Dreaming Of Tau Lepton Decays
    By Tommaso Dorigo | March 17th 2014 08:21 AM | 15 comments | Print | E-mail | Track Comments
    About Tommaso

    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    The tau lepton is a particle of very complex phenomenology. Although point-like as its lighter counterparts - the electron and the muon - the tau has a quite respectable mass, 1.77 GeV, which makes all the difference from the other charged leptons.

    The tau was discovered in 1975 by Martin Perl at the SPEAR electron-positron collider. The acceptance of that observation was quite slow: the events found by Perl and his team were complicated because of the peculiar properties of the newfound particle. Perl had found an excess of events featuring an electron and a muon and an energy imbalance, which were hard to explain unless hypothesizing the creation of a pair of short-lived, heavy leptons.

    The fact that neutrinos were carrying away energy and momentum prevented a measurement of the mass of the tau. Eventually, however, Perl got his Nobel prize for the discovery, in 1995!

    Today the tau lepton is extremely well studied, and although it is much harder to detect taus than electrons or muons in the hadron-hadron collisions of the LHC, the decays can be used to extract meaningful physics results. For instance, one can search for Higgs decays to tau lepton pairs! The graph below shows the signal found so far by CMS.

    Above: distribution of the reconstructed invariant mass of tau lepton pairs from CMS 2011-2012 data (black points) compared to backgrounds (mostly due to Z->ττ decays, in beige). The upper right inset shows the excess of data over backgrounds, compared to the predicted Higgs signal (red hatched histogram).

    Besides the fact that a tau lepton always yields at least one neutrino -a tau neutrino, in fact- in its decay, the other reason why it is complicated to study is that its large mass allows all sorts of decays: not just ones to an electron and two neutrinos or to a muon and two neutrinos, but also ones involving light hadrons. Let me first explain the leptonic decays however.

    The tau turns into a neutrino by emitting a virtual W boson. The latter can materialize either a electron - electron neutrino pair, or a muon - muon neutrino pair: in these "fully leptonic" decays the final state has a charged lepton and two neutrinos. They are those which were first spotted by Perl in 1975. In a modern-day detector the signature of a tau pair production (say when the two taus are the product of the decay of a Z boson) can thus be the one seen by Perl, of an electron and a muon of opposite sign, not balancing in transverse momentum. However, there are more frequent decay modes involving hadrons, and those are much harder to spot.

    The virtual W boson emitted when the tau turns into its own neutrino, in fact, has enough energy to materialize a few light hadrons: pions, kaons, or even more massive particles. If one looks in the Review of Particle Properties (here), one finds literally dozens of observed decays to hadrons. Most of them have small probability of occurring, but in total they make 66% of the total; the eνν and μνν modes take a share of 17% each.

    My general knowledge of tau lepton decays stops roughly there: I know that taus may generate "one prong" and "three prong" topologies whereby there is only one charged particle (of charge, of course, equal to that of the tau) or three charged particles. These charged particles are almost exclusively pions, and they may or may not be accompanied by additional neutral pions. And I know little else.

    So I was surprised last night to learn, during a dream, that the tau can also decay to a phi meson! The phi meson weighs 1020 MeV, so the decay of a tau to a phi plus a neutrino and a charged particle is energetically possible; but I had never really thought of that possibility. And I had to dream about it to learn it.

    In my dream, I was talking to Luca Perrozzi, formerly a graduate student who worked with my group in Padova at a few early measurements we did with the first data taken by CMS in 2010. One of the early measurements was to detect the very first signal of the phi meson in its decay to kaon pairs - something which is very boring physics in absolute terms, and yet something which at the very start of CMS data taking was interesting to measure, to verify the capabilities of the detector to track charged particles and the possibility of silicon sensors to provide a measurement of particle characteristics through the specific energy loss of charged particles in the sensors.

    The phi meson, which decays to kaon pairs, offers the chance to verify that one can discriminate the omnipresent pions from the less frequent kaons using the silicon energy deposition measurement. Indeed, by selecting tracks with "kaon-like" energy losses we extracted a very nice peak with data from the very first few days of running. But that is ancient history now.

    Luca nowadays is measuring the W boson mass with CMS data. In his measurement he is using muons and electrons only; in the dream, however, he was also using other signatures. And he was reporting to me that he had two events that he could not really understand: those events appeared to have two kaons making the mass of the phi meson, and one further track of high momentum; and he could not understand their origin; in particular, the phi meson appeared to have a long lifetime - while in truth we know that it decays too fast for its decay length to be detectable.

