Many-body Physics in Neutrino and Dark Matter Detection

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

Collaborators

• 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

Outline

• Introduction

• Why Bother with Low Energies?

• Theory Basics

• Selected Works

• Summary

Introduction

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

+ …

𝛘

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

detection

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:

E_𝛎 ~ 100 keV - 20 MeV

• Max. energy deposition by m_𝛎 to mA: 2E_𝛎2/(mA+2E_𝛎) < 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) 𝓛^int

• 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:

F1=mQ; F2=MM; FA=AM; FE=EDM

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anapole el. dipole

anomalous mag. dipole charge

EFT DM-matter Lagrangian

• Leading-Order

• Next-to-Leading-Order O(q)

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

ǿ_int^NLO  ೎

ܓܒܜܚ ഭܐ^ܓ_଒଑ স^ƒসܓ^ƒܕǖ঴_ܓ Θ ǖܝܓ ܐ^ܓ_଒଒ স^ƒܕǖ঴_স Θ ǖܝসܓ^ƒܓ ܑ^ܓ_଒଑ 

ܝ^ଓ স^ƒসܓ^ƒܕǖ঴_ܓ Θ ǖܝܓ ܑ^ܓ_଒଒ 

ܝ^ଓ স^ƒܕǖ঴_স Θ ǖܝসܓ^ƒܓറ ς ǿ_int^LO  ೎

ܓܒܜܚ ഭܐ^ܓ_଒ স^ƒসܓ^ƒܓ ܐ^ܓ_କ স^ƒǖ܆_সস Θ ܓ^ƒǖ܆_ܓܓ ܑ^ܓ_଒ 

ܝ^ଓ স^ƒসܓ^ƒܓ ܑ^ܓ_କ 

ܝ^ଓ স^ƒǖ܆_সস Θ ܓ^ƒǖ܆_ܓܓറ

SI SD

SR

LR

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

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ۼ ^ Ѣ۹^ܐ^ܒ_଒ লǖܝ^ۼѣ ^^ଓথ܇ ˥ ۸CM ˥ ۸_۹ ˥ ۸_ۼ  ܑ^ଔܗ_ଓ

঱^ଔ

Baseline:

Free Electron Approximation

• No atomic calculation needed (almost)

• Validity at sub-keV regimes needs justification


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FEA

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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

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Benchmark: Ge Photoionization

10^-2 10^-1 10⁰ 10¹

σ γ (Mb)

MCRRPA Exp. Fit

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

Pre

limi

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!

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W,CR MM mQ

Ge AI by MM

FEA works o.k.

FEA overshoots

typical for reactor 𝛎’s MM: 2.9×10^-11𝝁^B

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^-11𝝁^B (GEMMA ’13); 7.4×10^-11𝝁^B (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

• 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

Summary

Conclusions

• 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.

Thanks!