# A CP Properties of the SM Higgs boson

1. Apr 14, 2017

### welatiger

The SM Higgs-boson is a CP-even state, as far as I know this is confirmed in the Higgs decay to di Z bosons, so why there are dozen of papers that propose to measure CP quantum number of the Higgs in tau tau final state?, what is the difference between CP in ZZ and tt of Higgs decay ?

2. Apr 14, 2017

### ChrisVer

One thing that might answer your Q partially is that the Higgs could as well be a mixture of CP-odd and CP-even states... The decays to dibosons are only sensitive to the HVV couplings. This means that if only the CP-even part of the Higgs coupled to dibosons, you wouldn't be able to see the CP-odd component of it. On the other hand, the ditau are sensitive to both HVV (due to the Vector Boson Fusion production of the Higgs) and Hff ones.
This in general allows you to probe more BSM models (by a simple search I found that 2HDM enhances the couplings to ditau) as well as get more sensitive (I think), because the CP-odd scenarios for the dibosons couplings (HVV) appear in loops (higher-dimensional terms of the Lagrangian) while for the ditaus they appear on the tree-level.

Last edited: Apr 14, 2017
3. Apr 14, 2017

Staff Emeritus
Correct.

Not correct. The CP-odd Higgs in 2HDM does not decay to ZZ, but that's not because of CP. It's because it comes about from the purely imaginary parts of the introduced phi fields and the vev is real. So these are orthogonal. But even if that weren't the case, all the decays would tell you is that there is a CP-even component to the Higgs.

Who says what was discovered was the SM Higgs?

4. Apr 14, 2017

### ChrisVer

Also as a side-comment (I think for the moment the answers are given), let's say that we always want to check everything that is possible or available... to make sure it fits to what we observed before (so that's an additional "why not?" answer/question).

5. Apr 14, 2017

### Staff: Mentor

Not the decay itself leads to that assignment, but the angular distribution of the leptons leads to a parity measurement.
ATLAS and CMS ruled out negative parity and determined the spin to be zero.

The Higgs could be an admixture of CP odd and CP eigenstates - more precise measurements will reduce the limit on possible CP odd contributions. The decay to two taus can help there.

PDG has an overview

6. Apr 14, 2017

Staff Emeritus
Technically, they rules out 100% negative paritry. If it's an admixture of CP even and CP-odd (or equivalently, + and - parity) this is allowed provided that the CP-odd piece isn't too big. I don't know offhand what the limit is: 20% 30%?

Everyone thinks its the angles, but the separation power comes almost entirely from m_34, not the angles. m_h = m_12 + m_34 + kinetic energy, and the kinetic energy is L^2/2I. If m_12 is on shell, we have 34 GeV - L^2/2I = m_34, so m_34 is 100% anti-correlated with the decay's angular momentum. CP-even is S-wave and CP-odd is P-wave, so they have different m_34 distributions.

The angles have low separation power because the decay Z to leptons is almost purely axial, so there's very little parity violation, so the Z decay is not self-analyzing in the way the W decay is.

7. Apr 14, 2017

### Staff: Mentor

See the second part of my post.

m_34 is calculated based on the energies of the leptons and the angle between them.

8. Apr 16, 2017

### welatiger

thank you all,

but why the coupling of the Higgs to bososn HVV is through loops, what is meant by higher dimensional operators ?!

9. Apr 16, 2017

Staff Emeritus
That seems like a different question.

10. Apr 19, 2017

### ChrisVer

correction: of the CP-odd part of the Higgs (if it exists).... the CP-even part Higgs has tree-couplings.
For the (H/A)VV Lagrangian you can check Eq1 here: https://arxiv.org/pdf/1703.07675.pdf
The higher-dimension operators are written in it suppressed by some scale $\Lambda$. The first two terms are the VV couplings to the higgs on tree level.

Last edited: Apr 19, 2017