    In my dream we discussed in some detail the events, which Luca appeared to be willing to attribute to W production. And then it dawned on me: these were tau lepton decays to a phi meson, a pion, and a neutrino: the phi thus appeared to have a long lifetime, but that was in fact the long lifetime of the tau (the tau lives only a few tenths of a picosecond, but that is enough for it to travel a few millimeters before decaying). When I explained that to Luca in the dream he appeared convinced that I was right; but a dream is only a dream...

    So today I decided to check whether such a decay has ever been studied or seen in a previous experiment: and I was pleased to see that it indeed has been measured. It occurs 35 times every million decays, so it is rare, but not impossibly so. In particular, CMS may well have been collected a few of these events in the 2011-2012 data. Note, however, that a W boson decay to a tau-tau neutrino pair will be hard to trigger on if the tau goes on to decay to a phi and a pion: there is nothing distinctive in the event apart from the missing transverse energy due to the escaping primary neutrino. However, we might have collected some Z->ττ decays with a subsequent decay of one tau to electron or muon, and the other to phi and pion. But how many?

    The Z->ττ production rate in CMS is of about one nanobarn, so that means about 20 million such events in the whole data collected so far. Now if we ask for the final state of one fully-leptonic decay (eνν or μνν) and one φπν decay, we should be left with 20M x 2 x 0.34 x 0.000035 = 476 events, okay let's make it 500 to round it off. Now, of those 500 events one may expect that no more than a tenth has been collected by the trigger, as the electron and muon from tau decay do not always have enough energy to pass the trigger threshold, and further oftentimes they will be emitted at small angle with respect to the beam pipe, making their triggering impossible.

    That ballpark estimate leaves with about 50 events in the data. It should be possible to select them (in the middle of a really large background!), by requiring the presence of an isolated electron or muon recoiling against three charged particles vertexed together, two of which making the phi mass if assigned the kaon mass hypothesis. But would this be a worthwhile endeavour ? Probably not - the branching ratio of tau leptons into phi and pion is already measured to 15% accuracy, and not much there is left to learn from a more precise determination which would anyway be almost impossible to obtain with CMS.

    Still, it is fun to just play with these branching ratios and imagining how many reactions of some particular kind are present in the data that LHC has produced. Or, at least it is sort of fun to me -today you are probably much more interested in what will be said at the Harvard press conference on the B-modes !


    Thank you for your excellent color-coded diagram of the contributions of various decays to the production of tauons (tau leptons). In Standard Model theory, the tauon is coupling very strongly to the Higgs field, to cause its large (for leptons!) mass of 1.77 GeV. But, paradoxically, it is decaying very fast, which is why the universe is not filled with tauons.

    So why is it coupling so strongly to the Higgs field that it has the biggest mass of all leptons, yet also so unstable that it is so hard to detect because it disappears so fast as a result of rapid decay? The apparent paradox: strong coupling to the Higgs field, yet very unstable?

    What must happen is that the stronger the Higgs field coupling, the more unstable the particle, or in mathematical language (of Heisenberg's uncertainty principle):

    STABILITY (LIFETIME) = {h-bar} / MASS (in energy units)

    The mass is inversely proportional to the lifetime. Only massless particles last forever, if this Heisenberg law is true. Tomasso: what puzzles me endlessly in my dreams, is why physicists don't think of mass as being the "charge" for the theory of quantum gravity, so that the 125 GeV Higgs field boson is actually the golden particle - the fundamental charge - of quantum gravity.

    As you say in your other post, the Higgs boson has a 4.15 MeV resonate decay width. It seems to be to be a composite particle, a Bose-Einstein condensate. My argument is that electromagnetism is not Weyl's and Dirac's assumed U(1) gauge theory, because there is a chiral difference between matter and antimatter which expresses itself in electromagnetic theory by the handedness of the magnetic field lines around a moving electron.

    Maxwell himself in 1861 proved that magnetic fields are caused by the angular momentum transfer from the spin of gauge bosons. He used the simple language of gear boxes and mechanics, like "idler wheels", not vector or tensor calculus that was applied later by Heaviside and Einstein. But Maxwell's original 1861 theory was actually a two-charge theory, not a single charge plus antimatter theory. In other words, Maxwell's theory of electromagnetism was SU(2), requiring Yang-Mills equations. These Yang-Mills equations are Maxwell equations plus a "net charge transfer term", which is a special case of displacement current that is normally unobservable and thus excluded by Heaviside from the Abelian U(1) Maxwell equations, because massive charge gauge bosons ("idler wheels") can't propagate along a single-way path in the vacuum, due to the infinite magnetic self-inductance.

