Isospin Symmetry Breaking Research Articles

D * s0(2317) and B*s0 as Molecular States

Abstract We investigate the dynamical generation of the $D_{s0}^{*}(2317)$ and $B_{s0}^{*}$ mesons using a meson-exchange model with a coupled-channel formalism. Our primary focus is on the $D_s^+\pi ^0$ channel below the $DK$ threshold. First, we construct the invariant kernel amplitudes, incorporating effective Lagrangians based on heavy-quark symmetry, flavor SU(3) symmetry, and hidden local symmetry. Since the $D_{s0}^{*}(2317)$ state implies isospin symmetry breaking, we introduce $\pi ^0\!-\!\eta$ isospin mixing. We subsequently solve the coupled-channel integral equations, which include four different channels, i.e. $D_s^+\pi ^0$, $D^0 K^+$, $D^+ K^0$, and $D_s^+\eta$. We carefully analyze how the pole corresponding to the $D_{s0}^{*}(2317)$ state emerges from the coupled channels. Our findings reveal that the pole positions of the $D_{s0}^{*}(2317)$ meson are at $\sqrt{s_R}=(2317.9 - i 0.0593)$ MeV and those of the $\bar{B}_{s0}^{*}$ meson are at $(5756.43-i0.0215)$ MeV, respectively. We also discuss their decay widths and destructive interference of the two sources. In conclusion, our current results provide a clear indication supporting the interpretation of the $D_{s0}^{*}(2317)$ meson as a $DK$ molecular state within the present coupled-channel formalism. In addition, we discuss the possible existence of $\bar{B}_{s0}^{*}$.

Isospin Symmetry Breaking in Atomic Nuclei

In this paper, the importance of isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for the nuclear many-body problem is discussed. The experimental data on isobaric analogue states cannot be described only with the Coulomb interaction, and ISB terms in the nucleon–nucleon interaction are needed to discern the observed properties. In the present work, the ISB terms are explicitly considered in nuclear energy density functional and spherical shell model approaches, and a detailed investigation of the analogue states and other properties of nuclei is performed. It is observed that isospin mixing is largest for the N = Z system in the density functional approach

Phenomenology of isospin-symmetry breaking with vector mesons

We study the effect of isospin-symmetry breaking in the framework of the extended linear σ model in vacuum. In this model, several particles mix with each other at tree level, due to the three nonzero scalar condensates (nonstrange, strange, isospin). We resolve these mixings with the help of various field transformations. We compute all possible meson mixings and decay widths at tree level and perform a χ2 fit to PDG data. A very good fit is found if we exclude the (very small ∼130 keV) ω→ππ decay. We also investigate the violation of Dashen’s theorem. Published by the American Physical Society 2024

Quark mass difference effects in hadronic Fermi matrix elements from first principles

It was recently estimated that the strong isospin-symmetry breaking (ISB) corrections to the Fermi matrix element in free neutron decay could be of the order 10−4, one order of magnitude larger than the naïve estimate based on the Behrends-Sirlin-Ademollo-Gatto theorem. To investigate this claim, we derive a general expression of the leading ISB correction to hadronic Fermi matrix elements, which takes the form of a four-point correlation function in lattice gauge theory and is straightforward to compute from first principles. Our formalism paves the way for the first determination of such correction in the neutron sector with fully-controlled theory uncertainties.

Rethinking the Pc(4457)+ as the [formula omitted] isoquartet [formula omitted] molecule

The nature of the Pc(4312), Pc(4440) and Pc(4457) pentaquarks is a fascinating theoretical question. Within the molecular picture their more usual interpretation is that of I=12D¯Σc and D¯⁎Σc bound states. Here we argue in favor of interpreting the Pc(4457) pentaquark as a I=32D¯⁎Σc bound state (with spin J=12) instead. Owing to isospin symmetry breaking effects, with this identification the partial decay width of the Pc(4457)+ into J/ψp will be of the same order of magnitude as the Pc(4312)+ and Pc(4440)+, in contrast with the considerably larger partial decay width in the I=12 scenario. In turn, this leads to a different hidden-charm molecular pentaquark spectrum, in which there are only four or five PψN bound states instead of the usual seven, which might explain why the predicted J=12 and 32 (I=12) D¯⁎Σc⁎ molecular partners of the Pc(4312) and Pc(4440) have not been observed.

