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Many-body Physics in Neutrino and Dark Matter Detection


Academic year: 2022

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Many-body Physics in Neutrino and Dark Matter Detection

Cheng-Pang Liu

National Dong Hwa University

Nov. 09, 2017

RIKEN-TW Workshop of Recent Developments in QCD and QFT, NTU, Taipei



A collaboration consists of NP/HEP theorists, atomic theorists, and experimentalists.

Core members: Jiunn-Wei Chen (NTU), Hsin-Chang Chi (NDHU), CPL (NDHU), Lakhwinder Singh (AS), Henry T.

Wong (AS), Chih-Pan Wu (NTU)

Adjunct members: Keh-Ning Huang (Sichuan U.), Shin- Ted Lin (Sichuan U.), Qian Yue (Tsinghua, Beijing)

Former members: Hao-Tze Hsiao (NTU), Chih-Liang Wu (NTU)

Supported in part by NCTS-ECP (2015-2018) and MoST




Why Bother with Low Energies?

Theory Basics

Selected Works





Neutrino Physics

- An Interdisciplinary Study

+ Atomic Physics


DNP/DPF/DAP/DPB Joint Study on

the Future of Neutrino Physics (2004)

1/, "Ê" 9-- 9


3 Recommendations (APS 2004)

A phased program of sensitive searches for neutrinoless nuclear double beta decay

A comprehensive U.S. program to complete our

understanding of neutrino mixing, to determine the

character of the neutrino mass spectrum and to search for CP violation among neutrinos

Development of an experiment to make precise

measurements of the low-energy neutrinos from the sun


How NP/AP Becomes Relevant?

As sources: beta decay, double beta decay, electron capture …

As media: the Sun, supernovae, the Earth (atom. &

geo.) …

As detectors: neutrino-nucleus/atom scattering/capture


Dark Matter Physics

- An Interdisciplinary Study, too!

+ Atomic Physics




WIMP Paradigm

PandaX-II (PRL 117, 121303, ’16) LUX (PRL 118, 021303, ’17)

★ Racing towards the “neutrino floor” !


How about “Light Dark Sector”?

Snowmass 2013 Rep. “Dark Sectors and New, Light, Weakly-Coupled Particles” (arXiv:1311.0029), compelling cases:

Axions and Axion-Like Particles (<1eV)

Dark Photons (masses vary)

Light Dark Matter (sub-GeV, neutral/milli-charged)

Anomalies in X-ray (∼keV) and γ-ray (∼MeV–GeV) lines indirectly point to potential LDM particles.


How NP/AP Becomes Relevant?

As detectors: DM-nucleus/atom scattering/capture …

As media: DM captured/boosted, decay/annihilate in stellar environments …

As sources: dark bound states, mirror DM (dark nuclei, atoms etc.) …


In this talk, focus on the detector aspect in direct



Important Issues

Can a scattering event be constructed as completely as possible?

If not, how is a detector observable related to the primary scattering event?

Is the primary event predicted by theory reliable?


Why Low Energies?


Where Interests Are

Solar, supernova, reactor, geo-neutrinos (keV-MeV)

Sterile neutrinos (eV or keV)

Relic neutrinos (sub-eV)

Light DM (sub-GeV)


Fluxes Are Big


Potential Enhancement / Filter

Nuclei and atoms have rich structure, e.g., each energy level has its own specific quantum numbers, it can

provide potential

enhancement (resonance scattering …)

filter (selection rules in angular momentum, parity, isospin …)

to experimental observables.


Important Physical Scales

For reactor/solar/supernova neutrinos:

E𝛎 ~ 100 keV - 20 MeV

Max. energy deposition by m𝛎 to mA: 2E𝛎2/(mA+2E𝛎) < 10 keV (if elastic)

Atomic scales with effective charge Zeff (shell-dep.):

pe ~ Zeff me𝛂, E𝝌 ~ Zeff me𝛂2, me𝛂 = 3.7 keV

Current lowest detector thresholds:

Tmin ~ keV (nuclear), ~100 eV (electronic)

Atomic effects important for low-E neutrino detection!


Important Physical Scales

For NR (v/c ~ 10-3), LDM (m𝝌 ≤ 10 GeV):

p𝝌 ≤ 10 MeV, E𝝌 ≤ 5 keV

Max. energy deposition by m𝝌 to mA: 4m𝝌mA/(m𝝌+mA)2 E𝝌 < 2 keV (if elastic)

Atomic scales with effective charge Zeff (shell-dep.):

pe ~ Zeff me𝛂, E𝝌 ~ Zeff me𝛂2, me𝛂 = 3.7 keV

Current lowest detector thresholds:

Tmin ~ keV (nuclear), ~100 eV (electronic)

Atomic effects important for LDM detection!


Theory Basics


What Are Needed?

