Do Measurements Of The B_d Decay To Muon Pairs Indicate Four Generations Of Matter ?
    By Tommaso Dorigo | July 21st 2013 09:18 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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    I reported two days ago on the new measurements by the CMS Collaboration of the decay of B hadrons into muon pairs, revealed at the opening of the EPS 2013 conference in Stockholm and in a preprint. Funnily, I wrote the piece oblivious of the LHCb result, which is basically equivalent (in importance, precision, and sensitivity) to the CMS one; when I found out that LHCb had also a comparable result, I made up for that by pointing out the LHCb result in a "UPDATE" at the end of the post - I did not want to rewrite half of the piece!

    Today, however, I would like to do here for you what most phenomenologists are doing on their blackboards these days: take the two measurements of the B_d decay to μμ pairs by CMS and LHCb, and combine them in a quick-and-dirty way, and then use that result to speculate on what the combination can be taken to mean - or not.

    The motivation for the exercise is provided by figures such as the one below, which have been a common exercise among theoretician friends as of late: compare the limits - and now the measurements - on these branching fractions to the values that would be predicted by alternative models for new physics. The figure is taken by a paper by David Straub (arxiv:1205.6094).

    In the figure the branching ratio of the Bs and Bd to dimuons (in 10^-9 units) predicted by the SM (yellow star) is compared to possible values that the two quantities take in varions versions of new physics models. Notably, MSSM predictions extend all over the place, while the "SM4" version - a model with four generations of matter fields - provides either an enhancement (or a deficit) of the Bs decay rate, or an enhancement (or deficit) of the Bd decay rate, but not of both. The box at the lower corner indicates the allowed region of parameter space following limits on the branching fractions determined last year.

    I have already explained in some detail in the former post why the rare decay of a neutral B hadron to a muon pair is sensitive to the existence of new physics beyond the standard model. In a nutshell, it is because new very heavy particles (ones we might not have had a chance to discover yet) would contribute significantly to the probability of such decays. Their being very heavy does not keep them from contributing, in fact, because they take part in the decay within virtual quantum loops. A basic course of quantum field theory would allow you to understand in fact that when you need to compute the probability of a reaction A->B you need to sum the amplitudes of all possible processes that bring the state A into the state B. So if one may conceive a new particle circulating in a quantum loop intermediate between state A and state B, that will contribute to the total probability, in some way.

    So, since there are only few requirements on the kind of particles that can contribute to the B hadron decays to muon pairs, the range of new physics models that can be tested is wide. The graph shows that a bunch of them does predict enhanced (but even reduced, due to interference effects, in some cases) branching fractions.

    Let us then give a look at the most recent measurements of LHCb and CMS. CMS reports

    B(Bs->μμ) = (3.0+1.0-0.9) x10^-9
    B(Bd->μμ) = (3.5+2.1-1.8) x10^-10

    and LHCb reports

    B(Bs->μμ) = (2.9+1.1+0.3-1.0-0.1) x10^-9
    B(Bd->μμ) = (3.7+2.4+0.6-2.1-0.4) x10^-10.

    (the second uncertainty quoted for LHCb is systematical).

    The above measurements are not on equal footing: while the Bs ones are based on well-observed signals, with significances of 4.3σ and 4.0σ respectively, the Bd ones are both based on 2.0σ signals only. Nevertheless, if one believes that the Bd decay is there, with a non-zero rate, then one can tentatively use the measurements anyway - while keeping the caveat in mind.

    The two experimental results are based on different data and different detectors, but share some common systematic uncertainties - most notably, ones on some structure functions for the decay, which enter the equations because both CMS and LHCb measure the branching fractions by comparing the observed decays to the number of decays to dimuons to others much more frequent, the ones of the B+ meson to J/ψ K+ pairs. Because of that, the exercise of combining the numbers is not trivial if done correctly. Further, the error bars are asymmetric, and so one should combine the likelihood functions from which the measurements are derived rather than the measurements themselves.

    Despite all the above, I believe that a quick-and-dirty weighted average will end up being only marginally different from the result of a more accurate determination. And since I am lazy, I will discuss here the result of the simple weighted average (which, I remind you, assumes that the inputs are totally uncorrelated and that they are Gaussian distributed: neither assumption holds). [Disclaimer: Please note that I am doing this exercise just as anybody could, without using any internal information from my experiment (CMS) or the other experiment. What I am doing here for you, anybody can do on the back of an envelope! Also, the facts that I am a member of the CMS collaboration and the fact that I am publishing these publically-available numbers here have exactly zero mutual dependence. I am speaking for myself here!]

    So if you average the two results you obtain

    B(Bs->μμ) = (2.95 +0.75 -0.67) x 10^-9
    B(Bd->μμ) = (3.6 +1.6 -1.38) x 10^-10

    Again, bear in mind that the errors above are slightly underestimated - they do not account for positive correlations - and are approximate also because they do not treat the asymmetric errors in a proper way. I believe that the central values, on the other hand, are not going to be much different if one does the exercise correctly, because LHCb and CMS ended up with extremely similar inputs !

    So let us compare the above "estimates" with the predictions of the Standard Model: for the Bs the SM predicts B=(3.56+-0.30) x 10^-9 and for the Bd the SM predicts B=(1.07+-0.10) x10^-10. We thus see that the Bs rate is in perfect agreement with the standard model, while our quick-and-dirty weighted average of LHCb and CMS results for the Bd branching fraction turns out to be 3.5 times larger than the prediction.

    Is that something worth speculating that we are seeing the first indications of new physics ? This question was somehow asked by a reader in the comments thread of the former post.

    My answer ? I doubt it, and for several reasons.

