Determining the Expected Range of Angles Between the Muon and Neutrino Pair for the W Boson Decay

Analysis using the W boson decay to muon and a neutrino - data set

Zach Armstrong & Taylor Plantt





One decay pathway for the W boson is into a muon and a neutrino.  The CMS detector is well equiped to analyze the muon but the neutrino is notoriously difficult to detect, much less measure.  As a result the mass of the W boson is determined using transverse mass.  Transverse mass is used when the total energy of the decay products are not known. If the the decay particles can be considered massless then 


The W boson decay to muon and a neutrino data set contains about 2000 collisions.  The traansverse mass histagram shows potential particles between 60-70 GeV and one near 80 GeV (likely the W boson),(Figure 1).  The data is filtered to include only collisions with a missing transverse energy (MET) of 35 to 70 GeV.  This selection gives a single histigram peak near 80 GeV (Figure 2), the expected mass of the W boson.  In the proton-proton collision a W boson is produced and then quickly decays into muon-neutrino pair.  The muon-neutrino pair are produced in the transverse plane.  The angle between the pair should show a consistant range of angles that resulted from the W boson decay. 


To calculate the angle between the muon and neutrino, a transverse mass of 80GeV for the W boson candidate was used as well as a range of transverse energy for both the muon and the neutrino. The muon transverse energy ranged from 20 to 50 GeV (Figure 3) while the neutrino transverse energy ranged from 35-40 GeV (Figure 4). This resulted in a upper end of theta at 3.14 radians and a lower end of theta at 2.21 radians. Comparing these results with the histrograms of the phi angle of the lepton and the phi angle of the missing transver energy, a general angle separation of around 3 radians seems likely.


Discussion and Conclusions

The measure of the mass of the W boson relies on the transverse mass because the total energy of the decay products is not known.  The angle of seperation between the muon and the neutrino are required to determine the W boson mass.  By working backwards we are able to show that the angle between the two should be in the range of 2.21 and 3.14 radians if the decay is likely to be from a W boson.  Therefore, a reasonable filter or trigger for collecting W boson candidates would be the angle between the muon and neutrino. 


Transverse Mass, Wikipedia. 6/6/2017