Earthquake Forecast via Neutrino Tomography $^{1}$Department of Physics, Nankai University, Tianjin, 300071, China Bin Wang, 1 Ya-Zheng Chen, 1 and Xue-Qian Li 1 We discuss the possibility of forecasting earthquakes by means of (anti)neutrino tomography. Antineutrinos emitted from reactors are used as a probe. As the antineutrinos traverse through a region prone to earthquakes, observable variations in the matter effect on the antineutrino oscillation would provide a tomography of the vicinity of the region. In this preliminary work, we adopt a simplified model for the geometrical profile and matter density in a fault zone. We calculate the survival probability of electron antineutrinos for cases without and with an anomalous accumulation of electrons which can be considered as a clear signal of the coming earthquake, at the geological region with a fault zone, and fi nd that the variation may reach as much as 3% for ¯ ν e emitted from a reactor. The case for a ν e beam from a neutrino factory is also investigated, and it is noted that, because of the typically high energy associated with such neutrinos, the oscillation length is too large and the resultant variation is not practically observable. Our conclusion is that with the present reactor facilities and detection techniques, it is still a difficult task to makean earthquake forecast using such a scheme, though it seems to be possible from a theoretical point of view while ignoring some uncertainties. However, with the development of the geology, especially the knowledge about the fault zone, and with the improvement of the detection techniques, etc., there is hope that a medium-term earthquake forecast would be feasible. PACS numbers: 14.60.Pq, 13.15.+g 91.30.Px 91.35.Pn Introduction.— Earthquakes and tsunamis are natural catas- trophes. They occur on our globe so frequently and cost thou- sands of lives and immense loss of property. We lack an effi- cient way to forecast earthquakes at present. We believe that our knowledge of modern physics and sophisticated detection techniques and facilities may help. It has been proposed that we could explore oil storage with neutrino beams [1–3], whic h also find applications in various other fields [4, 5]. These cr e- ative ideas motivate us to investigate the possibility of fore- casting earthquakes and tsunamis in terms of matter effects on (anti)neutrino oscillations. probability in uniform matter is similar to the vacuum case, but the vacuum mixing angle θ$_{0}$ and mass-squared difference Δ m 2 = | m 2 − m 2 1 | should be replaced by the corresponding quantities in matter. That is P$_{ν}$$_{e}$ → ν$_{e}$ = 1 − sin $^{2}$2 θ$_{M}$ sin 2 ( Δ m M 4 E$_{ν}$ L ) , (1) where θ$_{M}$ and Δ m 2 M are the mixing angle and mass-squared difference in matter, respectively. E$_{ν}$ and L are, respectively, the energy of the neutrino and the length of the baseline. For θ$_{M}$ we have Various neutrino experiments are, or will soon be, in op- eration. With great effort, most neutrino parameters have been determined with certain accuracy. However, the complex phase δ$_{CP}$ and the sign of Δ m 2 31 are still unknown. Moreover, so far we only have the upper bound of θ$_{13}$ , which is man- ifestly smaller compared with the other two mixing angles. Precise measurement of θ$_{13}$ will be valuable for searches for CP violation in the lepton sector. Two reactor neutrino ex- periments, Daya Bay [6] in China and Double Chooz [7] in France, aiming to measure θ$_{13}$ are expected to reach very high precision at the percent level. For antineutrinos, the minus sign in Eq. (2) should be replaced by a plus sign, which implies that unlike the case of neutrino oscillation in the sun, no resonant stage exists, but an enhance- ment of the survival probability for antineutrinos, as discussed in [10]. In analogy to the X-ray tomography, the possibility that (anti)neutrinos could be treated as a probe to detect the in- ner structure of the earth has been discussed by several au- thors. Two approaches [11] have been suggested for different (anti)neutrino energies. Our simplified model for an earthquake fault zone.— Earthquakes are caused by rapid slippage along faults and re- lease of energy stored in the seismic zone. Generally, a seis- mic zone does not consist of one single fault. The term ” fault zone” implies that the zone is composed of several in- ner faults and undergoes tremendous deformation caused by severe shear and strain. On May 12 of 2008, an M$_{S}$ = 8.0 earthquake occurred in Wenchuan, Sichuan Province, China. It was caused by the fracture of faults in the Longmenshan fault zone. This fault Matter effects on the neutrino oscillation are crucial in some cases, for example, to explain the solar neutrino flux deficit . Wolfenstein [8] formulated the matter effect on neutrino oscil- lation and then Mikheev and Smirnov [9] applied and devel- oped the theory to successfully solve the solar neutrino prob- lem. The newest experimental data confirm the MSW model. As a neutrino traverses through matter, its oscillation length is no longer the same as in vacuum. Electron neutrinos acquire an extra potential V ( x ) = √$_{2}$$_{G}$$_{F}$$_{n}$$_{e}$$_{(}$$_{x}$$_{)}$ in the Hamiltonian due to their interaction with electrons, which exist in ordinary matter, where G$_{F}$ is the Fermi coupling constant and n$_{e}$ is the number density of electrons in matter. In a simplified ver - sion with only two generations, the expression of the survival tan 2 θ$_{M}$ = tan 2 θ$_{0}$ ( 1 − $_{2}$√$_{2}$$_{E}$$_{ν}$$_{G}$$_{F}$$_{n}$$_{e}$ Δ m $^{2}$cos 2 θ$_{0}$ ) − 1 . (2) arXiv:1001.2866v2 [hep-ph] 29 Mar 2011