    First of all, this is just a less than 2-sigma departure (and we have anyway underestimated the uncertainty due to our sloppy averaging above: when neglecting positive correlations that is a fact).

    Second, the effect is based on results which are not yet of observation-level quality.

    Third, there is an implicit trials factor of four in the probability that we observe a departure, since we could have been just as surprised to see a deficit, or to see an excess or a deficit in the Bs result (compare to the "cross-like" region of SM4 allowed models in the graph above); a p-value corresponding to less than 2-sigma multiplied by four is a p-value of one-point-something sigma, i.e. one hardly worth discussing!

    And Fourth, most models of new physics do not predict an enhancement in the Bd decay to dimuons but a straight-on-the-SM rate of decay to dimuons of the Bs. But then, if we like the four-families extension of the Standard Model, things are different.

    As was noted by Masaya Kohda at the EPS 2013 conference last Friday, if we assume that there are four generations of quarks, we need to also assume that the new-found Higgs boson at 125.5 GeV is an impostor - a true Higgs boson would enhance its production rate by a factor of nine (!) in the presence of more than three ordinary generations of quarks, because each new generation provides a contribution in another quantum loop, the one existing between two colliding gluons and the Higgs which provides for the largest part of the production probability of the Higgs at the LHC.

    So provided we are ready to make all those steep assumptions - that the particle at 125.5 GeV is not a Higgs and that there are new quarks out there to be found, then a x3.5 rate of Bd decays to dimuons does fit well with a four-generation quarks model.

    So... Are you a believer or not ?


    Dear Tommaso,

    I am somewhat surprised by the precision of CMS in their measurements and so, this is the chance to present my compliments. You have other "less than 2 sigma" measurements that can hide new physics (or not) depending you are a believer (or not). These seem like clashing numbers out of the chorus that is there saying "it is only Standard Model". I am not claiming there is SUSY somewhere but that these clashing numbers may unveil a better Standard Model than people was able to get in the sixties. Your colleagues at EPS-HEP are claiming that some of these numbers will improve during LS1. And we all know that, often, small cracks in physics can reveal themselves glaring and unexpected results. I am not a believer but we all know that our friendly neighborhood is always plenty of surprises to the eyes of the smart men.



    How is it possible, that the decay, which is presented as the very exact confirmation of Standard Model can serve as an evidence of its violation (as far I know, the SM doesn't predict the fourth generation)

    It seems, the contemporary particle physics appears rather flexible in its deductions...

    Rather than evidence, one might say that there is still a door that is left somewhat ajar.

    Welcome to the messiness of the macroscopic real.

    Be careful Zephir. Here we are not talking about the Bs, but about the Bd being off the SM expectation. The Bs is perfectly in line with expectations, the Bd is not. I believe you might have read the article a bit too quickly...

    I see... My apology for talking about BS...

    Daniel de França MTd2
    If there are infinite generations, what happens to the Higgs?
    Hi Daniel,

    the Higgs becomes practically invisible if there is an infinite number of generations, because it only decays to a pair of gluons...

    The first question is whether you want to give masses to all these infinite generations purely via the Higgs. If you would try to do that the resulting field theory would be infinitely unstable, not well-defined at all.

    There is however the extra-dimensions scenario where you have in principle an infinite tower of heavier and heavier resonances of the SM particle, and they are all coupled to the Higgs, but only receive an increasingly small portion of their mass from the Higgs. In this case the effect is more well-defined, but also there the Higgs field becomes unstable or breaks down at some energy scale. Since the theory breaks down at some scale, it is not really really true that ther is an infinite number of "generations" as this is only strictly true before you look at quantum corrections.

    John Duffield
    Do Measurements Of The B_d Decay To Muon Pairs Indicate Four Generations Of Matter?


    So... Are you a believer or not?


    The B_d result at best indicates that the Standard Model is incomplete. But we already knew that. It doesn't model gamma-gamma pair production or the electron, it doesn't cover the neutrino, and it doesn't give you any real understanding of what a B_s or B_d meson actually is. (Or a muon for that matter. Or a quark. Or a gluon. By the way gluons are virtual). Until then, you're winging it, and clutching at straws. SUSY is a classic example of that. How can anybody seriously propose a selectron when the electron is a black-box "fundamental particle". Which the PDG thinks is pointlike. Even though it's quantum field theory rather than quantum point-particle theory.

    Way to go, Tommaso.
    Hrm! Stop talking like the Oracle of Delphi and say what you want to say!

    > By the way gluons are virtual

    Says who?

    All QCD-based models describing the nucleon (lattice QCD, structure functions) do not distinguish between "real" and "virtual" particles. These two terms are only valid in a perturbative picture, but the description of bound states in QCD is essentially non-perturbative. In the analysis of deep inelastic scattering, for example, perturbative calculations are only used to probe the nucleon structure, which itself is intrinsically non-perturbative.

    Predicted without four generations:

    Isn't there also a look-else effect to take into account when looking for rare processes on the edge of observability?

    There are a number of such observations to be made, and the ones that fluctuate upwards by chance will show the most s.d.s of significance.

    Hi Ralph,

    in general your statement is true. However, here we are looking for a very specific process, and a particle whose mass is perfectly well known, and which has angular distributions predicted carefully by the theory. So much so that the fit to signal contamination is done in 12 different bins of angular variables and multivariate kinematic discriminant, and the fit uses the knowledge of the predicted ratio of signal expected in the 12 regions in order to fit the contribution.
    In other words, the fit is sensitive ONLY to the sought signal. So no look-elsewhere effect is present here.

    The relation between the four colour theorem and the SM is very precise and excludes a fourth generation. The SM Higgs at 125 GeV is absolutely true!