particle physics - Energy measurement of W- and Z- bosons

W bosons decay into an electron and electron-neutrino or into a muon and muon-neutrino. The W lifetime is about $3 \cdot 10^{-25} s$, that means the decay occurs close to the collision point, not in a detector.

The energy of the resulting electron or muon can be measured quite accurately, but for the neutrino the energy must be inferred (with a low accuracy).

How can one arrive at a precision like $80.385 \pm 0.015\ GeV$ for the W boson rest energy, as it is quoted in the literature?

(similar arguments apply to the Z)

Answer

The $Z$-boson mass is easily fully measurable since for e.g. the processes $Z\to e^+e^-$ and $Z\to\mu^+\mu^-$ the complete four-vectors $p_\mu$ of the two final state particles can be measured very precisely, and from this one can reconstruct the $Z$ four vector and therefore its mass: $$m_Z^2=(p_1^\mu+p_2^\mu)^2$$

For the $W$ mass it is indeed a little more tricky: as you say, the neutrino cannot be directly measured, since it does not interact with the detector and only shows up as missing transverse energy ("MET"). Since at hadron colliders, we do not know the what the momentum balance in the longitudinal direction is (beam remnants disappearing along the beam line, Lorentz boost due to unequal parton momentum fractions, etc.), we can only measure missing energy in the transverse plane, therefore for the neutrino we can only measure the transverse momentum $p_T^\nu$

The canonical method to determine the $W$-mass precisely at hadron colliders is to measure the so-called transverse mass, $m_T$. The spectrum of the transverse mass has a very visible feature often called the Jacobian Peak, at the point $m_W$.

$m_T$ is defined as $$m_T = \sqrt{2p_{T}^{l}p_{T}^{\nu}(1-\cos\Delta\phi_{l\nu})}$$,

where the $\Delta\phi_{l\nu}$ is the angle in the transverse plane between the lepton and the direction of the missing transverse energy.

The resulting histogram from the recorded data is fitted with a line-shape that has $m_W$ as a floating parameter.

(from http://arxiv.org/pdf/1203.0275v1.pdf)