Isospin Breaking Effects Research Articles

Isospin mixing effects in the low-energyK¯N−πΣinteraction

New strong coupled-channels $\overline{K}N\text{\ensuremath{-}}\ensuremath{\pi}\ensuremath{\Sigma}$ potential, reproducing all existing experimental data and suitable for using in an accurate few-body calculations, is constructed. Isospin breaking effects of direct inclusion of the Coulomb interaction and using of physical masses in calculations are investigated. The $1s$ level shift and width of kaonic hydrogen, consistent with the scattering data, was obtained and the corresponding exact strong ${K}^{\ensuremath{-}}p$ scattering length was calculated. One- and two-pole form of $\ensuremath{\Lambda}(1405)$ resonance was considered.

Isospin breaking in K l4 decays

Data on K e4 decays allow one to extract experimental information on the elastic π π scattering amplitude near threshold, and to confront the outcome of the analysis with predictions made in the framework of QCD. These predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin-breaking effects—generated by electromagnetic interactions and by the mass difference of the up and down quarks—are always present. We discuss the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, we note that there is a spectacular isospin-breaking effect in K e4 decays. Once it is taken into account, the previous discrepancy between NA48/2 data on K e4 decays and the prediction of π π scattering lengths disappears.

The dipion mass spectrum in e+e- annihilation and τ decay: a dynamical (ρ, ω, φ) mixing approach

We readdress the problem of finding a simultaneous description of the pion form factor data in e+e- annihilations and in τ decays. For this purpose, we work in the framework of the hidden local symmetry Lagrangian and modify the vector meson mass term by including the pion and kaon loop contributions. This leads us to define the physical ρ, ω and φ fields as linear combinations of their ideal partners, with coefficients being meromorphic functions of s, the square of the four-momentum flowing into the vector meson lines. This allows us to define a dynamical, i.e. s-dependent, vector meson mixing scheme. The model is overconstrained by extending the framework in order to include the description of all meson radiative (VPγ and Pγγ couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking (ω/φ→π+π-) decay modes. The model provides a simultaneous, consistent and good description of the e+e- and τ dipion spectra. The expression for the pion form factor in the latter case is derived from those in the former case by switching off the isospin breaking effects specific to e+e- and switching on those for τ decays. Besides, the model also provides a good account of all decay modes of the form VPγ and Pγγ as well as the isospin breaking decay modes. It leads us to propose new reference values for the ρ0→e+e- and ω→π+π- partial widths, which are part of our description of the pion form factor. Other topics (φ→KK̄, the ρ meson mass and width parameters) are briefly discussed. As the e+e- data are found to be perfectly consistent with τ data up to identified isospin breaking effects, one finds no reason to cast any doubt on them and, therefore, on the theoretical estimate of the muon anomalous moment aμ derived from them. Therefore, our work turns out to confirm the relevance of the reported 3.3σ discrepancy between this theoretical estimate of aμ and its direct BNL measurement.

Investigation ofa0–f0mixing

We investigate the isospin-violating mixing of the light scalar mesons ${a}_{0}(980)$ and ${f}_{0}(980)$ within the unitarized chiral approach. Isospin-violating effects are considered to leading order in the quark mass differences and electromagnetism. In this approach both mesons are generated through meson-meson dynamics. Our results provide a description of the mixing phenomenon within a framework consistent with chiral symmetry and unitarity, where these resonances are not predominantly $q\overline{q}$ states. Amongst the possible experimental signals, we discuss observable consequences for the reaction $J/\ensuremath{\Psi}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ in detail. In particular, we demonstrate that the effect of ${a}_{0}$--${f}_{0}$ mixing is by far the most important isospin-breaking effect in the resonance region and can indeed be extracted from experiment.

Improved estimates of rareKdecay matrix elements fromKℓ3decays

The estimation of rare K decay matrix elements from K{sub l3} experimental data is extended beyond LO in chiral perturbation theory. Isospin-breaking effects at next-to-leading order (and partially next-to-next-to-leading order) in the chiral perturbation theory expansion, as well as QED radiative corrections, are now accounted for. The analysis relies mainly on the cleanness of two specific ratios of form factors, for which the theoretical control is excellent. As a result, the uncertainties on the K{sup +}{yields}{pi}{sup +}{nu}{nu} and K{sub L}{yields}{pi}{sup 0}{nu}{nu} matrix elements are reduced by a factor of about 7 and 4, respectively, and similarly for the direct CP-violating contributions to K{sub L}{yields}{pi}{sup 0}e{sup +}e{sup -} and K{sub L}{yields}{pi}{sup 0}{mu}{sup +}{mu}{sup -}. They could be reduced even further with better experimental data for the K{sub l3} slopes and the K{sub l3}{sup +} branching ratios. As a result, the nonparametric errors for B(K{yields}{pi}{nu}{nu}) and for the direct CP-violating contributions to B(K{sub L}{yields}{pi}{sup 0}l{sup +}l{sup -}) are now completely dominated by those on the short-distance physics.

