Charge Symmetry Breaking Research Articles

The charge and mass symmetry breaking in the KK K¯ system

In the framework of the Faddeev equations in configuration space, we investigate the K(1460) meson as a resonant state of the KKK¯ kaonic system. We perform calculations for the particle configurations K 0 K + K − and K0K+K0¯ within two models: the ABC model, in which all three particles are distinguishable, and the AAC model when two particles are identical. The models differ in their treatment of the kaon mass difference and the attractive Coulomb force between the K + K − pair. We found that the Coulomb shift adds over 1 MeV to the three-body binding energy. The expected correction to the binding energy due to mass redistribution from AA to AB is found to be negligible, up to a maximum of 6% of the relative mass correction. At the same time, the symmetry of the wave function is distorted depending on the mass ratio value. We found that the repulsive KK interaction plays an essential role in the binding energy of the KKK¯ system and reports the mass of 1461.8 or 1464.1 MeV for the neutral K 0(1460) and 1466.5 or 1468.8 MeV for the charged K +(1460) resonances, respectively, depending on the parameter sets for KK and KK¯ interactions.

QCD-based charge symmetry breaking interaction and the Okamoto-Nolen-Schiffer anomaly

QCD-based charge symmetry breaking interaction and the Okamoto-Nolen-Schiffer anomaly

HYPERNUCLEI AND NEUTRON STARS WITH CHARGE SYMMETRY BREAKING HYPERONIC POTENTIAL

In this paper, we propose a method of taking charge symmetry breaking (CSB) in hypernuclei and neutron stars into account within the framework of the Hartree-Fock approach with Skyrme interaction. The parameters of the contribution of Λ𝑁-Skyrme force leading to CSB are derived from the corresponding parameters of the hyperon-nucleon interaction in the meson exchange models. Based on the obtained parameters, the effect of charge symmetry breaking on the hyperon binding energy in carbon hypernuclei is analyzed. The effect of charge symmetry breaking on the characteristics of neutron stars, such as their maximum mass and radii, is considered for the first time.

Impact of charge symmetry breaking on gluon and sea quark distributions in the pion and kaon

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the [Formula: see text] and [Formula: see text] quark-mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu–Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the charge symmetry (CS) gluon distribution for the pion has a good agreement with the prediction results obtained from the recent lattice QCD simulation and JAM global fit QCD analysis at a higher scale of [Formula: see text][Formula: see text]GeV2. The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of [Formula: see text] at [Formula: see text][Formula: see text]GeV2 are, respectively, estimated by 1.3% and 2.0% at [Formula: see text] in comparison with those for [Formula: see text], while those for the kaon are approximately about 0.3% and 0.5% at [Formula: see text], respectively. A remarkable result is found that the CSB effects on gluon distribution for the kaon are smaller than that for the pion, which has a similar prediction result as that for the CS case.

Effects of Coulomb and isospin symmetry breaking interactions on neutron-skin thickness

Both the Coulomb interaction and isospin symmetry breaking (ISB) parts of the nuclear interaction break the isospin symmetry in atomic nuclei. Effects of these two kinds of interaction on properties of atomic nuclei, especially, the mass difference of mirror nuclei and the neutron-skin thickness of $ N = Z $ and $ N \ne Z $ nuclei, are discussed. It is found that corrections to the Hartree-Fock-Slater approximation for the Coulomb interaction negligibly affect the neutron-skin thickness, while the charge-symmetry breaking term originating from the strong interaction might affect it non-negligibly. According to our calculations, the ISB terms other than the Coulomb interaction affect the estimation of the density dependence of the symmetry energy, $ L $, by about $ 0 $--$ 12 \, \mathrm{MeV} $ using the correlation with the neutron-skin thickness.

