The physical state of $ρ$-$ω$-$ϕ$ mesons can be mixed by the unitary matrix. The decay processes of $ω\rightarrow π^{+}π^{-}$ and $ϕ\rightarrow π^{+}π^{-}$ are from the isospin symmetry breaking. The $ρ-ω$, $ρ-ϕ$ and $ω-ϕ$ interferences lead to resonance contribution to produce the strong phases. The $CP$ asymmetry is considered from above isospin symmetry breaking due to the new strong phase for the first order. It has been found the $CP$ asymmetry can be enhanced greatly for the decay process of $B^{0}\rightarrowπ^+π^{-}η^{(')}$ when the invariant masses of the $π^+π^{-}$ pairs are in the area around the $ω$ resonance range and the $ϕ$ resonance range in perturbative QCD. We also discuss the possibility to search the predicted $CP$ violation at the LHC.
In Perturbative QCD (PQCD) approach we study the direct $CP$ violation in the pure annihilation decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$ induced by the $ρ$ and $ω$ double resonance effect. Generally, the $CP$ violation is small in the pure annihilation type decay process. However, we find that the $CP$ violation can be enhanced by double $ρ-ω$ interference when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$, the maximum $CP$ violation can reach 28.64{\%}.
We perform a theoretical study on direct $CP$ violation in $D^\pm\to π^\pm π^+π^-$ in phase space around the intermediate states $ρ^0(770)$ and $f_0(500)$. The possible interference between the amplitudes corresponding to the two resonances is taken into account, and the relative strong phase of the two amplitudes is treated as a free parameter. Our analysis shows that by properly chosen the strong phase, both the $CP$ violation strength and differential decay width accommodate to the experimental results.
In supersymmetric models with R-parity violating interactions, sneutrinos may be produced as $s$-channel resonances at $μ^+ μ^-$ colliders. We demonstrate that, for R-parity violating couplings as low as $10^{-4}$, sneutrinos can be discovered and their couplings measured to high accuracy. The excellent beam energy resolution of muon colliders is found to be especially useful for studying such resonances in certain cases.
In supersymmetric models with R-parity violation, sneutrinos may be produced as s-channel resonances at muon colliders. We demonstrate that, for R-parity violating couplings as low as 10^-4, sneutrino resonances may be observed and may be exploited to yield high precision SUSY parameter measurements. The excellent beam energy resolution of muon colliders may also be used to resolve MeV level splittings between CP-even and CP-odd sneutrino mass eigenstates.
Pion-pion scattering amplitude obtained from one-loop Chiral Perturbation Theory (ChPT) is crossing symmetric, however the corresponding partial wave amplitudes do not respect exact unitarity relation. There are different approaches to get unitarized partial wave amplitudes from ChPT. Here we consider the inverse amplitude method (IAM) that is often used to fit pion-pion phase shifts to experimental data, by adjusting free parameters. We measure the amount of crossing symmetry violation (CSV) in this case and we show that crossing symmetry is badly violated by the IAM unitarized ChPT amplitude…
Searching for two-body resonance decays is a central component of the high energy physics energy frontier research program. While many of the possibilities are covered when the two bodies are Standard Model (SM) particles, there are still significant gaps. If one or both of the bodies are themselves non-SM particles, there is very little coverage from existing searches. We review the status of two-body searches and motivate the need to search for the missing combinations. It is likely that the search program of the future will be able to cover all possibilities with a combination of dedicated …
Hadron resonances affect nonexotic $D^o$ decays but not $B$ decays which are far from the resonance region. We obtain new information from {\bf exclusive} decays and show that interference between colour favoured and colour suppressed diagrams is {\bf constructive} in $B$ and (some) $D$ decays in contrast to the inclusive decays where a net Pauli destructive interference is claimed. We suggest that a systematic study of $B$ decay final states containing excited mesons such as $a_1 D$ or $πD^{**}$ show opposite behaviour for $B^o$ and $B^+$ relative to the ground state channels. We give inequal…
We consider new s-channel scalar exchanges in top quark and massive gauge-bosons pair production in e+e- collisions, in supersymmetry with a small lepton number violation. We show that a soft bilinear lepton number violating term in the scalar potential which mixes the Higgs and the slepton fields can give rise to a significant scalar resonance enhancement in e+e- -> ZZ, W+W- and in e+e- -> t t(bar). The sneutrino-Higgs mixed state couples to the incoming light leptons through its sneutrino component and to either the top quark or the massive gauge bosons through its Higgs component. Such a sc…
A general theory of pseudomagnetic effects for the propagation of polarized neutrons through polarized target in multi resonance approach is presented. Some applications related to the proposed search for time reversal invariance violation in neutron scattering are considered.
