The proton structure probed by D0

The D0 collaboration has recently submitted for publication a new measurement of the inclusive jet cross section, using 0.7/fb of integrated luminosity of 1.96 TeV proton-antiproton collisions collected during Run II at the Tevatron collider. I wish to summarize the results of this new precise analysis here, but before I do, allow me to explain why this measurement is interesting.

When you collide a proton with an antiproton (or, for that matter, any other hadron) the most likely result is that they scatter one off the other without breaking apart, and exchange only a small fraction of their energy: they practically fly one across the other, retaining their integrity.

However, hadrons are composite objects made of quarks and gluons, and sometimes a collision does involve a close encounter between a pair of those constituents. They may thus get kicked off the hadron with high energy. But quarks and gluons feel the strong force, which binds them to the hadron they belong to with a potential which grows linearly with their separation from it. As they fly away (in the horizontal direction in the picture on the right) recalled back by the strong force they decelerate, pulling a string of gluons as a bunjee jumper stretches the rubber cord he is attached to. If they have been kicked with enough energy the string eventually breaks, releasing its energy in the form of a new pair of quarks (the antiblue-yellow one on top, and then the antired-blue and antiyellow-red one below).

The process described above continues until a stream of partons (this is the generic way we call both quarks and gluons when we only care about the strong force) moving roughly in the direction of the original one is created. This fragmentation ultimately produces hadrons -the circles each containing a colored-anticolored quark pair in the pic above-, because quarks and antiquarks bind together into colorless objects. The electrically charged ones can be individually tracked with modern detectors, while neutral ones are harder to measure; but they are more meaningfully described collectively in what we call a hadronic jet – or simply, a jet. By measuring the total energy of the jet, and its direction, one gains access to the kinematical characteristics of the quark or gluon which originated it.

Measuring a hadronic jet is not that difficult: the energy of both charged and neutral hadrons in fact can be determined by letting them traverse our calorimeters: sandwiches of thick slabs of dense material alternated with plastic scintillator or similar active detector components, where they create new interactions, produce streams of secondaries, and ultimately get absorbed. The process has a negligible effect in terms of macroscopic quantities: a 100 GeV proton brought to rest by a block of iron produces in it an increase in temperature of about a picodegree Celsius (a thousandth of a billionth of a degree Celsius). We rather rely on microscopic effects: the scintillation light from all the secondary charged tracks traversing the plastic material produces a signal proportional to energy in a very localized region of the solid angle surrounding the point where the collision took place.

In the figure, you see a cartoon showing the different phases of a jet formation and detection: the proton-antiproton collision produces two quarks emitted at large angle with respect to the beam; a quark then fragments into hadrons; and finally, hadrons interact in the calorimeter, getting destroyed by the interactions with the material, and producing a measurement of the originating parton.

Once we measure a jet’s energy and direction we can do wonderful things: for instance, we can study the relative frequency of collisions as a function of energy and angle. We thus find that more energetic collisions are increasingly less frequent. By comparing the functional dependence with a model of the proton, we are able to test how well we know the proton structure.

And indeed, we do understand the structure of the proton amazingly well, after forty years of deep-inelastic scattering and hadron collisions. We describe what’s in a proton with Parton Distribution Functions (PDF): functional forms , , …, that tell us how likely it is to find inside an energetic proton a quark of a given kind (u,d, …), or a gluon, carrying a definite fraction of the proton’s energy. To find the total energy available to the two partons that hit each other hard -the lucky times when that happens- we multiply the two fractions and together: here is the reason why a fixed-energy proton-antiproton collision produces a variety of processes of different total released energy, , where is 1.96 TeV at the Tevatron.

Above, you can see the PDFs of the proton: the curves describe the probability to find a quark or gluon of different kinds (u,d,s,c,b, and also antiquarks , , plus gluons g) as a function of their energy fraction in the proton, x.

Now, let us make an example. In order to produce two jets with an energy each with a proton-antiproton collision, we must provide two partons such that the product of the energy fraction they carry is . That means that each of them has to carry half of the energy of the (anti-)proton which contains them; or 0.75 and 0.33, respectively!

Recall that a proton is a bag with three valence quarks plus a host of quark-antiquark pairs and gluons: one rightfully expects that the three valence quarks usually carry a bit less than a third of the proton’s energy each (because of the gluons they actually share half of the proton’s energy, on average: a sixth each). It is very rare to find energetic partons such as those of the example above! That is the reason why events with two 500-GeV jets are really rare at the Tevatron. And the PDF are what determines the relative fraction of jet events as a function of jet energy and angle.

In the sketches on the left I tried to picture a proton in two different instants of time. Besides the three valence quarks (a red, a blue, and a green one), one sees gluons and quark-antiquark pairs. Occasionally, even a high-mass quark (the red one in the bottom pic) may fluctuate out of the vacuum, vanishing quickly enough that no energy imbalance is created. 

I do not know whether I made the above explanation clear enough to retain N>0 readers to this point. If I did, I ask them one further effort: I am going to explain what else is very interesting in a collision giving rise to very high energy jets. If quarks are pointlike particles, as we currently understand them to be, the PDF are enough to describe the frequency of energetic collisions. But if quarks have a structure, then there comes a point when, by hitting them hard enough, we start to break them apart. If we ever did that, we would see that the relative frequency of those really energetic collisions would be higher than what PDFs alone predict.

In 1996 the CDF collaboration produced a very accurate measurement of the inclusive jet cross section – the same quantity now measured by D0 with seven times more statistics – which disagreed with PDF predictions at high energy: we saw more events than we thought we would, when jets had energies in excess of 400 GeV (the data points on the right in the plot below). The analysis was scrutinized with great accuracy, but no mistake was found. Were we seeing the effect of preons, the quark constituents ? 

 

Indeed, fits which included a compositeness scale (the energy corresponding to it) hit the data points in the head much better than fits which assumed no new physics. Here is a very good example of what Michelangelo Mangano describes in his recent paper and warns us about: the assessment of a discrepancy from known physics sources and the interpretation in terms of new physics must be two separate phases of the analysis work. And in fact, the more mundane explanation turned out to solve the mystery: the gluon PDF at very high x was not known well enough, and by modifying it just slightly the CDF discrepancy vanished! Later in 1996, D0 data confirmed that the gluon distribution was the sole offender. No preons, unfortunately…

Quarks and gluons are pointlike at the energy we probe them today. D0, with its new analysis (submitted to Physics Review Letters, preprint here), carries the horizon a bit further. But what is impressive of their analysis is observing the various cross section curves – referring to the production of jets at different angles with respect to the beam axis – all described by QCD fits with such an excellent accuracy. Please examine the plot shown below:

In the figure you see different curves – QCD predictions – and different sets of points. The cross-sections have been displaced by powers of two (x2, x4, x8, x16, x32) just to separate the sets for clarity. The sets corresponds to bins of the variable , the jet rapidity – a function of the angle to the beam. The smaller the angle, the harder it is to find jets with a given transverse energy. Transverse energy is the variable of choice for the x axis: it represents the “acceleration” that the quark or gluon originating the measured jet was provided with by the hard interaction. Remember, in fact, that the collision is not, in general, between partons of equal energy: a global motion of the center of mass of the collision is to be expected along the beam axis, but whatever flows transverse to the beam is a genuine indication of a sound kick imparted to the quark or gluon!

As I look at the great agreement of QCD curves and data points it is clear to me that no, the proton – up to energy of about a TeV – is no mystery for us today.