Charge Symmetry Breaking Research Articles

Neutron structure function and inclusive deep inelastic scattering from3Hand3Heat large Bjorkenx

A detailed study of inclusive deep inelastic scattering (DIS) from mirror $A=3$ nuclei at large values of the Bjorken variable x is presented. The main purpose is to estimate the theoretical uncertainties in the extraction of the neutron DIS structure function from such nuclear measurements. On the one hand, within models in which no modification of the bound nucleon structure functions is taken into account, we have investigated the possible uncertainties arising from (i) charge symmetry breaking terms in the nucleon-nucleon interaction, (ii) finite ${Q}^{2}$ effects neglected in the Bjorken limit, (iii) the role of different prescriptions for the nucleon spectral function normalization providing baryon number conservation, and (iv) the differences between the virtual-nucleon and light-cone formalisms. Although these effects have not yet been considered in existing analyses, our conclusion is that all these effects cancel at the level of $\ensuremath{\approx}1%$ for $x\ensuremath{\lesssim}0.75,$ in overall agreement with previous findings. On the other hand, we have considered several models in which the modification of the bound nucleon structure functions is accounted for to describe the EMC effect in DIS scattering from nuclei. It turns out that within these models the cancellation of nuclear effects is expected to occur only at a level of $\ensuremath{\approx}3%,$ leading to an accuracy of $\ensuremath{\approx}12%$ in the extraction of the neutron to proton structure function ratio at $x\ensuremath{\approx}0.7--0.8.$ Another consequence of considering a broad range of models of the EMC effect is that the previously suggested iteration procedure does not improve the accuracy of the extraction of the neutron to proton structure function ratio.

The α particle based on modern nuclear forces

The Faddeev-Yakubovsky equations for the \ensuremath{\alpha} particle are solved. Accurate results are obtained for several modern nucleon-nucleon $(\mathrm{NN})$ interaction models, which include charge-symmetry breaking effects in the $\mathrm{NN}$ force, nucleon mass dependences as well as the Coulomb interaction. These models are augmented by three-nucleon forces of different types and adjusted to the $3N$ binding energy. Our results are close to the experimental binding energy with a slight overbinding. Thus there is only little room left for the contribution of possible $4N$ interactions to the \ensuremath{\alpha}-particle binding energy. We also discuss model dependences of the binding energies and the wave functions.

Some Effects on Λ Single Particle Energies**The project supported in part by National Natural Science Foundation of China and Foundation of the State Education Ministry of China for Doctoral Training

With the phenomenological Λ-nucleus potentials of Woods–Saxon shape, the effects of the mass-number dependence of the shrinkage, the effective mass and the charge-symmetry breaking (CSB) on the single particle energies are discussed. It is found that the single particle energies are not sensitive to the effective mass . But the radius parameter depended on the mass number can substantially improve the results. We also found that CSB effect is significant for heavy hypernuclei with a large neutron excess.

Charge symmetry breaking inNNscattering with an interaction from effective field theory

The effect of isospin breaking pion s-wave rescattering is included in elastic $\mathrm{NN}$ scattering at low energies using an interaction obtained from effective field theory. Although this mechanism gave a large contribution to charge symmetry breaking in $n\stackrel{\ensuremath{\rightarrow}}{p}d{\ensuremath{\pi}}^{0},$ the effect is rather small in $\mathrm{pp}$ vs $\mathrm{nn}$ scattering parameters and in the ${}^{3}\mathrm{H}{\ensuremath{-}}^{3}\mathrm{He}$ binding energy difference. This smallness is caused by large cancellation of the up-down quark mass difference contribution and electromagnetic effects to the $\mathrm{np}$ mass difference.

Magnetic spectrometer Big Karl for studies of meson production reactions

The paper describes modifications of the Jülich magnetic spectrometer Big Karl needed to study meson production and especially to investigate charge symmetry breaking effects—an experiment that requires a high-precision measurement. New elements that have been added to Big Karl have extended the spectrometer capabilities to a much wider momentum range. The new features also facilitate simultaneous detection of particles with very different rigidities. The experimental methods for improving background and determining relative acceptance of the spectrometer at various rigidities are presented.

Erratum to: “A full one-loop charge symmetry breaking effective potential”

Erratum to: “A full one-loop charge symmetry breaking effective potential”

Charge-dependent nucleon–nucleon potential from chiral effective field theory

We discuss charge-symmetry and charge-independence breaking in a chiral effective field theory approach for few-nucleon systems based on a modified Weinberg power counting. We construct a two-nucleon potential with bound and scattering states generated by means of a properly regularized Lippmann–Schwinger equation. We systematically introduce strong isospin-violating and electromagnetic operators in the theory. We use standard procedures to treat the Coulomb potential between two protons in momentum space. We present results for phase shifts in the proton–proton, neutron–proton and the neutron–neutron systems. We discuss the various contributions to charge dependence and charge-symmetry breaking observed in the nucleon–nucleon scattering lengths.

