Two papers describing results of searches for high-mass resonances decaying into jet pairs have appeared on the arxiv this week. They are authored by the CMS and ATLAS collaborations, and they both report lower limits on the mass of hypothetical particles predicted by several new physics signatures. Both collaborations base their results on the analysis of their full 2011 datasets.

Because of their simultaneity, the use of quite similar methodologies, and their relying on equivalent datasets, these two papers allow for a quite precise assessment of the discovery potential of the two detectors. It is not just an academic issue the one of whether one or  the other experiment is superior: they are based on different technologies, and their design forced difficult choices and compromises. We may learn a lot from the comparison.

Learning from experimental sensitivities: the case of CDF vs DZERO

To make an example from the past, consider the CDF and DZERO experiments in Run I at the Tevatron. During the nineties the two collaborations got  engaged in a competition on multiple levels: first and foremost,  the discovery of the top quark and the measurement of its characteristics; then, of course, the searches for new physics; and notably, also the precise  measurement of the W boson mass.

Indeed, critical construction choices had been made in the early eighties, and the importance of measuring the characteristics of W bosons had suggested DZERO to opt for a design which maximized the  precision measurement of electron energies. They thus put a lot of effort in building the most precise electromagnetic calorimeter allowed by the available technology, and
decided to not install a solenoidal magnet, specifically for the task of a precision W boson mass
measurement in the W->ev decay mode (a magnet inserted within the calorimeter will constitute a thick layer of inert material, spoiling in part the energy resolution of electromagnetic showers; a magnet external to the calorimeter involved other hard to overcome challenges).

CDF, on the other hand, was built with a broader scope in mind. The designers put more emphasis on the central tracking, and decided to use for the first time a silicon vertex tracker in
hadron collisions; the technology was still quite new, so the choice was not devoid of risks.

We know how the story ended: the absence of a solenoid in DZERO was a  serious shortcoming, sizably diminishing the physics potential of the experiment. CDF could benefit from the precise tracking to identify b-quark-originated jets from the secondary vertices in the jets, which  resulted in better measurements of top quark properties; the better tracking also allowed CDF to pull off a number of world's best measurements of B hadron properties.

And on the W mass, the supposed advantage of DZERO due to a better electromagnetic calorimeter did not win it much: the Run I measurements of the W mass of the two experiments ended up having quite similar total uncertainties: the slight advantage with electrons of DZERO was balanced with CDF's superior momentum resolution for muons.

It is not a surprise then to see DZERO in Run II coming equipped with  a solenoidal magnet and a state-of-the-art, redundant silicon tracking system! Lesson learned, we might say.

Back to CMS and ATLAS: Dijet Searches

Searching for new particles decaying to jet pairs is one quite important part of the investigations of the high-energy frontier at hadron colliders. A number of new physics objects would, if they existed, be first detected in that final state: this is due to the fact that in hadron collisions  one usually produces with large rates objects that feel the strong interaction.

So if, for instance, quarks existed in excited states, a collision with enough energy could produce these excitations, and the "deexcitation" mechanism would be analogous to the return to the fundamental state of an excited atom, with the quark in place of the atom, and the emission
of a energetic gluon in place of the photon. So one would expect to see two jets: one from the quark, and one from the gluon. Their combined mass would measure the excitation energy: in fact, a resonance.

Despite the hypothesis that quark come with their own excited energy levels too, the above is quite standard physics. But theorists have hypothesized much fancier objects which hadron collisions could copiously produce. I cannot go through them in detail, so be happy with a list: string resonances, axigluons, colorons, color-octet resonances, diquarks, new W' and Z' bosons, and quantum black holes.

All of these new objects can be searched for by collecting events containing pairs of energetic jets, computing their total invariant mass, and examining the spectrum in search for bumps with a shape compatible with the characteristics of the searched object. A "wide" resonance could result from states with a large natural width; resonances with width significantly smaller than the experimental resolution on their mass would instead all appear of the same shape.

So let us have a look at the dijet mass spectrum obtained by ATLAS, shown  on the right. In the main frame you see the data (black points) compared  with a smooth parametrization of the background (the thin black histogram). The middle frame shows the residuals of the fit to the data, in fractions of the fit results in each bin. The data are seen to wiggle around zero according to statistical fluctuations; the way a signal of a excited quark resonance of 1, 2, and 3 TeV would appear is exemplified by the red, blue, and magenta points. The lower frame shows the "significance" (this is what the figure reports) of each data bin. Please accept that this is not
really a significance, but rather a measure of the statistical deviation of the data from the model in each bin.

By a simple inspection of the figure, one gathers that ATLAS would have been able to detect a 2-TeV excited quark, while probably a 3-TeV one is at the edge of the experimental sensitivity. But of course reading the numerical results of the search is much more meaningful practice  than eyeballing a graph. The results are discussed below, but first let us give a look at the analogous CMS figure.

