## Archive for February, 2014

### Z decays to four leptons

A bit more than a year ago I was pleased to see a clear signal from CMS for the decay of Z bosons to four leptons. Of course there are literally millions of recorded Z decays to two leptons (e+ e and μ+ μ) used for standard model physics studies, lepton efficiency measurements, momentum/energy scale determinations and detector alignment. But Z→4L is cuter and of some intrinsic interest, being relatively rare.

It turned out the main interest of physicists who analyzed the signal was Higgs boson decays to four leptons. By now that Higgs signal is well established and plays an important role in the Higgs mass measurement, but at the time of the CMS publication (InSpire link, i.e., arXiv:1210.3844 October 2012), Z→4L provided the ideal benchmark for H→4L.

You might think that the rare decay Z→4L had been well studied at LEP. In fact, it was quite well studied because the ALEPH Collaboration had once reported an anomaly in the 4L final state when two of the leptons were tau leptons. (At the time, this observation hinted at a light supersymmetric Higgs boson signal.) The anomaly was not confirmed by the other LEP experiments. A perhaps definitive study was published by the L3 Collaboration in 1994 (InSpire link). Here are the plots of the two di-lepton masses:

L3 plots showing the minor and major di-lepton masses

Most of the events consist, in essence, of a virtual photon emitted by one of the primary leptons, with that virtual photon materializing as two more leptons – hence the peak at low masses for the Mmin distribution. Note there is no point in plotting the 4-lepton mass since the beam energies were tuned to the Z peak resonance – the total invariant mass will be, modulo initial-state radiation, a narrow peak at the center-of-mass-energy.

Here is the Z resonance from the CMS paper:

CMS distribution of four-lepton invariant mass

A rather clear and convincing peak is observed, in perfect agreement with the standard model prediction. This peak is based on the 5 fb-1 collected in 2011 at 7TeV.

ATLAS have released a study of this final state based on their entire 7 TeV and 8 TeV data set (ATLAS-CONF-2013-055, May 2013). Here is their preliminary 4-lepton mass peak:
Clearly the number of events is higher than in the CMS plot above, since five times the integrated luminosity was used. ATLAS also published the di-lepton sub-masses:

ATLAS di-lepton mass distributions

Notice that the minor mass is less peaked toward zero than in the L3 plot, above.

This calibration channel is not meant to be the place where new physics is discovered. Nonetheless, we have to compare the rate observed in the real data with the theoretical prediction – a discrepancy would be quite interesting since this decay is theoretically clean and the prediction should be solid.

Since the rate of pp→Z→2L is very well measured, and the branching ratio Z→2L already well known from LEP and SLD, we can extract branching fractions for Z decays to four leptons:
``` SM... BF(Z→4L) = (4.37 ± 0.03) × 10-6 CMS.. BF(Z→4L) = (4.2 ± 0.9 ± 0.2) × 10-6 ATLAS BF(Z→4L) = (4.2 ± 0.4 ) × 10^-6 ```
So, as it turns out, the SM prediction matches the observed rate very well.