Coulomb-free 1S0p − p scattering length from the quasi-free p + d → p + p + n reaction and its relation to universality

The Coulomb-free 1S0 proton-proton (p-p) scattering length relies heavily on numerous and distinct theoretical techniques to remove the Coulomb contribution. Here, it has been determined from the half-off-the-energy-shell p-p scattering cross section measured at center-of-mass energies below 1 MeV using the quasi-free p + d → p + p + n reaction. A Bayesian data-fitting approach using the expression of the s-wave nucleon-nucleon scattering cross section returned a p-p scattering length {a}_{pp}=-18.1{7}_{-0.58}^{+0.52}{| }_{stat}pm 0.0{1}_{syst} fm and effective range r0 = 2.80 ± 0.05stat ± 0.001syst fm. A model based on universality concepts has been developed to interpret this result. It accounts for the short-range interaction as a whole, nuclear and residual electromagnetic, according to what the s-wave phase-shift δ does in the description of low-energy nucleon-nucleon scattering data. We conclude that our parameters are representative of the short-range physics and propose to assess the charge symmetry breaking of the short-range interaction instead of just the nuclear interaction. This is consistent with the current understanding that the charge dependence of nuclear forces is due to different masses of up-down quarks and their electromagnetic interactions. This achievement suggests that these properties have a lesser than expected impact in the context of the charge symmetry breaking.

Ab initio calculation of charge-symmetry breaking in A=7 and 8 Λ hypernuclei

The separation energies of the isospin triplet $^7_\Lambda\mathrm{He}$, $^7_\Lambda \mathrm{Li^{*}}$, $^7_\Lambda$Be, and the $T=1/2$ doublet $^8_\Lambda$Li, $^8_\Lambda$Be are investigated within the no-core shell model. Calculations are performed based on a hyperon-nucleon potential derived from chiral effective field theory at next-to-leading order. The potential includes the leading charge-symmetry breaking (CSB) interaction in the $\Lambda $N channel, whose strength has been fixed to the experimentally known difference of the $\Lambda$ separation energies of the mirror hypernuclei $^4_\Lambda \mathrm{He}$ and $^4_\Lambda \mathrm{H}$. It turns out that the CSB predicted for the $A=7$ systems is small and agrees with the splittings deduced from the empirical binding energies within the experimental uncertainty. In case of the $A=8$ doublet, the computed CSB is somewhat larger than the available experimental value. Using other experimental input for $A=4$ can change this prediction moving it closer to experiment.

Bayesian estimation of the low-energy constants up to fourth order in the nucleon-nucleon sector of chiral effective field theory

We use Bayesian methods and Hamiltonian Monte Carlo (HMC) sampling to infer the posterior probability density function (PDF) for the low-energy constants (LECs) up to next-to-next-to-next-to-leading order (N3LO) in a chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) description of the nucleon-nucleon interaction. In a first step, we condition the inference on neutron-proton and proton-proton scattering data and account for uncorrelated $\ensuremath{\chi}\mathrm{EFT}$ truncation errors. We demonstrate how to successfully sample the 31-dimensional space of LECs at N3LO using a revised HMC inference protocol. In a second step we extend the analysis by means of importance sampling and an empirical determination of the neutron-neutron scattering length to infer the posterior PDF for the leading charge-dependent contact LEC in the $^{1}S_{0}$ neutron-neutron interaction channel. While doing so we account for the $\ensuremath{\chi}\mathrm{EFT}$ truncation error via a conjugate prior. We use the resulting posterior PDF to sample the posterior predictive distributions for the effective range parameters in the $^{1}S_{0}$ wave as well as the strengths of charge-symmetry breaking and charge-independence breaking. We conclude that empirical point-estimate results of isospin breaking in the $^{1}S_{0}$ channel are consistent with the PDFs obtained in our Bayesian analysis and that, when accounting for $\ensuremath{\chi}\mathrm{EFT}$ truncation errors, one must go to next-to-next-to-leading order to confidently detect isospin breaking effects.

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles.

