Below I offer a preview of the slides I will show tomorrow at an invited seminar on the rather technical topic of "The b-jet energy calibration with Z-->bb decays", which I have come to CERN to give at a meeting of the LHCb collaboration. As I mentioned already in the first part of this two-part article, the topic is rather technical, and I do not expect a large audience -but I will nonetheless make an attempt at explaining the meaning of the slides pasted below. Then, of course, I am available to provide some additional light on any specific issue among those dealt below which you may want to understand more about.
The first 21 slides dealt with an introduction of the issue of b-jet energy measurement. Here, we start right with the main topic of the talk: how the Run II data collected by the CDF experiment have allowed a calibration of b-jet energy using Z decays.
Slide 22: Above, just a table of contents of the section of the talk which discusses the search for a Z-->bb signal in Run II.
Slide 23: here I discuss some details of how b-quark jet pairs with relatively low transverse energy are collected by CDF. The trigger is based on the SVX -the wonderful device I have discussed in the first part of this article.
Slide 24: above, I show a graph of the cross section of the trigger as a function of luminosity. If you have not fallen asleep yet, here you might stand up and say: "What ? Is the cross section of a process depending on the luminosity ? What the heck are you talking about ? Cross sections depend on the physics of the collisions, not on how many collisions you make!". You would be right, but the problem is that triggers are not perfect tools. If you request the presence of tracks and jets in an event, you are making a request on the combination of different objects. Triggers are sometimes fired by fake objects, and this is increasingly likely as luminosity increases. So much so, that the increase is not even just linear, but it follows a power law. That is the black curve fitting the red points. Also note on the graph the blue contours, which show points of the graph of equal rate. Since the rate is the product of cross section and luminosity, these are in fact hyperboles.
Slide 25: here is described the selection of events useful for the Z search in CDF Run II data. The first thing to do is to select dijet events: this is shown by the two plots, where the transverse energy of the leading and sub-leading jet are shown before and after the requirement that the two jets be central and above 22 GeV of transverse energy. Notice that the 22 GeV cut has no effect on the leading jet (on the left): the reduction there is only due to the fact that some events have no other jet above 22 GeV, or have jets emitted in the forward region, where we discard them (they are not well-measured, and we would not be able to find b-quark tags in them).
Slide 26: a few points are made about the differences between gluon fusion processes yielding a b-quark pair and electroweak production of a Z boson. The latter process emits less QCD radiation, as shown in the cartoon on the top right corner: the two colliding objects do not "transfer" colour charge to the final state (the Z is colourless), and so the two quarks emitted by Z decay only extend a colour string among them, producing the pattern of radiation shown on the top right (the configuration shown on the right). Conversely, the QCD production of bb pairs occurs via the flow of colour charge from initial to final state, with the creation of two "antennas" that emit QCD radiation preferentially along the two swaths parallel to the beam axis, shown on the graph on the left. This whole thing does not have a large impact in the choice of cuts for the increase of the signal to noise fraction, however: the kinematic selection only relies on simpler variables, determining whether the two jets are back-to-back (lower left, the delta-phi angle between them), or whether there is an additional jet (lower right).
Slide 27: after the kinematical selection one must decide how strict a requirement to impose on the presence of hints about the content of b-quarks of the two leading jets. The two graphs show a variable which discriminates b-quark progenitors from c-quark and from light-quark ones. It is the combined mass of all charged tracks found to originate from a common "secondary vertex" (a particle's decay point). B-quarks, thanks to their large mass, yield a broader distribution than c-quarks and light-quarks. The study shows that in order to select events where both jets come from b-quarks it is mandatory to enforce the presence of a secondary vertex b-tag in both. This is not necessarily so obvious a priori, since b-quarks are almost always produced in pairs in proton-antiproton collisions: yet, the selection of clean two-jet topologies and a single b-tag is not enough: fake b-quark tags pollute the sample too much, and there are a significant number of events where one of the two b-quarks disappears along the beam line. Double b-tagging is thus mandatory to reduce backgrounds.
Slide 28: this shows the number of expected signal events in the selected data, and the uncertainties affecting that estimate. Among them, the largest comes from the insufficiently well known efficiency of the secondary vertex b-tagging -a fact that plagued the determinations of the top quark pair production cross section for many years.
Slide 29: the dijet mass distribution of the remaining QCD background -which still dominates the Z signal after all cuts- needs to be modeled with the utmost care, because the signal is very small in comparison. The way this is done is to select events failing the kinematical requirements, and compute there (the hatched green region in the graph on the right) the ratio between events possessing two secondary vertex b-tags and all events before b-tagging. This ratio can be computed as a function of the mass of the two jets. Then, it is applied to events before b-tagging in the signal region (the red box) to obtain a background prediction which depends on the mass. This shape (shown on the left) is then fit with a continuous parametrization, which allows its use in a unbinned likelihood fit later on.