HEP: 𝝂/𝝌-matter interaction (model-driven / EFT) 𝓛int

HEP/NP/AP: Differential cross section d𝝈/dT

AstroP: 𝝂/𝝌 energy / velocity spectrum 𝝓(v⃗)

Exp-Th: Energy loss of 𝝂/𝝌 in detectors


Neutrino EM Interactions

General EM current for spin-1/2 particles:

For 𝛎’s and q2=0:






˥ ܕ۹





˥ ܝܝ

ഩ ত




anapole el. dipole

anomalous mag. dipole charge


EFT DM-matter Lagrangian


Next-to-Leading-Order O(q)

Refs: Fan et. al., JCAP11(2010) 042; Fitzpatrick et. al., JCAP02(2013) 004

ǿintNLO  ೎

ܓܒܜܚ ഭܐܓ ଒଑ ƒস ܓƒܕǖ঴ܓ Θ ǖܝܓ ܐܓ ଒଒ ƒܕǖ঴ Θ ǖܝস ܓƒܓ ܑܓ ଒଑ 

ܝ ƒস ܓƒܕǖ঴ܓ Θ ǖܝܓ ܑܓ ଒଒ 

ܝ ƒܕǖ঴ Θ ǖܝস ܓƒܓ റ ς ǿintLO  ೎

ܓܒܜܚ ഭܐܓ ƒস ܓƒܓ ܐܓ ƒǖ܆স Θ ܓƒǖ܆ܓܓ ܑܓ 

ܝ ƒস ܓƒܓ ܑܓ 

ܝ ƒǖ܆স Θ ܓƒǖ܆ܓܓ റ





Reaction Channels

Elastic: 𝝂/𝝌 + A → 𝝂/𝝌 + A (2-body)

Discrete excitation: 𝝂/𝝌 + A → 𝝂/𝝌 + A* (2-body)

Ionization: 𝝂/𝝌 + A → 𝝂/𝝌 + e- + A+ (3-body, our focus)

Channel separation is not trivial


Differential Cross Section

Example: a c1(e) type interaction with NR DM

All dynamical information in response functions

ECM for CM recoil, EF-EI for internal state change

Biggest challenge: many-body wave functions for the initial and final states





ۼ ^ Ѣ۹^ܐܒ লǖܝ ^ۼѣ ^থ܇ ˥ ۸CM ˥ ۸۹ ˥ ۸ۼ ܑܗ




Free Electron Approximation

No atomic calculation needed (almost)

Validity at sub-keV regimes needs justification


ܑ܇ ഋ




ܕ଒ ঩܇ ˥ ۵ܕ ܑ঴


T>Bi atomic shell open free scat.


Our MB Approach: MCRRPA

An ab initio method improved upon Hartree-Fock theory

MC [multi-configuration]: open-shell atoms have more than one ground-state configuration. Eg. for Ge:

R [relativistic]: Zα~0.25(Ge) / 0.4(Xe)

RPA [random phase approximation]: residual 2e

correlation is important for atomic excited / ionized states

^۽  ѣ  ܐ



ѣ ܐ





Benchmark: Ge Photoionization

10-2 10-1 100 101

σ γ (Mb)


101 102 103 104

T (eV) -10

-5 0 5 10

Rel. Diff. (%)

5% agreement!

solid vs. atom

(PLB 731, 159, ’14)


Benchmark: Xe Photoionization



na ry

(PLB 774, 656, ’17)


Selected Works


Neutrino EM Moments

(PLB 731, 159, ’14; PRD 90, 011301(R), ’14; PRD 91, 013005, ’15)

Basic properties of elementary particles

Potential new physics

Implication for astrophysics & cosmology


Beauty of Low-T Detectors

Neutrinos scatter off free electron with energy deposition T:

Low threshold detectors:

GEMMA: Ge @ 1.5 keV; TEXONO: Ge @ sub keV

Price to pay:

Atomic binding effects!



˰ ܇







Ge AI by MM

FEA works o.k.

FEA overshoots

typical for reactor 𝛎’s MM: 2.9×10-11𝝁B


Ge AI by mQ

FEA works o.k.

FEA overshoots

typical for reactor 𝛎’s

FEA under!

FEA better EPA works o.k.

mQ = 1.0×10-12e


Current Direct Limits

From PDG 2016

MM: 2.9×10-11𝝁B (GEMMA ’13); 7.4×10-11𝝁B (TEXONO ’07)

mQ: [1.5×10-12e (from GEMMA); 2.1×10-12e (from TEXONO)]

CR: 3.3×10-32cm2 (TEXONO ’10)

All with reactor anti-𝛎 sources


Low-E Solar Neutrinos

(PLB 774, 656, ’17)

pp neutrinos (~hundreds of keV) still not fully observed

Multi-ton scale LXe (Xenon1T, LZ, DARWIN) detectors are capable (through electron recoil with sub-keV th.)

Can test solar models to 1% level (~100 ton-yr)

Important for DM detection background


Solar Neutrinos Detection

Liquid Xenon


Solar Neutrino-Xenon Scattering


Assume 1-ton liquid xenon & 1-year exposure:

FE overestimate!

Low-E Solar Neutrino Rate





Neutrino & DM physics is interdisciplinary.

Many-body physics is essential for sub-keV detectors of neutrinos and dark matter.

High-quality many-body calculations can substantially reduce theoretical errors.

Energy loss mechanism still needs better understanding.





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