The decays of $$\bar{B}^0$$, $$\bar{B}^0_s$$B¯s0 and $$B^-$$B- into $$\eta _c$$ηc plus a scalar or vector meson

We investigate the decays of \(\bar{B}^0_s\), \(\bar{B}^0\) and \(B^-\) into \(\eta _c\) plus a scalar or vector meson in a theoretical framework by taking into account the dominant process for the weak decay of \(\bar{B}\) meson into \(\eta _c\) and a \(q\bar{q}\) pair. After hadronization of this \(q\bar{q}\) component into pairs of pseudoscalar mesons we obtain certain weights for the pseudoscalar meson-pseudoscalar meson components. In addition, the \(\bar{B}^0\) and \(\bar{B}^0_s\) decays into \(\eta _c\) and \(\rho ^0\), \(K^*\) are evaluated and compared to the \(\eta _c\) and \(\phi \) production. The calculation is based on the postulation that the scalar mesons \(f_0(500)\), \(f_0(980)\) and \(a_0(980)\) are dynamically generated states from the pseudoscalar meson-pseudoscalar meson interactions in S-wave. Up to a global normalization factor, the \(\pi \pi \), \(K \bar{K}\) and \(\pi \eta \) invariant mass distributions for the decays of \(\bar{B}^0_s \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0_s \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0 \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^0 \eta \), \(B^- \rightarrow \eta _c K^0 K^-\) and \(B^- \rightarrow \eta _c \pi ^- \eta \) are predicted. Comparison is made with the limited experimental information available and other theoretical calcualtions. Further comparison of these results with coming LHCb measurements will be very valuable to make progress in our understanding of the nature of the low lying scalar mesons, \(f_0(500), f_0(980)\) and \(a_0(980)\).     

Coupled channels dynamics in the generation of the $$\Omega (2012)$$ resonance

We look into the newly observed \(\Omega (2012)\) state from the molecular perspective in which the resonance is generated from the \(\bar{K} \Xi ^*\), \(\eta \Omega \) and \(\bar{K} \Xi \) channels. We find that this picture provides a natural explanation of the properties of the \(\Omega (2012)\) state. We stress that the molecular nature of the resonance is revealed with a large coupling of the \(\Omega (2012)\) to the \(\bar{K} \Xi ^*\) channel, that can be observed in the \(\Omega (2012) \rightarrow \bar{K} \pi \Xi \) decay which is incorporated automatically in our chiral unitary approach via the use of the spectral function of \(\Xi ^*\) in the evaluation of the \(\bar{K} \Xi ^*\) loop function.     

Detection of relic gravitational waves in thermal case by using Adv.LIGO data of GW150914

The thermal spectrum of relic gravitational waves enhances the usual spectrum. Our analysis shows that there exist some chances for detection of the thermal spectrum in addition to the usual spectrum by comparison with sensitivity of Adv.LIGO of GW150914 and detector based on the maser light. The behavior of the inflation and reheating stages are often known as power law expansion like \(S(\eta )\propto \eta ^{1+\beta }\), \(S(\eta )\propto \eta ^{1+\beta _s}\), respectively, with constraints \(1+\beta <0, 1+\beta _{s}>0\). The \(\beta \) and \(\beta _s\) have an unique effect on the shape of the spectrum. We find some values of the \(\beta \) and \(\beta _s\) by considering the mentioned comparison. As obtained, the results give us more information as regards the evolution of inflation and reheating stages.     

Abelian cosmic string in the extended Starobinsky model of gravity

We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by \(f(R) = R - 2\Lambda + \eta R^2 + \rho R^m\), with \(m > 2\). As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters \(\eta \) and \(\rho \) increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant.     

Warm modified Chaplygin gas shaft inflation

In this paper, we examine the possible realization of a new inflation family called “shaft inflation” by assuming the modified Chaplygin gas model and a tachyon scalar field. We also consider the special form of the dissipative coefficient \(\Gamma ={a_0}\frac{T^{3}}{\phi ^{2 }}\) and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the \(n_s \)–\( \phi ,\, n_s \)–r, and \(n_s \)–\( \alpha _s\) planes (where \(n_s,\, \alpha _s,\, r\), and \(\phi \) represent the spectral index, its running, tensor-to-scalar ratio, and scalar field, respectively) are being developed, which lead to the constraints \(r< 0.11\), \(n_s=0.96 \pm 0.025\), and \(\alpha _s =-0.019 \pm 0.025\). It is quite interesting that these results of the inflationary parameters are compatible with BICEP2, WMAP \((7+9)\) and recent Planck data.     

Ricci curvature non-minimal derivative coupling cosmology with field re-scaling

In this letter, cosmology of a simple NMDC gravity with \(\xi R \phi _{,\mu }\phi ^{,\mu }\) term and a free kinetic term is considered in flat geometry and in presence of dust matter. A logarithm field transformation \(\phi ' = \mu \ln \phi \) is proposed phenomenologically. Assuming slow-roll approximation, equation of motion, scalar field solution and potential are derived as function of kinematic variables. The field solution and potential are found straightforwardly for power-law, de-Sitter and super-acceleration expansions. Slow-roll parameters and slow-roll condition are found to depend on more than one variable. At large field the re-scaling effect can enhance the acceleration. For slow-rolling field, the negative coupling \(\xi \) could enhance the effect of acceleration.     

