (g + u, d, c, s, b).
For our detector simulation we used Delphes 2.0.2 [5]. We modified the Delphes codebase to use FastJet 3.0.3 [6] 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 analysis pipeline.
The Delphes detector settings are tuned to ATLAS, with the hadronic calorimeter grid set to match that in the ATLAS TDR. The magnetic field is turned on in the simulation.

Cuts
We implement the following event cuts, designed to increase the significance S / √ S + B for our characteristic t + E T signature: 1. E T >300 GeV.
3. If there are no leptons w/ p T > 5 GeV, require subleading fat jet p T >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 T . For every lepton with p T > 5 GeV, require This selects against high E T arising from boosted leptonic W decays in tt+jets and W+jets, as the opening angle between the lepton and E T is likely to be much smaller in these processes than from a top partner decay.

5.
Hard subjet is not collimated with E T . For every subjet with p T > 50 GeV, require the same as above. This works against hadronic τ from W decays in tt+jets and W+jets, as well as highly collimated bsubjets from top decays in tt+jets.
6. Require at least one top tagged jet, using the procedure described in the next section.
7. 225 < M T 2 < 650 for 600 GeV stops, and 325 < M T 2 < 850 for 800 GeV stops. M T 2 is calculated for the leading and subleading jet, with m χ = 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.

Jet clustering and grooming
Hadrons are clustered as fat jets using the Cambridge/Aachen algorithm 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" [7] using the mass-drop condition where m j n−1 is the invariant mass of the hardest parent jet, and m j n is the invariant mass of the child jet at clustering step n. We also require the subjet separation condition where d k T is the k T distance between the two parents jets. This removes contamination from MPI and ISR, improving top reconstruction quality. We take the fat jet (and its subjets) at the clustering step where both conditions are satisfied.

Reconstruction and tagging
The trimmed fat jets are then fed to our top reconstruction algorithm. The following steps are attempted for each of these jets: 1. Require p T > 400 GeV for the untrimmed jet.
3. Require that one b-subjet j b is reconstructed in the jet. Kinematic region Efficiency p T < 30 GeV 0% 30 GeV < p T < 60 GeV 60% 60 GeV < p T < 450 GeV 70% 450 GeV < p T < 1000 GeV 60% 1000 GeV < p T 0% 4. Find the subjet combination j 1 j 2 j b , of which no pair of subjets are within ∆R of each other, and which gives the closest invariant mass to m t . Require also that this invariant 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 j 1 j 2 j 3 j b .
6. Optionally require one two-subjet combination to have an invariant mass in the loose W mass window (50, 110) GeV. We present our main results with this requirement.
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.

b-tagging subjets
We require b-tagging in our top reconstruction algorithm to reconstruct the observable cos θ tb 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 the b-tagging efficiencies (shown in Table 1) recently validated at 7 TeV LHC by CMS for their CSVM tagger [9]. We impose the upper limit p T = 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 p T = 670 GeV, though a recent ATLAS study [10] shows similar efficiencies up to 200 GeV.
However, we do not implement mistagging, as this depends on various factors that are 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.
We apply these b-tagging efficiencies at parton level. To reconstruct a b-subjet we sum 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 is rejected and is not top tagged.

Reconstruction quality
Our measurable is cos θ tb , where θ tb is the angle between the b daughter and the top spin axis in the top rest frame.
The usefulness of this measurable depends on the fidelity of the top jet reconstruction. Here we illustrate the effectiveness of our reconstruction method.
First, we show the jet invariant mass distribution at different stages in Figure 1. For signal processes and tt+jets, few jets are lost in the pruning phase; however, without jet cluster pruning, we find that the cos θ tb distribution loses fidelity compared to the parton-level expectation. The subsequent trimming step is essential for removing soft contamination, resulting in a shift of the invariant 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 p T cut is ∼ 60%. Conversely, top reconstruction suppresses Z+jets and W+jets by a factor of O(100). The quality of reconstruction is also apparent in the signal-only cos θ tb distributions shown in Figure 2. One sees that the parton-level and reconstructed distributions coincide up to statistical fluctuations. Near cos θ tb = −1 there is depletion due to poor b-tagging efficiency, whereas near cos θ tb = +1 there is depletion due to the W subjets being too soft to pass the trimming threshold. One sees for this reason that there is less contrast between left and mixed stops with mass 600 GeV than with mass 800 GeV. The distributions at pre-cut/tag partonlevel match Ref. [3], except they have a downward leftto-right tilt due to the harder b-partons losing energy to FSR.
Finally, we show sample M T 2 distributions for 600 GeV and 800 GeV mixed stops in Figure 3 at reconstruction level, signal only. One can clearly see the expected inflection points at M T 2 = 600 GeV and M T 2 = 800 GeV.

tt + jets control region
As experimenters are likely to rely on data rather than Monte Carlo for the tt+jets background, we demonstrate a control region by inverting cuts #4 and #5, requiring that there be at least one lepton or hard subjet highly collimated with E T . An array of cos θ tb distributions for this region is shown in Figure 4. They evince little contamination from signal and other backgrounds.
It may be of concern that the collimation cuts #4 and #5 might introduce distortions to the cos θ tb distributions obtained from top tagging. In Figure 5 we show that the polarization distribution for tt+jets is invariant under these cuts up to statistical fluctuations. We show also in Figure 6 that the M T 2 cut does not distort the polarization distribution of tt+jets in the control region. Thus, it is safe to use a data-driven tt+jets background from this region.  To calculate sensitivity, we sum the cos θ tb distributions from signal and background processes. For the tt+jets contribution, we use the control region distribution normalized to the total of the signal region distribution. This sum is shown in Figure 7, where we have rebinned the data to use only two bins in order to minimize the trials penalty. The corresponding p-values for distinguishing stop mixing hypotheses are shown in Tables 2, 3

Conclusion and outlook
In summary, we described a simulation and analysis methodology for the t + E T collider signature that can distinguish stop mixing hypotheses at 14 TeV LHC with ∼ 100 fb −1 of data using the substructure of boosted jets. There are several possible improvements to the methodology. The first and foremost is to include polarization information from leptonic decays. Also if, in consultation with experimenters, the trimming threshold of p T = 10 GeV or the subjet cone size ∆R = 0.2 can be reduced, this would enhance the performance of the top reconstruction algorithm. Finally, it may be useful to implement the top reconstruction technique of Ref. [11] to supplement b-tagging, especially at large boosts. Other possible improvements are to implement charm mistagging, use spin-correlated backgrounds, and to calculate backgrounds at NLO.