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39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 114 (2023). doi:10.22323/1.430.0114, We present results for the nucleon electromagnetic form factors using $N_f$=2+1+1 twisted mass lattice QCD with clover improvement and with quarks with masses tuned to their physical values. Our preliminary analysis includes three ensembles at similar physical volume and varying lattice spacing allowing us to take the continuum limit at the physical point. Both connected and disconnected contributions are evaluated, allowing us to take the isovector and isoscalar contributions as well as the individual proton and neutron form factors in the flavour isospin limit. For each ensemble we assess excited state effects using several sink-source time separations in the range 0.8 fm - 1.6 fm, exponentially increasing statistics with the separation., Published by SISSA, Trieste

We have achieved the isovector and isoscalar tensor form factors of the N ( 1535 ) state in the framework of the light-cone QCD sum rule approach. In numerical computations, we have considered the most general forms of the interpolating current for the nucleon and the tensor current together with the distribution amplitudes of the N ( 1535 ) resonance. We have shown that the squared momentum transfer, Q 2 , dependence of N ( 1535 ) tensor form factors is characterized by a multipole fit function. Our results provide a perspective of the momentum dependence of the tensor form factors and can help to improve our understanding of the internal structure of nucleon states.

The differential spectra of final particles in the reaction $$pn\to pp\pi^{-}$$ are presented according to data obtained at nine energy values with the aid of a deuterium-filled bubble chamber. These spectra are compared with the results of a partial-wave analysis of data obtained with a continuous neutron beam incident to a proton target. This analysis was used as basis for performing a global partial-wave analysis of data on proton–neutron, neutron–proton, and proton–proton collisions. As a result, it became possible to determine the contributions of both isovector and isoscalar partial waves to a precision substantially higher than that reached earlier.

Centroid energies, $$E_{\textrm{CEN}}$$ , of the isoscalar ( $$T=0$$ ) and isovector ( $$T=1$$ ) giant resonances of multipolarities $$L_{m}=0$$ –3 in $${}^{\mathrm{40,48}}$$ Ca, $${}^{\mathrm{68}}$$ Ni, $${}^{\mathrm{90}}$$ Zr, $${}^{\mathrm{116}}$$ Sn, $${}^{\mathrm{144}}$$ Sm, and $${}^{\mathrm{208}}$$ Pb, were calculated within the fully self-consistent spherical Hartree–Fock (HF)-based random-phase approximation (RPA) theory, using 33 different energy density functionals associated with Skyrme-type effective nucleon–nucleon interactions of the standard form commonly employed in the literature. We also calculate the Pearson linear correlation coefficients between each $$E_{\mathrm{CEN}}$$ and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of $$E_{\mathrm{CEN}}$$ to bulk properties of NM. By comparing the calculated values of $$E_{\textrm{CEN}}$$ to the experimental data, we constrain the values of the bulk NM properties. We find that interactions associated with the values of the NM effective mass, $$m^{\ast}/m=0.70$$ –0.90, incompressibility coefficient, $$K_{\textrm{NM}}=210$$ –240 MeV, and the enhancement coefficient of the energy-weighted sum rule of the isovector giant dipole resonance, $$\kappa=0.25$$ –0.70, best reproduce the experimental data.

Continuum strength function for the isoscalar monopole (IS0) and dipole (IS1) transitions in the α + 40 Ca system is investigated on the basis of the orthogonality condition model (OCM) under the...

The isoscalar dipole response of heavy spherical nuclei in the low-energy region is studied by using a semiclassical model, based on the solution of the linearized Vlasov kinetic equation for finite Fermi systems. In this translation-invariant model, the excitations of the center of mass motion are exactly separated from the internal ones. The isoscalar dipole strength function displays three resonance structures in the energy region up to 15 MeV. Calculations of the velocity fields associated with resonance structures at centroid energies show the vortex (toroidal) nature of two overlying resonances. The main toroidal resonance gives a qualitative description of the low-energy isoscalar dipole resonance, which is observed in heavy spherical nuclei. The origin of the lowest isoscalar dipole resonance structure is apparently related to dipole single-particle excitations. Its centroid energy is close to the minimum energy of the dipole single-particle spectrum, and taking into account the residual interaction leads only to an insignificant shift of the centroid energy towards lower energy. However, the inclusion of residual interaction noticeably enhances the velocity field associated with the lowest resonance, which indicates collective effects in this resonance structure.

An approach to describing main properties of isoscalar giant multipole resonances in medium-heavy closed-shell nuclei is proposed within the particle–hole dispersive optical model formulated recently. The description includes the energy-averaged strength function, projected transition density, and partial branching ratios for direct single-nucleon decay. The results obtained within this approach for the $${}^{208}$$ Pb nucleus are compared with available experimental data.

We introduce the concept of neutron-proton two-particle units (np-Weisskopf units) to be used in the analysis of the ($^{3}$He,p) and (p,3He) reactions on nuclei along the N=Z line. These are presented for the conditions relevant to the (n,j,ℓ) orbits expected from $^{16}$O to $^{100}$Sn. As is the case of the Weisskopf units for electromagnetic transitions, the np-WU's will provide a simple, yet robust, measure of isoscalar and isovector np pairing collective effects.

An exotic narrow state in the $D^0D^0\pi^+$ mass spectrum just below the $D^{*+}D^0$ mass threshold is studied using a data set corresponding to an integrated luminosity of 9 fb$^{-1}$ acquired with the LHCb detector in proton-proton collisions at centre-of-mass energies of 7, 8 and 13 TeV. The state is consistent with the ground isoscalar $T^+_{cc}$ tetraquark with a quark content of $cc\bar{u}\bar{d}$ and spin-parity quantum numbers $\mathrm{J}^{\mathrm{P}}=1^+$. Study of the $DD$ mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell $D^{*+}$ mesons is confirmed by the $D^0\pi^+$ mass distribution. The mass of the resonance and its coupling to the $D^{*}D$ system are analysed. Resonance parameters including the pole position, scattering length, effective range and compositeness are measured to reveal important information about the nature of the $T^+_{cc}$ state. In addition, an unexpected dependence of the production rate on track multiplicity is observed., Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2021-032.html

A systematic study of the effect of tensor force on the evolution of shell structure in even–even super-heavy nuclei in the region of proton numbers $$Z=114$$ , 120 and 126 and in the region of neutron numbers $$178 \le N \le $$ 188 is presented. We use, in this investigation, the Hartree–Fock framework by means of different types of Skyrme functionals in two cases with and without tensor force. The Bardeen–Cooper–Schriefer (BCS) approximation has been used to treat the pairing correlations. By investigating structural and decay properties of nuclei under consideration, it is found that $$N=184$$ shell gap is more enhanced by the tensor interaction which depends on the isoscalar tensor coupling constant $$C_0^J$$ of the used Skyrme interactions. In the case without tensor interaction, this gap is significant only for T22, T24, T42 and SLy5. So, it disappears with T46, T64 and T66 and is too weak for T26, T44 and T62. Without exception, the shell gap at $$N=184$$ becomes more pronounced when the tensor part is taken into account.

