Precise Measurement of W Boson Mass
 Figure 1 : Fundamental elements in the nature. |
 Figure 2 : The loop process of a W boson. (a): Quark loop, (b): Higgs loop. |
 Figure 3 : Transverse mass distribution of W boson events. The blue dots show the experimental data and the red histogram shows the computer simulation. (a):W→eν mode，(b):W→μν mode. |
 Figure 4 : The current status of the W boson mass measurements. A measurement with the most precise in the world was performed by CDF II this time. |
 Figure 5 : The predicted range of the Standard Model Higgs boson mass obtained from the mass of a top quark and that of a W boson. |
The W boson is a gauge particle that mediates the “weak interaction,” one of the four fundamental interactions in nature. According to the theory based on the gauge principle, one of the fundamental principles of modern particle physics, gauge particles that mediate forces (interactions) were originally considered to have zero mass. In fact, photons that mediate electromagnetic force have no mass. However, it has been confirmed that the W boson, which is the subject of this discussion, has a very heavy mass of about 80 GeV/c2. One answer to the mystery of where this mass comes from was provided by the British physicist P. W. Higgs. According to Higgs’ theory, elementary particles originally had no mass, but due to the “spontaneous symmetry breaking” of the Higgs field causing a phase transition in the vacuum, the vacuum expectation value of the field became non-zero, resulting in particles acquiring mass. At that time, a scalar particle known as the “Higgs particle” appears as a physical entity, but as of January 2007, the Higgs particle has not yet been discovered. However, if the mass of the W boson is also brought about by the Higgs field, then by closely examining the W boson, we can indirectly obtain information about the Higgs particle. Particularly by considering “radiative corrections” through loop processes as shown in Figure 2, the mass of the Higgs particle in the Standard Model of particle physics is closely related to the mass of the top quark and the mass of the W boson.
In this study, the CDF experiment, in which Osaka City University participates, successfully measured the mass of the W boson with extremely high precision. Generally, the mass (M) of an elementary particle is determined from its energy (E) and momentum (p) using the special relativity relation:
\begin{align*}
M = \sqrt{E^2 – p^2} \;.
\end{align*}
If the particle to be measured is unstable, the mass is calculated by measuring the energy and momentum of all decay products and reconstructing the state before decay:
\begin{align*}
M = \sqrt{\sum_i E^2_i – \sum_i p^2_i} \;.
\end{align*}
The W boson in this study decays into leptons or quarks as shown below:
W± → ℓ±ν, qq′ .
However, to alleviate the difficulty of distinguishing signal events from data containing many noise events, mainly the lepton mode, especially
W± → e±νe, μ±νμ
is often used for analysis. However, there is one problem here: it is technically impossible to measure the longitudinal component (along the proton-antiproton collision axis) of the neutrino’s (ν) momentum. Therefore, in the CDF experiment, instead of E and p, only their transverse components are extracted, and quantities called “transverse energy (ET)” and “transverse momentum (pT)” are used. Using these, “transverse mass (MT)” is defined as
\begin{align*}
M_T = \sqrt{E_T^2 – p_T^2} \;.
\end{align*}
At CDF, the mass of the W boson was measured with high precision by comparing the transverse mass distribution with computer simulations. Figure 3 shows the comparison between experimental data (points with error bars) and computer simulations (histograms). (a) analyzes W± → e±νe, and (b) analyzes W± → μ±νμ, resulting in W boson masses of 80483 ± 48(syst.) MeV/c2 and 80349 ± 54(syst.) MeV/c2, respectively. The final result, combining these values and including systematic errors, is
MW = 80413 ± 48 MeV/c² .
As of January 2007, this is the most precise measurement of the W boson mass in the world (Figure 4).
As mentioned earlier, the mass of the Standard Model Higgs particle can be theoretically predicted from the measured mass of the W boson and the mass of the top quark. From previous measurements, the mass of the top quark is
Mt = 171.4 ± 2.1 GeV/c² .
Combining this value with the above W boson mass, the predicted range of the Higgs particle mass can be obtained as shown in Figure 5. As the amount of collected data increases in the future, the statistical error in the mass measurements of the W boson and the top quark will decrease, making the predicted range of the Higgs particle mass more precise.