New physics field content in the nature, more specifically, from spin-1 resonances sourced by the extension of the SM local gauge symmetry to the larger local group $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$, may induce CP-violation signalling NP effects from higher energy regimes. In this work we completely list and study all the CP-violating operators up to the $p^4$-order in the Lagrangian expansion, for a non-linear left-right electroweak chiral context and coupled to a light dynamical Higgs. Heavy right handed fields can be integrated out from the physical spectrum, inducing thus a physic…
Electromagnetic resonant cavities form the basis of many tests of Lorentz invariance involving photons. The effects of some forms of Lorentz violation scale with cavity size. We investigate possible signals of violations in the naturally occurring resonances formed in the Earth-ionosphere cavity. Comparison with observed resonances places the first terrestrial constraints on coefficients associated with dimension-three Lorentz-violating operators at the level of 10^{-20} GeV.
Large CP violation is an interesting phenomenon both theoretically and experimentally. Last year, LHCb Collaboration found in some three-body decays of bottom mesons that large CP violations appear in regions of the Dalitz plots that are not dominated by contributions from narrow resonances. In this paper, we present a mechanism which can induce such kind of large CP violations. In this mechanism, large localized CP asymmetries in phase space can be induced by the interference of two intermediate resonances with different spins. We also apply this mechanism to the decay channel $B^\pm\to K^\pm…
Leptonic CP violation is one of the most important topics in neutrino physics. CP violation in the neutrino sector is strongly related to the nature of neutrinos: whether they are Dirac or Majorana particles. In \cite{Popov:2021icg} we have shown that for Majorana neutrinos arance of nonzero Majorana CP-violating phases combined with strong magnetic field during supernova core-collaple can induce new resonances in neutrino oscillations, for example in $ν_e \to \barν_τ$ channel. In this contribution we further study new resonances in Majorana neutrino oscillations, in particular energy dependen…
The low energy behaviour of Quantum Chromodynamics makes unreliable an expansion in terms of its coupling strength, since nothing guarantees the convergence of such expansion. To overcomer such difficulty one resorts to Lattice QCD or Effective Field Theories. In this thesis we compute hadronic processes at low energies, using Resonance Chiral Lagrangians as the effective theory of QCD. The processes we study are important background on the search for Lepton Flavor Violation, Lepton Universality Violation, Lepton Number Violation, Second Class Currents and study the Hadronic light-by-light con…
Quantitative understanding of CP violation is extremely important as naturalness reasoning strongly suggests that new physics should be accompanied by beyond the Standard Model CP-odd phases. In 2019 LHCb made the first $5 σ$ discovery of CP violation in the charm system, leading to the new world average $Δa_{CP}^{\mathrm{dir}} = -0.00161 \pm 0.00028$. While some calculations have found this observation as requiring new physics, we suggest that scalar resonances nearby to $m_{D^0}$, in particular, $f_0(1710)$ and/or $f_0(1790)$ cause enhancements for CP violation within the SM. Thereby, our ca…
The experimental data on pi N scattering in the elastic energy region T_pi < 250 MeV are analyzed within the multichannel K-matrix approach with effective Lagrangians. Isospin invariance is not assumed in this analysis and the physical values for masses of the involved particles are used. The corrections due to pi^+- pi^0 and p-n mass differences are calculated and found to be in a reasonable agreement with the NORDITA results. Analysis shows the good description of the all experimental observables. From the data, new values for mass and width of the Delta^0 and Delta^{++} resonances were obta…
The role of quantum mechanical time-energy uncertainty (TEU) is central in resonant neutrino (nue) reactions (3H to 3He to 3H) because of the unusual 18 y lifetime of 3H. The TEU explicitly manifests itself by a non-intuitive but quantitatively predictable spontaneous temporal growth of the nue resonance signal. A slower growth rate signifies violation of TEU via a larger than natural width of 3H, possibly imposed by a fundamental length in nature. Strong limits on TEU violation can be set in the unprobed virgin energy regime of ~10-24 eV.
We discuss direct CP violation in three-body decays of $B$ meson such as $B^\pm \to K^\pmπ^+π^-$, which involves various intermediate resonance states, such as $B^\pm \to K^*_i π^\pm$ and $B^\pm \to ρK^\pm$, where $K^*_i$ represents the $πK$ resonance. Due to the large final state interaction phases of the resonances, the CP asymmetry can be as large as the 25% level near the kinematical region where the $K^*_i$ and $ρ$ resonances overlap. By examining a Dalitz plot of this mode and combining a measurement of the branching ratio for $B^\pm \to ρ^\pm K$, it is possible to extract the weak phase…
We study the phenomenological implications of the Higgs sector CP violation at a photon collider. In our model, the CP violation is radiatively induced by the non-trivial CP phases of the third-generation scalar-quark sector in the MSSM. We re-evaluate the $s$-channel resonance production cross sections and the polarization asymmetries of the neutral Higgs bosons based on the calculation of the mass matrix of the neutral Higgs bosons which is valid for any values of the relevant SUSY parameters. The CP properties of the Higgs bosons can be precisely probed through their $s$-channel resonance p…
Yields of hadrons, their average masses and energies per hadron at the stage of chemical freeze-out in (ultra)relativistic heavy-ion collisions are analyzed within the statistical model. The violation of the scaling <E>/<N> = 1 GeV observed in Au+Au collisions at $\sqrt{s}$ = 130 AGeV is linked to the formation of resonance-rich matter with a considerable fraction of baryons and antibaryons. The rise of the energy-per-hadron ratio in baryon-dominated matter is discussed. A violation of the scaling condition is predicted for a very central zone of heavy-ion collisions at energies around 40 AGeV…
We study the possibility of measuring the muon Yukawa couplings in s-channel Higgs boson production at a muon collider with transversely polarized beams. We investigate sensitivity to the relative size of the CP-odd and CP-even muon Yukawa couplings. Provided the event rate observed justifies the operation of the mu+mu- Higgs boson factory, we find that 40% polarization for both beams is sufficient to resolve the CP nature of a single resonance as well as disentangle it from two overlapping CP conserving resonances.
The 750 GeV resonance observed by ATLAS and CMS may be explained by a gauge singlet scalar. This would provide an ideal candidate for a gauge singlet scalar alternative to Higgs Inflation, S-inflation. Here we discuss the relevant results of S-inflation in the context of the 750 GeV resonance. In particular, we show that a singlet scalar, if it is real, has a major advantage over the Higgs boson with regard to unitarity violation during inflation. This is because it is possible to restrict the large non-minimal coupling required for inflation, $ξ\sim 10^5$, to the real singlet scalar, with all…
We investigate a possibility of observing CP asymmetries in the partial widths for the decays B^- -> pi^+ pi^- K^- and B^- -> K^+ K^- K^- produced by the interference of the non-resonant decay amplitude with the resonant amplitudes. The resonant states which subsequently decay into pi^+ pi^- and K^+ K^- or K^- pi^+ are charmonium c(bar) c states with J^P = 0^+, 1^-, 1^+ or the phi(1020) meson. We find that the largest partial width asymmetry comes from the chi_c0 resonance, while the resonances K^*_0(1430) and psi(2S) give a partial width asymmetry of the order 10%.
Recent advances towards a model-independent description of hadronic few-body final states, relevant for the extraction of direct CP violation from the decays of heavy mesons, are presented.
A classic sum rule by Das et al. is extended to seven of the low-energy constants $K_i$, introduced by Urech, which parameterize electromagnetic corrections at chiral order $O(e^2p^2)$. Using the spurion formalism, a simple convolution representation is shown to hold and the structure in terms of the chiral renormalization scale, the QCD renormalization scale and the QED gauge parameter is displayed. The role of the resonances is studied as providing rational interpolants to relevant QCD n-point functions in the euclidian domain. A variety of asymptotic constraints must be implemented which ha…
We examine the isospin violation in the timelike pion form factor near threshold at next-to-leading order in the chiral expansion using the techniques of Chiral Perturbation Theory. This next-to-leading order contribution contains the first nonvanishing isospin violation. This isospin violation is found to be very small near threshold. In particular, the isospin violation at threshold is found to be of order 10^-4, which should be compared with the few percent level seen in the vector meson resonance region.