Nonsinglet structure function of the3He−3Hsystem and divergence of the Gottfried integral

We study shadowing and antishadowing corrections to the flavor nonsinglet structure function ${F}_{2}^{{}^{3}\mathrm{He}}\ensuremath{-}{F}_{2}^{{}^{3}\mathrm{H}}$ and show that the difference between the one-particle density distributions of ${}^{3}\mathrm{He}$ and ${}^{3}\mathrm{H}$ plays an important role at very small x. We find that the flavor nonsinglet structure function in these mirror nuclei is enhanced at small x by nuclear shadowing, which increases the nuclear Gottfried integral, integrated from ${10}^{\ensuremath{-}4}$ to 3, by 15--41 %. When integrated from zero, the Gottfried integral is divergent for these mirror nuclei. It seems likely that, as a consequence of charge symmetry breaking, this may also apply to the proton-neutron system.

High resolution spectroscopy of Λ hypernuclei: present status and perspectives

Recent results and future directions of the γ-ray spectroscopy of Λ hypernuclei are discussed. A further analysis of the last KEK experiment (E566) has revealed a new γ transition in 12ΛC at 6048keV (preliminary), which is ascribed to the M1(13−→11−) transition. At J-PARC, studies will be extended from p-shell to s-shell and sd-shell hypernuclei. In the first part of the J-PARC E13 experiment, we will measure the 4ΛHe(1+→0+) transition to study charge-symmetry breaking in the ΛN interaction and investigate the 19ΛF hypernucleus to study ΛN spin–spin interaction further using one of the sd-shell hypernuclei. In the second part of E13, we will precisely measure the spin-flip B(M1) value for the 7ΛLi(3/2+→1/2+) transition. Beyond E13, we plan to study impurity effects by observing possible changes in nuclear deformation caused by the presence of a Λ in sd-shell hypernuclei, as well as to investigate various heavier Λ hypernuclei in order to precisely determine the energies of Λ single-particle orbits.

QED–QCD INTERFERENCE EFFECT ON THE CHARGE-DEPENDENT N–N INTERACTION

The charge symmetry breaking and charge independence breaking N–N1 S 0 scattering length differences, Δa CSB and Δa CIB , are calculated by a resonating group method with a quark cluster model. By adding the QED–QCD interference effect to the quark mass difference and the electromagnetic interaction, the Δa CSB and Δa CIB values can be reproduced with model parameters constrained by the hadron isomultiplet mass splitting.

The u– d quark mass difference and nuclear charge symmetry breaking

The group theoretical analysis of the Coleman-Glashow tadpole picture of "meson-mixing" is quantitatively reproduced by the u-d constituent quark mass difference in quantum loop calculations of the self-energies of mesons. This demonstration that the Coleman-Glashow scales can be directly calculated from the constituent $u - d$ quark mass difference finishes the link between charge symmetry breaking in low energy nuclear physics and the $u - d$ quark mass difference in particle physics.

A full one-loop charge symmetry breaking effective potential

We calculate the one-loop contributions to the effective potential for the minimal supersymmetric model when scalar fields other than the Higgses have vacuum expectation values. The importance of these contributions for studies of charge and colour breaking bounds is discussed.

Symmetries and symmetry breaking

Several new proton-proton parity violation experiments are presently either being performed or are being prepared for execution in the near future. Similarly, a new measurement of the parity-violating gamma-ray asymmetry in polarized neutron capture on the proton is being developed with a ten-fold improvement over previous measurements. These experiments are intended to provide stringent constraints on the set of seven effective weak meson-nucleon coupling constants. Time-reversal-invariance non-conservation has now been unequivocally demonstrated in a direct measurement at CPLEAR. Tests may also be made of time-reversal-invariance non-conservation in systems other than the kaon system. There exist two classes of time-reversal invariance breaking interactions: P-odd/T-odd and P-even/T-odd interactions. Constraints on the first ones stem from measurements of the electric dipole moment of the neutron, while constraints on the second ones stem from the same and measurements of charge symmetry breaking in neutron-proton elastic scattering and from $K$ semi-leptonic decays. A series of precision experiments, either ongoing or being prepared, will determine the neutral weak current of the proton by measuring the parity-violating normalized asymmetry in electron-proton elastic scattering. A direct comparison between the electromagnetic and neutral weak ground state currents of the nucleon will allow a delineation of the contributions to these currents of the various quark flavours, including quarks which belong exclusively to the nucleon sea. An extension of these precision experiments to very low momentum transfer would permit stringent limits to be placed on physics beyond the standard model.