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion MonteCarlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Charge-symmetry-breaking effects on neutron β decay in nonrelativistic quark models

A formalism for the study of charge-symmetry-breaking (CSB) effects is discussed and used to analyze the effects of charge-symmetry breaking on neutron $\ensuremath{\beta}$ decay. The effect of including CSB reduces the $\ensuremath{\beta}$-decay matrix element by an amount on the order of ${10}^{\ensuremath{-}4}$, a value much larger than the previous estimate. The earlier calculation used the neutron-proton mass difference as the CSB operator instead of the matrix element of the sum of the individual terms between the ground and excited states. The electromagnetic and dynamic effects of the up-down quark mass difference oppose the up-down quark mass difference leading to a small $n\ensuremath{-}p$ mass difference, but add coherently in computing the excitation matrix elements causing large enhancements. The current uncertainty in the value of ${V}_{ud}$ is also on the order of ${10}^{\ensuremath{-}4}$. An improvement of that uncertainty by an order of magnitude would require that charge-symmetry-breaking effects should be included in future analyses.

K−d→πΛN reaction for studying charge symmetry breaking in the ΛN interaction

We propose to utilize the ${K}^{\ensuremath{-}}d\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}p$ and ${K}^{\ensuremath{-}}d\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\mathrm{\ensuremath{\Lambda}}n$ reactions in order to investigate the difference between the low-energy $\mathrm{\ensuremath{\Lambda}}p$ and $\mathrm{\ensuremath{\Lambda}}n$ interactions. In these reactions, the $\mathrm{\ensuremath{\Lambda}}p$ and $\mathrm{\ensuremath{\Lambda}}n$ scatterings appear as final state interactions. We calculate the differential cross sections of these reactions with stopped kaons theoretically. We introduce isospin breaking by using the physical masses for the participating hadrons and through the chiral unitary amplitudes for ${K}^{\ensuremath{-}}N\ensuremath{\rightarrow}\ensuremath{\pi}N$ and ${K}^{\ensuremath{-}}N\ensuremath{\rightarrow}\overline{K}N$. With stopped kaons, the $\mathrm{\ensuremath{\Lambda}}N$ interaction takes place dominantly in the spin-triplet state thanks to the deuteron spin and $s$-wave dominance of the scattering amplitudes at low energy. We find that the ratio of the $\mathrm{\ensuremath{\Lambda}}N$ invariant mass spectra of these reactions is useful for revealing qualitative properties of charge symmetry breaking in the low-energy $\mathrm{\ensuremath{\Lambda}}N$ interaction. We also find that the contributions coming from the $\ensuremath{\pi}$ and $\mathrm{\ensuremath{\Sigma}}$ exchange diagrams which have $\ensuremath{\pi}N$ final state interaction and $\mathrm{\ensuremath{\Sigma}}N\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}N$ conversion, respectively, are negligibly small around the $\mathrm{\ensuremath{\Lambda}}N$ threshold, while the contributions from the impulse diagram without final state interactions and the $\overline{K}$ exchange diagram containing the $\ensuremath{\pi}\mathrm{\ensuremath{\Lambda}}$ final state interaction are main sources of the background.

In-medium Λ isospin impurity from charge symmetry breaking in the Λ4H−Λ4He mirror hypernuclei

The $\Lambda$ separation energies in the mirror hypernuclei ${_{\Lambda}^4}{\rm H}-{_{\Lambda}^4}{\rm He}$ exhibit large charge symmetry breaking (CSB). Analyzing this CSB within pionless effective field theory while using partially conserved baryon-baryon SU(3) flavor symmetry, we deduce a $\Lambda -\Sigma^0$ induced in-medium admixture amplitude ${\cal A}_{I=1}\approx 1.5\%$ in the dominantly isospin $I=0$ $\Lambda$ hyperon. Our results confirm the free-space value ${\cal A}^{(0)}_{I=1}$ inferred directly within the SU(3) baryon octet by Dalitz and von-Hippel in 1964 and reaffirmed in a recent QCD+QED lattice calculation. Furthermore, exploring the consequences of SU(3) flavor symmetry on the $\Lambda$-nucleon interaction, we find that CSB is expected to impact the $S=1$ and $S=0$ spin channels in opposite directions, with the latter dominating by an order of magnitude. These observations explain a recent deduction of $\Lambda$-nucleon CSB strengths.

