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B hadron lifetimes – part 2 *May 15, 2007*

*Posted by dorigo in news, physics, science.*

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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.

## Comments

Sorry comments are closed for this entry

Hi Dorigo,

My comment has nothing to do with physics…I saw a photo you took of the Azores and wonder if we can use it in a TV broadcast in the States. You can contact me at the email I provided. Of course, we will give you screen credit.

Thanks,

Stacey

Dear Stacey,

sure – go ahead. There are several pictures of the island of San Miguel in the posts I wrote last September, and as far as I am concerned you can grab them all.

Cheers,

T.

Tomasso,

1.041+-0.057 for the ratio of Lambda_b to B lifetimes seems way to large… why is it also larger than the recent D0 measurement in the same channel (of course, they are consistent with each other)? I don’t think there is a single theory prediction out there that claims that the ratio is greater than one…

Regards,

–Alexey.

P.S. Also, the main effect that drives the diference of lifetimes comes from non-perturbative 1/m corrections, not from perturbative QCD corrections…

Hi Alexey,

yes, a value above 1 is not easy to accommodate, but 0.8 was also sounding fishy according to theoretical estimates.

I am not sure I understand the rest of your comment. As far as I know, at lowest order in Lambda_QCD/m the b is a static source of color, and it does not affect the hadron lifetime. The lowest order at which lifetime changes are predicted is (Lambda/m)^2, because of spin interactions.

Cheers,

T.

Hi Tommaso,

Theoretical value for the ratio of the Lamda_b and B lifetimes adopted by the Heavy Flavor Averaging Group (HFAG) is from my paper with two postdocs, Phys. Rev. D70, 094031, 2004 [hep-ph/0407004], which is a “1-sigma” range 0.82 to 0.92 (theoretical uncertainties are not gaussian, that’s why 1-sigma is in quotes). So lower values of that rario are theoretically more feasible — but of course not 0.7-sh that was experimentally favored some years ago. And it is still not clear why D0 gets lower value (granted, with larger uncertainites) than CDF from the same measurement…

To your other comment: While indeed at the leading order in 1/m expansion all heavy hadrons have the same lifetime (b-quark is a static source of color field), the main effects which drive ratios of lifetimes of different heavy mesons and baryons come from (Lambda/m)^3 corrections. These are matrix elements of four-fermion operators that are specifically sensitive to “spectator” effects (i.e. effects of the light quarks). They are numerically larger than (Lambda/m)^2 effects due to phase space factors. All of that is quite well-understood and accepted theoretically. I’ll be happy to talk more about that both here and off-line.

Regards,

–Alexey.

Hi Alexey,

ha! So I am talking to _the_ expert. Very good to know… I have always been fascinated by HQET, since it gives me some ground to visualize what is going on inside heavy hadrons and actually understand a bit about their dynamics. It is the first step towards understanding more, although I think I am bound to stop there…

As for the CDF measurement, if you take the CDF Lambda_b lifetime and divide by the B0 lifetime also measured with the same method by CDF, you get a number with a slightly larger error (due to the fact that the B0 lifetime in CDF is not as precise as the WA) but where you are much safer with respect to unknown systematic effects. In that case, CDF obtains R =1.018+-0.062, which is only 1.7sigma away from the upper bound of the interval you quote… So we are good, I think.

By the way, since you work with HQET and you are willing to explain things, I have a question. I have known for some time that the mass splitting between B** and B hadrons is independent on the heavy quark mass – and so, the same value should divide a hypothetical T** from a T hadron. The argument can be used to explain why top hadrons do not form, in fact. Do you have a simple explanation of the absence of mQ-dependent terms in the B**-B mass ?

Cheers,

T.

