Enhancing the ttH signal through top-quark spin polarization effects at the LHC

We compare the impact of top-quark spin polarization effects in Higgs boson production in association with top-quark pairs and in corresponding backgrounds at the LHC. Because of the spin-zero nature of the Higgs boson, one expects, in the chiral limit for the top quarks, a substantial complementarity in $t\bar t$ spin correlations for a Higgs decaying into fermions/gauge-bosons and $t\bar{t}$ spin correlations for the corresponding irreducible $t\bar t f\bar f/VV$ backgrounds. Although top mass effects in $t\bar t H$ production are in general dominant, and seriously spoil the chiral-limit expectations, one can find observables that capture the $t \bar t$ angular spin correlations and can help in separating the signal from irreducible backgrounds. In particular, we show that, for both $H\to b\bar b$ and $H\to \gamma\gamma$, taking into account $t\bar{t}$ spin correlations in $t\bar t H$ production and irreducible backgrounds could appreciably improve the LHC sensitivity to the $t\bar t H$ channel.


Introduction
After the Higgs boson discovery in 2012 [1], [2], with m H around 125 GeV, the LHC experiments are due to test the new particle properties at the highest possible accuracy in the forthcoming years. The direct verification of the Yukawa sector describing the Higgs couplings to fermions in the standard model (SM) plays a major role in establishing the actual nature of the observed new particle. The Higgs coupling Y t to the top quark, the heaviest fermion, is of particular phenomenological and theoretical interest, since on the one hand it rules the dominant oneloop production mechanism gg → H, and, on the other hand, it governs the leading Higgsmass corrections dependence on the theory cut-off energy scale, connected to the scalar-field naturalness problem in the SM.
Potential contributions from new virtual states circulating in the gg → H, possibly induced by some unknown new physics, make the Higgs-top coupling determination through gg → H production particularly model dependent. A model-independent test of the Y t coupling relies instead on lower cross-section processes, notably the Higgs boson production in association with a top-quark pair pp → ttH [3]- [13], where one can tag the actual presence of top quarks in the final state [14]- [15].
The ttH production is a very challenging channel, traditionally thought to require the highest LHC collision energies and integrated luminosities in order to be discriminated from background. The ttH cross section at 8-TeV pp collisions is quite depleted by the phase space of three heavy final particles, being just about 130 fb [16]. Nevertheless, both the ATLAS and CMS experiments have been performing better than expected, delivering a first set of quite constraining measurements of ttH signal strengths for different Higgs decay channels [17]- [22]. Dedicated analysis have been done even in the rarest channels, like H → γγ and multileptons, where a more favorable signal-to-background ratio (S/B) compensates for the lack of statistics. The latter turn out to have a constraining power similar to the highest-statistics channels. For instance, with the present data set of about 5 fb −1 at 7 TeV plus about 20 fb −1 at 8 TeV, a 95% C.L. observed upper limit of 5.4 (5.3) times the SM cross section in the H → γγ channel has been set by CMS [20] (ATLAS [18]), that is quite close to the corresponding upper bound for the H → bb channel based on the same data set by CMS [21]. By combining the H → bb, γγ, τ τ and multileptons analyses [20]- [22], CMS already delivered a first measurement of the ttH signal strength, based on the total present data set, as σ/σ SM ≃ 2.5 +1.1 −1.0 , assuming SM Higgs branching ratios [23]. The channel with highest statistic, arising from H → bb, suffers from large QCD backgrounds, mainly corresponding to the ttbb and ttjj final states. The reconstruction of the H → bb resonance is also plagued by a combinatorial background arising from incorrect b-jet assignment (due either to extra b's from t andt decays or misidentified light jets). The ttjj reducible background component amounts to more than 95% of the total [24], and can be normalized through control regions not contaminated by the signal. Requiring multiple b-jet tagging is also very effective in reducing it. On the other hand, the irreducible ttbb component is hard to separate or fit through data-driven methods, being much smaller than, and kinematically very similar to, the dominant ttjj. As a consequence, in order to separate the irreducible background, it is crucial to reach the highest possible control of theory predictions for the ttbb production. To this end, in [24] an up-to-date discussion on the consistent interfacing next-toleading-order (NLO) QCD perturbative predictions [25]- [29] 1 with parton showers at 14 TeV is presented. After applying, a particular set of cuts optimizing the signal to background ratio, present analysis foresee S/B < ∼ 1/20. Developing strategies aimed to better discriminate the ttH signal distributions versus the irreducible ttbb background is hence crucial, particularly in view of the much higher statistics that will be accumulated in forthcoming years at 14 TeV.
