We calculate the decay η → 3π at next-to-next-to-leading order or order p 6 in Chiral Perturbation Theory. The corrections are somewhat larger than was indicated by dispersive estimates. We present numerical results for the Dalitz plot parameters, the ratio r of the neutral to charged decay and the total decay rate. In addition we derive an inequality between the slope parameters of the charged and neutral decay. The experimental charged decay rate leads to central values for the isospin breaking quantities R = 42.2 and Q = 23.2.B. The order p 4 expression 29 C. The order p 6 LECs dependent part 30160 ± 50 which is still far from the experimental value, however with a large theoretical error. Given the importance of the unitarity correction at NLO, it was deemed necessary to estimate this part of the corrections to higher order. This can be done using dispersive methods. In [19], extended Khuri-Treiman equations are used to evaluate the two-pion rescattering to the decay η → πππ. They achieve a moderate modification, an increase of about 14% per cent in the amplitude at the center of the Dalitz plot. Moreover, another analysis, based on a somewhat different dispersive method, but also restricting itself to two-pion rescattering, represented in [20] suggests also a mild enhancement to the real part of the amplitude in the physical region. A more model-dependent analysis of dispersive corrections appeared recently [21] relying on combining U (3)×U (3) ChPT and a relativistic coupled-channels method, finds agreement with data.Given all these, our motivation to perform a full NNLO computation is twofold. First, due to a relatively large strange quark-mass, the convergence of three-flavour or SU (3) ChPT is an a priori question. The reason hinges on the fact that the ratio M 2 K /M 2 ρ is much larger than M 2 π /M 2 ρ and there are possibly large effects as a result of strange quark loops. Three-flavour ChPT is probably less convergent than two-flavour ChPT, see e.g.[22] for a discussion. In general, one needs to have several terms available in order to check convergence. The situation at present is not fully clear, The results for the vector form factors, K ℓ4 and ππ-scattering have an acceptable convergence, while the results for the masses and πK-scattering, seem to converge slower, see [23] and references therein. Therefore we would like to check explicitly whether one may treat the strange quarkmass perturbatively for this process, namely η → 3π. In addition, at NLO the unitarity correction provided only half of the total correction. It is therefore also of interest to know if the other corrections are important at NNLO as well. This is known to be the case for K ℓ4 by comparing [24] and [25].Our finding shows that the full amplitude up to and including order p 6 corrections converges reasonably acceptably but we find larger corrections than in [19,20].In this paper, we perform the full NNLO calculation of η → 3π in standard three-flavour ChPT. We do this to first order in the isospin breaking quantity m u − m d ...

We consider a renormalizable extension of the standard model whose fermionic dark matter (DM) candidate interacts with a real singlet pseudo-scalar via a pseudo-scalar Yukawa term while we assume that the full Lagrangian is CP-conserved in the classical level. When the pseudoscalar boson develops a non-zero vacuum expectation value, spontaneous CP-violation occurs and this provides a CP-violated interaction of the dark sector with the SM particles through mixing between the Higgs-like boson and the SM-like Higgs boson. This scenario suggests a minimal number of free parameters. Focusing mainly on the indirect detection observables, we calculate the dark matter annihilation cross section and then compute the DM relic density in the range up to m DM = 300 GeV. We then find viable regions in the parameter space constrained by the observed DM relic abundance as well as invisible Higgs decay width in the light of 125 GeV Higgs discovery at the LHC. We find that within the constrained region of the parameter space, there exists a model with dark matter mass m DM ∼ 38 GeV annihilating predominantly into b quarks, which can explain the Fermi-LAT galactic gamma-ray excess.keywords: Beyond the standard model, dark matter experiments, dark matter theory 1 kghorbani@ipm.ir

A general formula is derived for the finite volume dependence of vacuum expectation values analogous to Lüscher's formula for the masses. The result involves no integrals over kinematic quantities and depends only on the matrix element between pions at zero momentum transfer thus presenting a new way to calculate the latter, i.e. pion sigma terms.The full order p 6 correction to the vacuum condensate qq is evaluated and compared with the result from the Lüscher formula. Due to the size of the p 6 result no conclusion about the accuracy of the Lüscher formula can be drawn.

We consider a simple renormalizable dark matter model consisting of two real scalars with a mass splitting δ, interacting with the SM particles through the Higgs portal. We find a viable parameter space respecting all the bounds imposed by invisible Higgs decay experiments at the LHC, the direct detection experiments by XENON100 and LUX and the dark matter relic abundance provided by WMAP and Planck. Despite the singlet scalar dark matter model that is fragile against the future direct detection experiments, the scalar split model introduced here survives such forthcoming bounds. We emphasize on the role of the co-annihilation processes and the mixing effects in this feature. For m DM ∼ 63 GeV in this model we can explain as well the observed gamma-ray excess in the analyses of the Fermi-LAT data at Galactic latitudes 2 • ≤ |b| ≤ 20 • and Galactic longitudes |l| < 20 • . * kghorbani@ipm.ir † pghorbani@ipm.ir

We propose a renormalizable dark matter model in which a fermionic dark matter (DM) candidate communicates with the standard model particles through two distinct portals: Higgs and vector portals. The dark sector is charged under a U (1) ′ gauge symmetry while the standard model has a leptophobic interaction with the dark vector boson. The leading contribution of DM-nucleon elastic scattering cross section begins at one-loop level. The model meets all the constraints imposed by direct detection experiments provided by LUX and XENON100, observed relic abundance according to WMAP and Planck, and the invisible Higgs decay width measured at the LHC. It turns out that the dark matter mass in the viable parameter space can take values from a few GeV up to 1 TeV. This is a new feature which is absent in the models with only one portal. In addition, we can find in the constrained regions of the parameter space a DM mass of ∼ 34 GeV annihilating into b quark pair, which explains the Fermi-LAT gamma-ray excess. * kghorbani@ipm.ir † pghorbani@ipm.ir