## Archive for November 8, 2012

### GFITTER Plots

I accidentally hit the link to GFITTER in my bookmarks file while having an early morning cup of coffee. So I looked at the plots there – they’re interesting.

As most particle physicists know, GFITTER is a public computer program for calculating fits to the Standard Model based on precision measurements of electroweak observables. Such fits have a long tradition and have played a crucial role in the development of our field since the 1990s or before. During LEP days, for example, it was customary to infer values of the top quark mass from its influence on electroweak observables. The agreement of these inferred values with the directly measured value at the Tevatron was exciting at the time. Once the top quark mass was known, the fits turned to predicting the Higgs mass. As the years went by and all the crucial measurements improved, the indirect bounds on the Higgs mass sharpened. Once again, the measured value from the LHC agrees with the prediction:

If you want to break the SM in order to access new physics, this agreement is not good news, and now one has to hope for unexpected Higgs properties as revealed in branching ratios and angular distributions of the decay products.

We can continue to scrutinize the internal consistency of the SM, and the GFITTER plots help with that. The traditional plot shows contours in the plane of M_{W} versus M_{t} – here is the GFITTER version:

The yellow cross indicates the measured values of M_{t} and M_{W}, and the black point in the middle of the plot with error bars represents the joint measurement – what I will call the true value. The large grey areas show the expected ranges of (M_{W},M_{t}) based on a host of precision measurements of electroweak observables. It overlaps the true value so at that level the SM is internally consistent. The narrow blue areas show the expected range of (M_{W},M_{t}) based on precision measurements of electroweak observables *and the measured Higgs mass*. The contour is much narrower reflecting the major impact the measurement of M_{h} has. Notice that the agreement with the black point is not so good: the measured value of M_{W} is a little bit higher than predicted by the blue areas, while M_{t} agrees very well.

Looking at this plot, you might wish for “slices” along M_{W} and M_{t} to see a chi-squared contour. Happily, GFITTER provides these plots for us. First, the M_{t} plot:

The most precise measurement comes from the Tevatron experiments, taken together, closely followed by the CMS measurement alone. All of the measurements agree among themselves very well, and they agree with the prediction of the SM (blue parabola) at the level of one sigma.

Here is the corresponding plot for M_{W}:

The agreement between the world average value and the SM prediction is less good. Taken at face value, the central value of the measurement is three sigma above the prediction of the SM (blue curve). Taking the measurement error into account, the disagreement is much smaller than three sigma, but could there be a hint of something here?

If the Higgs mass increases, then the (admittedly modest) tension between the measured and predicted values of M_{W} will increase. Perhaps it would be nice to see contours in the plane of M_{W} versus M_{h}. I’m sure people who know how to run GFITTER can produce this plot easily.

More precise measurements of M_{W} are desirable, but difficult to achieve. People at the LHC talk about reducing the uncertainty to below 10 MeV, but this requires a lot of experimental work and better PDFs, so it is not around the corner. A measurement with a precision of 6 MeV or even better could be made at a new e^{+}e^{–} collider, but that is just a hope, now.