38th International Symposium on Lattice Field Theory , (LATTICE2021), Zoom/Gather@Massachusetts Institute of Technology, USA, 26 Jul 2021 - 30 Jul 2021; Proceedings of Science / International School for Advanced Studies (LATTICE2021), 250 (2022). doi:10.22323/1.396.0250, We present the nucleon axial and electromagnetic form factors using $N_\textrm{f}$=2+1+1 ensembles of twisted mass fermions with clover improvement and with masses tuned to their physical values. Excited state effects are studied using several sink-source time separations in the range 0.8 fm - 1.6 fm, exponentially increasing statistics with the separation such that statistical errors remain approximately constant. In addition, quark loop disconnected diagrams are included in order to extract the isoscalar axial form factors and the proton and neutron electromagnetic form factors, as well as their strange-quark contributions. The radii and moments are extracted by modelling the $Q^2$ dependence, including using the so-called $z$-expansion. A preliminary assessment of lattice cut-off effects is presented using two lattice spacings directly at the physical point., Published by SISSA, Trieste

We suggest an extension to isospin asymmetric matter of the quarkyonic model from McLerran and Reddy. This extension allows us to construct the $\beta$-equilibrium between quarks, nucleons and leptons. The concept of the quarkyonic matter originates from the large number of color limit for which nucleons are the correct degrees of freedom near the Fermi surface -- reflecting the confining forces -- while deep inside the Fermi sea quarks naturally appear. In isospin asymmetric matter, we suggest that this new concept can be implemented within a global isoscalar relation between the shell gaps differentiating the nucleon and the quark sectors. In addition, we impose the conservation of the isospin-flavor asymmetry in the nucleon and the quark phases. Within this model, several quarkyonic stars are constructed on top of the SLy4 model for the nucleon sector, producing a bump in the sound speed, which implies that quarkyonic stars are systematically bigger and have a larger maximum mass than the associated neutron stars. They also predict lower proton fraction at $\beta$-equilibrium, which potentially quenches fast cooling in massive compact stars., Comment: 11 pages, 9 figures

The detection of gravitational radiation, emitted in the aftermath of the excitation of neutron star quasi-normal modes, has the potential to provide unprecedented access to the properties of matter in the star interior, and shed new light on the dynamics of nuclear interactions at microscopic level. Of great importance, in this context, will be the sensitivity to themodelling of three-nucleon interactions, which are known to play a critical role in the high-density regime. We report the results of a calculation of the frequencies and damping times of the fundamental mode, carried out using the equation of state of Akmal, Pandharipande and Ravenhall as a baseline, and varying the strength of the isoscalar repulsive term the Urbana IX potential within a range consistent with multimessenger astrophysical observations. The results of our analysis indicate that repulsive three-nucleon interactions strongly affect the stiffness of the equation of state, which in turn determines the pattern of the gravitational radiation frequencies, largely independent of the mass of the source. The observational implications are also discussed.

New formula to describe the non-resonant background strength in the binary breakup is considered on the basis of the Migdal-Watson (MW) formula. The background strength is assumed to be generated by the direct breakup, which is the one step transition from the initial bound state to the final continuum state. The strength of the direct breakup is evaluated by the complex scaling method (CSM). We have found that the extended MW formula, which is proposed in the present study, nicely reproduces the strength of the direct breakup calculated by CSM. The relation of the parameters newly introduced in the extended MW formula and the spatial size of the initial wave function is also discussed.

Isoscalar and isovector effective masses of the nucleon in nuclear medium are explored in the quasi-elastic electron scattering of nuclei with KIDS (Korea-IBS-Daegu-SKKU) density functional model. Effective masses are varied in the range (0.7 ~ 1.0)$M$ where $M$ is the mass of the nucleon in free space. Parameters in the KIDS functional are adjusted to nuclear matter equation of state, energy and radius of selected nuclei, and effective mass of nucleons. Hartree-Fock equation is solved to obtain the wave functions of the nucleon in target nuclei, and they are plugged in the calculation of electron-nucleus scattering cross sections at the energies of incident electrons 300 MeV ~ 2.5 GeV. Theoretical prediction agrees well with measurement. Dependence on the effective mass is evident: cross section tends to increase with small isoscalar effective masses. However, effect of isovector effective mass is negligible. Spectroscopic factors are estimated for the protons in the outermost shells of $^{16}$O, $^{40}$Ca, and $^{208}$Pb. Results are consistent with the values in the literature., Comment: 20 pages, 9 figures

We study the nuclear iso-scalar giant quadruple resonance~(ISGQR) based on the Boltzmann-Uehling-Uhlenbeck~(BUU) transport equation. The mean-field part of the BUU equation is described by the Skyrme nucleon-nucleon effective interaction, and its collision term, which embodies the two-particle-two-hole ($2$p-$2$h) correlation, is implemented through the stochastic approach. We find that the width of ISGQR for heavy nuclei is exhausted dominated by collisional damping, which is incorporated into the BUU equation through its collision term, and it can be well reproduced through employing a proper in-medium nucleon-nucleon cross section. Based on further Vlasov and BUU calculations with a number of representative Skyrme interactions, the iso-scalar nucleon effective mass at saturation density is extracted respectively as $m^{*}_{s,0}/m$ $=$ $0.83\pm0.04$ and $m^{*}_{s,0}/m$ $=$ $0.82\pm0.03$ from the measured excitation energy $E_x$ of the ISGQR of $\isotope[208]{Pb}$. The small discrepancy between the two constraints indicates the negligible role of $2$p-$2$h correlation in constraining $m_{s,0}^*$ with the ISGQR excitation energy., Comment: 7 pages, 5 figures; accepted by Physical Review C

Physical review / D 104(5), 054503 (2021). doi:10.1103/PhysRevD.104.054503, We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost. We find non-zero results for the disconnected isoscalar and strange quark distributions. The determination of the quark parton distribution and in particular the strange quark contributions that are poorly known provide valuable input to the structure of the nucleon., Published by Inst., Melville, NY

The correspondence between the isoscalar monopole (IS0) transition strengths and $\alpha$ inelastic cross sections, the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence, is investigated for $^{24}$Mg($\alpha,\alpha'$) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for $^{24}$Mg obtained with antisymmetrized molecular dynamics to the ($\alpha,\alpha'$) cross sections. We aim at clarifying how the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon–nucleon effective interaction in the scattering process, and the coupled-channel effect. It is found that these effects are significant and the explanation of the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence tends to remain because of a strong constraint on the transition densities between the ground state and the $0^+$ excited states. The correspondence is found to hold at 386 MeV with an error of about 20%–30%, while it is seriously compromised at 130 MeV, mainly by the strong nuclear distortion. It is also found that when a $0^+$ state that has a different structure from a simple $\alpha$ cluster state is considered, the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence becomes less valid. For a quantitative discussion on the $\alpha$ clustering in $0^+$ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.

We investigate roles of the tensor force (TF) on the pairing correlations in the ground-state structure of C 12 , O 16 , Ne 20 , and S 32 nuclei within a deformed BCS model. For pairing matrix elements, we exploit the Brueckner G matrix derived from the charge-dependent Bonn potential. In particular, the isoscalar (IS) neutron-proton ( n p ) pairing is studied in detail in relation to spin-triplet even TF in the nucleon-nucleon interaction. Detailed analyses of the n p pairing and possible enhancement of the IS channel are performed by focusing on roles of attractive spin-triplet even and repulsive spin-triplet odd channels in the TF for the ground states of the nuclei with some deformation. It is also shown that the TF may play a crucial role of properly interpreting the experimental data of a two-nucleon knockout reaction from C 12 .

The measurement of strong-interaction shift and broadening in pionic hydrogen and deuterium yields pion-nucleon scattering lengths as well as the threshold pion-production strength on isoscalar NN pairs. Results from recent high-resolution experiments at PSI using crystal spectrometers allow important comparisons with the outcome of the modern low-energy description of QCD within the framework of effective field theories.

The low-lying excited states in the neutron-deficient $N = Z + 1$ nucleus $^{87}_{43}$Tc$_{44}$ have been studied via the fusion-evaporation reaction $^{54}$Fe $(^{36}Ar, 2n1p)$ $^{87}$Tc at the Grand Accelerateur National d'Ions Lourds (GANIL), France. The AGATA spectrometer was used in conjunction with the auxiliary NEDA, Neutron Wall, and DIAMANT detector arrays to measure coincident prompt γ rays, neutrons, and charged particles emitted in the reaction. A level scheme of $^{87}$Tc from the $(9/2^+_{g.s})$ state to the $( 33 / 2^+_1$) state was established based on six mutually coincident γ -ray transitions. The constructed level structure exhibits a rotational behavior with a sharp backbending at $ℏω ≈ 0.50$ MeV. A decrease in alignment frequency and increase in alignment sharpness in the odd-mass isotonic chains around $N=44$ is proposed as an effect of the enhanced isoscalar neutron-proton interactions in odd-mass nuclei when approaching the $N=Z$ line.

We present a comprehensive analysis of the $\ensuremath{\gamma}W$ interference radiative correction to the neutron $\ensuremath{\beta}$-decay matrix element. Within a dispersion relations approach, we compute the axial-vector part of the $\ensuremath{\gamma}W$ box amplitude ${\ensuremath{\square}}_{A}^{\ensuremath{\gamma}W}$ in terms of the isoscalar part of the ${F}_{3}^{\ensuremath{\gamma}W}$ interference structure function. Using the latest available phenomenology for ${F}_{3}^{\ensuremath{\gamma}W}$ from the nucleon elastic, resonance, deep-inelastic, and Regge regions, we find the real part of the box correction to be ${\ensuremath{\square}}_{A}^{\ensuremath{\gamma}W}=3.90(9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. This improved correction gives a theoretical estimate of the CKM matrix element $|{V}_{ud}{|}^{2}=0.94805(26)$, which represents a $4\ensuremath{\sigma}$ violation of unitarity.

We searched for the $\alpha$ condensed state in $^{13}$C by measuring the $\alpha$ inelastic scattering at $E_{\alpha} = 388$ MeV at forward angles including 0 degrees. We performed the distorted-wave Born-approximation calculation with the single-folding potential and the multipole decomposition analysis to determine the isoscalar transition strengths in $^{13}$C. We found a bump structure around $E_x = 12.5$ MeV due to the isoscalar monopole ($IS0$) transition. A peak-fit analysis suggested that this bump consisted of several $1/2^-$ states. We propose that this bump is due to the mirror state of the 13.5 MeV-state in $^{13}$N, which dominantly decays to the $\alpha$ condensed state in $^{12}$C. It was speculated that the $1/2^-$ states around $E_x = 12.5$ MeV were candidates for the $\alpha$ condensed state, but the $3\alpha + n$ orthogonality condition model suggests that the $\alpha$ condensed state is unlikely to emerge as the negative parity states. We also found two $1/2^+$ or $3/2^+$ states at $E_x = 14.5$ and 16.1 MeV excited with the isoscalar dipole ($IS1$) strengths. We suggest that the 16.1-MeV state is a possible candidate for the $\alpha$ condensed state predicted by the cluster-model calculations on the basis of the good correspondence between the experimental and calculated level structures. However, the theoretical $IS1$ transition strength for this state is significantly smaller than the measured value. Further experimental information is strongly desired to establish the $\alpha$ condensed state in $^{13}$C., Comment: 24 pages, 12 figures, published in PTEP

The role of dynamical pairing in induced fission dynamics is investigated using the time-dependent generator coordinate method in the Gaussian overlap approximation, based on the microscopic framework of nuclear energy density functionals. A calculation of fragment charge yields for induced fission of $^{228}$Th is performed in a three-dimensional space of collective coordinates that, in addition to the axial quadrupole and octupole intrinsic deformations of the nuclear density, also includes an isoscalar pairing degree of freedom. It is shown that the inclusion of dynamical pairing has a pronounced effect on the collective inertia, the collective flux through the scission hyper-surface, and the resulting fission yields, reducing the asymmetric peaks and enhancing the contribution of symmetric fission, in better agreement with the empirical trend., 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:2004.10089

Tensor couplings and Coulomb-exchange terms in the relativistic mean-field (RMF) model impact the neutron skin thickness of nuclei [N. Liliani, A. M. Nugraha, J. P. Diningrum, and A. Sulaksono, Phys. Rev. C 93, 054322 (2016)], and a significantly thicker skin of $^{208}\mathrm{Pb}$ predicted by PREX-II leads to the existence of a phase transition in the interior of neutron stars (NSs) [F. J. Fattoyev, J. Piekarewicz, and C. J. Horowitz, Phys. Rev. Lett. 120, 172702 (2018)]. In this work, we revisit the effects of tensors and Coulomb-exchange terms within the RMF model with the $\ensuremath{\delta}$-meson and isovector-isoscalar coupling on finite nuclei. We also perform a systematic investigation of the implicit effect of both terms on the nuclear matter and NS properties. We confirmed in our previous work [N. Liliani, A. M. Nugraha, J. P. Diningrum, and A. Sulaksono, Phys. Rev. C 93, 054322 (2016)] that the roles of tensor couplings, Coulomb exchange, and isovector-isoscalar coupling on the bulk properties of finite nuclei are crucial. Conversely, the $\ensuremath{\delta}$-meson term's inclusion yields no significant effect on the bulk properties of finite nuclei. The tensor couplings and Coulomb-exchange terms implicitly influence the isoscalar and isovector parts of nuclear matter. By contrast, the $\ensuremath{\delta}$-meson and isovector-isoscalar coupling significantly impact the isovector parts of nuclear matter predictions. Except for the binding energy and the equation of state of pure neutron matter in low-density cases, the nuclear matter property predictions of all parameter sets used are relatively compatible with experimental data and the chiral effective field theory result. Moreover, the tensor couplings, Coulomb-exchange, $\ensuremath{\delta}$-meson, and isovector-isoscalar coupling terms play a significant role in predicting the canonical NS radius but not in the maximum mass of NS. For relatively large ${\ensuremath{\eta}}_{2\ensuremath{\rho}}$, the compatibility of the canonical NS radius predicted by the model with all of the observation results used in this work is better than that with the tensor couplings and Coulomb exchange excluded. Moreover, the presence of tensor couplings, Coulomb exchange, and various isovector-isoscalar nonlinear coupling terms influence the relation between NS tidal deformation and neutron skin thickness of $^{208}\mathrm{Pb}$. However, tensor couplings and Coulomb-exchange terms play a crucial role in making the NS tidal deformability prediction compatible with the constraints from observations and experimental data. In conclusion, tensor couplings and Coulomb-exchange RMF models have an essential role in finite nuclei predictions and implicitly influence the nuclear matter and NS property predictions.

Spin-M1 excitations of nuclei are important for describing neutrino reactions in supernovae or in neutrino detectors since they are allowed transitions mediated by neutral current neutrino interactions. The spin-M1 excitation strength distributions in self-conjugate N=Z nuclei were studied by proton inelastic scattering at forward angles for each of isovector and isoscalar excitations as reported in H. Matsubara et al., Phys. Rev. Lett. 115, 102501 (2015). The experiment was carried out at the Research Center for Nuclear Physics, Osaka University, employing a proton beam at 295 MeV and the high-resolution spectrometer Grand Raiden. The measured cross-section of each excited state was converted to the squared nuclear matrix elements of spin-M1 transitions by applying a unit cross-section method. Comparison with predictions by a shell-model has revealed that isoscalar spin-M1 strengths are not quenched from the prediction although isovector spin-M1 strengths are quenched similarly with Gamow-Teller strengths in charged-current reactions. This finding hints at an important origin of the quenching of the strength relevant to neutrino scattering, that is, the proton-neutron spin-spin correlation in the ground state of the target nucleus. In this manuscript we present the details of the unit cross-section method used in the data analysis and discuss the consistency between the quenching of the isoscalar magnetic moments and that of the isoscalar spin-M1 strengths.

Background: Mg 24 is a strongly deformed nucleus in the ground state. Deformation effects can be observed in the structure of the isoscalar giant monopole and quadrupole resonances. Mg 24 is also a nucleus that is well known to present different types of cluster-oscillation modes. Both giant resonances and cluster states are strongly populated by isoscalar transitions. Purpose: To extract the E 0 , E 1 , and E 2 transition strengths via Li 6 scattering. The Li 6 probe is a powerful tool for investigating the isoscalar nuclear response with a very favorable ratio of resonance-to-continuum background. Method: Double-differential cross sections of Li 6 inelastic scattering, at the beam energy of 100 MeV/u, were measured in the excitation-energy range 10 – 40 MeV and scattering angles 0 − 3 ∘ . A multipole-decomposition analysis was performed for extracting the isoscalar E 0 , E 1 , and E 2 strength distributions. Results: The extracted multipole strengths were compared with predictions from consistent quasiparticle random phase approximation calculations. The theoretical predictions are in fair agreement with the experimental data. The E 0 strength was also compared with results from antisymmetrized molecular dynamics calculations found in the literature. A few peaks in the experimental data might be associated with clustering in Mg 24 . Conclusions: Ground-state deformation effects were observed in the isoscalar giant monopole resonance (ISGMR) and isoscalar giant quadrupole resonance (ISGQR) distributions. The ISGMR strength is split in two peaks around 19 and 28 MeV. The ISGQR exhibits a pronounced peak at 20 MeV with a broadening at the low-energy region, similar to predictions from microscopic calculations. Signatures of excitation of cluster states were observed in the E 0 response. Further studies including particle-decay measurements will be required to confirm the nature of the observed peaks.

We show that the symmetry-restored paired mean-field states (quasiparticle vacua) properly account for isoscalar versus isovector nuclear pairing properties. Full particle-number, spin, and isospin symmetries are restored in a simple SO(8) proton-neutron pairing model, and prospects to implement a similar approach in a realistic setting are delineated. Our results show that, provided all symmetries are restored, the pictures based on pair-condensate and quartet-condensate wave functions represent equivalent ways of looking at the physics of nuclear proton-neutron pairing., Comment: 16 pages, 2 figures

The paper aims at clarifying some issues associated with evaluation of surface-averaged quantities in Direct Numerical Simulation (DNS) of a turbulent reacting flow. For a quantity ϕ(t, x) averaged over an isosurface c(t,x)=c^ of a reaction progress variable c, there exist at least two different definitions of surface averages; an area-weighted surface average 〈ϕ〉 s | c^,t and an unweighted surface average 〈ϕ〉 v | c^,t . These two fine-grained averages can also be extended to coarse-grained surface averages 〈ϕ〉 S | c^,ϵ,t and 〈ϕ〉 V | c^,ϵ,t over an interval of c^≤c(t,x)≤c^+ϵ. In a highly turbulent medium, the difference 〈ϕ〉 s −〈ϕ〉 v between the area-weighted and unweighted surface averages can be significant for most quantities ϕ of basic interest. The sign of this difference depends on the sign of the correlation between ϕ and |∇c|, can be opposite for different ϕ or even for different isosurfaces of the same scalar field ϕ. For a quantity ϕ that can become singular in the zero-gradient points |∇c|(t,x)=0, its unweighted or area-weighted surface averages can still be bounded. The difference between area-weighted and unweighted surface averages of 1/|∇c| or |∇c| is relevant to explaining the well-known, but still challenging controversy between available data on the influence of turbulence on the local flame thickness.

This review paper concerns the research devoted to the study of the properties of dipole excitations in nuclei. The main focus is on questions related to isospin effects in these types of excitations. Particular attention is given to the experimental and theoretical efforts made to understand the nature and the specific structure of the low-lying dipole states known as the Pygmy Dipole Resonance (PDR). The main experimental methods employed in the study of the PDR are reviewed as well as the most interesting theoretical aspects. The main features of the experiments and of theoretical models are reported with special emphasis on the reaction cross sections populating the dipole states. Results are organized for nuclei according to different mass regions. The knowledge of the isovector dipole response as well as its low energy part is important in order to deduce the nuclear polarizability as accurate as possible. This issue is discussed in this paper together with the connection with the neutron skin and the nuclear equation of state. The important role played by the dipole response to deduce other physical quantities of general interest is discussed in the last two chapters. One concerns the level density and the other the isospin mixing in nuclei at finite temperature and its relation with beta decay.

In this work, we study the BK¯ molecule in the Bethe-Salpeter (BS) equation approach. With the kernel containing one-particle-exchange diagrams and introducing two different form factors (monopole form factor and dipole form factor) in the vertex, we solve the BS equation numerically in the covariant instantaneous approximation. We investigate the isoscalar and isovector BK¯ systems, and we find that X5568 cannot be a BK¯ molecule.

Fully self-consistent spherical Hartree–Fock HF based random-phase approximation RPA calculations were performed for tin isotopes 100,116,132Sn using five type of Skyrme interaction: QMC2, LNS5, BsK21, NRAPR and MSKA. Isoscalar E0, E1, E2 and E3 transition strength distribution, centroid energy and transition density distribution have been investigated and compared with the available experimental data. Relations between the parameters and properties of the investigated Skyrme force, with the calculated properties of nuclei are analyzed.

Coherent photoproduction of the neutral pion and eta meson on the deuteron, $$\gamma {d}$$ $$\rightarrow $$ $$\pi ^0\eta {d}$$ , has been experimentally studied at $$E_\gamma

We study the ability of variational approaches based on self-consistent mean-field and beyond-mean-field methods to reproduce exact energies and electromagnetic properties of the nuclei defined within the $sd$-shell valence space using the non-trivial USD Hamiltonian. In particular, Hartree-Fock-Bogoliubov (HFB), variation after particle-number projection (VAPNP) and projected generator coordinate methods (PGCM) are compared to exact solutions {obtained by} the full diagonalization of the Hamiltonian. We analyze the role played by the proton-neutron ($pn$) mixing as well as the quadrupole and pairing degrees of freedom (including both isoscalar and isovector channels) in the description of the spectra of even-even, even-odd and odd-odd nuclei in the whole $sd$-shell., 16 pages; 16 figures

The YGLO (Yang-Grasso-Lacroix-Orsay) functional is applied for the first time to investigate ground-state properties of different isotopic chains, from Oxygen to Lead. Mean-field Hartree-Fock calculations are carried out to analyze global trends for separation energies, binding energies, radii, neutron skins, and density profiles. We have three objectives: i) we study whether this functional leads to a reasonable description of ground-state properties (despite the fact that it was not adjusted on nuclei) and we discuss the associated limitations; ii) we investigate whether the correct description of the low-density nuclear gas, which is the peculiarity of this functional, has any relevant impact on predictions for nuclei; iii) we connect nuclear energies, radii and density profiles with properties of the corresponding equations of state of infinite matter. In particular, we identify a link existing between the isoscalar effective mass and spatial properties in neutron-deficient nuclei, namely proton radii and tails of proton densities. On the other side, we show that the slope of the symmetry energy is connected with spatial properties in neutron-rich nuclei: the slope computed at saturation density is related to neutron skin thicknesses, as already well known, whereas the slope calculated at lower densities is linked to the tails of neutron densities. The YGLO effective mass turns out to be quite low. Directions to improve this aspect are explored and suggested at the end of the manuscript., 14 pages, 12 figures

Background: Low-energy dipole states have been popular topics in studies of stable and unstable nuclei. In $^{24}\mathrm{Mg}$, two low-energy dipole modes, the toroidal and compressional states have been theoretically proposed recently. The former state has been associated with cluster structure, but there is no explicit analysis of the cluster structure.Purpose: Our purpose is to investigate low-lying ${1}^{\ensuremath{-}}$ states in $^{24}\mathrm{Mg}$ and clarify their properties such as the dipole transition strengths, nuclear vorticity, and cluster features.Method: Wave functions of ${1}^{\ensuremath{-}}$ states of $^{24}\mathrm{Mg}$ are described within the antisymmetrized molecular dynamics framework combined with the generator coordinate method. Excitation energies and dipole transition strengths are calculated. Cluster wave functions are explicitly taken into account to reveal the role of cluster correlations in ${1}^{\ensuremath{-}}$ states. Intrinsic matter density and transition current density are analyzed.Results: Two low-lying dipole states, the ${1}_{K=1}^{\ensuremath{-}}$ and ${1}_{K=0}^{\ensuremath{-}}$, are obtained. The ${1}_{K=1}^{\ensuremath{-}}$ state has the strongest isoscalar toroidal dipole strength and shows two-vortex structure in the intrinsic transition current density. The ${1}_{K=0}^{\ensuremath{-}}$ state features the isoscalar compressional dipole strength and exhibits the $^{16}\mathrm{O}+^{8}\mathrm{Be}$ cluster correlation.Conclusions: The toroidal and compressional dipole modes separately appear as $K=1$ and $K=0$ states in the deformed $^{24}\mathrm{Mg}$ system. The ${1}_{K=1}^{\ensuremath{-}}$ state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the ${1}_{K=0}^{\ensuremath{-}}$ state is the compressional dipole state having enhanced cluster structure but weaker vorticity.

We present an $\mathcal{O}(\ensuremath{\alpha})$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $\ensuremath{\beta}$ decays. We find that a priori contributions arise from the photonic vertex correction and $\ensuremath{\gamma}W$ box diagram. Upon evaluation most elastic contributions vanish due to crossing symmetry or cancellation between isoscalar and isovector photonic contributions, leaving only the polarized parity-odd contribution, i.e., the Gamow-Teller equivalent of the well-known axial $\ensuremath{\gamma}W$ box contribution for Fermi decays. We show that weak magnetism contributes significantly to the Born amplitude, and consider additional hadronic contributions at low energy using a holomorphic continuation of the polarized Bjorken sum rule constrained by experimental data. We perform the same procedure for the Fermi inner radiative correction through a combination of the running of Bjorken and Gross-Llewellyn Smith sum rules. We discuss heavy flavor, higher-twist, and target mass corrections and find a significant increase at low momentum from the latter. We find ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}=0.02532(22)$ and ${\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.02473(27)$ for axial and vector inner radiative corrections, respectively, resulting in ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.60(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which allows us to extract ${g}_{A}^{0}$ for the first time to our knowledge. We discuss consequences for comparing experimental data to lattice calculations in beyond Standard Model fits. Further, we show how some traditional $\ensuremath{\beta}$ decay calculations contain part of this effect but fail to account for cancellations in the full $\mathcal{O}(\ensuremath{\alpha})$ result. Finally, we correct for a double-counting instance in the isospin $T=1/2$ mirror decay extraction of $|{V}_{ud}|$, the up-down matrix element of the Cabibbo-Kobayashi-Maskawa matrix element, resolving a long-standing tension and leading to increased precision.

To identify the 3 $$\alpha $$ BEC state with the excess neutron, we have investigated the monopole strength of the excited states of $$^{13}\mathrm{C}$$ by using the theoretical framework of the real-time evolution method. The calculations have revealed several candidates of the Hoyle-analog states in highly excited region.

We present expressions for the matrix elements of the spin--spin operator $\vec S_{\rm n}\cdot\vec S_{\rm p}$ in a variety of coupling schemes. These results are then applied to calculate the expectation value $\langle\vec S_{\rm n}\cdot\vec S_{\rm p}\rangle$ in eigenstates of a schematic Hamiltonian describing neutrons and protons interacting in a single-$l$ shell through a Surface Delta Interaction. The model allows us to trace $\langle\vec S_{\rm n}\cdot\vec S_{\rm p}\rangle$ as a function of the competition between the isovector and isoscalar interaction strengths and the spin--orbit splitting of the $j=l\pm \frac{1}{2}$ shells. We find negative $\langle\vec S_{\rm n}\cdot\vec S_{\rm p}\rangle$ values in the ground state of all even--even $N=Z$ nuclei, contrary to what has been observed in hadronic inelastic scattering at medium energies. We discuss the possible origin of this discrepancy and indicate directions for future theoretical and experimental studies related to neutron--proton spin--spin correlations., 11 pages, 7 figures. Accepted for publication in the European Physical Journal A

Beginning with the Skyrme interaction, we study the properties of the isoscalar giant monopole resonances (ISGMR) of 132Sn. Using the finite-rank separable approximation for the particle-hole interaction, the coupling between one- and two-phonon terms in the wave functions of excited states is taken into account in very large configurational spaces. The inclusion of the phonon–phonon coupling (PPC) results in the formation of a low-energy 0+ state. The PPC inclusion leads to a fragmentation of the ISGMR strength to lower energy states and also to a higher energy tail. Using the same set of parameters, we describe the available experimental data for the ISGMR characteristics of 118,120,122,124Sn and give a prediction for 126,128,130,132Sn.

Elastic $K^+ n\to K^+ n$ and charge exchange $K^+n\to K^0p$ reactions at low momenta are investigated using the partial wave analysis. Isospin relation gives constrains for the partial $s$- and $p$-waves among elastic $K^+p$, $K^+n$ and charge exchange $K^+n\to K^0p$ amplitudes. Two sets of the phase shift for these partial waves in the isoscalar channel are obtained from the fit of experimental data on total and differential cross sections. Polarization observable leads to a good criterion to decide which set is valid. Differential cross section data near $P_{\rm Lab}=434$ MeV/$c$ suggests a possibility of a resonance, e.g., the exotic $\Theta^+(1540)$ baryon around $\sqrt{s}\simeq$ 1.54GeV., Comment: 6 pages, 9 figures, 1 table, Proc. APFB 2020 Conf

The low-lying dipole strength in the 90,94Zr nuclei was investigated via (p,p′γ) at 80 MeV and (α,α′γ) at 130 MeV. The experiments, made at RCNP, used the magnetic spectrometer Grand Raiden for the scattered particles and the array CAGRA with HPGe detectors for the γ-decay. For 94Zr these are the first data for both reactions and for 90Zr these are the first data with (p,p′γ) and the first ones at high resolution for (α,α′γ). The comparison of the present results for the two nuclei with existing (γ,γ′) data shows that both nuclear probes produce an excitation pattern different than that of the electromagnetic probes. DWBA calculations were made using form factors deduced from transition densities, based on RPA calculations, characterized by a strong neutron component at the nuclear surface. A combined analysis of the two reactions was performed for the first time to investigate the isoscalar character of the 1− states in 90,94Zr. The (p,p′γ) cross section was calculated using values for the isoscalar electric dipole energy-weighted sum rule (E1 ISEWSR) obtained from the (α,α′γ) data. The isoscalar strength for 90Zr was found to exhaust 20 ± 2.5% of the EWSR in the energy range up to 12 MeV. In case of 94Zr, a strength of 9 ± 1.1% of the EWSR was found in the range up to 8.5 MeV. Although an overall general description was obtained in the studied energy intervals, not all proton cross sections were well reproduced using the isoscalar strength from (α,α′γ). This might suggest mixing of isoscalar and isovector components and that this mixing and the degree of collectivity are not the same for all the 1− states below the particle binding energy.

Background: Nuclei in the $sd$ shell demonstrate a remarkable interplay of cluster and mean-field phenomena. The $N=Z$ nuclei, such as $^{24}\mathrm{Mg}$ and $^{28}\mathrm{Si}$, have been the focus of the theoretical study of both phenomena in the past. A variety of different cluster structures in these nuclei are predicted, characterized by isoscalar dipole and monopole transitions. For example, low-energy isoscalar vortical dipole states were predicted in $^{24}\mathrm{Mg}$. The cluster and vortical mean-field phenomena can be probed by excitation of isoscalar monopole and dipole states in scattering of isoscalar particles such as deuterons or $\ensuremath{\alpha}$ particles.Purpose: We investigate, both experimentally and theoretically, the isoscalar dipole $IS1$ and monopole $IS0$ strengths in three essentially different light nuclei with different properties: stiff prolate $^{24}\mathrm{Mg}$, soft prolate $^{26}\mathrm{Mg}$, and soft oblate $^{28}\mathrm{Si}$. We analyze possible manifestations of clustering and vorticity in these nuclei.Methods: Inelastically scattered $\ensuremath{\alpha}$ particles were momentum analyzed in the K600 magnetic spectrometer at iThemba LABS, Cape Town, South Africa. The scattered particles were detected in two multiwire drift chambers and two plastic scintillators placed at the focal plane of the K600. In the theoretical discussion, the Skyrme quasiparticle random-phase approximation (QRPA) and antisymmetrized molecular dynamics $+$ generator coordinate method ($\mathrm{AMD}+\mathrm{GCM}$) were used.Results: A number of isoscalar monopole and dipole transitions were observed in the nuclei studied. Using this information, suggested structural assignments have been made for the various excited states. $IS1$ and $IS0$ strengths obtained within QRPA and $\mathrm{AMD}+\mathrm{GCM}$ are compared with the experimental data. The QRPA calculations lead us to conclude that (i) the mean-field vorticity appears mainly in dipole states with $K=1$, (ii) the dipole (monopole) states should have strong deformation-induced octupole (quadrupole) admixtures, and (iii) near the $\ensuremath{\alpha}$-particle threshold there should exist a collective state with $K=0$ for prolate nuclei and $K=1$ for oblate nuclei, with an impressive octupole strength. The results of the $\mathrm{AMD}+\mathrm{GCM}$ calculations suggest that some observed states may have a mixed (mean-field $+$ cluster) character or correspond to particular cluster configurations.Conclusion: A tentative correspondence between observed states and theoretical states from QRPA and $\mathrm{AMD}+\mathrm{GCM}$ was established. The QRPA and $\mathrm{AMD}+\mathrm{GCM}$ analysis shows that low-energy isoscalar dipole states combine cluster and mean-field properties. The QRPA calculations show that the low-energy vorticity is well localized in $^{24}\mathrm{Mg}$, fragmented in $^{26}\mathrm{Mg}$, and absent in $^{28}\mathrm{Si}$.

In this work, we determine up/down-quark mass $m_{q=u/d}$ in the isoscalar scalar channel from both the Shifman-Vainshtein-Zakharov (SVZ) and the Monte-Carlo-based QCD sum rules. The relevant spectral function, including the contributions from the $f_0(500)$, $f_0(980)$ and $f_0(1370)$ resonances, is determined from a sophisticated $U(3)$ chiral study. Via the traditional SVZ QCD sum rules, we give the prediction to the average light-quark mass $m_q(2 \, \text{GeV})=\frac{1}{2}(m_u(2 \, \text{GeV}) + m_d(2 \, \text{GeV}))=(3.46^{+0.16}_{-0.22} \pm 0.33) \, \text{MeV}$. Meanwhile, by considering the uncertainties of the input QCD parameters and the spectral functions of the isoscalar scalar channel, we obtain $m_q (2\, \text{GeV}) = (3.44 \pm 0.14 \pm 0.32) \, \text{MeV}$ from the Monte-Carlo-based QCD sum rules. Both results are perfectly consistent with each other, and nicely agree with the Particle Data Group value within the uncertainties., 25 pages,7 figures,2 tables

The QCD axion remains experimentally viable in the mass range of $\mathcal{O}(10\text{ }\text{ }\mathrm{MeV})$ if (i) it couples predominantly to the first generation of SM fermions; (ii) it decays to ${e}^{+}{e}^{\ensuremath{-}}$ with a short lifetime ${\ensuremath{\tau}}_{a}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{s}$; and (iii) it has suppressed isovector couplings, i.e., if it is piophobic. Remarkably, these are precisely the properties required to explain recently observed anomalies in nuclear deexcitations, to wit: the ${e}^{+}{e}^{\ensuremath{-}}$ emission spectra of isoscalar magnetic transitions of $^{8}\mathrm{Be}$ and $^{4}\mathrm{He}$ nuclei showed a ``bumplike'' feature peaked at ${m}_{{e}^{+}{e}^{\ensuremath{-}}}\ensuremath{\sim}17\text{ }\text{ }\mathrm{MeV}$. In this paper, we argue that on-shell emission of the QCD axion (with the aforementioned properties) provides an extremely well-motivated, compatible explanation for the observed excesses in these nuclear deexcitations. The absence of anomalous features in other measured transitions is also naturally explained: piophobic axion emission is strongly suppressed in isovector magnetic transitions and forbidden in electric transitions. This QCD axion hypothesis is further corroborated by an independent observation: a $\ensuremath{\sim}2--3\ensuremath{\sigma}$ deviation in the measurement of $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})$ from the Standard Model theoretical expectation. This paper also includes detailed estimations of various axionic signatures in rare light meson decays, which take into account contributions from low-lying QCD resonance exchange, and, in the case of rare kaon decays, the possible effective implementations of $\mathrm{\ensuremath{\Delta}}S=1$ octet enhancement in chiral perturbation theory. These inherent uncertainties of the effective description of the strong interactions at low energies result in large variations in the predictions for hadronic signals of the QCD axion; in spite of this, the estimated ranges for rare meson decay rates obtained here can be probed in the near future in $\ensuremath{\eta}/{\ensuremath{\eta}}^{\ensuremath{'}}$ and kaon factories.

Nuclear equation of state is often described in the framework of energy density functional. However, the isovector channel in most functionals has been poorly constrained, mainly due to rather limited available experimental data to probe it. Only recently, the relativistic nuclear energy density functional with an effective point-coupling interaction was constrained by supplementing the ground-state properties of nuclei with the experimental data on dipole polarizability and isoscalar monopole resonance energy in 208Pb, resulting in DD-PCX parameterization. In this work, we pursue a complementary approach by introducing a family of 8 relativistic point-coupling functionals that reproduce the same nuclear ground-state properties, including binding energies and charge radii, but in addition have a constrained value of symmetry energy at saturation density in the range J = 29, 30, …, 36 MeV. In the next step, this family of functionals is employed in studies of excitation properties such as dipole polarizability and magnetic dipole transitions, and the respective experimental data are used to validate the optimal choice of functional as well as to assess reliable values of the symmetry energy and slope of the symmetry energy at saturation.

A coupled-channel analysis of BESIII data on radiative $J/\psi$ decays into $\pi\pi$, $K\bar K$, $\eta\eta$ and $\omega\phi$ has been performed. The partial-wave amplitude is constrained by a large number of further data. The analysis finds ten isoscalar scalar mesons. Their masses, widths and decay modes are determined. The scalar mesons are interpreted as mainly SU(3)-singlet and mainly octet states. Octet isoscalar scalar states are observed with significant yields only in the 1500-2100\,MeV mass region. Singlet scalar mesons are produced over a wide mass range but their yield peaks in the same mass region. The peak is interpreted as scalar glueball. Its mass and width are determined to $M=1865$\er25$^{+10}_{-30}$ {\rm MeV} and $\Gamma= 370$\er$50^{+30}_{-20}$ {\rm MeV}, its yield in radiative $J/\psi$ decays to ($5.8\pm 1.0)\,10^{-3}$., Comment: 11 pages, 4 figures

The semimicroscopic particle-hole dispersive optical model (PHDOM) is implemented to describe main properties of Isoscalar Giant Multipole Resonances (up to L=3) in medium-heavy closed-shell nuclei. The main properties are characterized by the strength distribution, transition density, partial and total probabilities of direct one-nucleon decay. Calculation results obtained for the 208Pb nucleus are compared with available experimental data., 33 pages, 6 tables, 8 figures

Background: The presence of nuclear ground states with stable reflection-asymmetric shapes is supported by rich experimental evidence. Theoretical surveys of odd-multipolarity deformations predict the existence of pear-shaped isotopes in several fairly localized regions of the nuclear landscape in the vicinity of near-lying single-particle shells with $\Delta\ell=\Delta j=3$. Purpose: We analyze the role of isoscalar, isovector, neutron-proton, neutron-neutron, and proton-proton multipole interaction energies in inducing the onset of reflection-asymmetric ground-state deformations. Methods: The calculations are performed in the framework of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory using two Skyrme energy density functionals and density-dependent pairing force. Results: We show that reflection-asymmetric ground-state shapes of atomic nuclei are driven by the odd-multipolarity neutron-proton (or isoscalar) part of the nuclear interaction energy. This result is consistent with the particle-vibration picture, in which the main driver of octupole instability is the isoscalar octupole-octupole interaction giving rise to large $E3$ polarizability., Comment: 11 pages, 12 figures

A light boson $U$ from an extra $U(1)$ interpolates between a generalized dark photon coupled to $Q$, $B$, and ${L}_{i}$ (or $B\ensuremath{-}L$), plus possibly dark matter, a dark $Z$ coupled to the $Z$ current, and one axially coupled to quarks and leptons. We identify the corresponding $U(1{)}_{F}$ symmetries, with $F={\ensuremath{\gamma}}_{Y}Y+{\ensuremath{\gamma}}_{B}B+{\ensuremath{\gamma}}_{{L}_{i}}{L}_{i}+{\ensuremath{\gamma}}_{A}{F}_{A}+{\ensuremath{\gamma}}_{{F}^{\ensuremath{'}}}{F}^{\ensuremath{'}}+{\ensuremath{\gamma}}_{d}{F}_{d}$, ${F}_{d}$ acting in a dark sector and ${F}^{\ensuremath{'}}$ on possible semi-inert Brout-Englert-Higgs (BEH) doublets uncoupled to quarks and leptons. The $U$ current is obtained from the $U(1{)}_{F}$ and $Z$ currents, with a mixing determined by the spin-0 BEH fields. The charge ${Q}_{U}$ of chiral quarks and leptons is a combination of $Q$, $B$, ${L}_{i}$, and ${T}_{3L}$ with the axial ${F}_{A}$. It involves in general isovector and isoscalar axial terms, in the presence of two BEH doublets. A longitudinal $U$ with axial couplings has enhanced interactions and behaves much as an axionlike particle. Its axial couplings ${g}_{A}$, usually restricted to $\ensuremath{\lesssim}\text{ }2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\text{ }{m}_{U}(\mathrm{MeV})$, lead to effective pseudoscalar ones ${g}_{P}={g}_{A}\ifmmode\times\else\texttimes\fi{}2{m}_{q,l}/{m}_{U}={2}^{1/4}{G}_{F}^{1/2}{m}_{q,l}\text{ }{A}_{\ifmmode\pm\else\textpm\fi{}}$. ${A}_{\ifmmode\pm\else\textpm\fi{}}$ is proportional to an invisibility parameter $r=\mathrm{cos}{\ensuremath{\theta}}_{A}$ induced by a singlet v.e.v., possibly large and allowing the $U$ to be very weakly interacting. This allows for a very small gauge coupling, expressed with two doublets and a singlet as ${g}^{\ensuremath{'}\ensuremath{'}}/4\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\text{ }{m}_{U}(\mathrm{MeV})\text{ }r/\mathrm{sin}2\ensuremath{\beta}$. We discuss phenomenological implications for meson decays, neutrino interactions, atomic-physics parity violation, naturally suppressed ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}U$ decays, etc. The $U$ boson fits within the grand unification framework, in symbiosis with a $SU(4{)}_{\mathrm{es}}$ electrostrong symmetry broken at the grand unification scale, with ${Q}_{U}$ depending on $Q$, $B\ensuremath{-}L$, ${F}_{A}$, and ${T}_{3A}$ through three parameters ${\ensuremath{\gamma}}_{Y}$, ${\ensuremath{\gamma}}_{A}$, and $\ensuremath{\eta}$.