QCD-based Charge Symmetry Breaking (CSB) Interaction

Hiroyuki Sagawa

RIKEN/University of Aizu

Kobe DFT meeting
February 20-22, Kobe Japan

1. Introduction
2. QCD-based CSB and Okamoto-Nolen-Schiffer anomaly
3. CSB in HyperNuclei
4. Summary

Isospin is one of the most important symmetries which is uniquefor nuclear and elementary particle physics.
Concept of Isospin proposed by J. Heisenberg, 1932 and E. P. Wigner, 1937
Isospin conservation[H,T ] = 0Isospin Breaking Interactions (ISB)[H,T ] = [VC +VCSB +V CIB ,T ] ¹ 0Scattering
LengthCharge independence breaking
VCIS=(Vnn+Vpp)/2 -Vnp

LQCD
ab initio no core shell model

Asymptotic Freedom,
Chiral symmetry

Chiral symmetry breaking
confinement

Hadron Physics
Nuclear Many-body Problems

Effective Theories (RMF, Ch EFT)

Lattice QCD

QCD sum rule

QCD Lagrangian

Quark Effective theories(Nambu–Jona-Lasinio model)
BCS/HF in nuclear physics
QCD sum ruleEnergy weighted sum rule for
Giant resonances (RPA)

Based on a slide of T. Hatsuda

Operator product expansion with nucleon current

Operator product expansion (OPE) method

Phenomenological hadron propagator

Derivatives after Borel transformation~1GeVQCD-based CSB interaction

HS, T. Naito, X. Roca-Maza and T. Hatsuda, PRC109, L011302 (2024)qതq / qതq 0

The in-medium chiral condensate has a generalform in the leading order of Fermi motion
corrections;pion
Goda and Jido

Partial restoration of Chiral condensation of quark pairs 𝑞തqT. Nishi et al., Nature Physics, March 23, 2023
Pionic atom experiments

p-nNuclear medium

The mass difference between (Z+/-1,N)and (Z, N+/-1) with N=Z

The chiral symmetry breaking effect onONS anomaly is formulated as

The Skyrme-type CSB and CIB interactions

Summary
QCD sum rule approach is adopted to obtain EDF CSB
parameters without introducing any free parameters;
all QCD parameters are determined by experimental observables.
QCD-based CSB interactions are applied to solve ONS anomaly of
A=16+/-1 and 40+/-1 mirror nuclei and cured all experimental
observed values within the theoretical uncertainties.
Empirical evidence of CSB in hypernuclei is pointed out by RMFcalculations.

Future perspectives
CIB interaction in nuclear medium
QCD based Λ − 𝑁 CSB interaction for hypernuclei
CSB and CIB effects of Isobaric Analogue states
CSB in Exotic nuclei near proton drip lines

Collaborators
Skyrme CSB,QCD-CSB
T. Naito, iTHEMS, RIKEN
T. Hatsuda, iTHEMS, RIKEN
Xavi Roca-Maza, INFN, University of Milano, Italy
Gianluca Colo, INFN, University of Milano, Italy
Hypernuclei
E Hiyama, RIKEN/Tohoku University
T.T. Sun, Zhengzhou University, China
Y. Tanimura, OMEG, Soongsil University, Korea

J-PARK and Jefferson Labs
Future experiments

Isospin Breaking Strong interactions

Coulomb interaction
Skyrme type ISB interactions

Charge symmetry breaking (CSB) interaction
𝑉𝑛𝑛 ≠ 𝑉𝑝𝑝
Charge Independence breaking (CIB) interaction
𝑉𝑛𝑝 ≠ (𝑉𝑛𝑛 + 𝑉𝑝𝑝 )/2Hadrons: Nucleon and Pion mass difference
mn-mp=1.29MeV. 𝜋 ±-𝜋 0=4.6MeV

CIB

Energy density functionals

Quarks: explicit chiral symmetry breaking
𝑚𝑢 ≠ 𝑚𝑑

Observables

Nolen-Schiffer anomaly
Energy of IAS
mass differences in isobar and isotriplet nuclei

Hatsuda et al. (QCD sum rule; PRL66, 2851 (1991))
290.+/-70. 530.+/-140. 420.+/-110. 570.+/-150.
M. Kimura et al.(𝜌 − 𝜔 coupling in RM; PLB367, 5 (1996))
70-290 keV

( p) = (uud )mu ¹ md(n) = (udd )qu ¹ qdppnn

CSB=

pppn

Theoryqതq / qതq 0Explicit chiralsymmetry breaking

Pionic AtomExperiment

nnp

pnn
QCD
sum rule+CIB=

pnp

p

2nn

Spontaneous symmetry breaking(SSB)QCD-based CSB interaction

HS, T. Naito, X. Roca-Maza and T. Hatsuda, PRC109, L011302 (2024)

1. QCD sum rule approach to evaluate mass difference of proton and neutron in
nuclear medium
2. Partial restoration of Spontaneous symmetry breaking (SSB) in nuclear medium
The mass difference between neutron and proton is formulated in nuclear matter by
the QCD sum rule approach in leading order of the quark mass difference and QED
effectIN VACUUM,