In this work, a hadron resonance gas under van der Waals (VDW) interactions has been studied. Both attractive and repulsive interactions between the meson-meson and (anti)baryon-(anti)baryon have been taken into consideration. Various transport properties such as electrical conductivity ($σ_{\rm el}$) and thermal conductivity ($κ_{\rm th}$) have been estimated by solving the Boltzmann transport equation under the relaxation time approximation. The effect of baryochemical potential ($μ_{\rm B}$) and temperature is also explicitly explored for the mentioned observables. Comparisons have been mad…
The CP properties of Higgs bosons can be probed through their s-channel resonance productions via photon-photon collisions by use of circularly and/or linearly polarized backscattered laser photons at a TeV-scale linear e^+ e^- collider. Exploiting this powerful tool, we investigate in detail the Higgs sector of the minimal supersymmetric Standard Model with explicit CP violation.
The IceCube neutrino spectrum shows a flux which falls of as $E^{-2}$ for sub PeV energies but there are no neutrino events observed above $\sim 3$ PeV. In particular the Glashow resonance expected at 6.3 PeV is not seen. We examine a Planck scale Lorentz violation as a mechanism for explaining the cutoff of observed neutrino energies around a few PeV. By choosing the one free parameter the cutoff in neutrino energy can be chosen to be between 2 and 6.3 PeV. We assume that neutrinos (antineutrinos) have a dispersion relation $E^2=p^2 - (ξ_3/M_{Pl})~p^3$, and find that both $π^+$ and $π^-$ deca…
We discuss different $\rm SU(5)$ low-energy realizations and illustrate their use with the diphoton excess and Higgs flavor violation, which require new physics at the TeV scale. In particular, we study two scenarios for a $750$ GeV resonance: in the first one the resonance belongs to the adjoint of $\rm SU(5)$, being either an $\rm SU(2)_L$ singlet or a triplet, while in the second case the signal is due to the CP-even and CP-odd states of a new $\rm SU(2)_L$ Higgs doublet belonging to a ${\bf 45}_H$ or a ${\bf 70}_H$ representations, giving rise to a two-Higgs doublet model at low energies. …
We consider possibilities of observing T-violation effects in neutrino oscillation experiments with very long baseline (~ 10000 km) using low energy neutrino (~ several hundreds MeV). We show that the matter effect effectively changes only the first-second generation mixing angle, respecting solar neutrino deficits and atmospheric neutrino anomalies. The effective mixing of the first-second generation in the Earth grows up to maximum by resonance. This effect enables one to search T violation in case the first-second mixing angle is small. We discuss its implications to the observations of T-v…
Jacobson and Sotiriou showed that rotating black holes could be spun-up past the extremal limit by the capture of non-spinning test bodies, if one neglects radiative and self-force effects. This would represent a violation of the Cosmic Censorship Conjecture in four-dimensional, asymptotically flat spacetimes. We show that for some of the trajectories giving rise to naked singularities, radiative effects can be neglected. However, for these orbits the conservative self-force is important, and seems to have the right sign to prevent the formation of naked singularities.
Charged and neutral B decays into two charged pions and a charged or a neutral kaon are analyzed within the QCD factorization scheme where final state interactions before and after hadronization are included. The K*(892) and K*(1430) resonance effects are taken into account using the presently known pion-Kaon strange vector and scalar form factors. The weak decay amplitudes, which are calculated at leading power in Lambda_QCD/m_b and at the next-to-leading order in the strong coupling constant, include the hard scattering and annihilation contributions. The end point divergences of these weak …
In the perturbative QCD (PQCD) approach we study the direct $CP$ violation in $B^+_{c}\rightarrow D_{(s)}^+ρ^0(ω) \rightarrow D_{(s)}^+π^+π^-$ via the $ρ-ω$ mixing mechanism. We find that the $CP$ violation can be enhanced by $ρ-ω$ mixing when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process $B^+_{c}\rightarrow D^+ρ^0(ω) \rightarrow D^+π^+π^-$, the maximum $CP$ violation can reach 7.5 {\%}.
