## The CP Nature of the Higgs Boson

*November 18, 2012 at 10:48 am* *
4 comments *

We are in the process of ascertaining the properties of the Higgs-like particle discovered by CMS and ATLAS last July 4th. It must be a boson because it decays to pairs of bosons. Since it decays to a pair of massless photons, it cannot be spin-1. The relative rates of decays to WW and ZZ on the one hand, and γγ on the other, are close to what is expected for spin-0 boson and not what is expected for a spin-2 graviton. John Ellis, Veronica Sanz and Tevong You wrote a nice paper about this earlier this week (arXiv:1211.3068, 13-Nov).

So let’s assume that the new particle X(126) is a Higgs boson (and I will use the symbol “H” for it). If it is the standard model Higgs boson, then its CP eigenvalue must be +1. If it is a member of a two-Higgs-doublet model, then its CP eigenvalue might be -1, and if there is CP-violation in the Higgs sector, then its CP eigenvalue would be something other than +1 or -1.

The new news about this comes from the Hadron Collider Physics Symposium that just finished in Tokyo last week. The CMS Collaboration presented results that indicate that CP = -1 is the wrong hypothesis for the H. They used the golden channel H→ZZ→4L, where the four leptons are electrons and muons. The H state is completely reconstructed in this channel, and backgrounds are low. The Z bosons themselves are massive spin-1 particles, which means that they can be transversely and/or longitudinally polarized, so that one can talk about the degree of their polarization. They are produced coherently in the decay of the H, so their quantum mechanical states are entangled and their joint quantum mechanical state reflects the properties of the parent particle, H. Their quantum mechanical state is manifested in the angular distributions of the four leptons, especially taken as pairs — two for the first boson Z_{1} and two for the second bosons Z_{2}. So a study of the angular distributions tells us, on a statistical basis, whether the parent particle H is spin-0 or spin-2, and what its CP eigenvalue is. This physics as been studied by many authors, some of whom work on the CMS analysis discussed here, and who published their ideas two years ago (Gao et al., InSpire link). Many theorists have discussed similar material, for example arXiv:1108.2274.

Checking the hypotheses spin-0 and spin-2 is not fruitful at this time, and anyway we have reasons to believe that is has spin-0. So *assuming that it does have spin-0*, we can check the hypotheses CP-even and CP-off.

With four leptons in the final state, several angular distributions are available. Here is a diagram from Gao et al. labeling the main ones in the H center-of-mass frame:

There is the polar angle θ

^{*}the two Z bosons make with the beam axis. There are the two polar angles θ

_{1}and θ

_{2}that the lepton pairs make in the rest frames of the two Z bosons. Finally, there is a relative azimuthal angle Φ that the two Z decay planes make with each other.

The most striking differentiation between CP-even and CP-odd comes from the polar angles θ_{1} and θ_{2} and the azimuthal angle Φ. Here are the ideal distributions:

The CP-even case is shown by the solid red dots and the CP-off case by the open blue dots — the distributions are plainly different.

The event sample available to CMS at present is not large enough to make a determination of the CP eigenvalue by simply plotting one of these distributions. Instead, the CMS physicists built a probability density function for the two hypotheses based on the measured decay angles. This gives them the highest achievable statistical power (i.e., ability to distinguish two hypotheses CP-even vs. CP-odd) for the observables that they measure. An abstract-like summary is available on a CMS web page and also in the public document CMS PAS HIG-12-041.

The authors take the SM expectation as the null hypothesis and the alternative is the CP-odd hypothesis. The test statistic is D = [1 + P(CP-odd)/P(CP-even)]^{-1}, where P is the probability density calculated from the lepton angles and the two Z masses. There are three terms in the theoretical expression for P, one of which is small for both hypotheses and neglected, and the other two that dominate; which one dominating depends on which CP eigenvalue is assumed. The method takes account of the correlations among all measured quantities — indeed this is the point of the method and the reason why it is more effective than simply projecting out the angular variables.

