## Studying the Higgs via Top Quark Couplings

Article: “Implications of CP-violating Top-Higgs Couplings at LHC and Higgs Factories”

Authors: Archil Kobakhidze, Ning Liu, Lei Wu, and Jason Yue

Reference: arXiv hep-ph 1610.06676

It has been nearly five years since scientists at the LHC first observed a new particle that looked a whole lot like the highly sought after Higgs boson. In those five years, they have poked and prodded at every possible feature of that particle, trying to determine its identity once and for all. The conclusions? If this thing is an imposter, it’s doing an incredible job.

This new particle of ours really does seem to be the classic Standard Model Higgs. It is a neutral scalar, with a mass of about 125 GeV. All of its couplings with other SM particles are lying within uncertainty of their expected values, which is very important. You’ve maybe heard people say that the Higgs gives particles mass. This qualitative statement translates into an expectation that the Higgs coupling to a given particle is proportional to that particle’s mass. So probing the values of these couplings is a crucial task.

Figure 1 shows the combined experimental measurements between ATLAS and CMS of Higgs decay signal strengths as a ratio of measurement to SM expectation. Values close to 1 means that experiment is matching theory. Looking at this plot, you might notice that a few of these values have significant deviations from 1, where our perfect Standard Model world is living. Specifically, the ttH signal strength is running a bit high. ttH is the production of a top pair and a Higgs from a single proton collision. There are many ways to do this, starting from the primary Higgs production mechanism of gluon-gluon fusion. Figure 2 shows some example diagrams that can produce this interesting ttH signature. While the deviations are a sign to physicists that maybe we don’t understand the whole picture.

Putting this in context with everything else we know about the Higgs, that top coupling is actually a key player in the Standard Model game. There is a popular unsolved mystery in the SM called the hierarchy problem. The way we understand the top quark contribution to the Higgs mass, we shouldn’t be able to get such a light Higgs, or a stable vacuum. Additionally, electroweak baryogenesis reveals that there are things about the top quark that we don’t know about.

Now that we know we want to study top-Higgs couplings, we need a way to characterize them. In the Standard Model, the coupling is purely scalar. However, in beyond the SM models, there can also be a pseudoscalar component, which violates charge-parity (CP) symmetry. Figure 3 shows a generic form for the term, where Cst is the scalar and Cpt is the pseudoscalar contribution. What we don’t know right away are the relative magnitudes of these two components. In the Standard Model, Cst = 1 and Cpt = 0. But theory suggests that there may be some non-zero value for Cpt, and that’s what we want to figure out.

Using simulations along with the datasets from Run 1 and Run 2 of the LHC, the authors of this paper investigated the possible values of Cst and Cpt. Figure 4 shows the updated bound. You can see from the yellow 2σ contour that the new limits on the values are |Cpt| < 0.37 and 0.85 < Cst < 1.20, extending the exclusions from Run 1 data alone. Additionally, the authors claim that the cross section of ttH can be enhanced up to 1.41 times the SM prediction. This enhancement could either come from a scenario where Cpt = 0 and Cst > 1, or the existence of a non-zero Cpt component.

Further probing of these couplings could come from the HL-LHC, through further studies like this one. However, examining the tH coupling in a future lepton collider would also provide valuable insights. The process e+e- à hZ contains a top quark loop. Thus one could make a precision measurement of this rate, simultaneously providing a handle on the tH coupling.

1. “Enhanced Higgs associated production with a top quark pair in the NMSSM with light singlets”. arXiv hep-ph 02353
2. “Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at √s = 7 and 8 TeV.” ATLAS-CONF-2015-044

## Inspecting the Higgs with a golden probe

Hello particle nibblers,

After recovering from a dead-diphoton-excess induced depression (see here, here, and here for summaries) I am back to tell you a little more about something that actually does exist, our old friend Monsieur Higgs boson. All of the fuss over the past few months over a potential new particle at 750 GeV has perhaps made us forget just how special and interesting the Higgs boson really is, but as more data is collected at the LHC, we will surely be reminded of this fact once again (see Fig.1).

Previously I discussed how one of the best and most precise ways to study the Higgs boson is just by `shining light on it’, or more specifically via its decays to pairs of photons. Today I want to expand on another fantastic and precise way to study the Higgs which I briefly mentioned previously; Higgs decays to four charged leptons (specifically electrons and muons) shown in Fig.2. This is a channel near and dear to my heart and has a long history because it was realized, way before the Higgs was actually discovered at 125 GeV, to be among the best ways to find a Higgs boson over a large range of potential masses above around 100 GeV. This led to it being dubbed the “gold plated” Higgs discovery mode, or “golden channel”, and in fact was one of the first channels (along with the diphoton channel) in which the 125 GeV Higgs boson was discovered at the LHC.