Search for Weak Side Branches in the Electromagnetic Decay Paths of the 6526-keV 10+ Isomer in 54Fe

High-spin nuclear isomers in N≈Z nuclei between doubly magic 40Ca and 56Ni provide an excellent testing ground for the nuclear shell model and questions related to isospin symmetry breaking in the vicinity of the proton drip line. The purpose of the present study is to investigate the possibility of weak electromagnetic decay branches along the decay paths of the 6526-keV 10+ isomer in 54Fe. The isomer was strongly populated by means of the fusion-evaporation reaction 24Mg(36Ar,α2p)54mFe. The Gammasphere array was used to detect γ-ray cascades emitted from the isomeric state. By means of γγγ coincidences, weak non-yrast decay branches can be discriminated, with the isomer’s half-life confirmed at T1/2=363(4) ns. The yrast 61+→21+ E4 cross-over transition was interrogated. The observations are compared with shell-model calculations.

Ab initio calculations of mirror energy difference in sd-shell nuclei* *Supported by the National Natural Science Foundation of China (12205340, 11975282); the Gansu Natural Science Foundation (22JR5RA123); the Special Research Assistant Project of the Chinese Academy of Sciences; the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000); the Key Research Program of the Chinese Academy of Sciences (XDPB15);

Mirror energy difference is a key observable in isospin symmetry breaking, containing rich information about nuclear structure. Understanding the mechanisms underlying mirror energy difference is important in nuclear physics. In the present work, we extensively investigated mirror energy difference using ab initio valence-space in-medium similarity renormalization group approach, focusing specifically on -shell nuclei. The low-lying spectra of Al isotopes and isotones, together with their mirror nuclei, were calculated, followed by a systematic analysis of the evolution of the mirror energy difference. The results suggest that the large mirror energy difference is mainly caused by the weakly-bound effects and large average occupations of the orbit. Lastly, we compare the results of our ab initio calculations with shell model results, elucidating the relationship and coherence between these two models.

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.

Analysis of localized CP asymmetry in {bar{B}}_{s}^{0} rightarrow pi ^+pi ^-pi ^{0}(K^{0})

An investigation about localized CP asymmetries for the processes of {bar{B}}_{s}^{0} rightarrow pi ^{+}pi ^{-}pi ^{0} (K^{0}) is presented in this paper. The innovation of this paper is that there is a consideration of three-particle rho ^0(770), omega (782) and phi (1020) interferences effect. Generally, omega (782) and phi (1020) both can decay into pi ^+pi ^- pair where can cause extremely small contribution from isospin symmetry breaking. Nevertheless, our analysis shows that {bar{B}}_{s}^{0} rightarrow pi ^+pi ^-pi ^{0}(K^{0}) decay process can bring differential CP asymmetry about 65% (36%) because of isospin symmetry breaking. To be better compared with the data from experimental in the future, we integrate CP asymmetry over the invariant mass and obtain localized CP asymmetry value for the decay {bar{B}}_{s}^{0} rightarrow pi ^+pi ^-pi ^{0} (K^{0}). We find that there is an evident signal about CP asymmetry at invariant mass value m(pi ^{+}pi ^{-}) below the mass of rho ^{0}(770) with the decay {bar{B}}_{s}^{0} rightarrow pi ^+pi ^{-}pi ^{0}.

Analysis of localized CP asymmetry in {bar{B}}_{s}^{0} rightarrow pi ^+pi ^-pi ^{0}(K^{0})

An investigation about localized CP asymmetries for the processes of {bar{B}}_{s}^{0} rightarrow pi ^{+}pi ^{-}pi ^{0} (K^{0}) is presented in this paper. The innovation of this paper is that there is a consideration of three-particle rho ^0(770), omega (782) and phi (1020) interferences effect. Generally, omega (782) and phi (1020) both can decay into pi ^+pi ^- pair where can cause extremely small contribution from isospin symmetry breaking. Nevertheless, our analysis shows that {bar{B}}_{s}^{0} rightarrow pi ^+pi ^-pi ^{0}(K^{0}) decay process can bring differential CP asymmetry about 65% (36%) because of isospin symmetry breaking. To be better compared with the data from experimental in the future, we integrate CP asymmetry over the invariant mass and obtain localized CP asymmetry value for the decay {bar{B}}_{s}^{0} rightarrow pi ^+pi ^-pi ^{0} (K^{0}). We find that there is an evident signal about CP asymmetry at invariant mass value m(pi ^{+}pi ^{-}) below the mass of rho ^{0}(770) with the decay {bar{B}}_{s}^{0} rightarrow pi ^+pi ^{-}pi ^{0}.

