Abstract

The purpose of this research is to measure the muon anomalous magnetic dipole moment (which will be referred to *aμ*=(*g*−2)/2 from now on) with improvement of a factor of about four, resulting in 0.14 ppm, so that we could reveal new physics beyond the Standard Model. In order to do this, we have participated in the experiment E989 at Fermi National Laboratory, which will start in late 2014. In the previous experiment E821 at Brookhaven National Laboratory, the *aμ* value has been determined with a precision of 0.54 ppm. The result shows a deviation of about 3.2*σ* from the Standard Model prediction. It has drawn much attention since it might suggest a hint of new physics beyond the Standard Model. In this experiment, it is planned to improve the precision by a factor of four. If the central value remains the same, it would give an uncertainty of 7.5*σ*, providing a definite indication of new physics beyond the Standard Model in elementary particle physics.

Academic Background of this Research

The muon anomalous magnetic dipole moment, *aμ*=(*g*−2)/2、is the fundamental parameter arising from quantum corrections and is known to be measurable with high precision. Here, *g* is the g factor of the magnetic dipole moment and *aμ* can be referred to (*g*−2). The previous experiment E821 at Brookhaven National Laboratory (BNL) in 2001 has determined *aμ*=0.54ppm [1], as follows.

This value shows a 3.2*σ* deviation from the Standard Model prediction. It has attracted much interest, since it could be potentially a hint of new physics beyond the Standard Model at the TeV energy region. However, the 3*σ*deviation is not enough for claiming the evidence of new phenomena. To establish this deviation, a new experiment with better precision is being demanded. Responding this demand, a new experiment at Fermi National Laboratory (FNAL) in the United State (US), which plans collection of 21 times larger data with improvement of systematic uncertainty, is being planned. It aims at improvement of the experimental uncertainty by a factor of four (namely, ) [2].

Figure 1 shows the experimental uncertainties obtained in the past experiments and the expected uncertainty of this research. If the central value remains the same, it would indicate about **7.5***σ* deviation and would suggest a strong indication of new physics beyond the Standard Model. In summary, the present experiment FNAL-E989 has shown its importance to verify the experimental result of the muon anomalous magnetic dipole moment.

The anomalous magnetic dipole moment in the Standard Model, without any quantum corrections, ￼, is known to be exactly zero. However, with quantum correction (as mentioned before), it could be given as follows.

The main contributions of the quantum corrections are those from QED, namely . Its leading term is given by *α*/(2*π*), which is called the Schiwinger term. The terms of and are well understood and can be evaluated with high precision. However, since the contribution from hadronic contribution, , cannot be directly calculated, the reaction cross sections of *e*+*e*− → *hadrons* and the dispersion relation are used for its estimation. At present, since the data of elecron-position colliders have been collected, the uncertainty of the hadronic contribution becomes smaller. Furthermore, the light by light terms in the hadronic contribution, which cannot be evaluated from the experimental data, is being studied extensively by lattice calculations. In near future, the uncertainty of the Standard Model prediction, , (in particular ) is expected to be improved down to ±34×10-11 from the value in Eq.(3). Therefore, combined this possible future value of the Standard Model prediction with the expected experimental uncertainty of this research of ±16×10-11, which will have an improvement of a factor of about four (from Eq.(1)), the net uncertainty could be ±34×10-11. It will be a significant improvement over the present limit of ±81×10-11.

The deviation of *aμ* between the Standard Model prediction and the measured value could be explained by new physics beyond the Standard Model. There are several theoretical models of such, and they are for instance, supersymmetric models, extra-dimension models, and Little Higgs models. In particular, in the supersymmetric (SUSY) models, its contribution to the anomalous magnetic moment can be given by

where Λ is the SUSY energy scale. This prediction can explain sufficiently the deviation. Furthermore, as seen in Figure 2, the measurement of the anomalous magnetic moment is known to be more effective than the LHC to determine tan*β* in SUSY models. At this moment (2013), there are no indication of SUSY found at the LHC. But, in general it could be said that the deviation of *aμ* can be explained by a large value of tan*β* in SUSY models.

Figure１：

The measurement errors of the muon anomalous magnetic moment and the expected measurement error of FNAL E989 experiment.

Figure 2:

determination of tan*β* in supersymmetric models from *aμ*

What is being studied in this research period ?

We, from Osaka University, have participated in the BNL P969 collaboration since 2006. Unfortunately, the BNL-P969 did not proceed and was not successful. However, the same collaboration submitted their experimental proposal to FNAL spring in 2009 and it was approved fall in 2009 [2]. Furthermore, in 2010, the budget request on E989 was submitted to Department of Energy (DOE) in the US. It was evaluated high, and a fraction of the budget has been approved. According to the presently planned schedule, the E989 experiment will start late in 2014. In our research plan, we will develop R&D on the electron calorimeter for the E989 experiment and will construct a part of the electron calorimeter. In late 2014 and 2015, data taking will be made. By the end of 2015, the data collected will be analyzed and the experimental result will be published.

Significance of this Research and Expected Results and Importance

The Standard Model of elementary particle physics has many ad-hoc parameters, which cannot be determined by its own, and is considered to be incomplete. In order to obtain a more complete framework with new physics beyond the Standard Model, searches for new physics phenomena that cannot be explained by the Standard Model have been made. However, many experiments so far, including the LHC experiment, have failed to find any new hints beyond the Standard Model. At this moment, the muon anomalous magnetic dipole moment, *aμ*, is the only one measurement which presents a possible deviation from the Standard Model prediction. If the confidence of the deviation of *aμ* will be improved significantly from this research, it would provide a definite indication of new physics beyond the Standard Model, forming a new paradigm of elementary particle physics.

Reference

[1] G.W. Bennett et al (Muon (g-2) Collaboration), Physical Review D **73**, 072003 (2006).

[2] New (g-2) Collaboration, “The New (g-2) Experiment: A Proposal to Measure the Muon Anomalous Magnetic Moment to *±*0.14ppm Precision”, submitted to the DOE office of High Energy Physics, April 5, 2010

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New Initiative of Precision Measurement of the Muon Anomolous Magnetic Dipole Moment