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Higgs decays to photon pairs! March 4, 2009

Posted by dorigo in news, physics, science.
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It was with great pleasure that I found yesterday, in the public page of the DZERO analyses, a report on their new search for Higgs boson decays to photon pairs. On that quite rare decay process -along with another not trivial decay, the H \to \tau \tau reaction- the LHC experiments base their hopes to see the Higgs boson if that particle has a mass close to the LEP II upper bound, i.e. not far from 115 GeV. And this is the first high-statistics search for the SM Higgs in that final state to obtain results that are competitive with the more standard searches!

My delight was increased when I saw that results of the DZERO search are based on a data sample corresponding to a whooping 4.2 inverse-femtobarns of integrated luminosity. This is the largest set of hadron-collider data ever used for an analysis. 4.2 inverse femtobarns correspond to about three-hundred trillion collisions, sorted out by DZERO. Of course, both DZERO and CDF have so far collected more than that statistics: almost five inverse femtobarns. However, it always takes some time before calibration, reconstruction, and production of the newest datasets is performed… DZERO is catching up nicely with the accumulated statistics, it appears.

The most interesting few tens of billions or so of those events have been fully reconstructed by the software algorithms, identifying charged tracks, jets, electrons, muons, and photons. Yes, photons: quanta of light, only very energetic ones: gamma rays.

When photons have an energy exceeding a GeV or so (i.e. one corresponding to a proton mass or above), they can be counted and measured individually by the electromagnetic calorimeter. One must look for very localized energy deposits which cannot be spatially correlated with a charged track: something hits the calorimeter after crossing the inner tracker, but no signal is found there, implying that the object was electrically neutral. The shape of the energy deposition then confirms that one is dealing with a single photon, and not -for instance- a neutron, or a pair of photons traveling close to each other. Let me expand on this for a moment.

Background sources of photon signals

In general, every proton-antiproton collision yield dozens, or even hundreds of energetic photons. This is not surprising, as there are multiple significant sources of GeV-energy gamma rays to consider.

  1. Electrons, as well as in principle any other electrically charged particle emitted in the collision, have the right to produce photons by the process called bremsstrahlung: by passing close to the electric field generated by a heavy nucleus, the particle emits electromagnetic radiation, thus losing a part of its energy. Note that this is a process which cannot happen in vacuum, since there are no target nuclei there to supply the electric field with which the charged particle interacts (one can have bremsstrahlung also in the presence of neutral particles, in principle, since what matters is the capability of the target to absorb a part of the colliding body’s momentum; but in that case, one needs a more complicated scattering process, so let us forget about it). For particles heavier than the electron, the process is suppressed up to the very highest energy (where particle masses are irrelevant with respect to their momenta), and is only worth mentioning for muons and pions in heavy materials.
  2. By far the most important process for photon creation at a collider is the decay of neutral hadrons. A high-energy collision at the Tevatron easily yields a dozen of neutral pions, and these particles decay more than 99% of the time into pairs of photons, \pi^\circ \to \gamma \gamma. Of course, these photons would only have an energy equal to half the neutral pion mass -0.07 GeV- if the neutral pions were at rest; it is only through the large momentum of the parent that the photons may be energetic enough to be detected in the calorimeter.
  3. A similar fate to that of neutral pions awaits other neutral hadrons heavier than the \pi^\circ: most notably the particle called eta, in the decay \eta \to \gamma \gamma. The eta has a mass four times larger than that of the neutral pion, and is less frequently produced.
  4. And other hadrons may produce photons in de-excitation processes, albeit not in pairs: excited hadrons often decay radiatively into their lower-mass brothers, and the radiated photon may display a significant energy, again critically depending on the parent’s speed in the laboratory.

All in all, that’s quite a handful of photons our detectors are showered with on an event-by-event basis! How the hell can DZERO sort out then, amidst over three hundred trillion collisions, the maybe five or ten which saw the decay of a Higgs to two photons ?

And the Higgs signal amounts to…

Five to ten events. Yes, we are talking of a tiny signal here. To eyeball how many standard model Higgs boson decays to photon pairs we may expect in a sample of 4.2 inverse femtobarns, we make some approximations. First of all, we take a 115 GeV Higgs for a reference: that is the Higgs mass where the analysis should be most sensitive, if we accept that the Higgs cannot be much lighter than that: for heavier higgses, their number will decrease, because the heavier a particle is, the less frequently it is produced.

The cross-section for the direct-production process p \bar p \to H + X (where with X we denote our unwillingness to specify whatever else may be produced together with the Higgs) is, at the Tevatron collision energy of 1.96 TeV, of the order of one picobarn. I am here purposedly avoiding to fetch a plot of the xs vs mass to give you the exact number: it is in that ballpark, and that is enough.

The other input we need is the branching ratio of H decay to two photons. This is the fraction of disintegrations yielding the final state that DZERO has been looking for. It depends on the detailed properties of the Higgs particle, which likes to couple to particles depending on the mass of the latter. The larger a particle’s mass, the stronger its coupling to the Higgs, and the more frequent the H decay into a pair of those: the branching fraction depends on the squared mass of the particle, but since the sum of all branching ratios is one -if we say the Higgs decays, then there is a 100% chance of its decaying into something, no less and no more!- any branching fraction depends on ALL other particle masses!!!

