by Tommaso Dorigo

The so-called Lambda_b baryon is a well-studied particle nowadays, with several experiments having measured its main production properties and decay modes in the course of the past two decades. It is a particle made of quarks: three of them, like the proton and the neutron. Being electrically neutral, it is easily likened to the neutron, which has a quark composition “udd”. In the space of quark configurations, the Lambda_b is in fact obtained by exchanging a down-type quark of the neutron with a bottom quark, getting the “udb” combination.
Since the bottom quark alone weighs over 4 GeV (more than four times the proton mass), and thus a full three orders of magnitude more than the lightweight down quark, one should expect that similarities with the neutron stop at what I described above. However, there is one further thing that accomunates them: both particles decay by the weak interaction. In the neutron beta decay (see picture on the right) it is one of the d-type quarks that turns into a up quark, emitting a negative W boson; in the main Lambda_b decay it is instead the bottom quark which turns into a charm quark, emitting again a negative W boson.

The speed at which the two reactions described above take place is quite different: 900 seconds in the case of the neutron, and one picosecond in the case of the Lambda_b. But it would be myopical to not see the same pattern. In fact, a Feynman diagram of the processes allow us to see more clearly that this is indeed the same good-old “charged current” weak interaction at work in both cases, with much higher speed in the latter case provided by the much higher energy available to carry it out.

Above, the lines describe the “time development” of the decay of a Lambda_b baryon. Time increases on the x axis, such that the system can be drawn as a series of lines – each tracking one particular body involved in the reaction. The y axis can be thought as a single spatial coordinate instead. As you see, the typical decay of a Lambda_b baryon (in the case pictured above the materialized lepton by the W- decay is a tauon, but this is just an example) is quite the same thing as the regular beta decay of a neutron.

The rare decay found by LHCb

Along the years, the Lambda_b has been studied in detail. While the neutron can only decay to proton-electron-antineutrino, the Lambda_b has many more possible final states to turn into, again because of the large mass of the decaying bottom quark in its interior. Physicists want to know everything about all these possibilities, as new physics processes might hide in the murk of those rare processes. Indeed, it is possible that new exotic particles of high mass make possible decays that the standard model forbids – or predicts to occur with extreme rarity. Measuring something which is predicted to be very close to zero is quite advantageous for an experimentalist, as seeing “something instead of nothing” is quite easier than seeing “something slightly different from something else”!

Enter LHCb. The experiment, which is one of the four main experiments of the Large Hadron Collider, aims at studying in detail particles containing the bottom quark. And indeed, the Lambda_b is one of its targets. By searching for a particular decay of the Lambda_b involving the emission of a non-resonant muon pair, the experiment can indeed be sensitive to possible new phenomena.

Let us see what is the decay mode studied in the latest LHCb analysis. This involves the emission of a proton, a negative pion, and a muon-antimuon pair. Now, there are two distinct, and quite different, reactions that may give rise to the final state indicated above. The simpler one has the muon pair come from the decay of an intermediate body produced in the Lambda_b decay: a J/Psi particle, thus:

Why a J/psi ? Because that particle is a charm-anticharm bound state. And charm is the most likely product of the decay of a bottom quark. With a little thought, one understands what is the mechanism giving rise to the reaction.

– One charm quark is the result of the bottom quark decay, which also emits a negative W boson
– The negative W boson immediately decays, providing another anticharm quark together with a down quark;
– The charm and anticharm can thus bind into the J/psi particle
– As for the extra down quark emitted by the W, this must find a anti-up quark to form a negative pion. The anti-up quark is provided by a gluon, emitted by the initial state of the reaction, which materializes a up-antiup quark pair.
– Finally, the extra up quark from the gluon binds in the baryon, taking the place of the bottom quark. The lambda_b has thus become a proton.

I could not find a simple graph of this reaction in a google search, so I made a quick sketch for you below. As you can see, there are four vertices in the graph: an emission of a W boson, the materialization of a anticharm-down quark pair from it, the emission of a glion from a quark line in the baryon, and the materialization of a up-antiup quark from it.  Then, the J/psi decay to a muon pair introduces two additional vertices.

The above is all well and clear (or is it?), but the LHCb collaboration explicitly avoided decays of the Lambda_b occurring as explained above: they removed from their data events where the two muons came from a J/Psi (or Psi(2S)) decay! In fact, they wanted to study a very different process, much more rare. This is one where the muons come from a neutral electroweak boson (a photon or a Z)!

The Feynman diagram of such a process is more complex: instead of a regular W emission, the reaction entails the emission and immediate reabsorption of the W by the same quark line, such that the bottom quark can transmute not in a +2/3 charge quark, but rather in another lighter quark of charge -1/3: in this case, a down quark. The muon pair is then emitted as electroweak neutral radiation off the “virtual” W boson leg. The graph below should clarify what I mean.

The rarity of the process shown above is mainly due to the fact that it requires a virtual top quark (the one in the “loop” in the graph) to turn into a down quark: this is a very rare occurrence, as the “Cabibbo-Kobayashi-Maskawa” matrix element for such a transition is tiny. It is because of this that the reaction had not been seen before.


Experimental results

LHCb searched for events featuring a proton, a negative pion, and a muon pair in its dataset, and found a mass distribution for these four-body configurations on the right. As you can see, there is a clear narrow peak for mass combinations corresponding to the true Lambda_b mass, well consistent with the red fit to a signal component. (The “shoulder” to the left of it is due to decays involving missing particles and other backgrounds). The process is thus observed, as LHCb can quantify the probability to obtain data at least as discrepant from the “null model” (one where the process does not contribute) at 5.5 standard deviations.

For the three of you who had the guts to follow the discussion until here, I invite you to follow the @cmsvoices account on twitter, as writing this post gave me the inspiration to explain a bit in more detail the rules of the game for drawing complex Feynman diagrams of hadronic decays. It is a lot of fun once you get it!