We present an improved Standard-Model (SM) prediction for the dilepton decay of the neutral pion. The loop amplitude is determined by the pion transition form factor for $pi^0togamma^*gamma^*$, for which we employ a dispersive representation that inc
orporates both space-like and time-like data as well as short-distance constraints. The resulting SM branching fraction, $ text{BR}(pi^0to e^+e^-)=6.25(3)times 10^{-8}$ , sharpens constraints on physics beyond the SM, including pseudoscalar and axial-vector mediators.
The stability of pasta phases in cylindrical and spherical Wigner-Seitz (W-S) cells is examined. The electric Bond number is introduced as the ratio of electric and surface energies. In the case of a charged rod in vacuum, other kinds of instabilitie
s appear in addition to the well known Plateau- Rayleigh mode. For the case of a rod confined in a W-S cell the variety of unstable modes is reduced. It comes from the virial theorem, which bounds the value of the Bond number from above and reduces the role played by electric forces. A similar analysis is done for the spherical W-S cell, where it appears that the inclusion of the virial theorem stabilizes all of the modes.
It is shown that recently proposed RMF model with $sigma$ and $delta$ meson interaction agrees with the observational data and presents an interesting structure with phase transition in the outer part of neutron star core.
We address the contribution of the $3pi$ channel to hadronic vacuum polarization (HVP) using a dispersive representation of the $e^+e^-to 3pi$ amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the a
nomalous magnetic moment of the muon $(g-2)_mu$, both to its absolute value and uncertainty. It is largely dominated by the narrow resonances $omega$ and $phi$, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for $(g-2)_mu$ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying $gamma^*to3pi$ amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various $e^+e^-to 3pi$ data sets. Overall, we obtain $a_mu^{3pi}|_{leq 1.8,text{GeV}}=46.2(6)(6)times 10^{-10}$ as our best estimate for the total $3pi$ contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the $2pi$ channel below $1,text{GeV}$, this covers nearly $80%$ of the total HVP contribution, leading to $a_mu^text{HVP}=692.3(3.3)times 10^{-10}$ when the remainder is taken from the literature, and thus reaffirming the $(g-2)_mu$ anomaly at the level of at least $3.4sigma$. As side products, we find for the vacuum-polarization-subtracted masses $M_omega=782.63(3)(1),text{MeV}$ and $M_phi=1019.20(2)(1),text{MeV}$, confirming the tension to the $omega$ mass as extracted from the $2pi$ channel.
If physics beyond the Standard Model enters well above the electroweak scale, its low-energy effects are described by Standard Model Effective Field Theory. Already at dimension six many operators involve the antisymmetric quark tensor $bar q sigma^{
mu u} q$, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.
Symmetry energy behavior of scalar mesons interactions is analyzed within the framework of the standard relativistic mean field model. Whereas the presence of the $delta$ meson itself makes the symmetry energy stiffer, the crossing term $deltatextrm{
-}sigma$ allows its slope to decrease to the suggested experimental value. Moreover, such controlling of the symmetry energy does not significantly affect the stiffness of the equation of state and acceptable neutron star masses result. Interestingly, for the most plausible value of the symmetry energy slope, the phase transition occurs in the neutron star core.
The $pi^0$ pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLbL) tensor, and thus provides the leading contribution in a dispersive approach to HLbL scattering in the anomalous magnetic moment of the muon $(g-2)_mu$. It
is unambiguously defined in terms of the doubly-virtual pion transition form factor, which in principle can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full space-like doubly-virtual form factor can be reconstructed very accurately based on existing data for $e^+e^-to 3pi$, $e^+e^-to e^+e^-pi^0$, and the $pi^0togammagamma$ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the $(g-2)_mu$ loop integral. The resulting value, $a_mu^{pi^0text{-pole}}=62.6^{+3.0}_{-2.5}times 10^{-11}$, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly-virtual measurements alone would allow one to further reduce the uncertainty in $a_mu^{pi^0text{-pole}}$.
Studies of the reaction $gammapitopipi$, in the context of the ongoing Primakoff program of the COMPASS experiment at CERN, give access to the radiative couplings of the $rho(770)$ and $rho_3(1690)$ resonances. We provide a vector-meson-dominance est
imate of the respective radiative width of the $rho_3$, $Gamma_{rho_3topigamma}=48(18)$ keV, as well as its impact on the $F$-wave in $gammapitopipi$. For the $rho(770)$, we establish the formalism necessary to extract its radiative coupling directly from the residue of the resonance pole by analytic continuation of the $gammapitopipi$ amplitude to the second Riemann sheet, without any reference to the vector-meson-dominance hypothesis.
We present an extraction of the pion-nucleon ($pi N$) scattering lengths from low-energy $pi N$ scattering, by fitting a representation based on Roy-Steiner equations to the low-energy data base. We show that the resulting values confirm the scatteri
ng-length determination from pionic atoms, and discuss the stability of the fit results regarding electromagnetic corrections and experimental normalization uncertainties in detail. Our results provide further evidence for a large $pi N$ $sigma$-term, $sigma_{pi N}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.
The stability of periodically placed slabs occurring in neutron stars (lasagna phase) is examined by exact geometrical methods for the first time. It appears that the slabs are stable against any shape perturbation modes for the whole range of volume
fraction occupied by the slab. The calculations are done in the framework of the liquid drop model and obtained results are universal - they do not depend on model parameters like surface tension or charge density. The results shows that the transition to other pasta shapes requires crossing the finite energy barrier
