Isospin Symmetry Breaking Research Articles

Spectra and decays of $\pi \pi$ and $\pi K$ atoms

We describe the spectra and decays of pi pi and pi K atoms within a non-relativistic effective field theory. The evaluations of the energy shifts and widths are performed at next-to-leading order in isospin symmetry breaking. We provide general formulae for all S-states, and discuss the states with angular momentum one in some detail. The prediction for the lifetime of the pi K atom in its ground-state yields tau = (3.7 \pm 0.4) * 10^{-15} sec.

Decay widths and energy shifts of ππ and πK atoms

We calculate the S-wave decay widths and energy shifts for π+π− and π±K∓ atoms in the framework of QCD + QED. The evaluation—valid at next-to-leading order in isospin symmetry breaking—is performed within a non-relativistic effective field theory. The results are of interest for future hadronic atom experiments.

Isospin symmetry breaking and the nuclear shell model

The effect of isospin symmetry breaking on level statistics has been examined with the nuclear shell model. The eigenvalues and electromagnetic transitions were calculated with the program OXBASH for the nuclide 26Al for conserved isospin and for broken isospin. The long-range correlations of the eigenvalues, as measured by Δ3, show good agreement between the experimental results and the calculations. However, there are discrepancies between data and calculations for the short-range correlations of the eigenvalues.

Exclusive $B \to (K^*, \rho) \gamma$ decays in general two-Higgs-doublet models

By employing the QCD factorization approach, we calculated the next-to-leading order new physics contributions to the branching ratios, CP asymmetries, isospin and U-spin symmetry breaking of the exclusive decays $B \to V \gamma$ ( $V = K^*, \rho$ ), induced by the charged Higgs penguins in general two-Higgs-doublet models. Within the considered parameter space, we found that (a) the new physics corrections to the observables are generally small in model I and model III-A, moderate in model II, but large in model III-B; (b) from the well measured branching ratios and upper limits, a lower bound of M H > 200 GeV in model II was obtained, while the allowed range of M H in model III-B is $ 226 \leq M_{H} \leq 293 $ GeV; these bounds are comparable with those from the inclusive $B \to X_s \gamma$ decay; (c) the NLO Wilson coefficient C 7(m b ) in model III-B is positive and disfavored by the measured value of isospin symmetry breaking $ \Delta_{0-}^{\mathrm{{exp}}} (K^*\gamma) = (3.9 \pm 4.8)\%$ , but it still cannot be excluded if we take the large errors into account; (d) the CP asymmetry $\mathcal{A}_{CP}(B \to \rho \gamma)$ in model III-B has an opposite sign to the one in the standard model (SM), which may be used as a good observable to distinguish the SM from model III-B; (e) the isospin symmetry breaking $ \Delta(\rho\gamma)$ is less than $10\%$ in the region of $\gamma = [ 40 \sim 70]^\circ$ preferred by the global fit result, but it can be as large as 20 to $40\%$ in the regions of $\gamma \leq 10^\circ$ and $\gamma \geq 120^\circ$ . The SM and model III-B predictions for $ \Delta(\rho\gamma)$ are opposite in sign for small or large values of the CKM angles; (f) the U-spin symmetry breaking $\Delta U(K^*,\rho)$ in the SM and the general two-Higgs-doublet models is generally small in size: $\sim 10^{-7}$ .

Isospin Symmetry Breaking Effects on the Properties of Asymmetrical Nuclear Matter and -Stable Matter

We have studied the influences of isospin symmetry breaking of nucleon-nucleon interaction on the various properties of asymmetrical nuclear matter and $\beta$-stable matter. For asymmetrical nuclear matter, it is found that by including this isospin symmetry breaking, the changes of bulk properties increase by increasing both density and asymmetry parameter. However, these effects on the total energy and equation of state of $\beta$-stable matter are ignorable. For asymmetrical nuclear matter, the validity of the empirical parabolic law in the isospin symmetry breaking case is shown. It is observed that the isospin symmetry breaking of nucleon-nucleon interaction affects the $\beta$-equilibrium conditions in $\beta$-stable matter.

Baryon charge radii and quadrupole moments in the1/Ncexpansion: The 3-flavor case

We develop a straightforward method to compute charge radii and quadrupole moments for baryons both with and without strangeness, when the number of QCD color charges is N_c. The minimal assumption of the single-photon exchange ansatz implies that only two operators are required to describe these baryon observables. Our results are presented so that SU(3) flavor and isospin symmetry breaking can be introduced according to any desired specification, although we also present results obtained from two patterns suggested by the quark model with gluon exchange interactions. The method also permits to extract a number of model-independent relations; a sample is r^2_Lambda / r_n^2 = 3/(N_c+3), independent of SU(3) symmetry breaking.

