## 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.

## New AMS Results – hints of TeV Dark Matter?

Yesterday the AMS Collaboration released updated results on the **positron excess**. The press release is available at the CERN press release site. (Unfortunately, the AMS web site is down due to syntax error – I’m sure this will be fixed very soon.)

The Alpha Magnetic Spectrometer was installed three years ago at the International Space Station. As the name implies, it can measure the charge and momenta of charged particles. It can also identify them thanks to a suite of detectors providing redundant and robust information. The project was designed and developed by Prof. Sam Ting (MIT) and his team. An international team including scientists at CERN coordinate the analysis of data.

There are more electrons than positrons striking the earth’s atmosphere. Scientists can predict the expected rate of positrons relative to the rate of electrons in the absence of any new phenomena. It is well known that the observed positron rate does not agree with this prediction. This plot shows the deviation of the AMS positron fraction from the prediction. Already at an energy of a couple of GeV, the data have taken off.

The positron fraction unexpectedly increases starting around 8 GeV. At first it increases rapidly, with a slower increase above 10 GeV until 250 GeV or so. AMS reports the turn-over to a decrease to occur at 275 ± 32 GeV though it is difficult to see from the data:

This turnover, or edge, would correspond notionally to a Jacobian peak — i.e., it might indirectly indicate the mass of a decaying particle. The AMS press release mentions dark matter particles with a mass at the TeV scale. It also notes that no sharp structures are observed – the positron fraction may be anomalous but it is smooth with no peaks or shoulders. On the other hand, the observed excess is too high for most models of new physics, so one has to be skeptical of such a claim, and think carefully for an astrophysics origin of the “excess” positrons — see the nice discussion in Resonaances.

As an experimenter, it is a pleasure to see this nice event display for a positron with a measured energy of 369 GeV:

Finally, AMS reports that there is no preferred direction for the positron excess — the distribution is isotropic at the 3% level.

There is no preprint for this article. It was published two days ago in PRL 113 (2014) 121101″

## Z decays to four leptons

A bit more than a year ago I was pleased to see a clear signal from CMS for the decay of Z bosons to four leptons. Of course there are literally millions of recorded Z decays to two leptons (e^{+} e^{-} and μ^{+} μ^{-}) used for standard model physics studies, lepton efficiency measurements, momentum/energy scale determinations and detector alignment. But Z→4L is cuter and of some intrinsic interest, being relatively rare.

It turned out the main interest of physicists who analyzed the signal was Higgs boson decays to four leptons. By now that Higgs signal is well established and plays an important role in the Higgs mass measurement, but at the time of the CMS publication (InSpire link, i.e., arXiv:1210.3844 October 2012), Z→4L provided the ideal benchmark for H→4L.

You might think that the rare decay Z→4L had been well studied at LEP. In fact, it was *quite* well studied because the ALEPH Collaboration had once reported an anomaly in the 4L final state when two of the leptons were tau leptons. (At the time, this observation hinted at a light supersymmetric Higgs boson signal.) The anomaly was not confirmed by the other LEP experiments. A perhaps definitive study was published by the L3 Collaboration in 1994 (InSpire link). Here are the plots of the two di-lepton masses:

Most of the events consist, in essence, of a virtual photon emitted by one of the primary leptons, with that virtual photon materializing as two more leptons – hence the peak at low masses for the M^{min} distribution. Note there is no point in plotting the 4-lepton mass since the beam energies were tuned to the Z peak resonance – the total invariant mass will be, modulo initial-state radiation, a narrow peak at the center-of-mass-energy.

Here is the Z resonance from the CMS paper:

A rather clear and convincing peak is observed, in perfect agreement with the standard model prediction. This peak is based on the 5 fb

^{-1}collected in 2011 at 7TeV.

ATLAS have released a study of this final state based on their entire 7 TeV and 8 TeV data set (ATLAS-CONF-2013-055, May 2013). Here is their preliminary 4-lepton mass peak:

Clearly the number of events is higher than in the CMS plot above, since five times the integrated luminosity was used. ATLAS also published the di-lepton sub-masses:

This calibration channel is not meant to be the place where new physics is discovered. Nonetheless, we have to compare the rate observed in the real data with the theoretical prediction – a discrepancy would be quite interesting since this decay is theoretically clean and the prediction should be solid.

Since the rate of pp→Z→2L is very well measured, and the branching ratio Z→2L already well known from LEP and SLD, we can extract branching fractions for Z decays to four leptons:

SM... BF(Z→4L) = (4.37 ± 0.03) × 10^{-6}

CMS.. BF(Z→4L) = (4.2 ± 0.9 ± 0.2) × 10^{-6}

ATLAS BF(Z→4L) = (4.2 ± 0.4 ) × 10^^{-6}

So, as it turns out, the SM prediction matches the observed rate very well.

## Inclusive W and Z cross sections

The inclusive W and Z production cross sections are benchmarks for any hadron collider. Excellent measurements were published by CDF and D0, but the superior detector capabilities of CMS and ATLAS allows for even better measurements. Fiducial cross sections are relatively free from theoretical uncertainties and can be used to constrain the parton distribution functions (PDFs), which are of central importance for nearly all measurements done at a hadron collider. In fact, ATLAS published an interesting constraint on the *strange*-quark density on the basis of inclusive cross section measurements. I’ll return to this result in a future post.

The first results were published back in 2010 and then updated in 2011 and 2012, based on 7 TeV data. Since W and Z bosons are produced copiously at the LHC, very small statistical uncertainties can be achieved with a rather small amount of integrated luminosity. (We have tens of millions of Z bosons detected in leptonic decay channels, for example, far more than the LEP experiments recorded. And we have roughly ten times the number of W bosons.) Remarkably, experimental systematic uncertainties are reduced to the 1% – 1.5% level, which is amazing considering the need to control lepton efficiencies and background estimates. (I am setting aside the luminosity uncertainty, which was about 3% – 4% for the early data.) The measurements done with only 35 pb^{-1} are nearly as precise as the theoretical predictions, whose errors are dominated by the PDF uncertainties. We knew, back in 2011, that a new era of electroweak physics had begun.

Experimenters know the power of ratios. We can often remove a systematic uncertainty by normalizing a measured quantity judiciously. For example, PDFs are a major source of uncertainty. These uncertainties are highly correlated, however, in the production of W and Z bosons. So we can extract the ratio (W rate)/(Z rate) with a relatively small error. Even better, we can plot the W cross section against the Z cross section, as ATLAS have done:

The elongated ellipses show that variations of the PDFs affect the W and Z cross sections is nearly the same way. The theoretical predictions are consistent with the data, and tend to lie all together. (The outlier, JR09, is no longer a favored PDF set.)

It is even more interesting to plot the W^{+} cross section against the W^{-} cross section, because the asymmetry between W^{+} and W^{-} production relates to the preponderance of up-quarks over down-quarks (don’t forget we are colliding two protons). Since the various PDF sets describe the d/u-ratio differently, there is a larger spread in theoretical predictions:

During the 8 TeV running in 2012, the instantaneous luminosity was much higher than in 2010, leading to high pile-up (overlapping interactions) which complicate the analysis. The LHC collaborations took a small amount of data (18 pb^{-1}) in a low pile-up configuration in order to measure the W and Z cross sections at 8 TeV, and CMS have reported preliminary results. They produced ellipses plots similar to what ATLAS published:

You might notice that the CMS ellipse appear larger than the ATLAS ones. This is because the ATLAS results are based on *fiducial* cross sections – i.e., cross sections for particle produced within the detector acceptance. One has to apply an acceptance correction to convert a fiducial cross section to a total cross section. This acceptance correction is easily obtained from Monte Carlos simulations, but it comes with a systematic uncertainty coming mainly from the PDFs. (If a PDF favors a harder u-quark momentum distribution, then the vector bosons will have a slightly larger momentum component along the beam, and the leptons from the vector boson decay will be missed down the beam pipe more often. Such things matter at the percent level.) Since modern theoretical tools can calculate fiducial cross sections accurately, it is not necessary to apply an acceptance correction in order to compare to theory. Clearly it is wise to make the comparison at the level of fiducial cross sections, though total cross sections are also useful in other contexts. The CMS result is preliminary.

Back when I was electroweak physics co-convener in CMS, I produced a plot summarizing hadron collider measurements of W and Z production. My younger colleagues have updated that plot to include the new 8 TeV measurements:

This plot nicely summarizes the history of these measurements, and suggests that W and Z production processes are well understood.

As I learned a the WNL workshop, the collaborations are learning how to measure these cross section in the high pile-up data. We may see even more precise values, soon.

## Resuming blogging: what I learned recently about electroweak physics at the LHC

I regret that I have nearly abandoned this blog. It has been a long time since I tried to point out interesting results in high energy physics. Happily, I was asked to give an hour-long talk about electroweak physics at the LHC, at the workshop hosted by the (TIFR) in Mumbai. I was able to spend many days reviewing the recent publications of the LHC experiments in order to prepare for my talk. On my way back to the US, I realized that I could use my new understanding as the basis for a series of posts. I hope I will manage to keep with it…

## Nice, short video on US contributions to CERN Science

I just heard about a youtube video written by Don Lincoln about the role the United States plays in CERN science – specifically, the LHC. You can view it here:

Apparently Ernie Monitz, the new Secretary of Energy, linked this to his facebook page: https://www.facebook.com/ErnestJMoniz/posts/222609781237091

A really good video “explaining” why the Higgs is important is associated with the one by Don. It comes from MinutePhysics and is fun. Take a look:

## Higgs couplings to fermions and massive vector bosons

Let’s review the tests of the Higgs couplings to fermions and massive vector bosons completed by CMS and ATLAS.

The Higgs mechanism generates mass terms in the standard model Lagrangian. Electroweak symmetry is broken at the same time that the W and Z bosons get their mass. Fermions masses, on the other hand, are generated via Yukawa terms, and have nothing to do with electroweak symmetry breaking. The Higgs coupling to the electroweak gauge bosons go as M_{V}^{2}/v, while the Higgs coupling to the fermions goes as M_{f}/v, where v is the Higgs vacuum expectation value (v = 246 GeV).

Could there be a new physics effect that modifies these tree-level couplings? CMS and ATLAS have taken all their Higgs data and performed a fit with two free scale factors: κ_{V} for the vector boson couplings and κ_{F} for the fermions. The effective couplings for the Higgs boson to gluon pairs and photon pairs are expressed as their standard model loops modified by κ_{V} and κ_{F} as appropriate.

The CMS result is here. The contours centered on the black cross are the constraints from CMS data, and the yellow diamond is the standard model expected values, that fall within the 1σ CMS curve. While best value for κ_{F} is less than the SM value, the best value for κ_{V} agrees perfectly with the SM. There is a second local minimum with κ_{F} < 0 but that one is not favored by the data. (Source: CMS public Higgs page)

This plot shows contours from ATLAS data including the solution with κ_{F} < 0. The best value is marked by the X and the SM value is marked by the blue cross. The ATLAS data agree with the SM for κ_{F} and are a bit above the SM for κ_{V}. (Source: ATLAS Higgs page)

I have tried to put the two curves on the same grid: