Thursday 8 April 2021

Why is it when something happens it is ALWAYS you, muons?

April 7, 2021 was like a good TV episode: high-speed action, plot twists, and a cliffhanger ending. We now know that the strength of the little magnet inside the muon is described by the g-factor: 

g = 2.00233184122(82).

Any measurement of basic properties of matter is priceless, especially when it come with this incredible precision.  But for a particle physicist the main source of excitement is that this result could herald the breakdown of the Standard Model. The point is that the g-factor or the magnetic moment of an elementary particle can be calculated theoretically to a very good accuracy. Last year, the white paper of the Muon g−2 Theory Initiative came up with the consensus value for the Standard Model prediction 

                                                                      g = 2.00233183620(86), 

which is significantly smaller than the experimental value.  The discrepancy is estimated at 4.2 sigma, assuming the theoretical error is Gaussian and combining the errors in quadrature. 

As usual, when we see an experiment and the Standard Model disagree, these 3 things come to mind first

  1.  Statistical fluctuation. 
  2.  Flawed theory prediction. 
  3.  Experimental screw-up.   

The odds for 1. are extremely low in this case.  3. is not impossible but unlikely as of April 7. Basically the same experiment was repeated twice, first in Brookhaven 20 years ago, and now in Fermilab, yielding very consistent results. One day it would be nice to get an independent confirmation using alternative experimental techniques, but we are not losing any sleep over it. It is fair to say, however,  that 2. is not yet written off by most of the community. The process leading to the Standard Model prediction is of enormous complexity. It combines technically challenging perturbative calculations (5-loop QED!), data-driven methods, and non-perturbative inputs from dispersion relations, phenomenological models, and lattice QCD. One especially difficult contribution to evaluate is due to loops of light hadrons (pions etc.) affecting photon propagation.  In the white paper,  this hadronic vacuum polarization is related by theoretical tricks to low-energy electron scattering and determined from experimental data. However, the currently most precise lattice evaluation of the same quantity gives a larger value that would take the Standard Model prediction closer to the experiment. The lattice paper first appeared a year ago but only now was published in Nature in a well-timed move that can be compared to an ex crashing a wedding party. The theory and experiment are now locked in a three-way duel, and we are waiting for the shootout to see which theoretical prediction survives. Until this controversy is resolved, there will be a cloud of doubt hanging over every interpretation of the muon g-2 anomaly.   

  But let us assume for a moment that the white paper value is correct. This would be huge, as it would mean that the Standard Model does not fully capture how muons interact with light. The correct interaction Lagrangian would have to be (pardon my Greek)

The first term is the renormalizable minimal coupling present in the Standard Model, which gives the Coulomb force and all the usual electromagnetic phenomena. The second term is called the magnetic dipole. It leads to a small shift of the muon g-factor, so as to explain the Brookhaven and Fermilab measurements.  This is a non-renormalizable interaction, and so it must be an effective description of virtual effects of some new particle from beyond the Standard Model. Theorists have invented countless models for this particle in order to address the old Brookhaven measurement, and the Fermilab update changes little in this enterprise. I will write about it another time.  For now, let us just crunch some numbers to highlight one general feature. Even though the scale suppressing the effective dipole operator is in the EeV range, there are indications that the culprit particle is much lighter than that. First, electroweak gauge invariance forces it to be less than ~100 TeV in a rather model-independent way.  Next, in many models contributions to muon g-2 come with the chiral suppression proportional to the muon mass. Moreover, they typically appear at one loop, so the operator will pick up a loop suppression factor unless the new particle is strongly coupled.  The same dipole operator as above can be more suggestively recast as  

The scale 300 GeV appearing in the denominator indicates that the new particle should be around the corner!  Indeed, the discrepancy between the theory and experiment is larger than the contribution of the W and Z bosons to the muon g-2, so it seems logical to put the new particle near the electroweak scale. That's why the stakes of the April 7 Fermilab announcement are so enormous. If the gap between the Standard Model and experiment is real, the new particles and forces responsible for it should be within reach of the present or near-future colliders. This would open a new experimental era that is almost too beautiful to imagine. And for theorists, it would bring new pressing questions about who ordered it. 

Thursday 1 April 2021

April Fools'21: Trouble with g-2

On April 7, the g-2 experiment at Fermilab was supposed to reveal their new measurement of the magnetic moment of the muon.  *Was*, because the announcement may be delayed for the most bizarre reason. You may have heard that the data are blinded to avoid biasing the outcome. This is now standard practice, but the g-2 collaboration went further: they are unable to unblind the data by themselves, to make sure that there is no leaks or temptations. Instead, the unblinding procedure requires an input from an external person, who is one of the Fermilab theorists. How does this work? The experiment measures the frequency of precession of antimuons circulating in a ring. From that and the known magnetic field the sought fundamental quantity - the magnetic moment of the muon, or g-2 in short - can be read off.  However, the whole analysis chain is performed using a randomly chosen number instead of the true clock frequency. Only at the very end, once all statistical and systematic errors are determined,  the true frequency is inserted and the final result is uncovered. For that last step they need to type the secret code into this machine looking like something from a 60s movie: 

The code was picked by the Fermilab theorist, and he is the only person to know it.  There is the rub... this theorist now refuses to give away the code.  It is not clear why. One time he said he had forgotten the envelope with the code on a train, another time he said the dog had eaten it. For the last few days he has locked himself in his home and completely stopped taking any calls. 

The situation is critical. PhD students from the collaboration are working round the clock to crack the code. They are basically trying out all possible combinations, but the process is painstakingly slow and may take months, delaying the long-expected announcement.  The collaboration even got a permission from the Fermilab director to search the office of the said theorist.  But they only found this piece of paper behind the bookshelf: 

It may be that the paper holds a clue about the code. If you have any idea what the code may be please email or just write it in the comments below. 

Update: a part of this post (but strangely enough not all) is an April Fools joke. The new g-2 results are going to be presented on April 7, 2021, as planned.  The code is OPE, which stands for "operator product expansion", which is an  important technique used in the theoretical calculation of hadronic corrections to muon g-2: