Charge Symmetry Breaking Effects Research Articles

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

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

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

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

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

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

Status of the hyperon-nucleon interaction in chiral effective field theory

The Jülich-Bonn group aims at an extensive study of the baryonbaryon (BB) interaction involving strange baryons (Λ, Σ, Ξ) within SU(3) chiral effective field theory. An overview of achievements and new developments over the past few years is provided. The topics covered are: 1) Derivation of the leading charge-symmetry breaking (CSB) interaction for the ΛN system and its application in a study of CSB effects in A=4 Λ-hypernuclei. 2) Updated results for the ΞN interaction at NLO and predictions for Ξ−p correlation functions. 3) Extension of the ΛN-ΣN interaction to next-to-next-to-leading order.

Properties of nuclear matter in relativistic Brueckner–Hartree–Fock model with high-precision charge-dependent potentials

Properties of nuclear matter are investigated in the framework of relativistic Brueckner–Hartree–Fock model with the latest high-precision charge-dependent Bonn (pvCD-Bonn) potentials, where the coupling between pion and nucleon is adopted as a pseudovector form. These realistic pvCD-Bonn potentials are renormalized to effective nucleon–nucleon (NN) interactions, G matrices. They are obtained by solving the Blankenbecler-Sugar (BbS) equation in nuclear medium. Then, the saturation properties of symmetric nuclear matter are calculated with pvCD-Bonn A, B, C potentials. The energies per nucleon are around −10.72 MeV to −16.83 MeV at saturation densities, 0.139 fm−3 to 0.192 fm−3 with these three potentials, respectively. It clearly demonstrates that the pseudovector coupling between pion and nucleon can generate reasonable saturation properties comparing with pseudoscalar coupling. Furthermore, these saturation properties have strong correlations with the tensor components of NN potentials, i.e., the D-state probabilities of deuteron, PD to form a relativistic Coester band. The equations of state of pure neutron matter from pvCD-Bonn potentials are almost identical, since the prominent difference of pvCD Bonn potentials are the components of tensor force, which provides very weak contributions in the case of total isospin T = 1. In addition, the charge symmetry breaking (CSB) and charge independence breaking (CIB) effects are also discussed in nuclear matter from the partial wave contributions with these high-precision charge-dependent potentials. In general, the magnitudes of CSB from the differences between nn and pp potentials are about 0.05 MeV, while those of CIB are around 0.35 MeV from the differences between np and pp potentials.

Charge symmetry breaking effects in pion and kaon structure

Charge symmetry breaking (CSB) effects associated with the $u$ and $d$ quark mass difference are investigated in the quark distribution functions and spacelike electromagnetic form factors of the pion and kaon. We use a confining version of the Nambu--Jona-Lasinio model, where CSB effects at the infrared scale associated with the model are driven by the dressed $u$ and $d$ quark mass ratio, which because of dynamical chiral symmetry breaking is much closer to unity than the associated current quark mass ratio. The pion and kaon are given as bound states of a dressed quark and a dressed antiquark governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with a pion mass difference given by $m_{\pi^+}^2 - m_{\pi^0}^2 \propto (m_u - m_d)^2$ as demanded by dynamical chiral symmetry breaking. We find significant CSB effects for realistic current quark mass ratios ($m_u/m_d \sim 0.5$) in the quark flavor-sector electromagnetic form factors of both the pion and kaon. For example, the difference between the $u$ and $d$ quark contributions to the $\pi^+$ electromagnetic form factors is about 8\% at a momentum transfer of $Q^2 \simeq 10\,$GeV$^2$, while the analogous effect for the light quark sector form factors in the $K^+$ and $K^0$ is about twice as large. For the Parton distribution functions, we find CSB effects which are considerably smaller than those found in the electromagnetic form factors.

Constraints on Coulomb energy, neutron skin thickness in Pb208 , and symmetry energy

The charge-symmetry-breaking (CSB) effect in a nuclear medium that gives rise to the first-order symmetry energy in finite nuclei is discussed in detail in the present paper. For heavy and superheavy nuclei with large neutron excesses, it should be nonnegligible in high-precision mass predictions, and importantly it affects the stability of these nuclei. Combined with this CSB effect, the Coulomb energy is constrained by using the experimental Coulomb displacement energy of mirror nuclei, and then the mass-dependent symmetry energy coefficients of heavy nuclei are reextracted with the experimental ${\ensuremath{\beta}}^{\ensuremath{-}}$-decay energies of heavy odd-$A$ nuclei and with the experimental mass differences. Based on these results, we probe the neutron skin thickness $\mathrm{\ensuremath{\Delta}}{R}_{np}$ of $^{208}\mathrm{Pb}$ and the density-dependent symmetry energy coefficient of nuclear matter. $\mathrm{\ensuremath{\Delta}}{R}_{np}$ in $^{208}\mathrm{Pb}$ is found to be $0.158\ifmmode\pm\else\textpm\fi{}0.014\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$, and the slopes $L$ of the symmetry energy coefficient at densities of $\ensuremath{\rho}=0.16$ and $\ensuremath{\rho}=0.11\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$ are estimated to be $42\ifmmode\pm\else\textpm\fi{}8$ and $42\ifmmode\pm\else\textpm\fi{}3\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, respectively. These results would be meaningful to discriminate between the models and the predictions that are relevant for the investigations on properties of nuclei and of neutron stars.

Precise determination of charge-dependent pion-nucleon-nucleon coupling constants

We undertake a covariance error analysis of the pion-nucleon-nucleon coupling constants from the Granada-2013 np and pp database comprising a total of 6720 scattering data below LAB energy of 350 MeV. Assuming a unique pion-nucleon coupling constant in the One Pion Exchange potential above a boundary radius $r_c=3 {\rm fm}$ we obtain $f^2=0.0763(1)$. The effects of charge symmetry breaking on the $^3P_0$, $^3P_1$ and $^3P_2$ partial waves are analyzed and we find $f_{p}^2 = 0.0761(4)$, $f_{0}^2 = 0.0790(9)$ and $f_{c}^2 = 0.0772(6)$ with a strong anti-correlation between $f_c^2$ and $f_0^2$. We successfully test normality for the residuals of the fit. Potential tails in terms of different boundary radii as well as chiral Two-Pion-Exchange contributions as sources of systematic uncertainty are also investigated.

Charge symmetry breaking effect for 3H and 3He within s-wave approach

Three-nucleon systems are considered assuming the neutrons and protons to be distinguishable particles. The configuration space Faddeev equations are exploited to calculate ground state energies of 3H and 3He nuclei within an [Formula: see text]-wave approach applying the Malfliet–Tjon, Tamagaki G3RS and Afnan–Tang ATS3 NN potentials. We modify the potentials by scaling strength parameters to define [Formula: see text], [Formula: see text] and [Formula: see text] singlet components. The scaling parameters are fixed to reproduce experimental scattering lengths. The charge symmetry breaking energy is numerically evaluated. The relation between [Formula: see text], [Formula: see text] and [Formula: see text] singlet potentials is discussed.

Ground-state binding energy of [formula omitted] from high-resolution decay-pion spectroscopy

A systematic study on the Λ ground state binding energy of hyperhydrogen HΛ4 measured at the Mainz Microtron MAMI is presented. The energy was deduced from the spectroscopy of mono-energetic pions from the two-body decays of hyperfragments, which were produced and stopped in a 9Be target. First data, taken in the year 2012 with a high resolution magnetic spectrometer, demonstrated an almost one order of magnitude higher precision than emulsion data, while being limited by systematic uncertainties. In 2014 an extended measurement campaign was performed with improved control over systematic effects, increasing the yield of hypernuclei and confirming the observation with two independent spectrometers and two targets of different thicknesses. The analysis of these data is in agreement with the previously published value for the HΛ4 binding energy as well as with a consistent re-analysis of the 2012 data. When compared to the HeΛ4 binding energy from emulsion data, a large charge symmetry breaking effect in the A=4 hypernuclear system is confirmed.