Measurement of [formula omitted] and [formula omitted] binding energy in Au+Au collisions at [formula omitted] = 3 GeV

Measurements of mass and Λ binding energy of Λ4H and Λ4He in Au+Au collisions at sNN=3 GeV are presented, with an aim to address the charge symmetry breaking (CSB) problem in hypernuclei systems with atomic number A = 4. The Λ binding energies are measured to be 2.22±0.06(stat.)±0.14(syst.) MeV and 2.38±0.13(stat.)±0.12(syst.) MeV for Λ4H and Λ4He, respectively. The measured Λ binding-energy difference is 0.16±0.14(stat.)±0.10(syst.) MeV for ground states. Combined with the γ-ray transition energies, the binding-energy difference for excited states is −0.16±0.14(stat.)±0.10(syst.) MeV, which is negative and comparable to the value of the ground states within uncertainties. These new measurements on the Λ binding-energy difference in A = 4 hypernuclei systems are consistent with the theoretical calculations that result in ΔBΛ4(1exc+)≈−ΔBΛ4(0g.s.+)<0 and present a new method for the study of CSB effect using relativistic heavy-ion collisions.

Hypernuclei based on chiral interactions

We present Λ separation energies for light hypernuclei based on chiral hyperon-nucleon interactions up to next-to-leading order. In the first part, we consider several sources of uncertainties with a focus on using different realizations of chiral hyperon-nucleon interactions to estimate three-baryon forces that enter at next-to-next-to leading order. We also demonstrate that the similarity renormalization group evolution of the hyperon-nucleon interactions induces a strong variation of the separation energies. The energies are however strongly correlated which allows one to define a preferred similarity renormalization group parameter for which hypernuclear binding energies can be predicted reliably. With these insights, we present in the second part three examples of recent applications of chiral interactions to hypernuclei. In the first application, we study the predictions for A = 4 and A = 7 hypernuclei based on the version of the hyperonnucleon interaction that yields a large hypertriton binding energy as suggested by the recent experiment of the STAR collaboration. The first predictions for A = 4 − 6 strangeness S = −2 hypernuclei are discussed in the second application. Finally, in the third application, we use the charge-symmetry breaking of A = 4 Λ separation energies to constrain the Λ-neutron interaction.

Radial overlap correction to superallowed 0+→0+ nuclear β decays using the shell model with Hartree-Fock radial wave functions

The radial overlap correction ${\ensuremath{\delta}}_{\mathrm{RO}}$ is reexamined for 30 superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ nuclear $\ensuremath{\beta}$ decays using the shell model with Hartree-Fock (HF) radial wave functions. Our mean-field calculation is based on the effective Skyrme interaction including Coulomb, charge-symmetry-breaking (CSB), and charge-independence-breaking (CIB) terms. In addition, the electromagnetic corrections such as those due to the gradient of charge density, vacuum polarization, Coulomb spin orbit, and finite size of nucleons are also considered. In order to avoid the spurious isospin mixing, the local equivalent potential is constructed from the solution of a HF calculation for the $Z=N$ nucleus with charge-dependent forces neglected. Then the obtained mean field is solved noniteratively for the parent and daughter nuclei. It turns out that the CIB term has no significant impact on ${\ensuremath{\delta}}_{\mathrm{RO}}$ throughout the mass range between 10 and 74. On the other hand, the CSB term makes ${\ensuremath{\delta}}_{\mathrm{RO}}$ increase systematically between 10% and 30%. Similarly, the gradient density leads to a further increase of ${\ensuremath{\delta}}_{\mathrm{RO}}$ between 2% and 14%, while other estimated electromagnetic corrections are negligible. The effect of the suppression of isospin spuriosity is somewhat complicated. In general, it produces a significantly larger value of ${\ensuremath{\delta}}_{\mathrm{RO}}$; however, there are a few cases for which ${\ensuremath{\delta}}_{\mathrm{RO}}$ is mostly unaffected or even reduced, especially the even-even emitters in the light mass region. All these improvements partly explain the long-standing discrepancy between the correction values obtained with Woods-Saxon (WS) and HF radial wave functions. Nevertheless, the remaining discrepancy is still significant, except for the emitters with $A\ensuremath{\le}26$. In addition, the local odd-even staggering present in the results obtained with the phenomenological potential [J. C. Hardy and I. S. Towner, Phys. Rev. C 102, 045501 (2020); L. Xayavong and N. A. Smirnova, Phys. Rev. C 97, 024324 (2018)] is not well reproduced by our calculations. This subsequently leads to a large difference in the predicted mirror $ft$ ratios. These problems might relate to the errors of the calculated charge radii as well as the deformation and other correlation effects on the data of separation energies used for constraining the asymptotic radial wave functions.

