Muon co­nun­drum

An ex­per­i­ment be­ing car­ried out at Fer­mi­lab to mea­sure the mag­netic prop­erty of the muon has the po­ten­tial to show the way to new physics.

FrontLine - - SCIENCE - BY

A HIGH-PRE­CI­SION, and very im­por­tant, ex­per­i­ment (chris­tened E989) to mea­sure the mag­netic prop­erty of the fun­da­men­tal par­ti­cle called muon got un­der way in Fe­bru­ary at Fer­mi­lab, the high-en­ergy par­ti­cle ac­cel­er­a­tor lab­o­ra­tory in Illi­nois, United States (Fig­ure 1). The im­por­tance of this ex­per­i­ment arises from the fact that the present mea­sured value of the muon’s mag­netic strength, or its “mag­netic mo­ment”, which de­ter­mines its be­hav­iour in a mag­netic field, is sig­nif­i­cantly higher than the the­o­ret­i­cal pre­dic­tions of the Stan­dard Model (SM) of par­ti­cle physics, the highly suc­cess­ful the­o­ret­i­cal frame­work with which sci­en­tists by and large un­der­stand the uni­verse to­day.

The cur­rently best mea­sured and ac­cepted value is due to an ex­per­i­ment (E821) car­ried out at the turn of the cen­tury at the Brookhaven Na­tional Lab­o­ra­tory (BNL) in New York, U.S., to the pre­ci­sion level pos­si­ble then. This al­ready was an im­prove­ment by a fac­tor of 14 over the 1970s’ mea­sure­ment of the quan­tity at CERN (the Euro­pean Coun­cil for Nu­clear Re­search). The ex­per­i­ment achieved 540 ppb (parts per bil­lion) ac­cu­racy in its mea­sure­ment, while the ac­cu­racy achieved in the SM the­o­ret­i­cal cal­cu­la­tions was about 420 ppb. The BNL ex­per­i­ments were per­formed be­tween 1997 and 2001, and the fi­nal cor­rected re­sults were pub­lished dur­ing 2004-06, ac­cord­ing to which the ex­per­i­men­tal value was higher at about 2.5 ppm (parts per mil­lion) level than the the­o­ret­i­cal pre­dic­tion in the SM. In sta­tis­ti­cal


ter­mi­nol­ogy, this is equiv­a­lent to a “3.5 sigma” dis­crep­ancy, which, in lay lan­guage, im­plies that there was less than a one in 750 chance that the dif­fer­ence was due to a sta­tis­ti­cal fluc­tu­a­tion or a fluke.

The physicists per­ceive this vari­ance be­tween the­ory and ex­per­i­ment to be a pointer to new physics—in­volv­ing par­ti­cles as yet not seen— that lies be­yond the SM (Front­line, May 25, 2001). It must be em­pha­sised, how­ever, that, in terms of sta­tis­ti­cal sig­nif­i­cance, the dis­crep­ancy is not yet enough for physicists to re­gard it as “proof” of ex­is­tence of new physics but only as strong ev­i­dence. It will be proof only when the dis­crep­ancy is at a “5 sigma” level— equiv­a­lent to a one in 3.5 mil­lion chance of it be­ing a ran­dom fluc­tu­a­tion—or more be­cause in par­ti­cle physics it has of­ten been seen that many dis­crep­an­cies be­tween the­ory and ex­per­i­ments at around 3 sigma have just dis­ap­peared with im­proved sta­tis­tics and more ac­cu­rate mea­sure­ments.

So, un­til Fer­mi­lab pro­duces con­clu­sive proof, muon mag­netic mo­ment data will re­main con­sis­tent with the SM al­though the de­par­ture is sig­nif­i­cantly large (Fig­ure 2). The BNL ex­per­i­ment was essen­tially sta­tis­tics lim­ited. Us­ing 21 times more data, and four times more pre­cise mea­sure­ments than the BNL ex­per­i­ment (140 ppb ac­cu­racy com­pared with 540 ppb), the new ex­per­i­ment is ex­pected to ei­ther con-

FIG­URE 1. The g-2 stor­age-ring mag­net at Fer­mi­lab for ex­per­i­ment E989. Orig­i­nally de­signed for the Brookhaven g-2 ex­per­i­ment (E821), it was moved to Fer­mi­lab. The ge­om­e­try al­lows for a very uni­form mag­netic field to be es­tab­lished in the ring.

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