Mass spectra of neutral mesons K0,π0,η,η′ at finite magnetic field, temperature and quark chemical potential

The mass spectra of neutral mesons $K_0, \pi_0, \eta, \eta'$ on temperature-quark chemical potential $(T-\mu)$ plane in the presence of a constant magnetic field is investigated in the $SU(3)$ NJL model. As a Goldstone boson of chiral symmetry breaking, the mass of $K_0$ meson increases with temperature and/or quark chemical potential, and we observe two kinds of mass jumps of $K_0$ meson in media, which is induced by the mass jump of constituent quarks and the magnetic field, respectively. Due to the breaking of isospin symmetry between $u$ and $d$ quarks in magnetic fields, the mixing of $\pi_0-\eta- \eta'$ mesons occurs and this leads to rich structures of their mass spectra. For instance, $\pi_0$ mass is influenced by the strange quark. There appear the change of increase ratio of $\pi_0$ mass at high $\mu$ and vanishing $T$ and the $\pi_0$ mass jump crossing over the threshold of two times of strange quark mass at finite $T$ and $\mu$. The mass ordering of $\pi_0, \ \eta,\ \eta'$ mesons varies in media, due to their mass jumps, which are induced by the mass jump of constituent quarks or the magnetic field.

Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments

The paper reviews the recent progress in the description of isospin-symmetry breaking within the nuclear shell model and applications to actual problems related to the structure and decay of exotic neutron-deficient nuclei and nuclei along the N=Z line, where N is the neutron number and Z the atomic number. The review recalls the fundamentals of the isospin formalism for two-nucleon and many-nucleon systems, including quantum numbers, the spectrum’s structure and selection rules for weak and electromagnetic transitions; and at the end, summarizes experimental signatures of isospin-symmetry breaking effects, which motivated efforts towards the creation of a relevant theoretical framework to describe those phenomena. The main approaches to construct accurate isospin-nonconserving Hamiltonians within the shell model are briefly described and recent advances in the description of the structure and (isospin-forbidden) decay modes of neutron-deficient nuclei are highlighted. The paper reviews major implications of the developed theoretical tools to (i) the fundamental interaction studies on nuclear decays and (ii) the estimation of the rates of nuclear reactions that are important for nuclear astrophysics. The shell model is shown to be one of the most suitable approaches to describing isospin-symmetry breaking in nuclear states at low energies. Further efforts in extending and refining the description to larger model spaces, and in developing first-principle theories to deal with isospin-symmetry breaking in many-nucleon systems, seem to be indispensable steps towards our better understanding of nuclear properties in the precision era.

Direct CP violation in K → ππ decay on the lattice with periodic boundary conditions

Following our recent publication on direct CP violation and the ΔI = 1/2 rule in K → ππ decay, which was made with G-parity boundary conditions, we revisit this problem with a conventional lattice setup employing periodic boundary conditions and two lattice spacings to check our previous result and to improve the precision. We show that the physical amplitude, which corresponds to an excited state in this case, can be obtained reliably with the Generalized Eigenvalue Problem (GEVP) method. Not only are periodic boundary conditions cheaper and allow the use of existing ensembles to take the continuum limit, but they provide a straightforward path to introduce electromagnetism and strong isospin symmetry breaking, which will be needed in the near future. In this article we show our preliminary results and discuss the prospect of the high-precision calculation of K → ππ decay with periodic boundary conditions.

Medium modification of singly heavy baryons in a pion-mean-field approach

We investigate how the masses of singly heavy baryons undergo changes in nuclear matter. The mass spectrum of the singly heavy baryons was successfully described in a pion-mean field approach even with isospin symmetry breaking, based on which we extend the investigation to the medium modification of the singly heavy baryons. Since all dynamical parameters were determined by explaining the mass spectrum of the SU(3) light and singly heavy baryons in free space, we can directly implement the density-dependent functionals for the dynamical parameters, of which the density dependence was already fixed by reproducing the bulk properties of nuclear matter and medium modification of the SU(3) light baryons. We predict and discuss the density dependence of the masses of the singly heavy baryons.

