Torsion contraints from the recent precision measurement of the muon anomaly

In this paper we consider non-minimal couplings of the Standard Model fermions to the vector (trace) and axial vector (pseudo-trace) components of the torsion tensor. We then evaluate the contributions of these vector and axial vector components to the muon anomaly and use the recent precision measurement of the muon anomaly to derive constraints on the torsion parameters. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] The Standard Model (SM) has been extremely successful in explaining the results of all experiments both at low, medium and high energies. In spite of this phenomenal success a majority of high energy physicists agree that the SM is at best a renormalizable effective field theory valid in a restricted energy range since it does not include quantum gravity. Many theorists further believe that the ultimate and fundamental theory of Nature will be provided some day by string theory since the low-energy effective Lagrangian of closed strings reproduces quantum gravity. The low-energy effective action of closed strings predicts, along with the a massless graviton, a massless antisymmetric second rank tensor field Bαβ (Kalb-Ramond tensor) which enters the action[1] via its antisymmetrised derivative Hαβγ = ∂[αBβγ]. The third rank tensor Hαβγ is referred to as the torsion field strength. Since torsion is always predicted by string theory it is highly interesting to investigate what low-energy observables and phenomenological effects torsion can produce. Some effects of both heavy (nonpropagating) and dynamical (propagating) torsion fields have already been considered [2] and bounds on the free parameters of the torsion action (torsion mass and couplings) have been derived using experimental data. In this paper we shall study the effects of the trace and pseudo-trace components of the torsion tensor on the anomalous magnetic moment of the muon. Precision measurements of the muon anomaly aμ = (gμ − 2)/2 currently constitutes one of the most stringent tests for the SM and for new physics, particularly in the light of the recent and future promised results from the E821 experiment at BNL[4]. Recently the E821 collaboration has reported a new improved measurement of aμ. The experimental value of the muon anomaly according to this latest measurement[5] is a μ = (11 659 204(7)(4))× 10 −10 . The SM prediction, according to the latest and improved calculation[6] of a μ , is a μ = (11 659 176± 6.7)× 10 −10 . The experimental value of the muon anomaly differs, therefore, from the SM prediction by δaμ = (28± 10.5)× 10 −10 i.e. by about 2.66σ. The BNL collaboration is expected to 1 reach an eventual precision of 4×10 during its final stage of operation[4]. If the central value does not change, this could eventually differ from the SM by about 7σ and provide, perhaps, the earliest proof of new physics beyond the SM. It is clear, therefore, that it is extremely important to see if (a) the presence of torsion fields can explain why the measured value of the muon anomaly is different from the SM prediction, and/or (b) the highly accurate measurements from the E821 experiment can be used to constrain the parameter space of the torsion action. Such an analysis forms the subject of the present article. §Torsion couplings to SM fermions: In dealing with quantum theory on curved space times with torsion the metric gμν and the rank-3 torsion tensor T α βγ should be considered as independent dynamical variables. In this paper, we shall consider the observable consequences of torsion only and therefore we shall set the metric to be flat Minkowskian everywhere i.e. gμν = ημν . The torsion field T βγ is defined[3] in terms of the non-symmetric connection Γ̃ α βγ T αβγ = Γ̃ α βγ − Γ̃ α γβ . (1) For convenience the torsion tensor T βγ can be divided[2] into three irreducible components. These are • trace: Tβ = T α βα; • pseudo-trace: S = ǫTαβμ; • the third rank tensor qαβγ , which satisfies the conditions q α βα = 0 and ǫ qαβμ = 0. Clearly T behaves as a vector field and S as an axial vector field. The simultaneous presence of both S and T as light dynamical fields could, therefore, be a likely signature of torsion. However, the simultaneous presence of both S and T as light dynamical fields in the low-energy effective field theory would lead to serious problems related to renormalizability. The predictions of the model about loop-induced corrections like the muon anomaly would then become cut-off dependent and somewhat uncertain. In this