Hi Tommaso,

Sure. For a mass of any hadron containing heavy quark,

m_H = m_Q + {some hadronic stuff} + {stuff suppressed by powers of 1/m_Q}

Here {some hadronic stuff} could be HQET parameter Lambda-bar (roughly, energy of light degrees of freedom, which is independent of HQ mass) or also some energy stored in angular momenum, etc. — but it’s all O(Lambda_QCD). Also, {stuff supressed by powers of 1/m_Q} includes spin effects, kinetic energy of a heavy quark (a.k.a as HQET parameters lambda_2 and lambda_1) and other stuff…

Thus, if you take a difference of m_H** and m_H the m_Q dependent part cancels out. The only m_Q-dependence you can get is via terms that are from {stuff suppressed by powers of 1/m_Q}-part, which disappears in the heavy quark limit.

Hope it helps,

–Alexey.

P.S. I used to give an argument that toponium cannot be formed simply because top quark decays faster than toponium forms. How does your argument for T-hadrons (that you mention above) work? Just curious…

Hi Alexey,

thank you for the explanation, which matches my slightly confused knowledge of the issue – it is always good to straighten out one’s doubts by talking to the expert.

As for toponium, I once wrote (FNAL-CONF-02-344-E):

“The large value of Mt implies that the decay time is very short: Gt ~ Mt^3 ~ 1.5 GeV. That value is one order of magnitude larger than the hadronization scale L_QCD: that implies that top quarks cannot bind to form hadrons, and they decay as free particles. The absence of top hadrons can also be inferred from the non-relativistic quark model: on one side, the mass splitting MB**-MB=450 MeV is independent on the heavy quark mass, and must hold for T** and T as well; on the other, the splitting between B* and B depends on 1/M_Q and is thus expected to be smaller for top hadrons. Moreover, toponium states cannot exist, since their width (Gtt ~ 2Gt ~ 3 GeV) is larger than the splitting between 1S and 2S states expected from the perturbative QCD potential. All top resonances therefore merge and act coherently, and what is left in the cross section is only a broad excitation curve.”

I had to quote my own paper because I had forgotten some details of that didactical argument. I included it in my 2002 paper because I was discussing the history of top quark searches, and I thought it was an interesting deductive reasoning.

Cheers,

T.

[…] that’s a really short lifetime on a human scale of things! Then, as nicely reported by Tomaso here, CDF had a new number for this lifetime, 1.593 + 0.083 – 0.078 +- 0.033 ps, which is clearly […]

[…] mixing matrix and other parameters in the B sector of the Standard Model, such as B lifetimes (1) (2) and a host of other […]

i am really searching for the problem in heavy light mesons, but wht i did earlier is a kind of fitting in D mesons with a mass formula given by T mehen, right now looking for something similar in B mesons, but as far as pdg data only few states are available which is not helping me in fitting. Can U suggest something which i can do ?

Alka

Will new PDG wil help me for further exctied states of B mesons

Hi alka,

I am unable to help you because I do not know 1) the environment you are working in (e+e- production ? hadronic production ?…) 2) “fitting in D mesons with a mass formula given by T Mehen” does not ring a bell to me. Do you mean to say you are fitting the D lineshape with some complex formula (not a simple gaussian or a lorentz*gaussian) ? Also, I do not exactly understand what exactly you are looking for. I think the new PDG will contain data on the new B baryons discovered at the Tevatron, like Sigma_b and Xi_b, but as far as mesons, I am unaware of new discoveries there.

Sorry to be unable to help. Maybe you have a link to more information ? What exactly are you trying to measure ?

Cheers,

T.

Hi

thanks a lot for your reply. I am actually trying to give the better prediction to the charm meson masses(0+ and 1+), which have been in arguments for Cleo and Babar. So for that, we must know coupling constants of these states with the ground states, and within themselve. The mass formula for these heavy light meson are in terms of the HQET parameters, which are given in literature and are calculated thru some pionic decays:) Donoo how to get them for the B mesons, as it has been given for some other decays with 30% of uncertainty…and also masses of B* and Bs* are not available/not yet confirmed. So i wanted to use either masses to get better bound over the HQET parameter, or if they can help to give the decays in terms of these parameter. Anything will serve my purpose..but i am stuck these days…

best

Alka

[…] by dorigo in news, physics, science. Tags: b lifetimes, CDF, ichep 2008 trackback One year ago I reported here about the measurements of the lifetime of the Lambda b baryon, a very heavy neutron-like particle […]