Neutron-proton mass difference in isospin-asymmetric nuclear matter

Isospin-breaking effects in the baryonic sector are studied in the framework of a medium-modified Skyrme model. The neutron-proton mass difference in infinite, asymmetric nuclear matter is discussed. In order to describe the influence of the nuclear environment on the skyrmions, we include energy-dependent charged and neutral pion optical potentials in the s- and p-wave channels. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it strongly decreases in neutron matter.

Neutron-proton mass difference in nuclear matter

Isospin-breaking effects in nuclear matter are studied in the framework of a medium-modified Skyrme model. The proposed effective Lagrangian incorporates both the medium influence of the surrounding nuclear environment on the single nucleon properties and an explicit isospin-breaking effect in the mesonic sector. The approach predicts that the neutron-proton mass difference decreases in isospin-symmetric nuclear matter but by a very small amount only.

Erratum:CPasymmetry, branching ratios, and isospin breaking effects inB→ργandB→ωγdecays with the perturbative QCD approach [Phys. Rev. D72, 094005 (2005)

Received 23 January 2006DOI:https://doi.org/10.1103/PhysRevD.73.039902©2006 American Physical Society

CPasymmetry, branching ratios, and isospin breaking effects inB→ργandB→ωγdecays with the perturbative QCD approach

The radiative $B\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\gamma}$, $B\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\gamma}$ decay modes are caused by the flavor-changing-neutral-current process, so they give us good insight towards probing the standard model in order to search for new physics. In this paper, we compute the branching ratio, direct $CP$ asymmetry, and isospin breaking effects using the perturbative QCD approach within the standard model.

CPasymmetry, branching ratios, and isospin breaking effects ofB→K*γwith the perturbative QCD approach

The main contribution to the radiative $B\ensuremath{\rightarrow}{K}^{*}\ensuremath{\gamma}$ mode is from penguin operators which are quantum corrections. Thus, this mode may be useful in the search for physics beyond the standard model. In this paper, we compute the branching ratio, direct $CP$ asymmetry, and isospin breaking effects within the standard model in the framework of perturbative QCD, and discuss how new physics might show up in this decay.

Chiral dynamics of kaon-nucleon interactions, revisited

The anti-kaon nucleon system close to threshold is analyzed in view of the new accurate DEAR kaonic hydrogen data. The calculations are performed using chiral SU(3) effective field theory in combination with non-perturbative schemes based on coupled channels. Several variants of such approaches are compared with experimental data and the differences in the results are discussed. Coulomb and isospin breaking effects turn out to be important and are both taken into account. The pole structure of the Lambda(1405) resonance close to the anti-kaon nucleon threshold is critically examined.

Kaonic Hydrogen andK−pScattering

Chiral SU(3) effective field theory in combination with a relativistic coupled-channels approach is used to perform a novel analysis of the strong-interaction shift and width in kaonic hydrogen in view of the new accurate DEAR measurements. Questions of consistency with previous K(-)p data are examined. Coulomb and isospin breaking effects turn out to be important and are both taken into account in this work.

Isospin-breaking effects onαextracted inB→ππ,ρρ,ρπ

Isospin-breaking in B --> pi pi caused by pi^0-eta-eta' mixing is studied in a model-independent way using flavor SU(3). Measured branching ratios for B^+ --> pi^+ pi^0, B^+ --> pi^+ eta^(') and B^0 --> pi^0 eta^(') imply an uncertainty in alpha smaller than 1.4 degree. We find a negligible effect of pi^0-eta-eta' mixing on alpha in B --> rho pi. Characterizing the effect of rho^0-omega mixing in B --> rho rho and in B --> rho pi by the two-pion invariant mass dependence, we point out a way of constraining this effect experimentally or eliminating it altogether. We show that a model-independent shift in alpha caused by electroweak penguin amplitudes in B --> pi pi and B --> rho rho, \Delta alpha_{EWP}=1.5+- 0.3 degree, may be slightly different in B --> rho pi. Other sources of isospin-breaking in these processes are briefly discussed.

Isospin breaking in $K\to3\pi$ decays II: radiative corrections

The five different CP conserving amplitudes for the decays $K\to3\pi$ are calculated using Chiral Perturbation Theory. The calculation is made to next-to-leading order and includes full isospin breaking. The squared amplitudes are compared with the corresponding ones in the isospin limit to estimate the size of the isospin breaking effects. In this paper we add the radiative corrections to the earlier calculated $m_u-m_d$ and local electromagnetic effects. We find corrections of order 5-10 percent.

