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A precise measurement of the W boson width May 1, 2007

Posted by dorigo in news, physics, science.

The W boson, discovered at CERN in 1983, is the carrier of the weak charged current interaction. It weighs about 86 protons, it has a lifetime of about 10^-24 seconds, and it is the particle responsible for the radioactive decay of nuclei. In nuclear weak decay a neutron transmutes into a proton, emitting a virtual W boson which materializes into an electron-antineutrino pair. W bosons, being quite massive, carry a very short-range force.

Besides governing the weak decay of heavy fermions into lighter ones, W bosons are quite interesting objects to study. Their large mass guarantees a rich phenomenology, in fact: the W can decay into any pair of fermions in a democratic way if the latter have a combined mass not exceeding their parent’s. That means all, except top quarks: the W decays equally likely into a electron-neutrino pair (ev), a muon-neutrino pair (mv), or a tau-neutrino pair (tn), and similarly in a up-down (ud) quark pair or a charm-strange (cs) quark pair. No, wait: since quarks come in three colors, these count three times, and in the total budget one has 3(ud)+3(cs)+ev+mv+tv = 9 possible decay pairs.

In fact, one observes a 100%/9=11% branching ratio of the W to electron-neutrino pairs, and the same to muon-neutrino and tau-neutrino pairs. These are the best studied decays, because the high-energy electrons and muons produced by W decay are quite easy to identify. Let us check in the Particle Data Group information: 10.75+-0.13% of decays produce a electron-neutrino pair, 10.57+-0.15% a muon-neutrino pair, and 11.25+-0.20% a tau-neutrino pair.

The above precise measurements were made by LEP II, which produced WW pairs with electron-positron collisions at and above 160 GeV of center-of-mass energy. LEP II also measured with some precision the branching ratios of W bosons to quarks: of course, quarks emitted in W disintegration immediately hadronize in a stream of light stable particles, jets. The flavor of the original quark is thus not immediately known, but careful statistical analysis can tell charm quark jets from the rest.

The W is not only interesting in its decay, of course. It is a vector particle, and as such it carries some three-dimensional information (as all vectors do): it has one unit of spin. The angle between the direction of motion and the direction of the spin is a quantity which electroweak theory predicts quite well in all processes, and therefore measuring the W boson spin constitutes a precise test of electroweak theory. I will talk about these studies elsewhere, because I now want to discuss the other peculiar property of W bosons: their natural width.

It is an elementary notion in quantum mechanics that the lifetime of a particle is the inverse of the indetermination in its rest mass. The less time a particle has to “resonate” at its natural frequency (mass and natural frequency are the same thing for a quantum physicist),  the more ill-determined its frequency is. Not too different from the fact that very low tones of your piano cannot be distinguished well if played for a very short time: if you cannot hear enough periods of oscillation of the low-frequency tone, your guess on its pitch will worsen.

W bosons live a very short life, and their natural width – the quantity sizing up the intrinsic indetermination in their mass – is large: roughly 2 GeV. The exact formula for the width of the W boson would not teach you much more than a simple fact: the more open channels there are for its decay, the faster that will happen. If the W could decay to a as-of-yet undiscovered particle, the width would depart from Standard Model predictions. Therefore, measuring the W boson width is an interesting way to invest one’s research time.

Now, how does one determine the width ? In principle, that is easy to do: you just fit the distribution of observed W masses to the shape characteristic of a resonance, the so-called Breit-Wigner distribution – a peaked structure not much different from a simple gaussian in shape. But there are experimental problems: the experimental resolution on the W mass is usually worse than 2 GeV, and the natural width gets washed up in measurement errors.

Other problems depend on the environment where you produce the W. While at LEP II the two W bosons are competing with quite manageable backgrounds, and even jet decays can be seen with ease, in proton-antiproton collisions things are much harder, and only leptonic decays to electron-neutrino or muon-neutrino pairs can be selected with good purity. Unfortunately, the neutrino emitted in the decay escapes the detector unmeasured, and only its component of momentum transverse to the beam direction can be inferred (from the imbalance of the transverse energy detected in the calorimeter system).

All one can do when the z-component of neutrino momentum is missing is to compute the so-called “transverse mass”. One simply ignores the energy flowing in the direction parallel to the beams. The result is a so-called Jacobian peak: an asymmetric structure which peaks just below the true W mass, has a narrow tail at higher masses, and a broad uneven tail towards lower masses, as in the picture below.

In the picture you see that the data (blue points with error bars) is understood as a sum of W decays (in white) and a small background contamination (in grey) from QCD processes yielding a lepton and fake missing Et. The interesting thing to note is that the Breit-Wigner distribution of W decays extends with tails to very large values of transverse mass, where the resolution effects have died away, and where backgrounds are still small. There is thus good sensitivity to the natural width of the W in the high-end tails, as can be seen by comparing the colored templates from Monte Carlo, which refer to varying values of the width.

CDF recently used both electron-neutrino and muon-neutrino decays of the W collected in 350/pb of Run II data to measure directly the W boson width with the technique discussed above. The result is the most precise determination of that quantity: Gamma(W) = 2.032+-0.071 GeV. Yes, even the very clean LEP II results have been beaten: the statistics collected by the Tevatron is much larger, and systematic uncertainties have been reduced by a careful study. Systematics include the knowledge of lepton resolution, background modeling at high mass, and the effects of a imprecise knowledge of parton distribution functions, which determine the relative population of higher and lower mass of the produced W bosons.

When comparing to previous measurements, the CDF result is in line although more precise. Combining everything together one obtains a World Average width well in agreement with Standard Model expectations, and with a uncertainty of only 47 MeV (it used to be 60 before this measurement). You can see a comparison of all measurements   here .  

[Apologies for being unable to paste the picture here, due to a technical problem].

Update: you can find the above picture in a post by Kea .



1. Kea - May 2, 2007

This is so amazingly clear and simple. If the W could decay to a as-of-yet undiscovered particle, the width would depart from Standard Model predictions. You know, I tried to make a few of those $1000 bets, but nobody would take me on because I don’t have any money. Well, I hope you make some anyway.

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