High resolution spectroscopic study ofBeΛ10

Spectroscopy of a $^{10}_{\Lambda}$Be hypernucleus was carried out at JLab Hall C using the $(e,e^{\prime}K^{+})$ reaction. A new magnetic spectrometer system (SPL+HES+HKS), specifically designed for high resolution hypernuclear spectroscopy, was used to obtain an energy spectrum with a resolution of 0.78 MeV (FWHM). The well-calibrated spectrometer system of the present experiment using the $p(e,e^{\prime}K^{+})\Lambda,\Sigma^{0}$ reactions allowed us to determine the energy levels, and the binding energy of the ground state peak (mixture of 1$^{-}$ and 2$^{-}$ states) was obtained to be B$_{\Lambda}$=8.55$\pm$0.07(stat.)$\pm$0.11(sys.) MeV. The result indicates that the ground state energy is shallower than that of an emulsion study by about 0.5 MeV which provides valuable experimental information on charge symmetry breaking effect in the $\Lambda N$ interaction.

The general configuration-space Faddeev formalism for studying pd scattering

The configuration-space Faddeev equations are derived for p-d scattering taking into account the difference in interaction between the participant particles. Appropriate modifications have been made in the well-known configuration-space equations for n-d scattering. To show the effect of these modifications, the s-wave calculations are performed for bound state and scattering problems. We model the charge symmetry breaking effect for 3 H and 3 He with a modified Malfliet-Tjon MT I-III potential. Results obtained for elastic n-d and p-d scattering at Elab =14.1 MeV are compared with our prediction (Ref. [1]) and those of the Los-Alamos/Iowa group (Ref. [2]) .

Observation of Spin-Dependent Charge Symmetry Breaking in ΛN Interaction: Gamma-Ray Spectroscopy of _{Λ}^{4}He.

The energy spacing between the spin-doublet bound state of _{Λ}^{4}He(1^{+},0^{+}) was determined to be 1406±2±2 keV, by measuring γ rays for the 1^{+}→0^{+} transition with a high efficiency germanium detector array in coincidence with the ^{4}He(K^{-},π^{-})_{Λ}^{4}He reaction at J-PARC. In comparison to the corresponding energy spacing in the mirror hypernucleus _{Λ}^{4}H, the present result clearly indicates the existence of charge symmetry breaking (CSB) in ΛN interaction. By combining the energy spacings with the known ground-state binding energies, it is also found that the CSB effect is large in the 0^{+} ground state but is vanishingly small in the 1^{+} excited state, demonstrating that the ΛN CSB interaction has spin dependence.

A collective coupled-channel model and mirror state energy displacements

The spectra of nucleon-nucleus mirror systems allow examination of charge symmetry breaking in nucleon-nucleus interactions. To date, such examination has been performed with studies using microscopic models of structure. Herein we seek characterisation with a coupled-channel model in which the nucleon-nucleus interactions are described using a collective model prescription with the Pauli principle taken into account. The neutron-nucleus Hamiltonian is chosen to give the best match to the compound system spectrum, with emphasis on finding the correct ground state energy relative to the neutron-nucleus threshold. The Coulomb interactions for the proton-nucleus partner of a mirror pair are determined using charge distributions that match the root-mean-square charge radii of the nuclei in question. With the Coulomb interaction so defined modifying the neutron-nucleus Hamiltonian, we then predict a spectrum for the relevant proton-nucleus compound. Discrepancies in that resulting spectrum with measured values we tentatively ascribe to charge-symmetry breaking effects. We consider spectra obtained in this way for the mirror pairs 13C and 13N, 15C and 15F, and 15O and 15N, all to ∼ 10 MeV excitation.

Comment on “Lattice determination ofΣ−Λmixing”

A recent lattice QCD (LQCD) calculation of $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing by the QCDSF-UKQCD Collaboration [Phys. Rev. D 91, 074512 (2015)] finds a mixing angle about half of that found from the Dalitz--Von Hippel (DvH) flavor SU(3) mass formula which relates the $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing matrix element to known octet baryon mass differences and which has been used widely to evaluate charge symmetry breaking effects in $\mathrm{\ensuremath{\Lambda}}$ hypernuclei. We show that the LQCD-calculated $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing matrix element and octet baryon masses satisfy the DvH mass formula, concluding thereby that a good LQCD evaluation of $\mathrm{\ensuremath{\Sigma}}\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ mixing requires an equally good reproduction of octet baryon mass differences which is yet to be demonstrated.

