A new experiment points to the world beyond the Standard Model of Elementary Particles.

FOR nearly three decades now, the fundamental particles of nature, and the forces of interaction among them except gravity, have been successfully described to a great degree of accuracy by what has come to be called the Standard Model of Elementary Particles. This theory is now being challenged. A recent high precision accelerator experiment at the Brookhaven National Laboratory (BNL), United States, has found that the behaviour of one of the elementary particles, known as the muon, in a magnetic field, as measured in this experiment, deviates significantly from the predictions of the Standard Model (SM).

"We are 99 per cent sure that the present SM calculations cannot describe our data," says Gerry Bunce, project manager of the experiment which involved 68 scientists from 11 institutions worldwide. "This work could open up a new world of exploration for physicists looking at new theories, such as Supersymmetry, which extend the Standard Model," says Lee Roberts of Boston University, one of the collaborating institutions. Until January, the scientists did not know whether the results of their five year long "muon g-2 (pronounced gee-minus-two)" experiment (1997-2001) was going to confirm or violate the SM predictions. This exciting result was announced on February 8.

According to the Standard Model, the world is made up of two kinds of fundamental particles: leptons and quarks. In each category there are six particles organised in three families of two particles each. The three forces of interaction among them whose effects are observable at currently attainable energy scales (up to hundreds of giga electron-volts, or GeV) are the familiar electromagnetism, the weak nuclear force (which causes radioactivity) and the strong nuclear force (which holds the nucleus together). The familiar electron belongs to the category of leptons. The electron and its companion, the electron neutrino, make up the 'electron family'. The other leptons are the muon (which is identical to the electron in every respect but is 200 times heavier) and its partner, the muon neutrino, and the tau (which is 3,500 times heavier than the electron) and its partner, the tau neutrino. The quark sector has six quarks which are the fundamental constituents of particles, like the neutron and the proton that make up the atomic nucleus.

The three forces are described in the SM through certain mediating particles. The different forces arise when specific carrier particles are exchanged between interacting particles. The electromagnetic force arises due to the exchange of the massless photon, the weak nuclear force due to the exchange of a triplet of massive particles called W+, W- and Z and the strong nuclear force is caused by an octet of massless particles called gluons.

All elementary particles have an intrinsic quantum mechanical property called 'spin'. This attribute has no analogue in the classical description of macrospcopic objects but each particle can be imagined to be spinning about its axis like a top. This intrinsic 'spin' can take only discrete values which are multiples of half (in some units). Thus the 'spin' value can be 0, =, 1, and so on. The value of 'spin' for leptons and quarks is 1/2 and they are called fermions. The force carriers, on the other hand, have an intrinsic spin of one and they are called bosons.

Within the framework of the Standard Model, the description of how the leptons and quarks interact through these forces is based on a principle that there exists an underlying (mathematical) symmetry, called gauge symmetry. It is this 'gauge symmetry' that enables a description of three disparate forces in a single unified mathematical structure. It is generally regarded that the SM is only a theory in progress and that there is new physics lurking round the corner waiting to show up as we move up on the energy scale. Supersymmetry is one such new physical concept that physicists have sought to introduce into the description of nature. Supersymmetry postulates that there exists a (mathematical) symmetry between the spin-1/2 particles (the fermions) and integer spin particles (the bosons) in the theory.

There is a price to be paid for the supersymmetry postulate. It predicts the existence of as yet unseen particles. A "minimal supersymmetric extension of the SM" requires the existence of superheavy partners to each one of the particles in the SM. That is, the fermions of the theory, the leptons and the quarks, have superheavy partners called 'sleptons' and 'squarks' but with zero spin which together form 'superfamilies'. Similarly, the force carriers or the gauge bosons have superheavy spin-1/2 partners called 'gauginos'. The question is: will hitherto unseen effects of arbitrary energies, such as supersymmetry if it existed, show up indirectly in precision experiments at lower energies? The result of the BNL experiment seems to suggest that indirect evidence of 'unknown physics' has indeed been observed.