The scope of the present study is to explore the potential of the spin-correlation properties in the associated Higgs top-pair production at the LHC as a possible tool to improve the separation of the signal from the ttH irreducible backgrounds. The ttH spin properties have recently been considered in the literature as a mean to characterize a SM signal versus possible non-SM effects. In particular, spin correlations could help in disentangling the SM scalar component from a pseudoscalar contribution in the top-Higgs coupling [33]. In [34] it was emphasized that the relative impact of spin correlations on the leading-order (LO) ttH lepton kinematical distributions is much more dramatic than the one of the corresponding QCD NLO corrections [12].
The top quark is unique among all quarks, its life time being shorter than the characteristic hadronization time scale. Top quarks are then expected to decay before their original spin is affected by strong interactions, so ensuring that spin polarization at production level is fully transferred to the top decay products. Hence, by reconstructing the individual top systems (which can actually be done even in presence of two neutrinos in the final state [35]), the topquark spin properties can be accessed by measuring angular distributions of the final decay products in t → W + b → ℓν(du) + b [36]. Among the top decay products, the charged lepton (or d quark) has the maximal spacial correlation with the original top-quark spin axis [37]- [38].
In a naive picture, in the chiral limit of vanishing top-quark mass (or for very high invariant masses of the tt system, m tt ≫ m t ) the top quark and antiquark spins are highly correlated and parallel to each other along the tt production axis. Top pairs are hence produced in the LR + RL helicity configurations, where L(R) stands for the left(right)-handed helicity polarization. In the same kinematical limits, when the tt is produced in association with a Higgs boson, the top quark and antiquark helicities are also correlated, but in a complementary way with respect to the previous case. Indeed the Higgs-boson emission from the top-quark final states via Yukawa interactions induces a chirality flip in the top-quark polarization. Then, in contrast with tt production, for large m tt invariant masses the dominant tt helicity configurations in the ttH final state will be LL+RR, while the LR+RL configuration is expected to be suppressed by terms of order O(m 2 t /m 2 tt ). We can now extend the same top-quark chiral limit to the irreducible backgrounds for 1 See also [30]- [32] for NLO QCD corrections to ttjj.
ttH. For H → γγ, the irreducible background arises from direct ttγγ production. In this case, the emission of photons from the quark lines in the gg → tt and qq → tt amplitudes is not expected to affect the basic LR+RL helicity correlation of the plain top-quark pair production. One then should have some complementarity in the spin-correlation properties of the ttH(→ γγ) signal and the ones of the ttγγ irreducible background. As for the decay channel H → bb, the ttH(→ bb) signal presents of course the same spin correlations as the ones in the ttH(→ γγ) channel. On the other hand, the analysis of the ttbb irreducible background is less straightforward than in ttγγ even in the top chiral limit, since many different topologies (presenting in general different tt spin correlations) contribute to the ttH(→ bb) amplitude. Nevertheless, one expects that the action of the Yukawa coupling in the signal channel should leave some imprint diversifying the signal polarization features of ttH(→ bb) with respect to the ttbb irreducible background also in this case.
Just as it actually happens for the tt production [45], when dropping the unrealistic (for LHC energies) top chiral-limit assumption, predicting polarization properties of the ttH signal and corresponding backgrounds gets much harder. Top mass effects are indeed dominant in the bulk production of top pair systems. In tt production, the structure of spin correlations changes significantly over the top production phase space, with modulations (arising from the interference of different helicity states) that widely vary from threshold production to boostedtop regime [46]. As a consequence, the top-antitop spin-correlation properties in ttH and corresponding irreducible backgrounds are in general not simple to predict on the basis of the previous naive arguments.
In this paper, we study LO distributions of top decay products in ttH versus corresponding irreducible backgrounds, by keeping the correct correlation effects between top polarization in production and decay. We try to identify polarization observables that are particularly sensitive to separate the signal from irreducible backgrounds. The dependence on the reference-frame choice is also discussed.
We focus on the two channels corresponding to the H → γγ and H → bb decays where the corresponding irreducible backgrounds ttγγ and ttbb are expected to play a major role with respect to reducible ones.
Note that, regarding the ttγγ background, there are extra contributions to the observed final state ℓνb ℓνb γγ due to photon brehmsstralung from charged top decay products [47]. The latter can fake the irreducible ttγγ background, and affect the reconstruction of the spin properties of tt pairs. Proper kinematical cuts on the decay products of the top quarks can help to reduce these contributions, although eventual tt spin correlations are in general quite affected by kinematical cuts 2 . NLO QCD corrections to ttγγ could be further incorporated through the MadGraph5 aMC@NLO framework [48].