The spectrum of dijet masses found by CMS is shown on the left. CMS reports the data already reduced into a rate measurement of picobarns per GeV, but apart from this difference one cannot fail to see how similar the spectrum is to the one shown by ATLAS. The data (black points) is here compared with a theory-inspired background model fit (the blue curve); here different potential signals are compared in the main distribution rather than in  the one of residuals (shown on the bottom). One difference with the ATLAS plot is that the fit here has a green band showing the effect of the jet energy scale systematic uncertainty.

The first thing worth noting when visually comparing the graphs is the highest dijet mass reported by the two experiments: this is in both cases in the 4-4.2 TeV bin. Also worth noting is the extreme smoothness of the spectra, and their good agreement with the fits.

Since the data is roughly equivalent in size, and the high-mass reach is equal (a fact totally expected, given that both experiments study proton-proton collisions at the same total energy, and their data size is equivalent), what may make the difference on the results is only the size of systematic uncertainties, and the experimental resolution in the dijet mass -a parameter which cannot be apparent from a look at a smooth spectrum.

So let us compare first of all the quoted systematic uncertainties of the two searches. CMS quotes a 2.2% uncertainty on jet energy scale, a 10% uncertainty on jet energy resolution, and a 2.2% uncertainty on integrated luminosity; ATLAS quotes a 4% uncertainty on jet energy scale,
a 3.9% uncertainty from integrated luminosity, and does not quote the systematic uncertainty on jet energy resolution, noting that its effect on the search is negligible. So, from these numbers we gather that CMS has smaller systematic uncertainties on the factors affecting the observable rates of new phenomena; these errors enter the calculation as nuisance parameters in a Bayesian calculation, and they affect the resulting upper limits on signal cross sections and hence the lower limits on the mass of the resonances.

(It is easy to understand that uncertainty in the total data size affects the limits: from the data one has one puts an upper limit on the number of signal events of some kind; the limit on the number of signal events gets translated in a cross section limit since N=σL, where N is the number of events, sigma the cross section, and L the luminosity. For uncertainties on jet energy scale, it is a bit more complicated, but the end result is similar).

The other parameter heavily affecting the sensitivity to narrow resonances is the relative dijet mass resolution -i.e., how wide would be a resonance peak if reconstructed, with respect to its mass. Of course a narrower peak stands out more clearly in a smoothly falling background spectrum, so it is easy to understand how this is critical. ATLAS quotes widths ranging from 7% to 15% as the mass is increased from 1 to 4 TeV. CMS does not quote their resolution in the paper, referring to other documents where the matter was studied in detail: in fact, CMS uses a "wide jet" reconstruction algorithm which significantly improves the core resolution of resonances of high mass. I believe this is one important factor in  the sensitivity that CMS obtains in the searches.

So what are the results, anyway ? Let us compare them in an itemized list, taking care of comparing expected limits, i.e. ones that do not depend on the statistical vagaries of the collected data. Bear in mind, though, that the observed limits show exactly the same trend -that is expected, since the experiments do not observe significant deviations of their data from the background models.

  • For excited quarks, CMS expected to exclude masses up to 3.05 TeV, at 95% confidence level; ATLAS expected to exclude masses up to 2.94 TeV, at the same confidence level.
  • For string resonances, CMS expected to reach 4.29 TeV; ATLAS expected to reach 3.47 TeV.
  • For S8 resonances, CMS expected to reach 2.24 TeV; ATLAS expected to reach 1.97 TeV.
  • For W' bosons, CMS expected to reach 1.78 TeV; ATLAS expected to reach 1.74 TeV.

In the above list I have excluded the case of quantum black holes (where the CMS limits are in the 4 to 5.3 TeV range and the ATLAS limits are in the 3.85-4.19 TeV range) because of the lack of a coincident set of assumptions in deriving the actual results, making it less meaningful to compare numbers. Also, coloron, diquarks, and Z' limits are only present in the CMS publication, as are specific limits for objects decaying to b-quark pairs; on the other hand, ATLAS has several other important results listed in their paper, including ones for contact interactions and model-independent signals. Other caveats should be mentioned because of small differences in the treamements of theory and simulation parameters, but they do not change the picture appreciably.

We see that CMS consistently surpasses the ATLAS limits, even though by a small margin in two of the four cases where a direct comparison is possible. As we noted, the difference is probably due to smaller systematic uncertainties and better dijet mass resolution in the CMS searches, but these facts are not structural and detector-driven as much as they are affected by the level of sophistication of the reconstruction and analysis methods. I in fact believe ATLAS will pay CMS back in the next round or results, when the two experiments will be analyzing five times more data taken at a centre-of-mass energy of 8 TeV. We'll see who wins the 2013 challenge!