Investigation of isospin-symmetry breaking in mirror energy difference and nuclear mass with ab initio calculations

Isospin-symmetry breaking is responsible for the energy difference of excited states in mirror nuclei. It also influences the coefficient of the isobaric multiplet mass equation. In the present work, we extensively investigate isospin-symmetry breaking in medium-mass nuclei within ab initio frameworks. For this, we employ the ab initio valence-space in-medium similarity renormalization group approach, in which charge-symmetry and charge-independence breakings are included in the adopted nuclear force. The mirror energies of $sd$- and $pf$-shell nuclei are computed for that matter. The effects of single-particle states on weakly bound and unbound nuclear states, especially those of the $s$ wave, are discussed. Predictions are also made concerning proton drip-line nuclei bearing large mirror energy difference. Finally, the coefficient of the isobaric multiplet mass equation in $T=1/2$ and $T=1$ isospin multiplets for $A=18$ to $A=76$ is calculated.

Electroweak nuclear radii constrain the isospin breaking correction to Vud

We lay out a novel formalism to connect the isospin-symmetry breaking correction to the rates of superallowed nuclear beta decays, δC, to the isospin-breaking sensitive combinations of electroweak nuclear radii that can be accessed experimentally. We individuate transitions in the superallowed decay chart where a measurement of the neutron skin of a stable daughter even at a moderate precision could already help discriminating between models used to compute δC. We review the existing experimental situation and make connection to the existing and future experimental programs.

Screening of the quark charge and mixing effects on transition moments and M1 decay widths of baryons

Motivated by the precision measurements of heavy flavor baryon masses, we analyze the modification of quark charge by employing the screening effect inside the baryon. In addition, we calculate the isospin mass splitting up to charmed baryons employing isospin symmetry breaking. Consequently, we obtain the masses, magnetic moments, and transition moments of $J^P=\frac{1}{2}^+$ and $\frac{3}{2}^+$ baryons to predict radiative decay widths for $\frac{1}{2}^{\prime +} \to \frac{1}{2}^+$ and $\frac{3}{2}^+\to \frac{1}{2}^{(\prime)+}$ transitions. Finally, we include the effects of state mixing in flavor degenerate baryon magnetic and transition moments, as well as M1 transition decay widths.

Isospin symmetry breaking in the charge radius difference of mirror nuclei

Isospin symmetry breaking (ISB) effects in the charge radius difference $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ of mirror nuclei are studied using the test example of $^{48}\mathrm{Ca}$ and $^{48}\mathrm{Ni}$. This choice allows for a transparent study of ISB contributions since pairing and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ with the nuclear equation of state and the effect of ISB on such a relation are discussed according to an energy density functional approach. We find that nuclear ISB effects may shift the estimated value for the symmetry energy slope parameter $L$ by about 6 to 14 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by ab initio calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron-skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the isobaric analog state energy.

Axial-vector transition form factors of the singly heavy baryons

We investigate the axial-vector transition form factors of the lowest-lying singly heavy baryons within the framework of the chiral quark-soliton model. We consider the linear ${m}_{\mathrm{s}}$ corrections, dealing with the strange current quark mass ${m}_{\mathrm{s}}$ as a small perturbation. Since we have various relations between different transitions because of isospin symmetry and flavor SU(3) symmetry breaking, only two axial-vector transition form factors are independent. We present the numerical results for these form factors. The effects of the flavor SU(3) symmetry breaking turn out tiny, so we neglect them. We also compute the decay rates for several strong decays of the singly heavy baryons and compare the results with the experimental data and those from other models. While the results for the ${\mathrm{\ensuremath{\Sigma}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}+\ensuremath{\pi}$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}+\ensuremath{\pi}$ decays are slightly overestimated in comparison with the corresponding experimental data, those for the ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}+\ensuremath{\pi}$ are in remarkable agreement with the data.

Direct CP violation of three body decay processes from the resonance effect* *Supported by National Natural Science Foundation of China (11605041)

The physical state of mesons can be mixed using the unitary matrix. The decay processes and originate from isospin symmetry breaking. The , , and interferences lead to a resonance contribution to produce strong phases. violation is considered from isospin symmetry breaking due to the new strong phase of the first order. violation can be enhanced greatly for the decay process when the invariant masses of pairs are in the area around the resonance range and resonance range in perturbative QCD. We also discuss the possibility of searching for the predicted violation at the LHC.