Isospin Symmetry Breaking Research Articles

Single flavour optimisations to Hybrid Monte Carlo

It has become increasingly important to include one or more individual flavours of dynamical fermion in lattice QCD simulations. This is due in part to the advent of QCD+QED calculations, where isospin symmetry breaking means that the up, down, and strange quarks must be treated separately. These single-flavour pseudofermions are typically implemented as rational approximations to the inverse of the fermion matrix, using the technique known as Rational Hybrid Monte Carlo (RHMC). Over the years, a wide range of methods have been developed for accelerating simulations of two degenerate flavours of pseudofermion, while there are comparatively fewer such techniques for single-flavour pseudofermions. Here, we investigate two different filtering methods that can be applied to RHMC for simulating single-flavour pseudofermions, namely polynomial filtering (PF-RHMC), and filtering via truncations of the ordered product (tRHMC). A novel integration step-size tuning technique based on the characteristic scale is also introduced. Studies are performed on two different lattice volumes, demonstrating that one can achieve significant reductions in the computational cost of single-flavour simulations with these filtering techniques.

Isospin-symmetry breaking corrections for the description of triplet energy differences

The charge-independence breaking of the nuclear interaction is analyzed by means of energy differences among analog states in $T=1$ isobaric multiplets. Data on triplet energy differences in the $sd, pf$, and $pfg$ shells, i.e., $18\ensuremath{\le}A\ensuremath{\le}66$, are reproduced with very good accuracy by large-scale shell-model calculations taking into account, aside from the Coulomb interaction, a single isotensor schematic interaction of monopole-pairing type. It is shown that the effect on the triplet energy differences of this isospin-breaking interaction is of the same magnitude as the Coulomb one. Moreover, its strength is the same for every single-particle orbital of the considered model space.

Nuclear Symmetry Energy and the Breaking of the Isospin Symmetry: How Do They Reconcile with Each Other?

We analyze and propose a solution to the apparent inconsistency between our current knowledge of the equation of state of asymmetric nuclear matter, the energy of the isobaric analog state (IAS) in a heavy nucleus such as ^{208}Pb, and the isospin symmetry breaking forces in the nuclear medium. This is achieved by performing state-of-the-art Hartree-Fock plus random phase approximation calculations of the IAS that include all isospin symmetry breaking contributions. To this aim, we propose a new effective interaction that is successful in reproducing the IAS excitation energy without compromising other properties of finite nuclei.

Electromagnetic transition form factors of baryons in the space-like momentum region

We present results from a calculation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only $\Sigma^0$ to $\Lambda$ transition. We work in the combined framework of Dyson-Schwinger equations and covariant Bethe-Salpeter equations with all elements, the baryon three body wave function, the quark propagators and the dressed quark-photon vertex determined from a well-established, momentum dependent approximation for the quark-gluon interaction. We discuss in particular the similarities among the different transitions as well as the differences induced by SU(3)-isospin symmetry breaking. We furthermore provide estimates for the slopes of the electric and magnetic $\Sigma^0$ to $\Lambda$ transitions at the zero photon momentum point.

Investigation of the isovector giant dipole resonance in excited nuclei

The present manuscript shows the importance of studying the isovector giant dipole resonance (IVGDR) to obtain information about the isospin-symmetry breaking and the shape evolution in excited nuclei. The $\gamma$ decay of the IVGDR was measured in the compound nuclei 80Zr and 81Rb formed at an excitation energy of $E^{\ast} = 54$ MeV and $ \langle J \rangle \approx 20\hbar$ . The reactions 40Ca+40Ca( $E_{beam} = 136$ MeV) and 37Cl+44Ca( $E_{beam} = 95$ MeV) were used to form the nuclei 80Zr and 81Rb, respectively. The experimental setup used for the $\gamma$ -rays detection was composed by the AGATA Demonstrator array coupled with large volume LaBr3:Ce detectors of the HECTOR+ array.

Isospin-symmetry breaking in masses of N ≃ Z nuclei

Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the N=Z line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton–neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the T=12 doublets and T=1 triplets, and TDEs for the T=1 triplets. Relative strengths of the obtained isospin-symmetry-breaking terms are not consistent with the differences in the NN scattering lengths, ann, app, and anp. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.

Pion properties at finite isospin chemical potential with isospin symmetry breaking**Supported by National Natural Science Foundation of China (11175088, 11475085, 11535005, 11690030) and the Fundamental Research Funds for the Central Universities (020414380074)

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI<0 and μI>0 in the phase diagram, and different values for the charged pion mass (or decay constant) and neutral pion mass (or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.

High-precision QEC -value measurement of the superallowed β+ emitter Mg22 and an ab initio evaluation of the A=22 isobaric triplet

A direct $Q_{EC}$-value measurement of the superallowed $\beta^+$ emitter $^{22}$Mg was performed using TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The direct ground-state to ground-state atomic mass difference between $^{22}$Mg and $^{22}$Na was determined to be $Q_{EC}=4781.40(22)$~keV, representing the most precise single measurement of this quantity to date. In a continued push towards calculating superallowed isospin-symmetry-breaking (ISB) corrections from first principles, ab-initio shell-model calculations of the $A=22$ IMME are also presented for the first time using the valence-space in-medium similarity renormalization group formalism. With particular starting two- and three-nucleon forces, this approach demonstrates a level of agreement with the experimental data that suggests reliable ab-initio calculations of superallowed ISB corrections are now possible.

Isospin-symmetry breaking in superallowed Fermi β-decay due to isospin-nonconserving forces

We investigate isospin-symmetry breaking effects in the sd-shell region with large-scale shell-model calculations, aiming to understand the recent anomalies observed in superallowed Fermi β-decay. We begin with calculations of Coulomb displacement energies (CDE's) and triplet displacement energies (TDE's) by adding the T=1,J=0 isospin nonconserving (INC) interaction into the usual isospin-invariant Hamiltonian. It is found that CDE's and TDE's can be systematically described with high accuracy. A total number of 122 one- and two-proton separation energies are predicted accordingly, and locations of the proton drip-line and candidates for proton-emitters are thereby suggested. However, attempt to explain the anomalies in the superallowed Fermi β-decay fails because these well-fitted T=1,J=0 INC interactions are found no effects on the nuclear matrix elements. It is demonstrated that the observed large isospin-breaking correction in the 32Cl β-decay, the large isospin-mixing in the 31Cl β-decay, and the small isospin-mixing in the 23Al β-decay can be consistently understood by introducing additional T=1,J=2 INC interactions related to the s1/2 orbit.

Low-lying baryon masses using Nf=2 twisted mass clover-improved fermions directly at the physical pion mass

The masses of the low-lying baryons are evaluated using an ensemble with two degenerate light twisted mass clover-improved quarks with mass tuned to reproduce the physical pion mass. The Iwasaki improved gluonic action is employed. The coupling constant value corresponds to a lattice spacing of $a=0.0938(3)(2)$ fm, determined from the nucleon mass. We find that the clover term supresses isospin symmetry breaking as compared to our previous results using $N_f=2+1+1$ twisted mass fermions. The masses of the hyperons and charmed baryons evaluated using this ensemble are in agreement with the experimental values. We provide predictions for the mass of the doubly charmed $\Xi_{cc}^*$, as well as of the doubly and triply charmed $\Omega$s that have not yet been determined experimentally.

τ−→η(′)π−ντγdecays as background in the search for second class currents

Observation of ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ decays at Belle-II would indicate either a manifestation of isospin symmetry breaking or genuine second class current (SCC) effects. The corresponding radiative ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}\ensuremath{\gamma}$ decay channels are not suppressed by $G$-parity considerations and may represent a serious background in searches of SCCs in the former. We compute the observables associated to these radiative decays using resonance chiral Lagrangians and conclude that vetoing photons with ${E}_{\ensuremath{\gamma}}&gt;100\text{ }\text{ }\mathrm{MeV}$ should get rid of this background in the Belle-II environment while searching for the ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ channel. Similar considerations hold inconclusive for decays involving the ${\ensuremath{\eta}}^{\ensuremath{'}}$, given the theory's uncertainties in the prediction of the ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ branching ratio. Still, additional kinematics-based cuts should be able to suppress this background in the ${\ensuremath{\eta}}^{\ensuremath{'}}$ case to a negligible level.

Isospin Symmetry Breaking in Mirror Nuclei $^{23}$Mg--$^{23}$Na

Mirror energy differences (MED) are a direct consequence of isospin symmetry breaking. Moreover, the study of MED has proved to give valuable information of several nuclear structure properties. We ...

Shell-model Calculation of Isospin-symmetry Breaking Correction to Superallowed Fermi beta Decay

We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed $0^+\to 0^+$-decay using the shell-model approach similar to that of Refs. [1, 2]. The 8 sd-shell emitters with masses between $A=22$ and $A=38$ have been re-examined. The Fermi matrix element is evaluated with realistic spherical single-particle wave functions, obtained from spherical Woods-Saxon (WS) or Hartree-Fock (HF) potentials, fine-tuned to reproduce the experimental data on charge radii and separation energies for nuclei of interest. The elaborated adjustment procedure removes any sensitivity of the correction to a specific parametrisation of the WS potential or to various versions of the Skyrme interaction. The present results are generally in good agreement with those reported in Refs. [3, 4]. At the same time, we find that the calculations with HF wave functions result in systematically lower values of the correction.

Phenomenological implications of a predictive formulation of the Nambu–Jona-Lasinio model having tensor couplings and isospin symmetry breaking terms

In the present work we consider the phenomenological consequences of a predictive formulation of the Nambu\char21{}Jona-Lasinio (NJL) model at the one loop level of perturbative calculations. The investigation reported here can be considered as an extension of previously made ones on the same issue. In the study made in this work we have included vector and tensor couplings, simultaneously, as well as $SU(2)$ isospin symmetry breaking terms. As a consequence of the last ingredient mentioned, there are different masses in the model amplitudes. In spite of this, within the context of the adopted procedure, we verify that it is possible to eliminate unphysical dependencies on the arbitrary choices for the routing of internal lines momenta as well as Ward identities violating contributions and scale ambiguous terms, from the corresponding one loop amplitudes, through the simple and universal Consistency Relations. The total content of divergence of the amplitudes is reduced to only two basic divergent objects. They are related to two inputs of the model in a way that, due to their scale properties, an unique arbitrariness remains. However, due to the critical condition found in the mechanism which generates the constituent quark mass, within our approach, this arbitrariness is also removed turning the model predictive in the sense that its phenomenological consequences is not dependent in possible choices made in intermediary steps of the calculations, as occurs in usual treatments. In this scenario, we investigate the most typical static properties of the scalar, pseudoscalar, vector and axial-vector mesons at low-energy. Special attention is given to the consequences of the $SU(2)$ isospin symmetry breaking for the phenomenological predictions. The implications of the tensor couplings for the model observables, which can be considered an original contribution of the present work, at the level of the content and not only in the form, is analyzed in a detailed way. The found values are in good accordance with the expectations and are globally consistent, having the obvious advantage that the predictions are not dependent in parameters aliens to the model Lagrangian as occurs in traditional approaches based in regularizations.

π0−η−η′mixing in a generalized multiquark interaction scheme

We investigate the isospin symmetry breaking effects within a recently derived Nambu-Jona-Lasinio related model by fitting the measured pseudoscalar meson masses and weak decay couplings $f_\pi$, $f_K$. Our model contains the next to leading order terms in the $1/N_c$ expansion of the effective multi-quark Lagrangian, including the ones that break the chiral symmetry explicitly. We show the important phenomenological role of these interactions: (1) they lead to an accurate fit of the low-lying pseudoscalar nonet characteristics; (2) they account for a very good agreement of the current quark masses with the present PDG values; (3) they reduce by $40\%$ the ratio $\epsilon/\epsilon'$ of the $\pi_0-\eta$ and $\pi_0-\eta'$ mixing angles, as compared to the case that contemplates explicit breaking only in the leading order, bringing it in consonance with the quoted values in the literature. The conventional NJL-type models fail in the joint description of these parameters.

Kondo effect in charm and bottom nuclei

We discuss the Kondo effect for isospin-exchange interaction between a $\bar{D}$, $B$ meson and a valence nucleon in charm/bottom atomic nuclei including the discrete energy-levels for valence nucleons. To investigate the binding energy by the Kondo effect, we introduce the mean-field approach for the bound state of the $\bar{D}$, $B$ meson in charm/bottom nuclei. Assuming a simple model, we examine the validity of the mean-field approximation by comparing the results with the exact solutions. We also estimate the effect of the quantum fluctuation beyond the mean-field approximation. We discuss the competition between the Kondo effect and the other correlations in valence nucleon, the isospin symmetry breaking and the nucleon pairings.

Isospin-symmetry breaking and shape coexistence in A∼70 analogs

Properties of proton-rich nuclei in the A∼70 region could bring insights into fundamental symmetries and interactions and may have relevance for the astrophysical scenarios on the rp-process path. Recent results concerning the interplay between isospin-symmetrybreaking and shape-coexistence effects on isospin-related phenomena in A=70 and A=74 isovector triplets obtained within the beyond-mean-field complex Excited Vampir variational model using an effective interaction obtained from a G-matrix based on the charge-dependent Bonn CD potential in a relatively large model space are presented.

Detailed study of Ke4 decay properties by the NA48/2 experiment at CERN

A sample of 1.13 million Ke4+−(K±→π+π−e±ν) decays and 65210Ke400(K±→π0π0e±ν) decays has been collected in 2003–2004 by the NA48/2 collaboration at the CERN SPS. Branching ratio and form factors in the S- and P-wave have been measured at a percent level precision. The comparison of Branching ratio and form factor values in both modes sheds new light on isospin symmetry breaking effects. Form factor measurements are major inputs to the study of low energy QCD and bring stringent tests of Chiral Perturbation Theory predictions.

Theoretical corrections and world data for the superallowedftvalues in theβdecays ofTi42,Cr46,Fe50, andNi54

Prompted by recent measurements, we have surveyed world data and calculated radiative and isospin-symmetry breaking corrections for the superallowed 0+ -to- 0+ Fermi transitions from 42Ti, 46Cr, 50Fe and 54Ni. This increases the number of such transition with a complete set of calculated corrections from 20 to 23. The results are compared with their equivalents for the mirror superallowed transitions from 42Sc, 46V, 50Mn and 54Co. The predicted ft-value asymmetries of these mirror pairs are sensitive to the correction terms and provide motivation for improving measurement precision so as to be able to test the corrections. To aid in that endeavor, we present a parameterization for calculating the f values for the new transitions to plus/minus 0.01%.

Probing isospin-symmetry breaking with the modern storage rings and other advanced facilities

The Lanzhou storage ring has demonstrated its power in the experimental determination of heavier neutron-deficient masses, which has motivated theoretical discussions of isospin-symmetry breaking in the fp-shell mass regions and beyond. We summarize the recent theoretical studies of displacement energies and other related quantities within the framework of nuclear shell model. We emphasize the importance of the isospin non-conserving nuclear interactions for the upper fp shell nuclei.