Isospin symmetry breaking and scaling observed in pion production in p+d reactions

A stack of annular detectors made of high purity germanium was used to measure p+d→3He+π0 and p+d→3H+π+ differential and total cross sections at beam momenta from 900 to 1050 MeV/c. The total cross sections are consistent with Δ-excitation. The differential data consist of two components. One corresponds to large momentum transfer from the projectile to the pion, the other to small momentum transfer. The former shows an independence of the slope as function of the momentum transfer t (scaling). The scale parameter is different for π+ and π0 emission which violates isospin symmetry. The second component which is almost isotropic is in agreement with isospin symmetry. It is approximately a quarter of the total yield in the Δ resonance region.

Three-body approach to theK−dscattering length in particle basis

We report on the first calculation of the scattering length A_{K^-d} based on a relativistic three-body approach where the two-body input amplitudes coupled to the Kbar N channels have been obtained with the chiral SU(3) constraint, but with isospin symmetry breaking effects taken into account. Results are compared with a recent calculation applying a similar set of two-body amplitudes,based on the fixed center approximation, considered as a good approximation for a loosely bound target, and for which we find significant deviations from the exact three-body results. Effects of the hyperon-nucleon interaction, and deuteron $D$-wave component are also evaluated.

Calculated corrections to superallowed Fermiβdecay: New evaluation of the nuclear-structure-dependent terms

The measured $ft$-values for superallowed $0^{+} \to 0^{+}$ nuclear $\beta$-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. An essential requirement for this test is accurate calculations for the radiative and isospin symmetry-breaking corrections that must be applied to the experimental data. We present a new and consistent set of calculations for the nuclear-structure-dependent components of these corrections. These new results do not alter the current status of the unitarity test -- it still fails by more than two standard deviations -- but they provide calculated corrections for eleven new superallowed transitions that are likely to become accessible to precise measurements in the future. The reliability of all calculated corrections is explored and an experimental method indicated by which the structure-dependent corrections can be tested and, if necessary, improved.

Tests of the standard model from superallowed Fermi β-decay studies: The 74Rb β-decay

Precise measurements of the intensities of superallowed Fermi 0+ → 0+β-decays have provided a powerful test of the CVC hypothesis at the level of 3×10-4 and also led to a result in disagreement with unitarity for the CKM matrix at the 98% confidence level. It is essential to address possible trivial explanations for the apparent non-unitarity such as uncertainties in the isospin symmetry-breaking corrections. We have carefully studied the 74Rb →74Kr β-decay in order to measure the non-analog β-decay branching to the 0+ state at 508 keV in 74Kr. We have determined that this branching is < 3×10-4, far smaller than any published theoretical estimate. We also show that high-precision, complete spectroscopy, measuring the major β-branches to excited 0+ and 1+ states, must be performed if one is to obtain a meaningful branching ratio to the excited 0+ state and concomitantly deal, in a substantial way, with the possibility of β feeding to an array of 1+ states.

Isospin symmetry breaking in ρ→πγ decay

In terms of effective field theory and mixed-propagator approach, we show that there is a larger hidden effect of isospin breaking in rho(0) --> pi(0)gamma decay due to a w exchange, rho(0) --> w --> pi(0)gamma. The branching ratio is predicted as B(rho(0) --> pi(0)gamma) = (11.67 +/- 2.0) x 10(-4), which is much larger than Particle Data Grolip's datum (6.8 +/- 1.7) x 10(-4) and one of charged mode, B(rho(+/-) --> pi(+/-)gamma) = (4.5 +/- 0.5) x 10(-4).

Resonating-group study of baryon-baryon interactions for the complete baryon octet:NNinteraction

We upgrade a SU_6 quark-model description for the nucleon-nucleon and hyperon-nucleon interactions by improving the effective meson-exchange potentials acting between quarks. For the scalar- and vector-meson exchanges, the momentum-dependent higher-order term is incorporated to reduce the attractive effect of the central interaction at higher energies. The single-particle potentials of the nucleon and Lambda, predicted by the G-matrix calculation, now have proper repulsive behavior in the momentum region q_1=5 - 20 fm^-1. A moderate contribution of the spin-orbit interaction from the scalar-meson exchange is also included. As to the vector mesons, a dominant contribution is the quadratic spin-orbit force generated from the rho-meson exchange. The nucleon-nucleon phase shifts at the non-relativistic energies up to T_lab=350 MeV are greatly improved especially for the 3E states. The low-energy observables of the nucleon-nucleon and the hyperon-nucleon interactions are also reexamined. The isospin symmetry breaking and the Coulomb effect are properly incorporated in the particle basis. The essential feature of the Lambda N - Sigma N coupling is qualitatively similar to that obtained from the previous models. The nuclear saturation properties and the single-particle potentials of the nucleon, Lambda and Sigma are reexamined through the G-matrix calculation. The single-particle potential of the Sigma hyperon is weakly repulsive in symmetric nuclear matter. The single-particle spin-orbit strength for the Lambda particle is very small, in comparison with that of the nucleons, due to the strong antisymmetric spin-orbit force generated from the Fermi-Breit interaction.