In the Section 2, we start with a more quantitative analysis of the polarization effects in the ttH production. We then proceed to a detailed analysis of the signal and corresponding irreducible backgrounds for H → γγ and H → bb, in Section 3 and 4, respectively. We then draw our conclusions in the Section 5.

Spin correlations in ttH production
Before entering the details of the signal and background analysis for the ttH production, we show in Fig. 1, the integrated top p T distributions projected on the tt LL+RR and LR+RL helicity configurations (normalized to the total cross section), for the tt (left plot) and ttH (right plot) productions, in the Lab frame. Here, p top T is the minimum transverse momentum of the hardest top. We can see that helicity correlations as a function of p top T (which is directly connected to the invariant mass m tt of the tt system adopted before) for tt and ttH productions are not complementary as in the top chiral limit, but present a quite different behavior. In tt production, one indeed observes the chiral limit emerging at large p top T , with the LR+RL component saturating the production rate. On the other hand, in the ttH production one does not have a complementary LL+RR dominance at high p top T as expected from the Higgs-sstralung chirality flip discussed in Section 1. Top mass effects and the presence in the final state of a further massive (Higgs) particle makes the LL+RR and LR+RL helicity components in ttH less unbalanced in all the statistically relevant top transverse-momentum range. One expects that the actual chiral limit is reached in ttH production for much higher p top T values than the ones that can be experimentally covered with the actual LHC energy and luminosity. While in tt production the fraction of the chiral-limit LR+RL configuration is above 80% for p top T > ∼ 400 GeV, in ttH it moderately gets the upperhand for p top T > ∼ 600 GeV, effectively dampened by Higgs radiation.
We then compare the fraction of LL+RR and LR+RL helicity configurations that contribute to the total ttH cross section, with the corresponding fractions in the irreducible backgrounds corresponding to the H → γγ and H → bb channels. We find that about 61% of the total ttH cross section corresponds to the LL+RR combination, with a remaining 39% for LR+RL. Regarding the ttγγ background (with basic cuts defined in the Fig. 2 caption later on), we have 28% of the total cross section with LL+RR combination, and a remaining 72% for LR+RL. As for the ttbb background (with basic cuts defined in the Fig. 7 caption later on), we have an almost equal fraction of LL+RR and LR+RL configurations. One can see that in the ttγγ background one indeed finds an opposite trend in the helicity configurations with respect to the H → γγ signal. In the ttbb background the effect is washed out in the integrated cross section.
We now proceed to scrutinize the effects of ttH top spin properties through the study of angular variables involving decay products of the top pair into two semileptonic final states t → bℓν,t →bℓν. We will focus in particular on charged-lepton pair and b-jet pair variables, where the b jets originate from top and antitop decays, applying strategies previously explored in tt production. Spin correlations in hadronic tt production can be measured by studying angular distributions of top decay products in specific frames and coordinate basis [39]- [41]. The following observables and corresponding distributions have been extensively used 3 : is the polar angle of any of the top (antitop) decay products.
• Distributions of three-dimensional opening angles (ϕ) between one top decay products and one anti-top decay products ( dσ d cos ϕ ). • More compact one-dimensional observables given by combinations of azimuthal angles φ ±φ of two top and antitop decay products ( dσ d(φ±φ) ).
In this work we focus on the second kind of observables as they capture most of the tt-system spin-correlation effects at moderate values of the top-quark p T [46]. Apart from the laboratory frame, we will consider two further reference frames. The latter, although unusual, have been introduced in [40], being particularly sensitivite to the tt spin correlations compared to the lab frame.
We define the angle between the direction of flight of ℓ + (b) in the t rest system and ℓ − (b) in thet rest system [40]. Two different rest systems are involved in the above angular-variable definition, and to avoid ambiguities one has to specify the common initial frame where Lorentz boosts are applied to separately bring the t andt at rest.
The two aforementioned frames are defined as follows. The t andt rest systems are obtained by two corresponding rotation-free Lorentz boosts : • (Frame-1) with respect to the tt-pair c.m. frame, • (Frame-2) with respect to the laboratory frame.
In this paper we analyze the tt spin-correlations in both signal and background for two relevant Higgs decay channels H → γγ and H → bb. For both signal and background the t → bℓν decay has been performed in MadGraph5 [49] by retaining the full spin information, while in the uncorrelated case, the decay has been included by interfacing MadGraph5 with PYTHIA [50] at the ttH level, so neglecting the spin polarization effects. In our analysis, we do not include shower nor hadronization effects. In the following, we will show the results for angular and rapidity distributions for the decay products of the top and antitop, in both the signal ttH, with H → γγ and H → bb, and corresponding irreducible backgrounds ttγγ and ttbb, respectively.
