Ionization cross sections of neutrino electronagnetic interactions - PowerPoint PPT Presentation

Ionization cross sections of neutrino electronagnetic interactions with electrons Chih-Pan Wu Dept. of Physics, National Taiwan University P. 1

Constrain ν EM Properties by Ge Reference : Phys. Lett. B 731 , 159, arXiv:1311.5294 (2014). Phys. Rev. D 90 , 011301(R), arXiv:1405.7168 (2014). Phys. Rev. D 91 , 013005, arXiv:1411.0574 (2015). P. 2

ν -e Non-standard Interactions (NSI) E E   E  T  ( ) ( T  ) , q , q ( T  ) , q Weak = − g 1 / 2 Magnetic moment A =  + Interaction g 2 sin 1 / 2 v w     2 2 1 1   +  −   2   m e T E  An Example for enhanced signals at low T! P. 3

Solar ν Background in LXe Detectors 99.98% ER rejection J. Aalbers et. al. (DARWIN collaboration), JCAP 11 , 017, arXiv:1606.07001 (2016). P. 4 J.-W. Chen et. al ., Phys. Lett. B 774 , 656, arXiv:1610.04177 (2017).

Outline • Atomic ionization cross sections of neutrino- electron scattering – Why & when atomic effects become relevant? – MCRRPA: a framework of ab initio method • Discovery potential of ton-scale LXe detectors in neutrino electromagnetic properties – arXiv: 1903.06085 – solar nu v.s. reactor nu + Ge detector P. 5

Why Atomic Responses Become Important? The space uncertainty is inversely proportional to its incident momentum: λ ~ 1/p • 2 important factors: Atomic Size is inversely proportional to its – neutrino momentum orbital momentum: Zm e α ~ Z *3.7 keV – Energy transfer T Z: effective charge P. 6

Atomic Ionization Process for ν | 𝑁 | 2 The weak scattering amplitude: The EM scattering amplitude: P. 7

Electroweak Currents Lepton current: Atomic (axial-)vector current: , 1 , 0 Sys. Error: ~ 𝛽 ≈ 1% P. 8

The Form Factors & Related Physical Quantities neutrino millicharge : : charge form factor charge radius squared : : anomalous magnetic neutrino magnetic moment : : anapol e ( P -violating) electric dipole moment : : electric dipole anapole moment : ( P , T -violating) P. 9

“effective” Magnetic Moment µ ν and d ν interactions are not distinguishable where f and i are the mass eigenstate indices for the outgoing and incoming neutrinos, A ie ( E ν , L ) describes how a solar neutrino oscillates to a mass eigenstate ν i with distance L from the Sun to the Earth. P. 10

Bound Electron Wave Function |w > |u > ⅇ 𝛿 𝜈 ⅇ 𝑔 | 𝛿 𝜈 |Ψ 𝑗 > ത < Ψ < 𝑥| 𝛿 𝜈 |𝑣 > EM interaction Weak interaction Non-standard interactions 𝛿 𝜈 → 𝑕 𝑊 𝛿 𝜈 + 𝑕 𝐵 𝛿 𝜈 𝛿 5 → NSI Opⅇrators P. 11

One-Electron Dirac Spinors Then the radial Dirac equations can be reduced to P. 12

Atomic Response Functions Do multipole expansion with J Initial states could be Final continuous wave functions approximated by could be obtained by MCRRPA bound electron orbital and expanded in the ( J , L ) basis wave functions given of orbital wave functions by MCDF P. 13

Ab initio Theory for Atomic Ionization MCDF: multiconfiguration Dirac-Fock method   u a ( r , t ) ( t ) Dirac-Fock method: is a Slater determinant of one-electron orbitals 𝜔(𝑢) 𝑗 𝜖 𝜀 ሜ 𝜖𝑢 − 𝐼 − 𝑊 𝐽 (𝑢) 𝜔(𝑢) = 0 and invoke variational principle 𝑣 𝑏 (റ 𝑠, 𝑢) . to obtain eigenequations for  ( t ) multiconfiguration: Approximate the many-body wave function  ( t ) by a superposition of configuration functions   For Ge: ቐ𝜔 1 = Zn 4𝑞 1/2 2  =  ( t ) C ( t ) ( t )   𝜔 2 = Z𝑜 4𝑞 3/2 2  MCRRPA: multiconfiguration relativistic random phase approximation  u a ( r , t ) RPA: Expand into time-indep. orbitals in power of external potential        −   = + + + i t i t i t u ( r , t ) e u ( r ) w ( r ) e w ( r ) e ... a + − a a a a = + −  +  + i t i t C ( t ) C [ C ] e [ C ] e ... + − a a a a P. 14

Here use square brackets with subscripts to designate the coefficients in powers of e ± i ω t in the expansion of various matrix elements: 𝛿 𝛽𝛾 : Lagrange multipliers MCDF Equations: † : functional derivatives 𝜀 𝛽    0 + = EC C H 0 † with respect to 𝑣 𝛽 a b ab b    0  −  = † δ * C C H u 0     a b ab  ab The zero-order equations are MCDF equations for unperturbed orbitals u a and unperturbed weight coefficients C a . MCRRPA Equations: ( )         ( )   − + = E C H C H C V C   a ab b ab  b ab  b 0 b b ( ) ( )         †  − − + † δ δ * * * C C i H C C C C H      a b ab ab a m b a b ab 0 ab ab ( )     −  +  = † * δ w u C C V         a b ab  ab The first-order equations are the MCRRPA equations describing the linear response of atom to the external perturbation v ± . P. 15

Atomic Structure of Ge Multiconfiguration of Ge Ground State (Coupled to total J =0) : Selection Rules for J =1, λ =1: Angular Momentum Selection Rule: Parity Selection Rule: P. 16

Multipole Expansion Transition matrix elements of atomic ionization by nu-EM interactions: P. 17

Benchmark: Ge & Xe Photoionization Exp. data: Ge solid Theory: Ge atom (gas) Above 100 eV error under 5%. B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data and Nuclear Data Tables 54 , 181-342 (1993). J. Samson and W. Stolte, J. Electron Spectrosc. Relat. Phenom. 123 , 265 (2002). I. H. Suzuki and N. Saito, J. Electron Spectrosc. Relat. Phenom. 129 , 71 (2003). P. 18 L. Zheng et al ., J. Electron Spectrosc. Relat. Phenom. 152 , 143 (2006).

Approximation Schemes Longitudinal Photon Approx. (LPA) : V T = 0 V L = 0, q 2 = 0 Equivalent Photon Approx. (EPA) :  Strong q 2 -dependence in the denominator : long-range interact ion Real photon limit q 2 ～ 0 :  relativistic beam or soft photons q μ ～ 0 Free Electron Approx. (FEA) : q 2 = -2 m e T  Main contribution comes from the phase space region similar with 2-body scattering  Atomic effects can be negligible : E ν >> Z m e α T ≠ B i (binding energy) P. 19

Numerical Results: Weak Interaction = = E 10 k eV E 1 M eV v v e e (1) short range interaction 2 2 E =  v cutoff : T 0 . 38 k eV e (2) neutrino mass is tiny + Max 2 E m v e e (3) E ν >> Z m e α Kinematic forbidden by the inequality:      − FEA works well away from p 2 m T q 2 E T  r e Max e → the ionization thresholds. (backward scattering , m 0 ) ν e P. 20

Numerical Results: NMM = E 1 M eV v e = E 10 k eV v e Similar with WI cases. FEA still faces a cutoff with lower E ν . For right plot, EPA becomes better when T approaches to E ν ( q 2 -> 0). Consistent with analytic Hydrogen results. P. 21

Numerical Results: Millicharge = = E 1 M eV E 10 k eV v v e e EPA worked well due to q 2 dependence in the denominator of scattering formulas of F 1 form factor (a strong weight at small scattering angles). P. 22

Double Check on Our Simulation • We perform ab initio many-body calculations for atomic initial & final states WF in ionization processes, and test by – Comparing with photo-absorption experimental data, for typical E1 transition, the difference is <5%. – In general, we have confidence to report a 5~10% theoretical errors. – It agrees with some common approximations under the crucial condition as we know in physical picture P. 23

Solar ν As Signals in LXe Detectors P. 24 J.-W. Chen et. al ., arXiv:1903.06085 (2019).

Expected Experimental Limits Assuming an energy resolution from the XENON100 experiment P. 25 J.-W. Chen et. al ., arXiv:1903.06085 (2019).

What Else? Portals to the Dark Sector: 1. Remain a large region for the possibility of LDM (Ex: Dark Sectors) 2. Other interactions, or interacted with electrons K. Olive et al . (Particle Data Group), Chin. Phys. C 38 , 090001 (2014). P. 26 R. Essig, J. A. Jaros, W. Wester, P. H. Adrian, S. Andreas et al ., arXiv:1311.0029.

Spin-Indep. DM-e Scattering in Ge & Xe P. 27 J.-W. Chen et. al ., arXiv:1812.11759 (2018).

Sterile Neutrino Direct Constraint q 2 < 0 q 2 > 0 • Non-relativistic massive sterile neutrinos decay into SM neutrino. At m s = 7.1 keV, the upper limit of μ ν sa < 2.5*10 -14 μ B at 90% C.L. • • The recent X-ray observations of a 7.1 keV sterile neutrino with decay lifetime 1.74*10 -28 s -1 can be converted to μ ν sa = 2.9*10 -21 μ B , much tighter because its much larger collecting volume. P. 28 J.-W. Chen et al ., Phys. Rev. D 93 , 093012, arXiv:1601.07257 (2016).

Constraints on millicharged DM P. 29 L. Singh et. al . (TEXONO Collaboration), arXiv:1808.02719 (2018).