    To use highway traffic as an analogy, a two-way path like a motorway with a return carriageway, is perfectly permissible in "gauge boson exchange", because the returning traffic - which by charge conservation is in equilibrium with the outgoing charge - has a magnetic field vector that precisely cancels out the magnetic field curls from the other "lane" on the motorway. So I believe like Maxwell in 1861 that electromagnetism is an SU(2) gauge theory, and that Weyl-Dirac-Pauli got it wrong with the U(1) model in 1929. By the time Pauli started to see sense in 1956 when U(2) parity conservation in weak interactions was finally debunked and SU(2) became vital for weak interactions, he was dying and unable to go back and re-examine parity conservation dogma in electromagnetism.

    So SU(2) is both the correct gauge symmetry for weak interactions and also electromagnetic interactions. U(1) hypercharge is then free for use to model the force of dark energy, which also gives us quantum gravity by a LeSage mechanism. All the "objections" have been debunked as ignorant nonsense.

    Hi Nige,

    "So why is it coupling so strongly to the Higgs field that it has the biggest mass of all leptons, yet also so unstable that it is so hard to detect because it disappears so fast as a result of rapid decay? The apparent paradox: strong coupling to the Higgs field, yet very unstable?"

    No paradox here.

    First of all, one simple rule is that the larger is the mass of a particle,  the faster it decays: the final state can be imparted with a wider range of possible momenta. This is called "phase space". Alone, the larger phase space of tau decay as opposed to e.g. muon decay explains most of the difference between the speed of the two processes (tau decay is ten million times faster).

    But then you must consider that the tau has also a much wider choice of possible final states: while the muon can only go into an e ν_e ν_μ final state, the tau can do that AND decay to μ v_μ ν_τ, but it can also decay to a multitude of hadronic final states. More choices, more speed.

    Thank you very much for replying Tommaso!

    The phase space concept from path integrals for radioactive decay: yes, thanks, the more possible ways a decay can occur, the faster it does decay. Also, Heisenberg's law says that lifetime is inversely proportional to the mass of the particle.

    All I was trying to say, was that "normally" stronger couplings mean more stability, and slower decay rates! For example, the virtual pion-mediated attractive force of the strong interaction in a nucleus makes light elements very much less liable to break up (spontaneous fission) than very heavy elements like Fermium or Einsteinium.

    (I'm aware that the strong interaction also has repulsive components mediated by virtual mesons other than pions, but it is the attractive pion-mediated force which confines the protons in the nucleus against the Coulomb repulsive force.)

    The reason of course is that the pion exchange between neutrons and protons binds the nucleus together, against the Coulomb repulsion force between protons that is trying to explode the nucleus. For light nuclei like helium, the strong nuclear attraction mediated by virtual pions wins out very effectively against Coulomb's electromagnetic repulsion. But as you know, for extremely heavy nuclei, the very short -range of the strong nuclear force prevents it from properly offsetting the long-range (inverse square law) electromagnetic repulsion between protons due to Coulomb's law. So very heavy nuclei are liable to spontaneous fission, unlike light nuclei.

    Applying this idea to the coupling between the Higgs field and leptons, you might expect stronger coupling to indicate greater stability and longer half-lives, when in fact the opposite occurs. This was what I was trying to say! Thanks for your response, Tommaso. I realise you are very busy with particle physics experiments data interpretation.

    Hi Nige,

    not too busy.

    I believe it is confusing to use the pion-exchange idea for deductions about subnuclear physics. It is a nice schematization that people put forth when they knew the pion existed but nothing more; but we have treaded further, and we know it is not the way things actually go. The gluon is the mediator of strong interactions, not the pion...

    Hi Tomasso,

    Thanks for your time in discussing. But isn't it a fact that the QCD gluon strong interaction SU(3) theory only works for very high energy, because the strong coupling decreases with increasing energy, allowing asymptotic freedom of quarks at very short ranges?

    Surely, virtual mesons (like pions) do mediate the strong force between nucleons, while gluons by themselves just bind together the quarks within nucleons? Or do you mean that Yukawa's strong force theory of mesons is replaced by quark theory? Cheers, Nigel

    Yes to the second one. The Yukawa theory was an effective field theory developed to model the observed features of hadrons, but it worked until it worked. Also note that the theory existed before the pion, and when the pion was found it was identified with the quantum of that interaction, but it was only by chance that it had more or less the right properties.

    You can understand some of the low-energy phenomenology that way, by single pion exchange, but that does not make you smarter -as instead knowing the details of the true underlying theory, QCD.