Charge symmetry breaking of the nucleon-nucleon interaction: ρ-ω mixing versus nucleon mass splitting

We investigate three models for the charge symmetry breaking (CSB) of the nucleon-nucleon ($NN$) interaction (based upon $\rho$-$\omega$ mixing, nucleon mass splitting, and phenomenology) that all reproduce the empirical value for the CSB of the $^1S_0$ scattering length ($\Delta a_{CSB}$) accurately. We reveal that these models make very different predictions for CSB in $^3P_J$ waves and examine the impact of this on some observable quantities of $A\geq 3$ nuclear systems. It turns out that the $^3$H-$^3$He binding energy difference is essentially ruled by $\Delta a_{CSB}$ and not very sensitive to CSB from $P$ waves. However, the Coulomb displacement energies (which are the subject of the Nolen-Schiffer anomaly) receive about 50% of their CSB contribution from $NN$ partial waves beyond $^1S_0$. Consequently, the predictions by the various CSB models differ here substantially (10-20%). Unfortunately, the evaluation of the leading Coulomb contributions carry a large uncertainty such that no discrimination between the competing CSB models can presently be made. To decide the issue we suggest to look into nuclear few-body reactions that are sensitive to CSB of the nuclear force.

Apparatus for a measurement of charge symmetry breaking in np→dπ 0

TRIUMF experiment E704 is a study of Charge Symmetry Breaking in the reaction np→dπ 0. The observable is the forward–backward asymmetry in the centre-of-mass differential cross-section, predicted to be −0.0035 at 5 MeV above threshold. As a check on the understanding of certain systematic effects the reaction pp→dπ +, which cannot have an asymmetry, is measured also. Similarly, neutron–proton elastic scattering is used to verify spectrometer acceptance. We describe the beams, target, and detectors developed for this experiment.

Measurement of charge symmetry breaking by the comparison ofπ+d→ppηwithπ−d→nnη

Measurement of charge symmetry breaking by the comparison of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>pp</mml:mi><mml:mi>η</mml:mi></mml:math>with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>−</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>nn</mml:mi><mml:mi>η</mml:mi></mml:math>

High-precision, charge-dependent Bonn nucleon-nucleon potential

We present a charge-dependent one-boson-exchange nucleon-nucleon $(\mathrm{NN})$ potential that fits the world proton-proton data below 350 MeV available in the year 2000 with a ${\ensuremath{\chi}}^{2}$ per datum of 1.01 for 2932 data and the corresponding neutron-proton data with ${\ensuremath{\chi}}^{2}/\mathrm{datum}$ $=1.02$ for 3058 data. This reproduction of the $\mathrm{NN}$ data is more accurate than by any phase-shift analysis and any other $\mathrm{NN}$ potential. This is achieved by the introduction of two effective $\ensuremath{\sigma}$ mesons the parameters of which are partial-wave dependent. The charge dependence of the present potential (which we call ``CD-Bonn'') is based upon the predictions by the Bonn full model for charge symmetry and charge-independence breaking in all partial waves with $J&lt;~4.$ The potential is represented in terms of the covariant Feynman amplitudes for one-boson exchange which are nonlocal. Therefore, the off-shell behavior of the CD-Bonn potential differs in a characteristic way from commonly used local potentials and leads to larger binding energies in nuclear few- and many-body systems, where underbinding is a persistent problem.

Density dependence of charge symmetry breaking

We study the Okamoto-Nolen-Schiffer (ONS) anomaly in the binding energy of mirror nuclei at high density by adding a single neutron or proton to a quark gluon plasma. In this high-density limit we find an anomaly equal to two-thirds of the Coulomb exchange energy of a proton. This effect is dominated by quark electromagnetic interactions---rather than by the up-down quark mass difference. At normal density we calculate the Coulomb energy of neutron matter using a string-flip quark model. We find a nonzero Coulomb energy because of the neutron's charged constituents. This effect could make a significant contribution to the ONS anomaly.

Deep inelastic scattering on asymmetric nuclei

We study deep inelastic scattering on isospin asymmetric nuclei. In particular, the difference of the nuclear structure functions and the Gottfried sum rule for the lightest mirror nuclei, 3He and 3H, are investigated. It is found that such systems can provide significant information on charge symmetry breaking and flavor asymmetry in the nuclear medium. Furthermore, we propose a new method to extract the neutron structure function from radioactive isotopes far from the line of stability. We also discuss the flavor asymmetry in the Drell–Yan process with isospin asymmetric nuclei.

Charge and isospin symmetry breaking via external π0– η meson mixing

A simple model of isospin and charge symmetry breaking due to external π 0– η meson mixing is presented. It is based on amplitudes extracted from the available experimental data for pd→ 3He π 0 , pd→ 3He η and dd→ 4He η reactions. Predictions of the strength of isospin symmetry breaking in pd→ 3H π +/ 3 He π 0 reactions are given. Within the same model, the cross section for the charge symmetry breaking dd→ 4He π 0 reaction is calculated.