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    The Quote of the Week: Richter on Blind Analyses
    By Tommaso Dorigo | November 29th 2012 08:14 AM | 8 comments | Print | E-mail | Track Comments
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    "While looking for the decay pi+ ->  e+ nu_e, we focused all our attention on reducing backgrounds, since a prior experiment had set a limit at the level of 10^-6 on the branching ratio. When we heard that an experiment at CERN had seen a signal around 10^-4 I switched from delayed to prompt. The signal was right there, and could have been seen on the first day."

    Burton Richter, quoted in  J. Klein, A.Roodman, "Blind Analysis in Nuclear and Particle Physics"

    A reader correctly mentions that it is not exactly trivial to understand the above quote without some explanation, so here it is.

    Pions ordinarily decay to muons (within some nanoseconds), and only in a very rare fraction do they go directly into electrons. Muons themselves decay to electrons, but do so after 2.2 microseconds (on average).

    A digression: why pions don't decay to electrons as frequently as to muons ?

    Incidentally, while the lifetimes of pions and muons can only be understood by studying quantitatively the weak interaction, the strongly difference in relative frequency of pi->mu and pi->e is easy to figure out. Pions are spin-zero particles, and they produce two-body decays when they turn into a fermion-antifermion pair (muon/muon antineutrino, or electron/electron antineutrino). Fermions have spin 1/2. The spin of neutrinos, which are massless (to an excellent approximation), can only be aligned opposite to their direction of motion: they are left-handed, and antineutrinos are right-handed (their spin being always pointing in their direction of motion).

    Now, for simplicity imagine that you are sitting in the center-of-mass frame of the decaying pion. You see a spin-zero particle decaying into two spin-1/2 particles, leaving the scene in opposite direction at high momentum. Given that the antinetrino wants to have its spin pointing in the direction of their motion, the charged fermion emitted in the opposite direction is bound to do the same, such that the two spin vectors cancel: conservation of angular momentum forces them to. But while the antineutrino is a anti-fermion, and thus wants to be right-handed (spin perfectly aligned with direction of motion, as we specified above), the charged fermion -be it a muon or an electron- is a fermion, and thus prefers to be left-handed. The charged fermion has mass, and this allows it to have its spin misaligned with its momentum vector; but the smaller the mass, the less probable is a non-aligned configuration.

    Muons weigh 200 times as much as electrons do. This makes them much more willing to be "right-handed", when they travel at speeds smaller than the speed of light (in the ultra-relativistic limit they would also be exactly left-handed as the neutrinos) than electrons.
    So this is the basic difference: the pion decay to fermion-antifermion pair forces the charged fermion to have the "wrong" alignment of spin and momentum. This is much easier to do for the muon because of its large mass. Therefore the decay of pions to electrons is highly suppressed, despite the fact that there would be a larger phase space for that decay if compared to the muon decay. Oh, I have not explained what phase space is: stuff for another post, but in a nutshell the larger the energy release not going into mass of the decay products, the faster is a decay.

    Back to Richter's experiment

    Now, if you search for pion decays to electrons without the intermediate muon, you want to look for immediate decays (when the pion enters your apparatus). But muons will always be present as a background, so you need to estimate that.

    Richter studied muons by placing a delay between the timing of pion detection and the timing of electron detection. He could thus study the pi->mu->e reaction, to determine the background he would have when at some point he would look at the immediate pi->e reactions. By doing this he was doing things "blindly", to avoid involuntary biasing himself. When he heard that a signal of the direct decay pi->e had been seen elsewhere he realized this was not such a rare thing, and so by removing the delay in his detection electronics he saw that there was a ready signal of pi->e events which he could have seen on day one.

    Comments

    The article is not free, so I looked at another paper by Roodman
    (which does not contain the Richter quote, but does discuss blinding)
    at arxiv physics/0312102 and it says:
    "... dificult example is ... bump-hunting ...
    since the signal region is not known a-priori,
    there is no one place to put a hidden signal box ...".

    How does blinding work in Higgs digamma bump-hunting
    in which the bump-signal is very small compared
    to the large background smooth curve ?

    If the background curve is determined by something like
    polynomial smoothing of the data
    then
    would introduction of spurious blinding data cause
    the analysis process to see a distorted background curve
    and therefore a distortion in the location of a bump ?

    In that event, would the process of unblinding
    (removal of the spurious blinding data)
    be very difficult because it might not be a simple shift
    of the bump location
    but might also involve
    a subtle distortion of the smooth background curve?

    Tony

    What does "I switched from delayed to prompt" mean?

    dorigo
    Right - I should have explained this in the post. Pions decay to muons most of the time, and only in a very rare fraction directly to electrons. Muons themselves decay to electrons, but do so after 2.2 microseconds (on average). So if you search for pion decays to electrons without the intermediate muon, you want to look for immediate decays (when the pion enters your apparatus). But muons will always be present as a background, so you need to estimate that.
    Richter studied muons by placing a delay between the timing of pion detection and the timing of electron detection. He could thus study the pi->mu->e reaction, to determine the background he would have when at some point he would look at the immediate pi->e reactions. By doing this he was doing things "blindly", to avoid involuntary biasing himself. When he heard that a signal of the direct decay pi->e had been seen elsewhere he realized this was not such a rare thing, and so by removing the delay in his detection electronics he saw that there was a ready signal of pi->e events which he could have seen on day one.

    Cheers,
    T.
    Thanks for the explanation.

    Bornerdogge
    If I get it right, the rate of decay of pi+ -> e+ v has been found to be 2 orders of magnitude higher than expected?

    What are the implications of that?
    dorigo
    ... two orders of magnitude higher than expected... fifty years ago!
    Of course the implications back then were more precise determination of weak interaction parameters.
    Cheers,
    T.
    Any idea what went wrong with the previous experiment?

    dorigo
    Excellent question. No, sorry - I might ask around though. But my guess is that it was simply a very imprecise determination.

    Best,
    T.