Letter of Intent for an Experiment at the Spallation Neutron Source Precise Measurement of the Neutron Beta Decay Parameters

We propose to perform a precise measurement of a, the electronneutrino correlation parameter, and b, the Fierz interference term in neutron beta decay, at the Fundamental Neutron Physics Beamline at the SNS, using a novel electric/magnetic field spectrometer and detector design. The experiment is aiming at the 10−3 accuracy level in a, and will provide an independent measurement of λ = GA/GV , the ratio of axial-vector to vector coupling constants of the nucleon. We will also perform the first ever measurement of b in neutron decay, which will provide an independent limit on the tensor weak coupling. Precise measurement of a, b LoI for an experiment at SNS 1. Scientific motivation Neutron β decay, n → peνe, is one of the basic processes in nuclear physics. Its experimental study provides the most sensitive means to evaluate the ratio of axial-vector to vector coupling constants λ = GA/GV . The precise value of λ is important in many applications of the theory of weak interactions, especially in astrophysics; e.g., a star’s neutrino production is proportional to λ. More precise measurements of neutron β-decay parameters are also important in the search for new physics. Measurement of the neutron decay rate Γ, or lifetime τn = 1/Γ, allows a determination of Vud, the Cabibbo-Kobayashi-Maskawa (CKM) matrix element, independent of nuclear models, because Γ is proportional to |Vud|, as seen in the leading order expression: Γ = 1 τn = fmec 4 2π3~7 ( |GV | + 3|GA| ) ∝ |GV | ( 1 + 3|λ| ) = |Vud| |gV | GF (1 + 3|λ|) , (1) where f = 1.71482(15) is a phase space factor, me is the electron mass, gV,A the vector and axial-vector weak nucleon form factors at zero momentum transfer, respectively, and GF is the fundamental Fermi weak coupling constant. While the conserved vector current (CVC) hypothesis fixes gV at unity, two unknowns, Vud and λ, remain as variables in the above expression for Γ. Hence, an independent measurement of λ is necessary in order to determine Vud from the neutron lifetime. Several neutron decay parameters can be used to measure λ; they are discussed below. Precise knowledge of Vud helps greatly in establishing the extent to which the three-generation CKM matrix is unitary. CKM unitarity, in turn, provides an independent crosscheck of the presence of certain processes and particles not included in the Standard Model (SM) of elementary particles and interactions, i.e., an independent constraint on new physics. Currently, the most accurate value of the CKM matrix element Vud is obtained from measurements of 0 → 0 nuclear β-decays, the so-called superallowed Fermi transitions [1]. However, the procedure of the extraction of Vud involves calculations of radiative corrections for the Fermi transition in nuclei. Despite the fact that these calculations have been done with high precision (see [2] and references therein), it is impossible to verify the values of these nuclear corrections from independent experiments. A problem with CKM matrix unitarity at the 2− 3σ level persisted for over two decades in the first row sum; e.g., the 2002 Review of Particle Properties [3] reported values of CKM matrix elements that yield ∆ ≡ 1− |Vud| − |Vus| − |Vub| = 0.0032± 0.0014 . (2) The situation changed drastically in 2003 and 2004 when a series of experiments at Brookhaven, Fermilab and CERN reported revised values of Kl3 decay branching ratios which led to an upward adjustment, by about 2.5σ, of the CKM matrix element Vus [4, 5, 6]. Without getting into the details of this revolutionary development, it will suffice to note that a revised CKM unitarity check yields [7] ∆ = (3± 14)× 10−4 , (3) which indicates that, at least for the time being, the question of the CKM matrix unitarity appears to be closed. However, several questions related to Vud still remain open. Firstly,