Golden Probe of the Top Yukawa

We describe how the Higgs decay to four leptons can be used to probe the nature and $CP$ structure of the top Yukawa coupling.

h Z µ Z µ or h Z µν Z µν or h Z µν F µν (1) where h is the putative Higgs, Z µν = ∂ µ Z ν − ∂ ν Z µ , and F µν is the equivalent field strength for the photon. We showed that with O(50) events at the LHC, these different possibilities can be distinguished.

PROBING LOOP PROCCESSES
Having seen that kinematic distributions in h → 4 can be useful, we now turn our attention to measuring loop processes in this channel, namely the next-to-leading order (NLO) corrections to the tree level effect induced by the h Z µ Z µ operator. The largest of these are shown in Figure 1, showing that this channel can be sensitive to the couplings of the Higgs to the top and W. Here we examine the sensitivity of this channel to the top Yukawa coupling, so we keep all other couplings (Higgs to W and Z and gauge boson couplings to fermions) at their SM values. We parameterize the top Yukawa coupling as ht y + iỹ γ 5 t .
In the SM, y ≈ 1 andỹ ≈ 0. The pseudo-scalar operator is P and CP odd, so if both y andỹ are non-zero, then CP is violated in the top Yukawa coupling. This effect is tiny in the SM, so a detection of this would be a clear sign of new physics.

Other Probes of CP Violation
If there is CP violation in the top Yukawa coupling, this contributes to the electric dipole moments (EDM) of the electron, neutron, and Hg atom [2] at two loops. These bounds, particularly the electron EDM, constrainỹ to be less than O(1%), with future experiments expected to reduce the bound to one in ten thousand.

DANIEL STOLARSKI September 2, 2015 LHCP 6
fter the W and top, the next largest contribution he e↵ective Z and couplings comes from the tom quark contribution. This e↵ect is suppressed ⇠ (m b /m t ) 2 in the matrix element relative to the contribution which is itself subdominant to the W . Thus, to a very good approximation, the Z and e↵ective couplings only receive contributions at onefrom the W boson and top quark. he h ! 4`process receives additional one-loop eleceak (EW) corrections that are not of the form wn in Fig. 1. Since the Z and e↵ective couplings q. (1) are only first generated at one loop, they do receive a contribution from these additional EW corions at this loop order. These include processes such orrections to the Z propagator and coupling to leps as well as various other non-local interactions all of ch are computable [82,83]. Thus in principle we can e a precise prediction for all contributions not ining the top Yukawa coupling. This allows us to treat part of the amplitude which does not depend on the Yukawa as part of the SM 'background' to our top awa 'signal'.

Discussion of Signal and 'Backgrounds'
o be more explicit, we can write the h ! 4`amplitude to one loop as follows, leading term M 0 SM arises from the tree level hZZ pling, ch is generated during EWSB and is responsible for ng the Z boson its mass. The second term M 1 EW ines all SM one-loop contributions independent of the Yukawa, though there are one-loop corrections from quark loops to the Z boson propagator for exam-Finally, M 1 t encodes the one-loop contribution sensito the top Yukawa coupling and which enters via the diagram in Fig. 2. 1 In this work, we will treat M 1 t as here is also a wave function renormalization for the Higgs that pends on the top Yukawa, but this does not a↵ect kinematic our signal and fit for the parameters in Eq. (2), while we will treat the rest of the matrix element as 'background' which we keep fixed. There are also real non-Higgs backgrounds, whose leading contributions must be accounted for as well and will be discussed below. We can further characterize the 'background' in M 1 EW by isolating those contributions which are generated by hV V (where V V = ZZ, Z , ) e↵ective couplings of the form shown in Fig. 1 to write, where we have defined, These contributions all have the form of Fig. 1 and will be examined more closely below. There are many contributions toM 1 EW , all of which are computable and can in principle be extracted from [82,83]. Some of these one loop contributions can be absorbed into shifts of the tree level couplings. Others can be modeled using e↵ective operators. There are also real photon emission e↵ects in h ! 4`[82-84] which can be non-negligible in certain regions of phase space, but which can also be included [85]. The key point however is that these corrections do not depend on the top Yukawa, allowing us to treat them as fixed when fitting for the top Yukawa. Furthermore, since at one loop these corrections do not contribute to the Z or e↵ective couplings to which we are most sensitive in h ! 4`[66, 68], and since they are sub-dominant over most of the phase space [85], we will neglect them in this preliminary study. However, a detailed investigation of their e↵ects is worthwhile and will be done in future work. Thus in the end, for the present study we define the Higgs part of our 'background' (in contrast to non-Higgs background to be discussed) as, This part of the h ! 4`amplitude will be treated as fixed during the parameter extraction procedure. As mentioned, our 'signal' is then the top quark loop in the Z and e↵ective couplings which we call M Z Z/ Z/ h rates measurements can.
Put this to use with loop processes. The computations of EDM bounds assume SM couplings for other fields. In particular, the Yukawa coupling of the first generation fermions to the Higgs play a key role. As we have no direct experimental evidence that these couplings are SM-like, one could also consider the scenario where those couplings are zero, and in that case O(1) values ofỹ are allowed. In this case, the neutron EDM is still somewhat sensitive due to the Weinberg operator, and future experiments are expected to boundỹ at the per mille level, but they could also see a discovery. In that case, direct measurements of the top Yukawa coupling will be critical to characterizing the nature of CP violation responsible.