The variables that we found particularly sensitive to spin correlations are cos θ ℓℓ and ∆η ℓ (with ∆η ℓ ≡ |η ℓ + − η ℓ − |), where θ ℓℓ is the three-dimensional polar angle between the ℓ + and ℓ − directions of flight, and η ℓ is the pseudo rapidity of individual leptons in a specific frame. Analogously, we adopt the cos θ bb and ∆η b variables (with ∆η b ≡ |η b − ηb|) involving the two b quarks from t andt decays. This set of variables has been pinpointed after a careful scrutiny including different proposals adopted in tt production studies [45], [46].
In all the following plots, the signal (background) distributions will be shown via red (green) lines, while spin-correlated (-uncorrelated) cases will be reported through solid (dashed) lines. All distributions are normalized to 1. In the following, in each case we will show distributions that we found to be particularly sensitive to spin effects.  In Fig. 2, we show the cos θ ℓℓ distributions for ttγγ signal and irreducible background with and without correlations in the t,t spin polarizations. In the left and right plots we report the results in the Frame-1 and Frame-2, respectively, as defined above. Here, we impose just the following kinematical cuts on the photons transverse momenta, p γ 1,2 T > 20 GeV, pseudorapidities, |η γ 1,2 | < 2.5, and isolation, ∆R γ 1 γ 2 > 0.4, in addition to a diphoton invariant mass cut 123 GeV < m γγ < 129 GeV, where ∆R ij is as usual ∆R ij = η 2 ij + φ 2 ij , with η ij (φ ij ) the rapidity (azimuthal) separation.
In the uncorrelated analysis, the angular distributions for the signal and background are both flat in cos θ ℓℓ , in both reference frames. On the contrary, when the spin information is taken into account, the signal and background distributions are different and almost complementary. In particular, the signal (background) distributions is monotonically increasing (decreasing) as a function of cos θ ℓℓ . This is a consequence of the aforementioned complementarity in the tt helicity correlations of the signal and irreducible background for the H → γγ channel, that we have previously discussed. Although the correlation effect is remarkable both in Frame-1 and Frame-2, the separation between the correlated cos θ ℓℓ distributions for signal and background is more enhanced in Frame-1, where one gets an improvement in S/B (computed by integrating angular distributions over the range 0 < cos θ ℓℓ < 1) of about 17%, compared to the uncorrelated case.
In Fig. 3 , we show the corresponding distributions in the cos θ bb variable in Frame-1 (analogous results hold in Frame-2). The distributions are all approximately flat, and no significant effect is found in this case.
In Fig. 4, for comparison, we consider various distributions in the laboratory frame, where the variables studied are more straightforward to reconstruct experimentally. We analyze the correlated and uncorrelated distributions in cos θ ℓℓ and ∆η ℓ (top), and cos θ bb and ∆η b (bottom) (with ∆η ℓ ≡ |η ℓ + − η ℓ − |), ∆η b ≡ |η b − ηb|). In all plots in the Lab Frame the inclusion of spin correlations increases the difference in distribution shapes between signal and background, although the relative effect is quite smaller than in Frame 1 and Frame 2 for leptonic distributions. The cos θ bb distribution in the Lab Frame is instead much more effective in separating signal and background with respect to Frame 1 (where it is almost flat in all cases cf. Fig. 3). Distributions in rapidity separations turns out to be more selective in the ∆η ℓ < 1.5 range.
In Fig. 5 we show the effects of including both photon radiation from t,t decay products and the new set of kinematical cuts defined in Eq.(3-6) on signal and background. We show the cos θ ℓℓ distributions in Frame-1 (left) and Frame-2 (right), to be compared to the ones not including extra background radiation in Fig. 2. One can see that the cos θ ℓℓ distributions for signal are basically unaffected by the new selection cuts, while in the background the extra photon radiation tends to reduce the gap between the correlated and uncorrelated cos θ ℓℓ distributions.
In Frame-1 one gets an improvement by 14% in S/B.
In the Lab frame, Fig. 6 shows the cos θ ℓℓ (top left), ∆η ℓ (top right), cos θ bb (bottom left) and ∆η b (bottom right) distributions including extra photon radiation and new selection cuts. One can see that the effects of photon emission from the top decay products do not dramatically affect the previous results where these contributions where ignored (cf. Fig. 4). Differences are found mainly for low separations of lepton and b pairs (that is for cos θ ℓℓ , cos θ bb ∼ 1 and ∆η ℓ , ∆η b < 1), where the new set of cuts is more effective. In conclusion, we find that the analysis of the cos θ ℓℓ distributions for the channel ttH(H → γγ) and its irreducible background in a study that correctly takes into account spin-correlation effects could significantly help in enhancing the signal-to-background ratio with respect to the uncorrelated analysis. The use of dedicated reference frames for reconstruction, like Frame-1 and Frame-2, can improve S/B by about 15%. More modest improvements can be obtained in the laboratory frame.