Charge symmetry breaking in electromagnetic nucleon form factors in elastic parity-violating electron-nucleus scattering

The effects of charge symmetry breaking in nucleon electromagnetic form factors on parity- violating elastic electron-12C scattering is studied, and found to be much smaller than other known effects. The analysis of a planned experiment is discussed.

ΣNNquasibound states inHe3(K−,π∓) reactions at 600 MeV/c

We theoretically demonstrate the inclusive and semiexclusive spectra in the $^{3}\mathrm{He}$(${K}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{\ensuremath{\mp}}$) reactions at 600 MeV/$c$ (4${}^{\ensuremath{\circ}}$) within a distorted-wave impulse approximation, using a coupled ($2N\ensuremath{-}\ensuremath{\Lambda})+(2N\ensuremath{-}\ensuremath{\Sigma}$) model with a spreading potential. We present the possible existence of the $\ensuremath{\Sigma}\mathit{NN}$ quasibound state with ${J}^{\ensuremath{\pi}}=$ 1/2${}^{+}$, $T\ensuremath{\simeq}$ 1 near the $\ensuremath{\Sigma}$ threshold, predicted by a $2N\ensuremath{-}Y$ folding-model potential derived from $\mathit{YN}$ $g$-matrices. The result shows that a signal of the ${}_{\ensuremath{\Sigma}}^{3}$He quasibound state is clearly confirmed near the $\ensuremath{\Sigma}$ threshold in the ${\ensuremath{\pi}}^{\ensuremath{-}}$ spectrum, whereas a peak of the ${}_{\ensuremath{\Sigma}}^{3}n$ quasibound state is rather reduced in the ${\ensuremath{\pi}}^{+}$ spectrum owing to the interference effects caused by the ${}^{3}{S}_{1}$-${}^{1}{S}_{0}$ admixture in the $\mathit{NN}$ pair. The mechanism of $\ensuremath{\Sigma}$ production for these spectra and charge symmetry breaking effects are also discussed.

Electro-Production of Light Lambda Hypernuclei

Through the study of light hypernuclei, we can learn about hyperon nucleon interaction. The hypernuclear spectroscopy with electron beams is one of most powerful methods to study detailed structure of light hypernuclei thanks to its high energy resolution. With a decade of efforts at Jefferson Lab, the spectroscopy of Λ hypernuclei with an electron beam is now established. Observation of \({_{\Lambda}^{7}}\) He which gave the last missing binding energy of the A = 7, T = 1 iso-triplet hypernuclei provides an important experimental input for the charge symmetry breaking (CSB) effect of the ΛN interaction. Further study about A = 4 hypernuclear iso-doublet, \({_{\Lambda}^{4}}\) H and \({_{\Lambda}^{4}}\) He, is necessary and such experiments are now planned.

Observation of theHeΛ7Hypernucleus by the (e,e′K+) Reaction

An experiment with a newly developed high-resolution kaon spectrometer (HKS) and a scattered electron spectrometer with a novel configuration was performed in Hall C at Jefferson Lab (JLab). The ground state of a neutron-rich hypernucleus, He 7 Lambda, was observed for the first time with the (e,e'K+) reaction with an energy resolution of ~0.6 MeV. This resolution is the best reported to date for hypernuclear reaction spectroscopy. The he 7 Lambda binding energy supplies the last missing information of the A=7, T=1 hypernuclear iso-triplet, providing a new input for the charge symmetry breaking (CSB) effect of \Lambda N potential.

The impact of charge symmetry and charge independence breaking on the properties of neutrons and protons in isospin-asymmetric nuclear matter

We investigate the effects of charge independence and charge symmetry breaking in neutron-rich matter. We consider neutron and proton properties in isospin-asymmetric matter at normal densities as well as the high-density neutron matter equation of state and the bulk properties of neutron stars. We find charge symmetry and charge independence breaking effects to be very small.