Experimental Sensitivity
In [3] we analyzed the experimental sensitivity of h → 4 to y andỹ. The sensitivity depends on the number of such decays which in turn depends on the integrated luminosity. To get an O(1) precision on y andỹ, one needs about ten thousand events, which corresponds to a few thousand fb −1 of luminosity and depends on the experimental efficiencies. The scaling of the sensitivity is shown in Figure 2. From there, we see that the sensitivity toỹ is better than to y, and this is because there is no SM contribution of the W to compete with in the P odd channel.  The sensitivity depends on the experimental cuts used to collect h → 4 . Current cuts are designed for discovery and to maximize the ratio of signal to background. As an example, they require one of the lepton pairs to have invariant mass bigger than 40 GeV at CMS. Since we already have the discovery, current measurements would be more sensitive to NLO effects if they aimed to maximize signal efficiency [4], even if that means having more background events in the sample. In particular, by loosening the invariant mass cut down to 4 GeV, the experiments will be much more sensitive to effects with photon intermediate states. This will increase the amount of background, but [4] showed that the sensitivity to loop effects is much improved even with background taken into account.
We can plot the the 1 − σ contours in the y −ỹ plane for different numbers of events, and this is done Figures 3,  4, and 5. All our simulations use a crude modelling of detector effects including energy smearing described in [4]. We show three different contours for different assumptions about how events are collected. The outermost is using current CMS cuts, the middle is using the realistic "Relaxed-Υ" cuts described in [4], and the innermost is with zero background, the theoretically best possible result. We see that definite improvements can be made relative to current cuts, but it is possible that a still better method exists. )   )  There are other measurements that are sensitive to the top Yukawa coupling, and we have put some of them in the figures for comparison. The green oval is the bound from tth production which is quadratically sensitive to y and y. The thickness of the oval represents putative uncertainty of that measurement, but even with an infinitely precise measurement, tth alone will never be able to determine at what point in the oval the true theory lies. The blue band )  is h → γγ, which is again an oval, but displaced from the origin because of the contribution from the W loop to that process. The pink curve is h → Zγ which is much less sensitive.
In Figure 3, we show the projected sensitivity with 800 events which corresponds to roughly 300 fb −1 , where we see the h → 4 measurement is only barely competitive with the others. On the other hand, with higher luminosity the other measurements do not gain much sensitivity, while h → 4 will always be statistics limited. Therefore we see in Figure 4, which corresponds to roughly 3,000 fb −1 , the high luminosity run of the LHC, that this measurement gets substantially better, allowing for strong constraints. Finally, we see that with 20,000 events, the measurement is even further improved, and this quantity of events could be achieved with a 100 TeV collider recording 3 ab −1 .
If tth and h → γγ are both measured to be SM-like in the asymptotic future of the LHC, then they can mutually break each others degeneracy in y −ỹ plane. On the other hand, there are assumptions about no other new physics that have to go into this measurement, particularly in the loop induced h → γγ decay. Furthermore, if there is a deviation from the SM prediction in one or both of these measurements, then the h → 4 analysis described here will be crucial in characterizing the deviation.

CONCLUSIONS
The four lepton decay of the Higgs is an excellent channel to make detailed measurements. The four body final state gives rise to a rich structure of kinematic variables that can be exploited to measure the properties of the Higgs. This analysis is complementary to rate measurements and can give information not available in other ways. In particular, this channel is sensitive to NLO effects that interfere with the tree level contribution, giving access to the Higgs' coupling to the top quark and W boson. Furthermore, because the NLO effects interfere with the leading order, one can measure signs and phases of the Yukawa coupling. Therefore, this measurement can be used to place model independent bounds, or possibly even discover new physics.