The ttbb channel
We now turn to the spin-correlated analysis for ttH(H → bb). With respect to the H → γγ channel, here the (ttbb) irreducible background receives contributions from many components that have different top spin correlations. This makes even more difficult to guess by general arguments how the correlated/uncorrelated background distributions may behave, especially when kinematical cuts can affect predictions. We stress that the following analysis is an idealized one where we assume to be able to distinguish the b quarks coming from top (anti top) decays. T > 20 GeV, |η b,b | < 2.5 and ∆R bb > 0.4 has been imposed on the two b-quarks not coming from t decays, in addition to the invariant mass cut m bb > 100 GeV.
In Fig. 7 we show the results for the cos θ ℓℓ (left) and cos θ bb (right) distributions for signal and irreducible background, in Frame-1 (top) an Frame-2 (bottom). In both frames spin effects are quite relevant. In particular, while uncorrelated distribution are in general flat, the correlated ones behave differently for signal and background. In Frame-1, signal cos θ ℓℓ slope is quite increased by spin correlations, while background distribution keeps flat. The opposite occurs for cos θ bb distributions in Frame-1, where the background is very sensitive to spin correlations, while signal stays flat. A similar behavior for cos θ bb distributions one has in Frame-2, while cos θ ℓℓ slopes are quite large for both signal and background for the correlated case.
Also in the present case, retaining the full spin information can then help in enhancing S/B, as in the case of the H → γγ channel. In particular, in Frame-1 including spin correlations improves S/B by 7% using the cos θ ℓℓ variable, and by 12% using cos θ bb .
For comparison we present in Fig. 8  correlated and uncorrelated cases. The advantage of employing a full spin-correlated analysis in the Lab frame is quite modest.
Finally, in Fig. 9 we explore the boosted top regime, by imposing that the highest top p T satisfies the cut p T > 250 GeV in the laboratory frame. In particular, we plot the cos θ ℓℓ distributions for the signals ttH (H → γγ) (left) and ttH (H → bb) (right) with their corresponding backgrounds ttγγ and ttbb, imposing the cuts p T > 20 GeV, |η| < 2.5 and ∆R > 0.4 on the final state photons or b quarks (where b's are not from top decays) in addition to the invariant mass cut 123 GeV< m γγ < 129 GeV, and m bb > 100 GeV, respectively. The left and right plots in Fig. 9 should be compared with the top-left plots of Fig. 4 and Fig. 8, respectively. Requiring a boosted top increases the lepton-pair angular separation in general. Then, in the H → γγ, one obtains practically identical correlated and uncorrelated curves. There is instead  Figure 9: The cos θ ℓℓ distributions for the signals (red) ttH (H → γγ) (left) and ttH (H → bb) (right) with their corresponding backgrounds (green) ttγγ and ttbb in the Lab frame, after demanding one highly-boosted top by imposing that the highest top p T satisfies the cut p T > 250 GeV. Same cuts as in Fig. 2 and 7 have been applied, respectively. some advantage for the H → bb signal, where the separation of cos θ ℓℓ distributions for signal and background increases both in the correlated and uncorrelated case.
Summing up, as for the H → γγ signal, we can see that the most significant deviations between the correlated and uncorrelated analysis is observed in the cos θ ℓℓ distributions, evaluated in Frame-1 and Frame-2. Hence, also for the H → bb signal, an analysis taking into account spin correlations in a suitable frame could significantly help in enhancing the S/B ratio with respect to the uncorrelated analysis.

Conclusions
The top-quark polarization observables are quite powerful tools that can be used to enhance the sensitivity to the dynamics involved in the top-production processes. The main purpose of the present study was to investigate the advantages of taking into account the full tt spincorrelation effects in the measurement of the ttH process versus its irreducible backgrounds, using a simplified framework (not including NLO QCD corrections and parton-shower effects). We found that, for the two processes ttH (H → γγ) and ttH (H → bb), where irreducible backgrounds are bound to have a dominant role when increasing the LHC data set at 14 TeV, there are indeed angular variables defined in dedicated reference frames that sizably increase the separation of signal and background, with a gain of about 15% in S/B. We conclude that spin-correlation features in the ttH production should be definitely included in future analysis of the process at high luminosities to enhance the signal sensitivity over the background.