One of the characteristics that makes the golden channel so valuable as a probe of the Higgs is that it is very precisely measured by the ATLAS and CMS experiments and has a very good signal to background ratio. Furthermore, it is very well understood theoretically since most of the dominant contributions can be calculated explicitly for both the signal and background. The final feature of the golden channel that makes it valuable, and the one that I will focus on today, is that it contains a wealth of information in each event due to the large number of observables associated with the four final state leptons.

Since there are four charged leptons which are measured and each has an associated four momentum, there are in principle 16 separate numbers which can be measured in each event. However, the masses of the charged leptons are tiny in comparison to the Higgs mass so we can consider them as massless (see Footnote 1) to a very good approximation. This then reduces (using energy-momentum conservation) the number of observables to 12 which, in the lab frame, are given by the transverse momentum, rapidity, and azimuthal angle of each lepton. Now, Lorentz invariance tells us that physics doesnt care which frame of reference we pick to analyze the four lepton system. This allows us to perform a Lorentz transformation from the lab frame where the leptons are measured, but where the underlying physics can be obscured, to the much more convenient and intuitive center of mass frame of the four lepton system. Due to energy-momentum conservation, this is also the center of mass frame of the Higgs boson. In this frame the Higgs boson is at rest and the $\emph{pairs}$ of leptons come out back to back (see Footnote 2) .

In this frame the 12 observables can be divided into 4 production and 8 decay (see Footnote 3). The 4 production variables are characterized by the transverse momentum (which has two components), the rapidity, and the azimuthal angle of the four lepton system. The differential spectra for these four variables (especially the transverse momentum and rapidity) depend very much on how the Higgs is produced and are also affected by parton distribution functions at hadron colliders like the LHC. Thus the differential spectra for these variables can not in general be computed explicitly for Higgs production at the LHC.

The 8 decay observables are characterized by the center of mass energy of the four lepton system, which in this case is equal to the Higgs mass, as well as two invariant masses associated with each pair of leptons (how one picks the pairs is arbitrary). There are also five angles ($\Theta, \theta_1, \theta_2$, Φ, Φ1) shown in Fig. 3 for a particular choice of lepton pairings. The angle $\Theta$ is defined as the angle between the beam axis (labeled by p or z) and the axis defined to be in the direction of the momentum of one of the lepton pair systems (labeled by Z1 or z’). This angle also defines the ‘production plane’. The angles $\theta_1, \theta_2$ are the polar angles defined in the lepton pair rest frames. The angle Φ1 is the azimuthal angle between the production plane and the plane formed from the four vectors of one of the lepton pairs (in this case the muon pair). Finally Φ is defined as the azimuthal angle between the decay planes formed out of the two lepton pairs.

To a good approximation these decay observables are independent of how the Higgs boson is produced. Furthermore, unlike the production variables, the fully differential spectra for the decay observables can be computed explicitly and even analytically. Each of them contains information about the properties of the Higgs boson as do the correlations between them. We see an example of this in Fig. 4 where we show the one dimensional (1D) spectrum for the Φ variable under various assumptions about the CP properties of the Higgs boson.

This variable has long been known to be sensitive to the CP properties of the Higgs boson. An effect like CP violation would show up as an asymmetry in this Φ distribution which we can see in curve number 5 shown in orange. Keep in mind though that although I show a 1D spectrum for Φ, the Higgs to four lepton decay is a multidimensional differential spectrum of the 8 decay observables and all of their correlations. Thus though we can already see from a 1D projection for Φ how information about the Higgs is contained in these distributions, MUCH more information is contained in the fully differential decay width of Higgs to four lepton decays. This makes the golden channel a powerful probe of the detailed properties of the Higgs boson.

OK nibblers, hopefully I have given you a flavor of the golden channel and why it is valuable as a probe of the Higgs boson. In a future post I will discuss in more detail the various types of physics effects which can enter in the grey blob in Fig. 2. Until then, keep nibbling and don’t let dead diphotons get you down!

Footnote 1: If you are feeling uneasy about the fact that the Higgs can only “talk to” particles with mass and yet can decay to four massless (atleast approximately) leptons, keep in mind they do not interact directly. The Higgs decay to four charged leptons is mediated by intermediate particles which DO talk to the Higgs and charged leptons.

Footnote 2: More precisely, in the Higgs rest frame, the four vector formed out of the sum of the two four vectors of any pair of leptons which are chosen will be back to back with the four vector formed out of the sum of the second pair of leptons.

Footnote 3: This dividing into production and decay variables after transforming to the four lepton system center of mass frame (i.e. Higgs rest frame) is only possible in practice because all four leptons are visible and their four momentum can be reconstructed with very good precision at the LHC. This then allows for the rest frame of the Higgs boson to be reconstructed on an event by event basis. For final states with missing energy or jets which can not be reconstructed with high precision, transforming to the Higgs rest frame is in general not possible.