    Thank you for these clarifications. All I meant was that QCD breaks down at low energy because the coupling runs the opposite way as QED with energy. The QCD coupling is small at high energy giving asymptotic freedom, so the gluon theory works there. But QCD has always been a complete failure at distances on the order of a nucleus. For this reason, I was taught Yukawa's theory as an effective theory. At the time, Yukawa's theory was so popular people tried to claim that the muon was the meson just because it was observed with roughly the right mass, before the pion was seen. The pion contains a quark-antiquark pair with overall neutral color (color and anti-color cancel), so I don't understand how QCD is expressed in Yukawa's proof-tested theory. Surely QCD is tested for particle physics and Yukawa theory for nuclear physics?

    Maybe the word "effective" has different meanings, but I was taught that effective means better than ineffective, like QCD. What practical physicists want and need are effective theories, maybe, not beautifully ineffective theories. I don't see how anyone can believe that the nucleus is a product of QCD mathematics, because QCD can't be calculated for nucleus-sized distances due to the blow-up in the perturbative expansion to the path integral. This is due to the large QCD coupling at low energies. So it is an ineffective theory. I agree on what is an effective theory, Tommaso. I wonder is the QCD theory really the "underlying theory" at all. How can a series that can't calculate anything in the IR limit (low energy limit) for nuclear physics due to the large strong coupling in that limit, be called the "true theory"? Not even God can calculate with such a theory. Surely, the Yukawa theory can be viewed as the solid theory, and QCD is an extension. Has anyone ever isolated a gluon or glue-ball? But they have seen pions. :-)

    Well, I don't think that a theory needs to be fully calculable to be the true theory. After all that would be asking for too much, I believe. It is already extraordinary that we can understand the laws of nature, I don't think we should insist that we can calculate them.

    Hi Tommaso, that's exactly what the string theorists say! Feynman said that scientists should be less romantic and emotional, and more calculating! Thank you for your discussion with me. Normally, debates are prohibited. :-)

    What is it, do you have Ebola ?
    Anyway, QCD has produced tremendously precise theoretical predictions that have been checked extensively. If there is a restricted energy domain where we do not calculate, while still understanding every phenomenon in detail without recurring to new entities, science is fine. String theory is all another matter.

    Thanks for clarifying, Tommaso. QCD is an empirical theory based on Gell-Mann's SU(3) correlation patterns for hadron spins and charges, so it's hardly surprising that it gives good predictions for particle physics (a circular argument) ... what's really surprising, or rather telling, is that it fails to make any predictions for nuclear physics. Mesons have no color charge because the quark and anti-quark in the meson have opposite color charges, which cancel out. This says it all, for the pipe dream of using QCD for nuclear physics, quite apart from the failure of perturbative QCD in its IR limit due to its large running coupling at low energy ...

    String theory is not at all a different matter, is it, Tommaso? You must please admit that the string theory's AdS-CFT correspondence (really only an unproved, failed conjecture) was the best hope in science for making non-perturbative QCD predictions for nuclei. Maldacena's AdS-CFT hype claimed that string theory would allow a conformal field theory of particle physics for QCD's strong force nuclear physics interactions to be calculated non-perturbatively by identifying a corresponding anti-de Sitter space. I studied anti-de Sitter spaces 25 years ago, and remember that anti-de Sitter space is a universally attractive force, akin to the pion-mediated Yukawa force that binds nuclei together against Coulomb interactions. So, Tommaso, the failure of string theory's AdS-CFT surely kills your dreams of claiming that QCD is a theory of nuclear physics. And no, I do not have ebola! :-)

    You are getting it wrong Nige, QCD is not an empirical theory. QCD is based on a different SU(3) group than the flavour one of Gell-Mann, and it has nothing of empirical in it. Confirmations of theory predictions have been astounding and the fact that we do not know how to calculate the low-energy limit should not fool you into thinking it is non-predictive.

    The SU(3) group of hadrons is strong isospin and that of quarks is color, Tommaso: one suggested the other! The quark theorys checked by the Omega minus baryon, which was predicted and has 3 identical strange quarks, which would be forbidden under Pauli's exclusion principle if an SU(3) color charge didn't exist. The Omega minus proved that three color charges exist. The basis idea behind its prediction was influenced by the SU(3) hadronic pattern! I thought you knew from college, Tommaso. It's a shame you have to argue over kids stuff and won't discuss frontiers. Cheers.

    For clarity, since some effort seems now to be made to take things out of context: The SU(2) isospin theory, mediated by pions with charges 0, +1, and -1, is not what I'm referring to above. The SU(3) symmetry patterns for quarks and for baryons can be compared in Figures 12.3 and 12.4 of and many texts. I won't continue reading/commenting this blog, or it will just lead to further time-wasting for you and annoyance for everybody. It's sad that there's no possibility of discussing physics anymore anywhere. Cheers, Nigel.