“Wait a minute,” I would like to hear you say now, “the photon is massless! How can the Higgs couple to it?!”. Right. H does not couple directly to photons, but it can nevertheless decay into them via a virtual loop of electrically charged particles. Just as happens when your US plug won’t fit into an european AC outlet! You do not despair, and insert an adaptor: something endowed with the right holes on one side and pins on the other. Much in the same way, a virtual loop of top quarks, for instance, will do a good job: the top has a large mass -so it couples aplenty to the Higgs- and it has an electric charge, so it is capable of emitting photons. The three dominant Feynman diagrams for the H \to \gamma \gamma decay are shown above: the first two of them involve a loop of W bosons, the third a loop of top quarks.

So, how much is the branching ratio to two photons in the end ? It is a complicated calculus, but the result is roughly one thousandth. One in a thousand low-mass Higgses will disintegrate into energetic light: two angry gamma rays, each roughly carrying the energy of a 2 milligram mosquito launched at the whooping speed of four inches per second toward your buttocks.

Now we have all the ingredients for our computation of the number of signal events we may be looking at, amidst the trillions produced. The master formula is just

N = \sigma L B

where N is the number of decays of the kind we want, \sigma is the production cross section for Higgs at the Tevatron, L is the integrated luminosity on which we base our search, and B is the branching ratio of the decay we study.

With \sigma = 1pb, L=4.2 fb^{-1} = 4200 pb^{-1}, and B=0.001, the result is, guess what, 4.2 events. 4.2 in three hundred trillions. A needle in the haystack is a kids’ game in comparison!

The DZERO analysis

I will not spend much of my and your time discussing the details of the DZERO analysis here, primarily because this post is already rather long, but also because the analysis is pretty straightforward to describe at an elementary level: one selects events with two photons of suitable energy, computes their combined invariant mass, and compares the expectation for Higgs decays -a roughly bell-shaped curve centered at the Higgs mass and with a width of ten GeV or so- with the expected backgrounds from all the processes capable of yielding pairs of energetic photons, plus all those yielding fake photons. [Yes, fake photons: of course the identification of gamma rays is not perfect -one may have not detected a charged track pointing at the calorimeter energy deposit, for instance.] Then, a fit of the mass distribution extracts an upper limit on the number of signal events that may be hiding there. From the upper limit on the signal size, an upper limit is obtained on the signal cross-section.

Ok, the above was a bit too quick. Let me be slightly more analytic. The data sample is collected by an online trigger requiring two isolated electromagnetic deposits in the calorimeter. Offline, the selection requires that both photon candidates have a transverse energy exceeding 25 GeV, and that they be isolated from other calorimetric activity -a requirement which removes fake photons due to hadronic jets.

Further, there must be no charged tracks pointing close to the deposit, and a neural-network classifier is used to discriminate real photons from backgrounds using the shape of the energy deposition and other photon quality variables. The NN output is shown in the figure below: real photons (described by the red histogram) cluster on the right. A cut on the data (black points) of a NN output larger than 0.1 accepts almost all signal and removes 50% of the backgrounds (the hatched blue histogram). One important detail: the shape of the NN output for real high-energy photons is modeled by Monte Carlo simulations, but is found in good agreement with that of real photons in radiative Z boson decay processes, p \bar p \to l^+ l^- \gamma. In those processes, the detected photon is 100% pure!

After the selection, surviving backgrounds are due to three main processes: real photon pairs produced by quark-antiquark interactions, compton-like gamma-jet events where the jet is mistaken for a photon, and Drell-Yan processes yielding two electrons, both of which are mistaken for photons. You can see the relative importance of the three sources in the graph below, which shows the diphoton invariant mass distribution for the data (black dots) compared to the sum of backgrounds. Real photons are in green, compton-like gamma-jet events are in blue, and the Drell-Yan contribution is in yellow.

The mass distribution has a very smooth exponential shape, and to search for Higgs events DZERO fits the spectrum with an exponential, obliterating a signal window where Higgs decays may contribute. The fit is then extrapolated into the signal window, and a comparison with the data found there provides the means for a measurement; different signal windows are assumed to search for different Higgs masses. Below are shown four different hypotheses for the Higgs mass, ranging from 120 to 150 GeV in 10-GeV intervals. The expected signal distribution, shown in purple, is multiplied by a factor x50 in the plots, for display purposes.

From the fits, a 95% upper limit on the Higgs boson production cross section is extracted by standard procedures. As by now commonplace, the cross-section limit is displayed by dividing it by the expected standard model Higgs cross section, to show how far one is from excluding the SM-produced Higgs at any mass value. The graph is shown below: readers of this blog may by now recognize at first sight the green 1-sigma and yellow 2-sigma bands showing the expected range of limits that the search was predicted to set. The actual limit is shown in black.

One notices that while this search is not sensitive to the Higgs boson yet, it is not so far from it any more! The LHC experiments will have a large advantage with respect to DZERO (and CDF) in this particular business, since there the Higgs production cross-section is significantly larger. Backgrounds are also larger, however, so a detailed understanding of the detectors will be required before such a search is carried out with success at the LHC. For the time being, I congratulate with my DZERO colleagues for pulling off this nice new result!

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.