The BNL experiment was designed to make a high precision (1.3 parts per million) measurement of the "anomalous" component in muon's magnetic moment. The magnetic moment of a particle is a measure of the strength with which it couples to a magnetic field and every charged particle with spin behaves like a dipole magnet with a magnetic moment. Now purely relativistic quantum effects make certain anomalous contributions to the value of the magnetic moment of spin-1/2 particles like the electron and the muon to alter it from the simplistic prediction of the theory. A convenient way to describe or measure this anomaly quantitatively is by studying the value of the parameter called the 'gyromagnetic ratio' or the 'g-factor'.

The gyromagnetic ratio is simply the ratio of the magnetic moment to the intrinsic spin angular momentum of the particle. The theory at its simplest level (the Dirac equation) tells us that g = 2 or g-2 = 0. This is the case when the particle is strictly point-like or the mass and the charge distribution of the particle are identical. These idealised situations are not obtained in the real world description of particles. The departure of the 'g-factor' from 2 gives us the extent of the anomalous contribution. For the proton, g-2 = 3.6 and the large value of the anomaly is due to the mass distribution of its constituent particles: the quarks and other neutral particles. For the electron and the muon, which are thought to be almost point-like, g-2 is about 0.002. The reason for the non-zero value of g-2 is the interaction of the particle with 'virtual fields' and these contributions are called 'radiative corrections'.

These 'virtual fields' arise because of Heisenberg's uncertainty principle. The principle implies that, for example, a charged particle like the electron or the muon constantly emits and reabsorbs photons, producing a fluctuating 'virtual' electromagnetic field associated with the particle. When the particle travels through an external magnetic field, the external field sees the bare electrical field of the particle as well as the fluctuating field. Essentially, g-2 is a measure of the average of the effects of interactions of the particle with the virtual field. In fact, even more complex virtual processes - such as emission and absorption of heavier particles like W and Z, creation of fleeting virtual quark-antiquark or electron-positron pairs by the emitted virtual photons - can take place, all of which contribute to the value of g-2. That is, the g-2 value measures the effects of the strong, weak and electromagnetic forces on the magnetic moment of a particle. Their combined effect is calculated in the SM to a precision level of 0.6 ppm.

The g-2 values for the electron and the muon are, in fact, the most precisely calculated quantities in the SM. A remarkable fact is that the muon g-2 can not only be predicted to a high degree of precision, but it can be measured to equally high precision. So, the greater the precision with which g-2 is measured, the better is the understanding of what quantum mechanical effects contribute to the magnetic moment and how well the SM fares. That is, a precise determination of g-2 becomes a powerful test of the SM. If there is physics beyond the SM, and such new physics is of a kind that will contribute to the muon g-factor, then the difference should show up as experimental precision increases with improved techniques. Till now the measurements have been in good agreement with the SM.

Most models that go beyond SM, like supersymmetry, predict the existence of heavier particles than those that the SM describes. The muon, because of its greater mass, is more sensitive than the electron to the effects of virtual fields of such heavier particles. This increased sensitivity is proportional to the square of the mass. Muon being 200 times heavier than the electron, its precision g-2 value is 40,000 times more sensitive to contributions from emission and absorption of heavier virtual particles. This is why measurement of g-2 of the muon has always been regarded as an important experiment.

Measurements of g-2 have been going on since the 1960s. The last high precision measurement carried out in the 1970s at CERN, the European Centre for Particle Physics, the electron and the muon g-2 were the same at levels of precision achievable then. The present experiment is more precise to a factor of 5.6 than the CERN experiment and finds that the value of g-2 is numerically greater than the SM predication, suggesting virtual field effects beyond the SM.

