A Quantum Diaries Survivor

I started the first part of a tale of B hadron lifetimes a few days ago by discussing in simple terms what happens when a b hadron, produced in a particle collision, awaits its own decay by means of the weak force. Not all hadrons containing a b-quark need weak interactions to disintegrate: those which are “excited” can transmute into their “fundamental” state by means of the strong or electromagnetic force, and they in fact do so quite fast. But those quick “radiative” decay processes produce fundamental states which can then only decay if they change their b-quark into a c- or a u-quark by emitting a W boson: those are the ones which are condemned to a long waiting list.

Now, what are these fundamental states, anyway ? The lowest mass mesons - composed of a quark-antiquark pair orbiting around each other - are of two kinds: (anti-)B0 and B-, respectively formed by a (b anti-d) or (b anti-u) quark pair. Of course, the antiparticles of these two mesons have the same behavior, as well as  B_s mesons (b-bar s), which I will leave aside in this discussion. As for baryons (formed by triplets of quarks), there is not much to play with: only the Lambda_b (udb) or its antiparticle can be considered - the recently discovered Sigma_b states have a mass larger than the Lambda_b, and they decay quite fast into it by emitting a pion - again, a sort of “radiative” strong interaction process of which we need not be concerned here.

From a phenomenological standpoint, the fact that the b-quark weighs so much more than the d- or the u- quark means that we have a quite simple way to picture the structure of these particles. B mesons are pretty much like miniature hydrogen atoms: a heavy body - the b-quark - around which jiggles around a much lighter one. These two are not exchanging a cloud of virtual photons, however, as the electron and proton of a H atom do: they exchange a cloud of gluons, the carriers of the strong force which binds the hadron together. On the other hand, the Lambda_b can be pictured as a negative H ion: a b-quark plays the role of the proton, and the two lighter quarks act as the two electrons, again jiggling around and exchanging a cloud of gluons with the b and with each other to keep themselves tied in.

The above picture is much more than a didactic explanation of the basic physics involved in the structure of these bodies: it is in fact the core of a framework called Heavy Quark Effective Theory (HQET). HQET allows theorists to compute the detailed behavior of these bodies quite effectively, in fact. The method involves an “expansion” of the quantity to be measured (say, the lifetime of the body) as a perturbation series where smaller and smaller effects are considered in turn and given coefficients proportional to inverse powers of the mass of the heavy quark.

Brilliant! the fact that the mass of the b-quark (about 4.5 GeV) is so much larger than the characteristic energy of strong interactions - a quantity called Lambda_QCD, equal to a few tenths of a GeV (QCD stands for quantum chromodynamics, the insiders’ name of the strong force)- allows a perturbative expansion, something which QCD usually disallows.

[In simple terms, a perturbative series is a sum of many terms. If each term (the "perturbation" at a given order) is much smaller than the previous ones (something that the heavy quark expansion grants, in the case of the b-quark), the result is already quite precise after only the first few terms have been computed: so one is not condemned to compute an infinite number of large contributions, which is usually embarassing.]

These HQE calculations predict that B mesons and Lambda_b baryons should have a comparable lifetime, despite the extra light quark contained in the latter. This is not altogether surprising, but please note that strong interactions could indeed modify heavily the phenomenology of a weak decay by the added interactions of the extra quark, as they in fact do in other systems.

Theorists can only guess the relative strength of the coefficients of the perturbative series which they have not computed, and so their estimates of the lifetimes of these particles carry some uncertainty - which in turn is not easy to quantify; but the predictions appear to be rather precise in assessing the ratio between lambda_b and B meson lifetimes to be slightly smaller than, but consistent with, unity. That is thus a place where a precise experimental input can be useful to settle the matter - or, if a strong disagreement with predictions is observed, to start wondering whether some new, exciting physics is lurking in the studied phenomena.

The nice part comes when one considers the experimental measurement of the lifetimes. Usually, measuring the lifetime of a B-hadron is not a simple task: one needs to reconstruct the decay vertex (the point where the hadron decayed into lighter bodies) from the tracks left by daughter particles; the measured distance traveled by the hadron is then used in a formula together with its mass and momentum to extract the time it took for the disintegration to take place. And then, comparing two different decays in order to extract their lifetime ratio may be complicated by the different systematic uncertainties that each different decay topology implies. But not for neutral B mesons and Lambda B: they can both be detected in their decay to a J/psi meson and a “V-zero” particle. 

“V-zero” is a term used in the fifties to describe in generic terms neutral long-lived hadrons which materialized in a bubble chamber in a pair of oppositely-charged tracks, in a point displaced from the point where a collision originated them. Neutral kaons do that, but also Lambda baryons do. Kaons decay to pairs of pions, Lambda baryons in a proton and a negative pion. The long lifetime of these decays is driven by the fact that they are, again, weak: the neutral kaon is (d anti-s), the Lambda is (uds) in quark content, and they decay by transforming the s-quark into a lighter one. In the picture shown on the left, a pion-proton collision in a bubble chamber produces a K-zero and a Lambda, and they both produce the signature of  a “V-zero” I discussed above. 

CDF measured lifetimes of neutral B hadrons and Lambda_b baryons with a large sample of events extracted from a dataset rich of J/psi signals (the J/psi is a meson formed by two c-quarks, which often decays into pairs of muons, and are thus easy to identify and collect): they measured the B0 decay into J/psi K-zero, and the Lambda_b decay into J/psi Lambda. Exactly the same kinematics, save small differences in the available energy of the decay products.  

When one has two very similar measurements, the ratio of the two becomes an excellent thing to compute, since the systematic uncertainties are common to both, and -a joy to behold- they perfectly annihilate and dissolve like gin and Martini dry in your glass.

The precision of the new measurement, based on an inverse femtobarn of data, beats the previous world average for the lambda_b lifetime. Above you can see the exponential distribution of measured decay lengths of Lambda_b baryons obtained by CDF (the decay length is the quantity used to determine the lifetime). The blue points with error bars are the data, the black line is the fit, and the red line is the background distribution, while the contribution from real Lambda_b decays is in light blue. The measurement has a precision of 5%. Below you can compare the new measurement, this time quoted in picoseconds, with the previous determinations of the same quantity in CDF (with less data) and in other experiments.

You can see that indeed, the new data point fights a little with the previous ones.

By taking the ratio of the above measurement with the better determined world average of the B-zero lifetime, CDF measures that the Lambda_b lives 1.041+-0.057 times more than the neutral B meson.  It turns out that the HQET predictions are not far from the new measured value. All is well - b mesons and b baryons decay alike, and HQET is still a quite useful tool for the understanding of quantum chromodynamical influences to the weak-interaction mediated decay of these particles.

[A note for experts: while it is true that the ratio of lifetimes is indeed computed with the world-average of B-zero lifetime, and not with the single determination produced by CDF with J/psi V-zero topologies, the fact that the latter is perfectly compatible wit the former, while slightly more imprecise, is the best test one can show that indeed, systematics in the Lambda_b measurements are well under control... ]

If you want to know more about this intriguing measurement, please have a look at the web page of the analysis , which also contains a link to the recent publication which ensued.