Slide 30: this shows that the choice of the area where the ratio between tagged events and untagged ones, discussed in the previous slide, has an impact on the mass background shape one can obtain with the method. The blue region in the plot is the one corresponding to selection cuts for the control region which do not bias much the dijet mass distribution -as measured by the chisquared of fits to data excluding the region where the Z boson might give an additional contribution. These regions are called "mass sidebands".
Slide 31: the mass shape expected for the signal also requires a suitable parametrization. Here are shown 21 different shapes, obtained from Monte Carlo simulation and a variation of the b-Jet Energy Scale -the number we want to measure. The b-JES is a factor describing how under- or over-estimated is the b-jet energy in the Monte Carlo simulation with respect to the real data. In a ideal world, it would be equal to 1.0; however, deficiencies of the simulation of the detector, insufficient knowledge of B-meson phenomenology, and other issues may make the b-JES depart from 1.0. The fit to the Z boson peak gives a direct answer on how well the simulation is matched to the data.
Slide 32: here the formula for the fit to the dijet mass distribution is detailed. The results of the fit to the mass spectrum are also shown : the fit identifies more than five thousand Z boson decays to b-quark jet pairs.
Slide 33: and here is the mass spectrum, fit with the functional form shown in the previous slide. The top right inset shows the excess of data over the fitted background shape (which is in green in the distribution shown on the lower part of the graph). The "excess" of blue points is well fit by the signal shape alone, as it should.
Slide 34: this shows the main uncertainties on the measurement of the b-jet energy scale factor, which is extracted by the dijet mass fit as a shift of the signal peak from its nominal position.
Slide 35: The data also allow to measure the cross section for Z boson production, multiplied by the branching fraction to b-quark pairs. The result is larger, but in agreement, with theoretical predictions.
Slide 36: Here a few conclusions are drawn from the Z->bb analysis of Run II data performed by CDF (that is, me and eight collaborators within CDF).
Slide 37: here a hint is given at the new trigger which superseded the old one for the collection of b-jet pairs at CDF, when the Tevatron luminosity started to exceed 10^32 cm^-2 s^-1 , forcing the rethinking of all triggers to reduce the accept rate and keep it at a level manageable by the data writing capabilities.
Slide 38: here some ideas are collected about the possibility of calibration the b-jet energy scale using events where a high-energy photon recoils against a single b-quark jet. There are several problems in this technique, first of all the insufficient purity of b-jets achievable by secondary vertex b-tagging. As the graph on the bottom shows, the b-quark component is only half of the total selected sample (this is however just a simulation).
Slide 39: this discusses the existing measurements of the gamma-B production at the Tevatron, to size up how much data may be needed for a meaningful determination of the b-jet energy scale using those processes.
Slide 40: this is an idea I have caressed for about ten years, but have never found the time to investigate in detail. The idea is that if one manages to select Z+gamma events -Z boson production when the Z recoils against a high-energy photon- with the Z decaying to b-quark jets, the calibration of the b-JES becomes a child trick, since the system is kinematically over-constrained by the very well-measured transverse energy of the photon. The trick is that Z->bb +gamma events do not suffer from the usual background of Z->bb events, because the requirement of the additional photon automatically kills all initial states with gluons in the QCD background -and those are the largest source of background. The drawback of using Zgamma events for b-JES calibration is of course the lack of statistics: this is a rare process. However, the graph on the top right shows that CDF has already collected hundreds of them. At LHC this might be a useful way to work out a calibration.
Slide 41: some concluding remarks are collected here about the whole seminar. On the right, I placed a few figures showing significant hadronic signals recently collected by the CDF collaboration.
Slide 42: here is my personal conclusion: since LHC will hardly ever be able to measure the top-quark mass with a precision higher than what is being provided by the Tevatron experiments, the LHC experiments should consider using the top quark as a calibration line: the mass is known, and the large cross section for top-quark pairs makes this a no-brainer...
Of course, this is a provoking statement. Atlas and CMS will one day measure the top mass with a precision better than that of the Tevatron experiments. However, this is expected to take a long time, since such a precision measurement requires a lot of effort spent understanding the detectors in all their nuisances. By the way, the plot on the left shows the most precise measurements of the top quark mass by the Tevatron experiments, which have been combined in the world average shown at the bottom; the plot on the right shows the expectations for the precision on the top mass measurement by CDF alone, as a function of integrated luminosity used for the measurement. As you can see, the experiment has been doing exceedingly well so far, out-doing the pre-run II predictions (the red star) by a factor of two already. By the end of Run II, CDF alone might have a <1 GeV total uncertainty on the top mass.
Energy Calibration Of B-Jets: Part II