In the present experiment at BNL, scientists used an intense "polarised" beam of positively charged muons from an accelerator called the Alernating Gradient Synchrotron (AGS). In a polarised beam the spins of all the particles in the beam are aligned in one direction. In the present case, the muon spins were all made to align along the direction of the momentum. The polarised muon beam of 3.09 GeV energy was directed into the world's largest, 14 metre diameter, circular superconducting magnet which has a uniform field applied in the direction perpendicular to the direction of motion. As the muons race around the ring (at speeds close to the speed of light), an electric field is used to confine the circulating muons. That is, the circulating polarised muons are "stored" in the doughnut shaped magnet ring. Such a set-up is called a "muon storage ring". Very sensitive detectors are then used to measure the muon magnetic moment anomaly.

The basic principle behind this experiment is that as the muon circulates around the ring, its spin, which was originally aligned along the direction of the muon motion, rotates or precesses (much like a spinning top) in the magnetic field that acts on it at right angles. The precession occurs because the magnetic field exerts a torque to make the spin align along the direction of the field, just as a bar magnet aligns itself in a magnetic field. If the muon were not spinning, this is what would happen. But the muon is spinning. So instead of aligning with the magnetic field, the axis of the muon spin precesses slowly in the horizontal plane. The rate of precession depends on the force of the magnetic field (its torque), the size of the magnetic moment and how fast the muon is spinning. An accurate measurement of the difference between these two quantities is directly proportional to g-2. This is the key idea of the experiment.

How does one measure the muon precession? Each muon is unstable and undergoes radioactive decay into a positron (a positively charged electron, the antiparticle to the electron) and two neutrinos. A 3.09 GeV muon exists an average of 64 microseconds. The emitted positron remembers the spin direction of the parent muon. A measurement of the positron energy carries information on the instantaneous direction of the muon spin at the time of decay. A detector system measures the time and energy of these positrons. The data of events versus time looks like any other (exponential) radioactive decay with a wiggle superimposed due to the precession of the spin direction. It is this spin precession frequency that is measured with great precision to yield g-2. About a billion muon decay events were analysed. The value measured turns out to be significantly different from SM predictions.

According to scientists, the probability that the result is still consistent with the SM, and that the deviation is only a statistical fluctuation, is low. Moreover, the experimenters have obtained an additional body of similar data, with four times as many events. The analysis of this data is currently on, which will reduce the error margins significantly. Another possible interpretation is that the SM is basically right but there are uncertainties arising from the errors in the experimental data that serve as inputs to the g-2 calculation. One such input is the estimate of quark-antiquark contributions to the radiative corrections to g-2. This estimate is made by making use of data on quark production gathered over the years in experiments carried out in certain accelerators called "electron-positron collid- ers". Although the error in this is much smaller than the deviation of the measured value of g-2 from the SM prediction, new electron-positron results from Russia, China and the U.S. should bring down the uncertainty further, says the BNL research team. The last interpretation, which seems to be the most plausible, is that the SM is either inadequate or wrong.

While the BNL team does say that "there is new physics out there and it affects the muon g-factor at a certain level", the measurement does not offer any clue to what this new physics is likely to be. In any case, the BNL finding augurs well for the next run of the new accelerator experiments at the Tevatron Collider at the Fermi National Accelerator Laboratory (FNAL) in the U.S., at the upcoming Large Hadron Collider (LHC) at CERN or at future electron-positron or a muon colliders. If high mass particles that are not part of the SM indeed exist, all these will be able to observe them directly.

Of course, many theorists believe that the BNL result represents evidence for supersymmetry. "The size and the sign of the difference between theory and data is in the right ball park for supersymmetry to be discovered or ruled out at the Tevatron, LHC, etc. The additional reduction in the experimental error when the analysis is complete should also help clarify the picture," says Rohini Godbole, a particle theorist at the Centre for Theoretical Studies (CTS), Indian Institute of Science, Bangalore. There are also models which invoke novel ideas like muon substructure and W-boson substructure to explain the departure. That is, the muon and the weak force carrier W-boson may themselves not be elementary and may have substructures which may be revealed at higher energies. In any case, the BNL experiment has proved to be a harbinger of new physics, whatever that may eventually be. What is certain is there is world beyond the Standard Model.

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