Coherency in Neutrino-Nucleus Elastic Scattering

Transcription

1 Coherency in Neutrino-Nucleus Elastic Scattering S. Kerman, V. Sharma, M. Deniz, H. T. Wong, J.-W. Chen, H. B. Li, S. T. Lin, C.-P. Liu and Q. Yue (TEXONO Collaboration) Institute of Physics, Academia Sinica, Taipei, Taiwan 4 th International Workshop on Dark Matter, Dark Energy and Matter-Antimatter Asymmetry December 29-31, 2016, NTHU, Hsinchu, Taiwan Coherency in Neutrino-Nucleus Elastic Scattering, Phys. Rev. D 93, (2016)

2 Outline 1 2 3

3 Motivation νa el process: A convenient channel to study the quantum mechanical coherency effects in electroweak interactions. The generic scale for coherency is: E ν < 50 MeV. We focesed on quantitative studies on the transitions towards decoherency. Our theme s objective is to quantify this transition the first such investigation in the literature. The degree of coherency is described by a measurable parameter (α) and the dependency of α parameter to the incoming neutrino energy, detector threshold, and target nucleus are examined.

4 νa el : ν + A(Z, N) ν + A(Z, N). The SM differential cross section of νa el scattering: dσ νael dq 2 (q2, E ν ) = 1 [ ] ] G 2 F [1 q2 2 4π q 2 = 2MT + T 2 2MT. σ νael = 4E 2 ν [ εzf Z (q 2 ) NF N (q 2 ) ] 2, (1) The total cross section: [ ] dσνael dq 2 (q2, E ν ) dq 2. (2) q 2 max q 2 min For nuclear form factors the effective method is adapted, [ ] 3 F(q 2 ) = J 1 (qr 0 ) exp[ 1 qr 0 2 q2 s 2 ], (3) with parameters: R 2 0 = R2 5s 2 and s = 0.5 fm.

5 Neutron and several different nuclei (n, Ar, Ge, Xe), compatible with exp. interest, are selected for studies {Z = (0, 18, 32, 54)}. Fig. 1.(a) Nuclear form factor F (q 2 ) as a function of T: Fig. 1.(b) Total cross section (σ νael ) at T min = 0 as a function of E ν : Figure 1: (a) Nuclear form factor F (q 2 ) as a function of T, related by q 2 = 2MT ; (b)total cross section (σ νael ) at T min = 0 as a function of E ν. (n, Ar, Ge, Xe) nuclei are selected for illustrations.

6 Decoherency Decoherency for σ νael is characterized by deviations from the [εz N] 2 scaling as q 2 increases. The scattering amplitude of individual nucleons adds with a finite relative phase angle to contribute to the cross section. The combined amplitude A: A = Z N e iθ j X j + e iθ k Y k, (4) j=1 k=1 (X j, Y k ) = ( ε, 1): the coupling strengths for protons and neutrons; ( ) e iθ j e iθ k : the phase for protons (neutrons).

7 σ νael AA = Z j=1 X 2 j + j=l+1 l=1 N k=1 Y 2 k Z Z 1 [ ] e i(θ j θ l ) + e i(θ j θ l ) X j X l N k=m+1 m=1 Z j=1 k=1 N 1 [ ] e i(θ k θ m) + e i(θ k θ m) Y k Y m N [ e i(θ j θ k ) + e i(θ j θ k ) ] X j Y k. (5) The decoherence effects between any nucleon pairs is described by the average phase misalignment angle φ [0, π/2]: [ e i(θ j θ k ) + e i(θ j θ k ) ] = 2cos(θ j θ k ) = 2cos φ. (6)

8 The degree of coherency can therefore be quantified by a measurable parameter α cos φ [0, 1]. The cross-section ratio between A and neutron is: σ νael (Z, N) σ νael (0, 1) = {ε 2 Z + N + ε 2 Z (Z 1)α + N(N 1)α 2εZNα} = {Z ε 2 [1 + α(z 1)] + N [1 + α(n 1)] 2αZN}. (7) The limiting conditions: Full coherency: α = 1; σ νael [εz N] 2 Total decoherency: α = 0; σ νael [ε 2 Z + N]. Partial coherency, the relative change in cross section, ξ: ξ [ σ νael (α) (ε 2 ] Z + N) = α + (1 α) σ νael (α = 1) (εz N) 2, (8) which varies linearly with α, and both are unity at full coherency.

9 Numerical Numerical Analysis The α contours on the (N, E ν ) plane at T min = 0: Figure 2: The α contours on the (N, E ν) plane at T min = 0, with bands of realistic neutrino sources and target nuclei superimposed.

10 Variations of α and ξ as functions of (a) E ν at T min = 0; (b) T min at E ν = 50 MeV : Figure 3: Variations of α and ξ for Ar, Ge, Xe as functions of (a) E ν at T min = 0, and (b) T min at E ν = 50 MeV where the end points correspond to maximum recoil energies.

11 Experimental studies of coherency would be performed with realistic neutrino sources. The current projects: reactor ν e, DAR π (ν µ, ν e, ν µ ) & the high energy solar- 8 B ν e. Figure 4: Neutrino spectra (Φ ν) from reactor ν e, DAR π (ν µ, ν e, ν µ), and solar- 8 B ν e, normilized by their maxima. (b)distributions of [ Φ ν σ νael ] at Tmin = 0, which are the weights in the averaging of (α, ξ) to provide measurements of ( α, ξ ).

12 The values of α at T min = 0: ν Half maxima of [Φ ν σ νael ] α with source in E ν (MeV) Ar Ge Xe Reactor ν e solar- 8 B ν e DAR πν µ DAR πν e DAR πν e Table 1: The half maxima in the distributions of [ Φ ν σ νael ] at Tmin = 0 for the different neutrino sources, and the values of α probed by the selected target nuclei.

13 For Ge variations of ( α, ξ ) with T min with different ν sources : Figure 5: Variations of ( α, ξ ) as a function of T min with reactor ν e, solar- 8 B ν e and DAR π (ν µ, ν e, ν µ) for Ge. The end points correspond to maximum recoil energies allowed by kinematics. The low energy reactor ν e and solar- 8 B ν e probe the full coherency region (α > 0.9), while DAR πν s allow measurements in the transition regions (0.9 > α > 0.1).

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