## Archive for September 27, 2014

### CMS resolves states with a mass difference of 19 MeV

This week the CMS Collaboration released a paper reporting the measurement of the ratio of production cross sections for the χb2(1P) and the χb1(1P) heavy meson states (arXiv:1409.5761). The motivation stems from the theoretical difficulties in explaining how such states are formed, but for me as an experimenter the most striking feature of the analysis is the impressive separation of the χ states.

First, a little background. A bottom quark and an anti-bottom anti-quark can form a meson with a well-defined mass. These states bear some resemblance to positronium but the binding potential comes from the strong force, not electromagnetism. In the past, the spectrum of the masses of these states clarified important features of this potential, and led to the view that the potential *increases* with separation, rather than decreasing. As we all know, QCD is absolutely confining, and the first hints came from studies of charmonium and bottomonium. The masses of these and many other states have been precisely measured over the years, and now provide important tests of lattice calculations.

The mass of the χb2(1P) is 9912.21 MeV and the mass of the χb1(1P) is 9892.78 MeV; the mass difference is only 19.4 MeV. They sit together in a fairly complicated diagram of the states. Here is a nice version which comes from an annual review article by Patrignani, Pedlar and Rosner (arXiv:1212.6552) – I have circled the states under discussion here:

So, even on the scale of the bottomonium mesons, this separation of 19 MeV is quite small. Nonetheless, CMS manages to do a remarkably good job. Here is their plot:

Two peaks are clearly resolved: the χb2(1P) on the left (and represented by the green dashed line) and the χb1(1P) on the right (represented by the red dashed line). The two peaks are successfully differentiated, and the measurements of their relative rates can be carried out.

How do they do it? The χ stated decay to the Y(1S) by emitting a photon with a substantial branching fraction that is already known fairly well. The vector Y(1S) state is rather easily reconstructed through through its decays to a μ+μ- pair. The CMS spectrometer is excellent, as it the reconstruction of muons, so the Y(1S) state appears as a narrow peak. By detecting the photon and calculating the μμγ invariant mass, the χ states can be reconstructed.

Here is the interesting part: the photons are *not* reconstructed with the (rather exquisite) crystal electromagnetic calorimeter, because its energy resolution is not good enough. This may be surprising, since the Higgs decay to a pair of photons certainly is well reconstructed using the calorimeter. These photons, however, have a very low energy, and their energies are not so well measured. (Remember that electromagnetic calorimeter resolution goes roughly as 1/sqrt(E).) Instead, the CMS physicists took advantage of their tracking a second time, and reconstructed those photons that had cleanly converted into an e+e- pair. So the events of interest contained two muons, that together give the Y(1S) state, and an e+e- pair, which gives the photon emitted in the radiative decay of the χ state. The result is the narrow peaks displayed above; the yield is obtained simply by integrating the curves representing the two χ states.

This technique might conceivably be interesting when searching for peculiar signals of new physics.

It is difficult to ascertain the reconstruction efficiency of conversion pairs, since they tend to be asymmetric (either the electron or the positron gets most of the photon’s energy). By taking the ratio of yields, however, one obtains the ratio of cross sections times branching fractions. This ratio is experimentally clean, therefore, and robust. The mass spectrum was examined in four bins of the transverse momentum of the Y(1S); the plot above is the second such bin.

Here is the results of the measurement: four values of the ratio σ(χb2)/σ(χb1) plotted as a function of p_{T}(Y):

LHCb have also made this measurement (arXiv:1202.1080), and their values are presented by the open circles; the CMS measurement agrees well with LHCb. The green horizontal band is simply an average of the CMS values, assuming no dependence on p_{T}(Y). The orange curved band comes from a very recent theoretical calculation by Likhoded, Luchinsky and Poslavsky (arXiv:1409.0693). This calculation does not reproduce the data.

I find it remarkable that the CMS detector (and the other LHC detectors to varying degrees) can resolve such a small mass difference when examining the debris from an 8 TeV collision. These mass scales are different by a factor of two million. While there is no theoretical significance to this fact, it shows that experimenters must and can deal with such a huge range within one single apparatus. And they can.