Isovector density and isospin impurity in 40Ca

We study isoscalar (IS) and isovector (IV) densities in Ca40 in comparison with theoretical densities calculated by Skyrme Hatree-Fock (HF) models. The charge symmetry breaking and the charge independence breaking forces are introduced to study the effect on the IV density. The effect of isospin mixing in the ground-state density is examined by using the particle-vibration coupling model taking into account the collective IV giant monopole excitation. We show a clear correlations in the IV density and isospin impurity of Ca40 within the HF and the particle-vibration coupling model. We extract for the first time the experimental information of isospin impurity from the magnitude of IV density.

Hunting for Direct CP Violation in B ¯ s 0 ⟶ π + π − K ∗ 0

In perturbative QCD approach, based on the first order of isospin symmetry breaking, we study the direct CP violation in the decay of B ¯ s 0 ⟶ ρ ω K ∗ 0 ⟶ π + π − K ∗ 0 . An interesting mechanism is applied to enlarge the C P violating asymmetry involving the charge symmetry breaking between ρ and ω . We find that the CP violation is large by the ρ − ω mixing mechanism when the invariant masses of the π + π − pairs are in the vicinity of the ω resonance. For the decay process of B ¯ s 0 ⟶ ρ ω K ∗ 0 ⟶ π + π − K ∗ 0 , the maximum CP violation can reach − 59.12 % . Furthermore, taking ρ − ω mixing into account, we calculate the branching ratio for B ¯ s 0 ⟶ ρ ω K ∗ 0 . We also discuss the possibility of observing the predicted C P violation asymmetry at the LHC.

Toward ab initio charge symmetry breaking in nuclear energy density functionals

We propose a new approach to determine the strength of the charge symmetry breaking (CSB) term in the framework of nuclear density functional theory. It is shown that once ab initio calculations are available including accurate description of isospin symmetry breaking terms in medium and heavy nuclei, the mass difference of mirror nuclei as well as the neutron-skin thickness of doubly-closed-shell nuclei can be used to constrain the strength of the CSB interaction with an uncertainty less than 6%, separately from other isospin symmetry breaking forces. This method opens a new vista of ab initio nuclear energy density functionals.

Recent progress on few-body hypernuclei

Few-body Λ hypernuclei provide valuable information towards understanding strange matter. Recent experimental progress by the STAR Collaboration at the RHIC facility and by the ALICE Collaboration at the LHC has been matched by theoretical progress reviewed here: (i) lifetimes of the hypertritonΛ3H,Λ3n if particle-stable,Λ4H andΛ4He and their charge symmetry breaking, and (ii) the onset of ΛΛ hypernuclear binding.

Hypernuclear gamma-ray spectroscopy: summary and future prospect

The present status and prospects of hypernuclear γ-ray spectroscopy are summarized. In particular, 4-body hypernuclear γ-ray spectroscopy, the recent result of 4ΛHe and the future plan of 4ΛH and charge symmetry breaking in the ΛN interaction are presented. In addition, future plans to measure the Λ-spin-flip B(M1) values of 7Λ(3/2+ → 1/2+) and 12ΛC(2− → 1−) transitions are introduced. They aim to study the g-factor of Λ in the nuclear medium.