The distribution of the discriminating variable shows some a priori power of discrimination:

The discrimination is not dramatic, but it is not negligible either. The few data entries do land more to the right of the plot than to the left, favoring the CP-even hypothesis.

The hypothesis test boils down to one number, namely, the log of the ratio of likelihoods. The distribution of this variable is typically Gaussian, and the two hypotheses show up as Gaussians with different means and more or less the same width. The power of the test amounts to the separation of the two peaks (which depends on the separation of the means and the narrowness of the peaks); for a powerful test there is very little overlap between them. The power of the test depends on the number of events, so the authors made the plot for the number of events observed:

The magenta peak on the right represents the CP-even hypothesis (as expected in the SM), and the blue peak on the left represents the CP-odd hypothesis. The two peaks do overlap, so there are some values for this quantity for which a conclusion would be difficult or impossible. As it turns out, the value from the CMS data lands a bit to the right — see the position of the green arrow. If the H particle truly has CP-odd, then the probability to observe the value indicated by the green arrow is low, about 2.4%. In this sense, the CMS analysis disfavors the CP-odd hypothesis at the 2.5σ level. It is completely compatible with the CP-even hypothesis.

So the conclusion is that the new particle is probably CP-even, as expected in the SM.

While this indication is fairly strong and extremely important, 2.5σ can be a fluctuation. We have seen larger fluctuations in other places in the grand landscape of Higgs searches. We will have to see whether ATLAS can perform this analysis and what their data will indicate. Furthermore, the possibility of CP-violation is completely set aside in this analysis, since only two hypotheses are tested – one cannot do better with the present data sample. At some point physicists will define an angle in CP space that quantifies the deviation from the CP-even hypothesis, and experimenters will start to constrain or measure that angle.

Note: Tommaso Dorigo wrote about this briefly, last Wednesday.

**Update** (21-Nov): The witty author of one of my favorite blogs, In the Dark, wrote yesterday about interesting new CP-violation results in the B system (link: Time will say nothing but I told you so…) and provided a very nice, succinct description of what C, P and CP violation means. Take a read!

Entry filed under: Particle Physics.

1.telescoper | November 21, 2012 at 2:49 amReblogged this on In the Dark and commented:

After my little dabble in particle physics yesterdays I thought I’d reblog this from a proper particle physicist – it’s a long and rather technical post about the Higgs-like Boson recently discovered at the LHC. Enjoy.

2.Durgadas Datta | November 21, 2012 at 3:47 amPossibility of CP VIOLATION can not be set aside when the stage is a gravitoetherton soup itself. The wrong theories are applied to prove SM right which can not be contemplated from asymmetry largely responsible in the function. The spin has to be 2 and if we devise the model in mono magnetic coupling arm then the ideas of spin dissolves into a coupling reaction from earths magnetism as well as gravitoetherton spin. We are avoiding the vicinity of side track which also seen from bias of particles path. More intelligent way of thinking in polar coordinates taking the concept out of FEYNMAN MODEL may help to un cover the gravitoetherton or graviton or ether or dark energy what ever you say. Read balloon inside balloon theory of atom model and universe by Durgadas Datta. Do not dabble again at this juncture of NEW PHYSICS. Abandon relativity and present day quantum physics of uncertainty and vagueness on Feynman diagrams and wrong atomic model of Bohr and others. BE CAREFUL NOW AS OUR STATE OF MIND IS FILLED WITH WRONG PHYSICS.

3.Measurement of the Mass of the Higgs Boson « Collider Blog | November 21, 2012 at 4:34 pm[…] Let’s use the word “Higgs boson” for the new state discovered by ATLAS and CMS. The collider physics community is trying to measure everything they can about this new particle. One of the “easiest” properties to measure is its mass, MH. (One of the more difficult is the CP Nature of the Higgs boson.) […]

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