Pion-pion scattering amplitude obtained from one-loop Chiral Perturbation Theory (ChPT) is crossing symmetric, however the corresponding partial-wave amplitudes do not respect exact unitarity relation. There are different approaches to get unitarized results from ChPT. Here we consider the inverse amplitude method (IAM) and, using the Roskies relations, we measure the amount of crossing symmetry violation when IAM is used in order to fit pion-pion phase-shifts to experimental data in the resonance region. We also show the unitarity violation of the crossing symmetric ChPT amplitude with its pa…
We investigate the isospin-violating mixing of the light scalar mesons a0(980) and f0(980) within the unitarized chiral approach. Isospin-violating effects are considered to leading order in the quark mass difference and electromagnetism. In this approach both resonances 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 quark-antiquark states. We discuss in detail the reactions J/Psi to phi S, where S denotes a suitable pair of pseu…
We consider the sneutrino resonance reaction l^+ l^- -> sneutrino -> tau^+ tau^- in the MSSM without R-parity. We introduce new CP-violating and CP-conserving tau-spin asymmetries which are generated already at the tree-level if there is sneutrino - sneutrino-bar mixing and that are forbidden in the SM. It is remarkable that these spin asymmetries can reach ~75% around resonance for a sneutrino mass splitting of Δm ~ Γand ~10% for a splitting as low as Δm ~ 0.1Γ, where Γis the sneutrino width. We show that they are easily detectable already at LEP2 so long as the beam energy is within ~10 GeV …
Weak decays of beauty baryons like Λ_b (\barΛ_b) into Λ(\barΛ) and V (J^P = 1^-), where both decay products are polarized, offer interesting opportunities to perform tests of time reversal and CP violations and of CPT invariance. We propose a model independent parametrization of the angular distribution and of the polarization of the final resonances, by means of the spin density matrix. The transverse component of the polarization is sensitive to time reversal violations, moreover CP-and CPT-sensitive observables are defined.
In the QCD factorization (QCDF) approach we study the direct $CP$ violation in $\bar{B}^{0}\rightarrowρ^0(ω)ρ^0(ω)\rightarrowπ^+π^-π^+π^-$ via the $ρ-ω$ mixing mechanism. We find that the $CP$ violation can be enhanced by double $ρ-ω$ mixing when the masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance, and the maximum $CP$ violation can reach 28{\%}. We also compare the results from the naive factorization and the QCD factorization.
In perturbative QCD approach, we study the direct $CP$ violation in the decay of $\bar{B}_s^0\toρ(ω)ϕ\to {π^+}{π^-}ϕ$ via isospin symmetry breaking. An interesting mechanism involving the charge symmetry violating between $ρ$ and $ω$ is applied to enlarge the $CP$ violating asymmetry. We find that the $CP$ violation can be enhanced by the $ρ-ω$ mixing mechanism when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\toρ(ω)ϕ\to{π^+}{π^-}ϕ$, the maximum $CP$ violation can reach $5.98\%$. The possibility of detecting the $C…
Resonances and final state interactions (FSI) play a role in the formation of CP violation (CPV) constrained by CPT invariance. We provide a general formulation of CPV including resonances and FSI starting from the CPT constraint. Our discussion is elaborated within a simple $B$ decay model with the $ρ$ and $f_0(980)$ resonances plus a non resonant background including the $ππ\to KK$ coupled amplitude. We consider few illustrative examples to show the interference patterns appearing in the CP asymmetry, namely, that from the $ρ$ resonance plus a non-resonant amplitude, and that from the interf…
We demonstrate that the explanation of the neutron anomaly around $W\sim 1685$MeV in $γN\to ηN$ reactions provided by the $η$MAID2018 isobar model is based on large violation of the flavour SU(3) symmetry in hadron interactions. This is yet another example of how conventional explanation (without invoking exotic narrow nucleon resonance) of the neutron anomaly metamorphoses into unconventional physics picture of hadron interactions. A possibility to mend the flavour SU(3) symmetry for some of resonances in $η$MAID model is discussed.
