A Quantum Diaries Survivor

"I have made this letter longer than usual, because I lack the time to make it short"

(Blaise Pascal)

This is dedicated to Mia, who is pestering me with pages of her would-be master's thesis!

So, in a former post here I discussed in some detail what the jet energy scale is. Here I would like to show why we take so much of our time to compute the shift of our jet energy measurement from the true value.

I discussed why we care for the top quark mass measurement in another post. In short, the top quark mass is one fundamental parameter of the standard model, the theory that explains most -if not all- of the phenomenology of particle physics we have discovered so far. The standard model has several limitations, but alternatives have so far either failed to produce predictions for measurable quantities, or have been disproven by the data.

The top mass is important because the physics of the standard model is very sensitive to its value, and by measuring it, together with other parameters -most notably the W mass and the Weinberg angle (this latter is accessible with precision in neutrino scattering experiments, so it is not CDF's job)- we obtain either a perfect consistency and an indication of what is the mass of the Higgs boson, or a proof that the model is incomplete. 

The standard model has accustomed us to success after success for thirty years and we, as kids who have grown tired of their favorite toy, now want to break it in pieces ….

Anyway, b-jets.  First of all, why is the b-jet scale is different from that of other jets ?

Because b-quarks are very different from the others. They are heavy - more or less as much as five protons. And when they produce a jet, the latter has very peculiar characteristics, which make its measurement different from that of generic jets.

To make matters worse, with data we can determine energy corrections that only apply to generic jets, because b-jets are rare in generic processes. So the scale for b-jets is less well determined.

However, a top-antitop pair always (that is, 999 times out of 1000) produces a pair of b-quark jets. And these will have an energy that to first order is proportional to the top quark mass. So, if we err by 1 GeV on their energy measurement, we will err by 1 GeV on the top mass measurement. Generic jets coming out of top decay are less critical in the top mass indetermination, because they emerge in pairs from the decay of W bosons: t -> Wb -> jj b . The two jets must make the W mass, and this by itself is a very strong constraint on their energy - less need for a precise energy scale for them!

The figure aside shows a top pair production event, with the subsequent decay to a pair of W bosons and a pair of b-jets. W bosons in the picture have decayed to an electron-neutrino and a muon-neutrino pair, but they can also decay to pairs of jets.

The figure below instead shows the projected uncertainty that the CDF and D0 experiments will be able to reach on the top quark mass measurement, as a function of the amount of data they collect. The x scale runs to a value that corresponds to the total dataset achievable by the Tevatron collider experiments before 2009 - if all is well.

One sees that the generic jet energy scale (purple curve) will contribute appreciably to the total uncertainty, but the remaining uncertainties (blue curve) will dominate more and more as we move towards the full data we think we can collect. Among the contributions to the blue curve, the residual systematic uncertainty due to the b-jet energy scale -that is, the part not constrained by a precise knowledge of generic jet scale - is one of the largest.

One more thing to note: the figure above only considers the so-called "lepton plus jets" final state of top pair production. An additional measurement will come from the "dilepton" decay, where only b-jets appear (as in the first figure above). For those events, the mass cannot be measured with great precision, but the b-jet energy scale is more important there.

By measuring the Z->bb decay peak (the 91.19 GeV calibration line!), we can constrain b-jets more or less with the same level of precision of the W->jj calibration line (at 80.36 GeV). We have much larger statistics of Z decays, but backgrounds are much larger too.

The measurement we will try to produce this summer for the b-jet scale in CDF has a total uncertainty of the order of 2%. That is one thing we have been working on in Padova since my PhD thesis in 1998!