Constraining the Unitarity Triangle with B→Vγ

We discuss the exclusive radiative decays $B\to K^{*}\gamma$, $B \to\rho\gamma$, and $B\to\omega\gamma$ in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Special emphasis is placed on constraining the CKM-unitarity triangle from these observables. We propose a theoretically clean method to determine CKM parameters from the ratio of the $B\to\rho l\nu$ decay spectrum to the branching fraction of $B\to\rho\gamma$. The method is based on the cancellation of soft hadronic form factors in the large energy limit, which occurs in a suitable region of phase space. The ratio of the $B\to\rho\gamma$ and $B\to K^{*}\gamma$ branching fractions determines the side $R_{t}$ of the standard unitarity triangle with reduced hadronic uncertainties. The recent Babar bound on $B(B^0\to\rho^0\gamma)$ implies $R_t < 0.81 (\xi/1.3)$, with the limiting uncertainty coming only from the SU(3) breaking form factor ratio $\xi$. This constraint is already getting competitive with the constraint from $B_{s}$-$\bar B_{s}$ mixing. Phenomenological implications from isospin-breaking effects are briefly discussed.

Isospin violating effects in e+e− vs. τ measurements of the pion form factor |Fπ|2(s)

We study possible so far unaccounted isospin breaking effects in the relation between the pion form factor as determined in e+e− experiments and the corresponding quantity obtained after accounting for known isospin breaking effects by an isospin rotation from the τ-decay spectra. In fact the observed 10% discrepancy in the respective pion form factors may be explained by the isospin breaking which is due to the difference between masses and widths of the charged and neutral ρ mesons. Since the hadronic contribution to the muon anomalous magnetic moment can be calculated directly in terms of the e+e−-data the corresponding evaluation seems to be more reliable. Our estimate is aμhad(1)=(694.8±8.6)×10−10. The τ-data are useful at the presently aimed level of accuracy only after appropriate input from theory.

Theoretical precision in estimates of the hadronic contributions to (g − 2)μ and αQED(Mz)

I review recent estimates of the non-perturbative hadronic vacuum polarization contributions. Since these at present can only be evaluated in terms of experimental data of limited precision, the related uncertainties pose a serious limitation in our ability to make precise predictions. Besides e+e−-annihilation data also τ decay spectra can help to get better predictions. Here, it is important to account for all possible iso-spin violations in τ-decay spectra, from which e+e− cross sections may be obtained by an iso-spin rotation. The observed 10% discrepancy in the region above the π may be understood as a so far unaccounted iso-spin breaking effect.

Constraining the unitarity triangle with B→ K*γ and B→ργ

We discuss the exclusive radiative decays B -> K* gamma and B -> rho gamma in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Phenomenological implications for branching ratios and isospin breaking effects are discussed. Special emphasis is placed on constraining the CKM unitarity triangle from these observables.

Nucleon axial charge from quenched lattice QCD with domain wall fermions

We present a quenched lattice calculation of the nucleon isovector vector and axial-vector charges gV and gA. The chiral symmetry of domain wall fermions makes the calculation of the nucleon axial charge particularly easy since the Ward-Takahashi identity requires the vector and axial-vector currents to have the same renormalization, up to lattice spacing errors of order O(a^2). The DBW2 gauge action provides enhancement of the good chiral symmetry properties of domain wall fermions at larger lattice spacing than the conventional Wilson gauge action. Taking advantage of these methods and performing a high statistics simulation, we find a significant finite volume effect between the nucleon axial charges calculated on lattices with (1.2 fm)^3 and (2.4 fm)^3 volumes (with lattice spacing, a, of about 0.15 fm). On the large volume we find gA = 1.212 +/- 0.027(statistical error) +/- 0.024(normalization error). The quoted systematic error is the dominant (known) one, corresponding to current renormalization. We discuss other possible remaining sources of error. This theoretical first principles calculation, which does not yet include isospin breaking effects, yields a value of gA only a little bit below the experimental one, 1.2670 +/- 0.0030.

Confronting spectral functions from e+e− annihilation and τ decays: Consequences for the muon magnetic moment

Vacuum polarization integrals involve the vector spectral functions which can be experimentally determined from two sources: ( i) e + e − annihilation cross sections and ( ii) hadronic τ decays. Recently results with comparable precision have become available from CMD-2 on one side, and ALEPH, CLEO and OPAL on the other. The comparison of the respective spectral functions involves a correction from isospin-breaking effects, which is evaluated. After the correction it is found that the dominant ππ spectral functions do not agree within experimental and theoretical uncertainties. Some disagreement is also found for the 4π spectral functions. The consequences of these discrepancies for vacuum polarization calculations are presented, with the emphasis on the muon anomalous magnetic moment. Adding quadratically experimental and theoretical uncertainties, we find that the full Standard Model prediction of a μ deviates from the recent BNL measurement at the level of 3.0 ( e + e −-based) and 0.9 (τ-based) standard deviations.