We re-examine direct CP violation in the quasi-two-body $D\to V\!P$ decays and study CP asymmetries in three-body $D$ decays proceeding through intermediate vector resonances within the framework of the topological amplitude approach for tree amplitudes and the QCD factorization approach for penguin amplitudes. Using the same mechanism of incorporating long-distance penguin-exchange amplitude induced from final-state rescattering that nicely accounts for the CP asymmetry difference between $D^0\to K^+K^-$ and $π^+π^-$ modes, we find that CP asymmetry can also occur at the per mille level in ma…
It is proposed to search for $C\!P$ violation through the two-fold angular distributions in the four-body decays of bottom and charmed hadrons. The two polar angles in the two-fold angular distributions are correlated, to which the interferences of intermediate resonances are one important origin. These interferences will leave tracks in the two-fold angular distributions, with which the $C\!P$ violation can be studied. Special attention is paid to the case when all the intermediate resonances are different, which is unique to four-body decays. It is suggested to look for $C\!P$ violation in f…
The formulae for D^0-\bar{D}^0 or B^0-\bar{B}^0 mixing and CP violation at the τ-charm or B-meson factories are derived, for the case that only the decay-time distribution of one D or B meson is to be measured. In particular, we point out a new possibility to determine the D^0-\bar{D}^0 mixing rate in semileptonic D decays at the Ψ(4.14) resonance; and show that both direct and indirect CP asymmetries can be measured at the Υ(4S) resonance without ordering the decay times of two B_d mesons or measuring their difference.
Recently, the large CP asymmetries in $B^\pm\toπ^\pmπ^+π^-$ decays were found by the LHCb Collaboration to localize in the region $m_{π^+π^-}^2<0.4 \text{GeV}^2$. We find such large localized CP asymmetries may be due to the interference between a light scalar and $ρ^0(770)$ intermediate resonances. Consequently, we argue that the distribution of CP asymmetries in the Dalitz plots of three-body B decays could be very helpful for identifying the presence of the scalar resonance.
We discuss resonant squark production at the LHC via baryonic $R$-parity violating interactions. The cross section easily exceeds pair-production and a new set of signatures can be used to probe squarks, particularly stops. These include dijet resonances, same-sign top quarks and four-jet resonances with large $b$-jet multiplicities, as well as the possibility of displaced neutralino decays. We use publicly available searches at $\sqrt{s}=8$ TeV and first results from collisions at $\sqrt{s}=13$ TeV to set upper limits on $R$-parity violating couplings, with particular focus on simplified mode…
We develop a comprehensive description of three flavor neutrino oscillations inside the Earth in terms of neutrino oscillograms in the whole range of nadir angles and for energies above 0.1 GeV. The effects of the 1-2 mass splitting and mixing as well the interference of the 1-2 and 1-3 modes of oscillations are quantified. The 1-2 mass splitting and mixing lead to the appearance, apart from the resonance MSW peaks, of the parametric resonance peak for core-crossing trajectories at E_nu ~= 0.2 GeV. We show that the interference effects, in particular CP violation, have a domain structure with …
We consider the ATLAS and CMS searches for dijet resonances, as well as the ATLAS search for like-sign dimuon pairs at the LHC with 7 TeV center of mass energy. We interpret their exclusions in terms of bounds on the supersymmetric R-parity violating parameter space. For this we focus on resonant slepton production followed by the corresponding decay.
We present a new determination of the strong coupling constant alpha_s through the scaling violations in the fragmentation functions for charged pions, charged kaons, and protons. In our fit we include the latest e+e- annihilation data from CERN LEP1 and SLAC SLC on the Z-boson resonance and older, yet very precise data from SLAC PEP at center-of-mass energy sqrt(s)=29 GeV. A new world average of alpha_s is given.
A quantitative understanding of isospin violation is an increasingly important ingredient for the extraction of the nucleon's strange vector form factors from experimental data. We calculate the isospin violating electric and magnetic form factors in chiral perturbation theory to leading and next-to-leading order respectively, and we extract the low-energy constants from resonance saturation. Uncertainties are dominated largely by limitations in the current knowledge of some vector meson couplings. The resulting bounds on isospin violation are sufficiently precise to be of value to on-going ex…
