## Omega b: the new baryon nailed by D0September 19, 2008

Posted by dorigo in news, physics, science.
Tags: , ,

Three weeks ago my attention was focused on the LHC start-up and on other less exciting things, and I overlooked a new important find by the D0 Collaboration: the discovery of the Omega_b baryon. Let me do justice to this new scientific result, although belatedly, in this post. I will first give a short introduction for non-experts in the following, and then discuss the details of the analysis in brief.

The Omega_b baryon, $\Omega_b$, is a funny particle. It is made up of a b-quark and two s-quarks. Since the b-quark has -1/3 electric charge like the s-quark, the Omega_b carries one unit of negative electric charge. It belongs to a baryon octet, eight particles of similar characteristics which you may obtain one from the other by successive exchanges of the three quarks. To explain what a baryon multiplet is, let me neglect the b-quark for a second and rather discuss a simpler scheme with just the three lightest quarks u, d, and s, which are the building blocks of the symmetrical states first compiled in the sixties, when particle theorists were just starting to fiddle with group representations to try and categorize the observed new particle states.

The simplest baryon decuplet is shown in the scheme shown on the left. As you might notice, there are three different axes along which one can classify the ten baryons belonging to the scheme. One, labeled by the letter “Q“, describes the electric charge of the states, and goes from -1 to +2, increasing toward the top right corner. The second, labeled by the letter “S”, describes the “strangeness” of the states. S is the number of strange quarks the baryons contain, and it increases instead as one moves down. Forget the third axis, it is of no use for you.

The one above is an example of the many possible representations of the symmetry group SU(3), in this case applied to describe the symmetries of quark flavors. You exchange a quark flavor with another by jumping along one of the three directions along the sides of the triangle, and you obtain a new baryon, whose properties are somehow connected to those of the former one.

In 1964, exactly the scheme above was drawn to predict that a new state should exist, the $\Omega^-$, at the bottom of the triangle. All nine other baryons had been already observed, and their organization in a decuplet was highlighted by the similarity of the mass of baryons belonging to each row: the upper four states are called Deltas: $\Delta^-, \Delta^0, \Delta^+, \Delta^{++}$, and all have masses of about 1.232 GeV; the second row contains three states called Sigmas: $\Sigma^-, \Sigma^0, \Sigma^+$, all with a mass of about 1.384 GeV; the third row has the two states called Xi, $\Xi^-, \Xi^0$, with a mass of about 1.533 GeV. It does not take a very smart crackpot to guess that a single state should exist to occupy the lower vertex of the triangle, and its mass could be well inferred from the linear progression above: each step down increased the mass by 140-150 MeV, the contribution due to the substitution of a “heavy” strange quark for one of the lighter d or u quarks. So the new state had to have a mass of about 1.533+0.145=1.680 GeV.

The discovery of the $\Omega^-$, in 1964, from the single, gold-plated event shown above (left, the bubble chamber image, and right, the decoding into particle tracks; the particle is produced by a beam entering from below, hitting a target in the chamber) was a true success of Gell-Mann’s and Zweig’s threefold way, the classification scheme of hadrons based on the SU(3) symmetry, which implied the existence of quarks, if only as mathematical descriptive tools. The discovery also made clear that a new quantum number was needed to describe these objects: if the $\Delta^-$, the $\Delta^{++}$, and the $\Omega^-$ were each composed of three quarks of equal type, lying in the same quantum state (with their half-integer spins completely aligned, to give those baryons a total spin of 3/2), there was the absolute need for an additional quantum number for quarks, to make each component of the trio different from the others, or the Pauli exclusion principle would have to be abandoned. This new characteristics was soon identified with colour, the “charge” of strong interactions, which binds quarks together inside hadrons.

Now, let us fast-forward to 2008. We know baryons are quark triplets, we know we can organize them in multiplets of well-defined symmetry properties, we have found most of them. The $\Xi_b$ states have recently been seen by both CDF and D0. So in principle, having observed the cousins of the Omega_b, nobody can really pretend to be surprised by the new discovery: it is just needed by the scheme. Nevertheless, finding the $\Omega_b$ -measuring its properties, its mass, and the rate of its production in hadron collisions- is important. Actually, for theorists the thing which is way the most important is the production rate: understanding the production mechanisms is tough.

Our current understanding of the mechanisms whereby a energetic collision creates states like the $\Omega_b$ is still rather sketchy. Quantum chromodynamics, the theory of strong interactions that bind colored quarks in colorless hadrons, can be used to calculate precisely the production rate of b and s quarks only in special cases; for others, some parametrizations are needed. The possibility that s-quarks come directly from inside the projectiles is also parametrized by “parton distribution functions”, which are measured experimentally; as for b-quarks, they  are hardly contained in the proton or antiproton. All in all, it is possible to predict, with some degree of uncertainty, how frequently we may obtain those three quarks in the final state; but predicting the probability of their binding into a (bss) triplet requires to understand the action of lower-energy phenomena, and it currently still requires a good dealof black magic. Because of these difficulties, the number of $\Omega_b$ events produced for a given amount of Tevatron proton-antiproton collisions is an intrinsically interesting quantity.

The analysis by D0 searches for a very well-defined final state of the $\Omega_b$ decay, one which does not include any neutral particles. It is shown in the graph on the right, where only full lines represent particles which are detected and measured in the detector. The presence of only charged particles in the final state allows the measurement of all the relevant particle momenta, and the reconstruction of the mass of the Omega_b candidate. The decay chain is spectacular, since it involves first the decay $\Omega_b \to J/ \Psi \Omega$, and then the cascade of the $\Omega \to \Lambda K^- \to p \pi^- K^-$, with three charged tracks in the final state which form a backward-reconstructed path, similar (although less striking) to the one of the first Omega- event observed in 1964. As for the $J/ \Psi$, it is easily reconstructed from the two muons it decays into.

D0 uses a method called “Boosted Decision Trees”, BDT for insiders, to increase the signal-to-noise ratio of their $\Omega^-$ candidates, before combining their signal with that of the J/Psi decays. Several kinematic variables are used to discriminate the real $\Omega^-$ decays from random track combinations. The method does a good job, as you may judge yourself by comparing the invariant mass spectrum of $\Lambda \pi$ combinations before (left) and after (right) the BDT selection in the graphs. Notice that the red histogram comes from combining three tracks which have the wrong sign combination: a $\Lambda$ signal with a positive kaon, which cannot possibly come from a $\Omega^-$ decay. The combination carries exactly the same biases of the right-sign combination, and in fact it well-reproduces the shape and normalization of the background in the right-sign sample, both before and after the selection.

In the end, D0 reconstructs the mass of the $\Omega_b$ baryon (see below) with a rather simple-minded approach. This is the only part of the analysis which made me frown. Why did they not do a full-fledged kinematical fit to extract the candidate mass with the best possible accuracy ? They in fact apply some hoonga-doonga correction to the reconstructed mass, forgetting for a moment that they have the moral obligation to use the full information provided by their precious detector. Here is what they do: they first compute the J/Psi mass from the two muon quadrimomenta; then they compute the $\Omega^-$ mass from the lambda-kaon combinations; and then they go hoonga-doonga:

$M_{\Omega_b}=M_{\Omega_b^{rec}} + (3.097 - M_{J/\Psi}) + (1.6724 - M_{\Omega^{-,rec}})$.

That is, they just add the residual differences between true and reconstructed J/Psi and Omega masses to the measured $\Omega_b$ mass. This is like putting a pair of flints as a cigarette lighter in a Ferrari Enzo. Rather hard to digest for me, but this is a first observation paper, so I will keep my criticism constrained. So, my congratulations to D0 for pulling this new result off! You can read the details of the analysis in this paper.

UPDATE: I made a typo in the post above (at least one, that is). The one I am referring to is important, however. It is in the part where I discuss hadron multiplets. Can you spot it ?