Brane Fluctuation and anomalous muon magnetic moment

We study the effects of extra dimensions on the muon anomalous magnetic moment with brane fluctuation. Since the coupling is naturally suppressed if brane fluctuation is considered by exponential softening factor for heavier states, the contribution from the whole Kaluza-Klein graviton tower is shown to be finite. The recent BNL E821 result is accomodated with D = 4 + δ dimensional gravitational scale, MD, in the range of MD ≃ 1.0 − 5.1 TeV (δ = 2), and MD ≃ 1.0 − 8.0 TeV (δ = 6) with the brane tension parameter f = (4π2τ)1/4, in the range f = 1− 10 TeV. PACS number(s): 11.30.Pb, 11.30.Er [email protected] [email protected] The report of measurement of the anomalous g value for the positive muon from Brookhaven AGS experiment 821, based on data collected in 1999, has attracted great interests [1]. Combining recent theoretical and experimental uncertainties, the new world average shows 2.6σ deviation from the standard model(SM) prediction. It may be the first evidence that the standard model must be extended by new physics at TeV scale. The reported result is given as δaμ ≡ aμ(exp)− aμ(SM) = 43(16)× 10 , (1) where aμ(exp) is world averaged value. Since four times larger data is already recorded in 2000 and measurements with negative muon are undertaking now, it is very interesting situation to consider the implications of the speculative advocates of the new phycis on the anomaly. Most popular approaches include weak scale supersymmetry, large or warped extra dimensional scenario, extension of the gauge structure and many other alternatives (see e.g., [3]). In this paper, we consider the extra dimensional scenario suggested by Arkani-Hamed et.al. with brane fluctuation. If all the matter fields are confined on the brane-world, 1-loop contribution of the KaluzaKlein excitations of the graviton is known to explain the recent BNL anomaly [4], [5], [6]. (The case in which SM fields propagate in the bulk is also studied [7].) We note that in both cases-with large or warped extra dimensionsphysical cutoff at weak scale should be imposed to get finite results from the non-renormalizable theory. Even these truncation procedures are not un-natural in treating effective theory [8], it seems not generally true that the exactly same expressions for the muon anomalous moment remains valid until the cutoff scale. In this letter, we study the another possibility to get rid of divergence by considering brane fluctuation [9], [10]. We take the case that all the gauge and fermion fields of SM are confined on 3-brane and only the gravitational field can propagate through the bulk. In that case, D = 4 + δ dimensional gravitational scale, MD, is related to our four dimensional Planck scale MP by M P = M 2+δ D R . Where R is the size of the extra dimension. From this relation, we 2 can understand weakness of gravity or largeness of Planck energy scale: if the size of the extra dimesion is large enough, the Planck scale also is very big. It is phenomenologically interesting case, if MD is as small as TeV scale. The gravitational interaction with SM fields which are confined on the fluctuating brane can be described by the action: S ⊃ − 1 MP ∫ dxTμν(x)g (x, ~y)δ(~y − ~ φ(x)) (2) where the Nambu-Goldstone boson ~ φ(x), which came from the spontaneous translational symmetry breaking, represent the brane fluctuating in the ~y direction at point x in our 3-brane. The Nambu-Goto action with tension τ = f /4π describe the dynamics of ~ φ(x): ∫ dx(−τ + τ 2 ∂μ~ φ(x) · ∂ μ~ φ(x) + · · ·) (3) on the flat background. After expanding the gravitational field around the compact extra dimension as gμν(x, ~y) = ∑ ~n g μν(x)e i~n·~ , (4) and taking normal ordering the exponential in perturbation framework, the interaction action includes an exponential ‘softening factor’: