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Events with photons, b-jets, and missing Et June 17, 2008

Posted by dorigo in news, physics, science.
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A recent analysis by CDF, based on 2 inverse femtobarns of data (approximately 160 trillion proton-antiproton collisions) has searched for events featuring a rare mixture of striking objects: high-energy photons, significant missing transverse energy, and energetic b-quark jets. Photons at a proton-antiproton collider are by themselves a sensitive probe of several new physics processes, and the same can be said of significant missing energy. The latter, in fact, is the single most important signature of supersymmetric decays, since the latter usually feature a non-interacting, neutral particle, as I had a chance of explaining in a lot of detail in two posts on the searches for dark matter at colliders (see here for part 1, here for part 2, and here for part 3). Add b-quark jets to boot, and you are looking at a very rare signature within the standard model, but one that may in fact be due to hypothetical exotic processes.

The idea of such a signature-based search is simple: verify whether the sum of standard model processes account for the events observed, without having to be led by any specific model for new physics. The results are much easier to interpret in terms of models that theorists might not have cooked up yet. A specific process which could provide the three sought objects together is not hard to find, in any case: in supersymmetric models where a photino decays radiatively emitting a photon and turning into a Higgsino -a lightest particle which escapes the detector, one gets both photons and missing energy; the additional b-jet is then the result of the decay of an accompanying chargino.

If the above paragraph makes no sense to you, worry not. Just accept that there are possible models of new physics where such a trio of objects arise rather naturally in the final state.

However, there is another, much more intriguing, motivation for the search described below. So let me open a parenthesis.

In Run I, CDF observed a single striking, exceedingly rare event which contained two high-energy electrons, two high-energy photons, and significant missing transverse energy. A unexplicable event by all means! Below you can see a cut-away view of the calorimeter energy deposits: pink bars show electromagnetic energy (both electrons and photons leave their energy in the electromagnetic portion of the calorimeter), but photon candidates have no charged track pointing at them. The event possesses almost nothing else, except for the large transverse energy imbalance, as labeled.

The single event shown above was studied with unprecedented detail, and some doubts were cast on the nature of one of the two electron signals. Despite that, the event remained basically unexplained: known sources were conservatively estimated at a total of 1 \pm 1 millionth of an event! A definitive answer on it was thought would be given by the larger dataset that the Tevatron Run II would soon provide. You can read a very thorough discussion of the characteristics of the infamous ee \gamma \gamma \not E_t event in a paper on diphoton events published in 1999 by CDF.

Closing the parenthesis, we can only say that events with photons and missing transverse energy are hot! So, CDF looked at them with care, by defining each object with simple cuts -such that theorists can understand them. No kidding: if an analysis makes complicated selections, a comparison with theoretical models coming after the fact becomes hard to achieve.

The cuts are indeed straightforward. A photon has to be identified with transverse energy above 25 GeV in the central calorimeter. Two jets are also required, with E_T>15 GeV and |\eta|<2.0; Rapidity \eta is just a mesure of how forward the jet is going; a rapidity of 2.0 corresponds to about 30 degrees away from the beam line, if I remember correctly. Selecting these events leads to about 2 million events! These are dominated by strong interactions where a photon is faked by a hadronic jet.

The standard selection is tightened by requiring the presence of missing transverse energy above 25 GeV. Missing transverse energy is measured as the imbalance in the energy flowing in the plane transverse to the beam axis; 25 GeV are usually already a significant amount, which is hard to fake by jets whose energy has been under- or overestimated. The two jets are also required to be well separated between each other and from the photon, and this leads to 35,463 events: missing Et has killed alone about 98% of our original dataset. But missing Et is most of the times due to a jet fluctuation, even above 25 GeV: thus it is further required that it is not pointing along the direction of a jet in the azimuthal angle (the one describing the direction in the plane orthogonal to the beam, which for missing transverse energy is indeed defined). A cut \Delta \Phi >0.3 halves the sample, which now contains 18,128 events.

Finally, a b-tagging algorithm is used to search for the secondary vertex B mesons produce inside the jet cones. Only 617 events survive the requirement that at least a jet is b-tagged. These events constitute our “gold mine” and they are interpreted as a sum of standard model processes, to the best of our knowledge.

One last detail is needed: not all the b-tagged jets are originated from real b-quarks! A sizable part of them is due to charm quarks and even lighter ones. To control the fraction of real b-quarks in the sample, one can study the invariant mass of the system of charged tracks which are fit together to a secondary vertex inside the jet axis. The invariant mass of the tracks is larger for b-jets, because b-quarks weigh much more than lighter ones, and their decay products reflect that difference. Below, you can see the “vertex mass” for b-tagged jets in a loose control sample of data (containing photons and jets with few further cuts): the fraction of b-jets is shown by the red histogram, while the blue and green ones are the charm and light-quark components. Please also note the very characteristic “step at about 2 GeV, which is due to the maximum mass of charmed hadrons.

The vertex mass fit in the 617 selected events allows to extract the fractions of events due to real photons accompanied by b-jets, c-jets, and fake b-tags (light quark jets). In addition, one must account for fake photon events. Overall, the background prediction is extracted by a combination of methods, well-tested by years of practice in CDF. The total prediction is of 637 \pm 54 \pm 128 events (the uncertainties are statistical and systematic, respectively), in excellent agreement with observed counts. A study of the kinematics of the events, compared with the sum of predicted backgrounds, provides a clear indication that Standard Model processes account very well for their characteristics. No SUSY appears to be lurking!

Below you can see the missing transverse energy distribution for the data (black points) and a stack of backgrounds (with pink shading for the error bars on background prediction).

Below, a similar distribution for the invariant mass of the two jets.

A number of kinematic distirbutions such as those shown above is available in the paper describing the preliminary results. Interested readers can also check the public web site of the analysis.