Chaos and isospin symmetry breaking in rotational nuclei

For nuclei with N≈ Z, the isospin degree of freedom is important and, for deformed systems, rotational bands of different isospin may be expected at low excitation energies. We have investigated, in a simple model space, the influence of the isospin-breaking Coulomb interaction on the degree of chaoticity of these rotational bands. The statistical measures used rely on an analysis of level-spacing distributions, which are extremely difficult to measure experimentally. We show, however, that the overlap integrals between states of similar frequency reflect well the degree of chaoticity. This quantity is closely related to the experimentally more accessible γ-decay “spreading width”.

Meson production in p + d reactions

Total and differential cross sections for the reactions p + d → 3He + m 0 with m=π, η and p + d → 3H+π+ were measured with the GEM detector at COSY for beam momenta between threshold and the maximum of the corresponding baryon resonance. For both reactions a strong forward-backward asymmetry was found. The data were compared with model calculations. The aspect of isospin symmetry breaking is studied.

Isospin symmetry breaking within the HLS Model: A full ( $\rho, \omega, \phi$ ) mixing scheme

We study the way isospin symmetry violation can be generated within the Hidden Local Symmetry (HLS) Model. We show that isospin symmetry breaking effects on pseudoscalar mesons naturally induces correspondingly effects within the physics of vector mesons, through kaon loops. In this way, one recovers all features traditionally expected from $\rho-\omg$ mixing and one finds support for the Orsay phase modelling of the $e^+e^- \ra \pi^+ \pi^-$ amplitude. We then examine an effective procedure which generates mixing in the whole $\rho$, $\omg$, $\phi$ sector of the HLS Model. The corresponding model allows us to account for all two body decays of light mesons accessible to the HLS model in modulus and phase, leaving aside the $\rho \ra \pi \pi$ and $K^* \ra K \pi$ modes only, which raise a specific problem. Comparison with experimental data is performed and covers modulus and phase information; this represents 26 physics quantities successfully described with very good fit quality within a constrained model which accounts for SU(3) breaking, nonet symmetry breaking in the pseudoscalar sector and, now, isospin symmetry breaking.

Meson production in p+d reactions

Total and differential cross sections for the reactions p + d → 3He + m0 with m=π, η and p + d → 3H+π+ were measured with the GEM detector at COSY for beam momenta between threshold and the maximum of the corresponding baryon resonance. For both reactions a strong forward-backward asymmetry was found. The data were compared with model calculations. The aspect of isospin symmetry breaking is studied.

Isospin symmetry breaking and direct CP violation in B → ϱγ within and beyond the standard model

We discuss the isospin symmetry breaking quantity Δ ±0 ≡ Γ( B ± → ϱ ±γ)/2Γ( B 0 → ϱ 0γ)−1, and the direct CP violation in B ± → ϱ ±γ within and beyond the standard model. After showing that the leading-order calculation would be a good approximation in such models, we argue that measurements of these quantities would be able to disentagle physics beyond the standard model.

Precise half-life measurement for the superallowed 0(+)-->0(+) beta emitter (74)Rb: first results from the new radioactive beam facility (ISAC) at TRIUMF.

Presently, the world data for superallowed beta decay leads to a result in disagreement (at the 98% confidence level) with the predictions of the minimal standard model for the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. Precise data for the superallowed 0(+)-->0(+) beta decay of (74)Rb would provide a critical test of the nucleus-dependent isospin symmetry-breaking corrections that must be calculated for these superallowed Fermi beta decays. The present work reports the first precise measurement of the half-life for (74)Rb ( t(1/2) = 64.761+/-0.031 ms). The data were obtained at the radioactive beam facility (ISAC) at TRIUMF using a beam of approximately 4000 (74)Rb ions s(-1).

Supersymmetric effects on isospin symmetry breaking and directCPviolation inB→ργ

We argue that one can search for physics beyond the standard model through measurements of the isospin-violating quantity $\Delta^{-0} \equiv \Gamma(B^- \to \rho^- \gamma)/2\Gamma(B^0 \to \rho^0 \gamma)-1$, its charge conjugate $\Delta^{+0}$, and direct CP violation in the partial decay rates of $B^\pm \to \rho^\pm \gamma$. We illustrate this by working out theoretical profiles of the charge-conjugate averaged ratio $\Delta \equiv {1 \over 2}(\Delta^{+0} +\Delta^{-0})$ and the CP asymmetry $A_{CP}(B^\pm \to \rho^\pm \gamma)$ in the standard model and in some variants of the minimal supersymmetric standard model. We find that chargino contributions in the large $\tan \beta$ region may modify the magnitudes and flip the signs of $\Delta$ and $A_{CP}(B^\pm \to \rho^\pm \gamma)$ compared to their standard-model values, providing an unmistakeable signature of supersymmetry.

Electromagnetic self-energies of neutral pions: contributions from vector resonances

By employing vector-meson dominance to establish the electromagnetic interactions of hadrons, the electromagnetic self-energy of the neutral pions, which receives the contributions from the vector resonances due to chiral anomaly, is evaluated. This part of the electromagnetic mass, which can contribute to the mass difference of π ±– π 0, is finite and as expected, is smaller than the contributions due to isospin symmetry breaking and electromagnetic chiral logs corrections, however, could be compared with the contribution from the short-distance QCD.