Hyperscaling for Oriented Percolation in $$$$ Space–Time Dimensions

Consider nearest-neighbor oriented percolation in \(d+1\) space–time dimensions. Let \(\rho ,\eta ,\nu \) be the critical exponents for the survival probability up to time t, the expected number of vertices at time t connected from the space–time origin, and the gyration radius of those vertices, respectively. We prove that the hyperscaling inequality \(d\nu \ge \eta +2\rho \), which holds for all \(d\ge 1\) and is a strict inequality above the upper-critical dimension 4, becomes an equality for \(d=1\), i.e., \(\nu =\eta +2\rho \), provided existence of at least two among \(\rho ,\eta ,\nu \). The key to the proof is the recent result on the critical box-crossing property by Duminil-Copin et al. [6].     

Spin density matrix of the $$\omega $$ in the reaction $${\bar{p}p}\,\rightarrow \,\omega \pi ^0$$p¯p→π0

The spin density matrix of the \(\omega \) has been determined for the reaction \({\bar{p}p}\,\rightarrow \,\omega \pi ^0\) with unpolarized in-flight data measured by the Crystal Barrel LEAR experiment at CERN. The two main decay modes of the \(\omega \) into \(\pi ^0 \gamma \) and \(\pi ^+ \pi ^- \pi ^0\) have been separately analyzed for various \({\bar{p}}\)momenta between 600 and 1940 MeV/c. The results obtained with the usual method by extracting the matrix elements via the \(\omega \) decay angular distributions and with the more sophisticated method via a full partial wave analysis are in good agreement. A strong spin alignment of the \(\omega \) is clearly visible in this energy regime and all individual spin density matrix elements exhibit an oscillatory dependence on the production angle. In addition, the largest contributing orbital angular momentum of the \({\bar{p}p~}\)system has been identified for the different beam momenta. It increases from \(L^{max}_{{\bar{p}p~}}\) \(=\) 2 at 600 MeV/c to \(L^{max}_{{\bar{p}p~}}\) \(=\) 5 at 1940 MeV/c.     

Predictions for $$\Xi _b^- \rightarrow \pi ^- (D_s^- ) \ \Xi _c^0 (2790) \left( \Xi _c^0 (2815) \right) $$ and $$\Xi _b^- \rightarrow \bar{\nu }_l l \ \Xi _c^0 (2790) \left( \Xi _c^0 (2815) \right) $$Ξb-→ν¯llΞc0(2790)Ξc0(2815)

We have performed calculations for the nonleptonic \(\Xi _b^- \rightarrow \pi ^- \ \Xi _c^0 (2790) \left( J=\frac{1}{2}\right) \) and \(\Xi _b^- \rightarrow \pi ^- \ \Xi _c^0 (2815) \left( J=\frac{3}{2}\right) \) decays and the same reactions replacing the \(\pi ^-\) by a \(D_s^-\). At the same time we have also evaluated the semileptonic rates for \(\Xi _b^- \rightarrow \bar{\nu }_l l \ \Xi _c^0 (2790)\) and \(\Xi _b^- \rightarrow \bar{\nu }_l l \ \Xi _c^0 (2815)\). We look at the reactions from the perspective that the \(\Xi _c^0 (2790)\) and \(\Xi _c^0 (2815)\) resonances are dynamically generated from the pseudoscalar–baryon and vector–baryon interactions. We evaluate ratios of the rates of these reactions and make predictions that can be tested in future experiments. We also find that the results are rather sensitive to the coupling of the \(\Xi _c^*\) resonances to the \(D^* \Sigma \) and \(D^* \Lambda \) components.     

CP violations in predictive neutrino mass structures

We study the CP-violation effects from two types of neutrino mass matrices with (i) \((M_\nu )_{ee}=0\), and (ii) \((M_\nu )_{ee}=(M_\nu )_{e\mu }=0\), which can be realized by the high-dimensional lepton number violating operators \(\bar{\ell }_R^c\gamma ^\mu L_L (D_\mu \Phi )\Phi ^2\) and \(\bar{\ell }_R^c l_R (D_\mu {\Phi })^2\Phi ^2\), respectively. In (i), the neutrino mass spectrum is in the normal ordering with the lightest neutrino mass within the range \(0.002\,\mathrm{eV}\lesssim m_0\lesssim 0.007\,\mathrm{eV}\). Furthermore, for a given value of \(m_0\), there are two solutions for the two Majorana phases \(\alpha _{21}\) and \(\alpha _{31}\), whereas the Dirac phase \(\delta \) is arbitrary. For (ii), the parameters of \(m_0\), \(\delta \), \(\alpha _{21}\), and \(\alpha _{31}\) can be completely determined. We calculate the CP-violating asymmetries in neutrino–antineutrino oscillations for both mass textures of (i) and (ii), which are closely related to the CP-violating Majorana phases.     

Study of the weak annihilation contributions in charmless $$\varvec{B_s\rightarrow VV}$$ decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless \(B_s\rightarrow VV\) (where V stands for a light vector meson) decays, we perform the \(\chi ^2\)-analyses for the endpoint parameters within the QCD factorization framework, under the constraints from the measured \(\bar{B}_{s}\rightarrow \) \(\rho ^0\phi \), \(\phi K^{*0}\), \(\phi \phi \) and \(K^{*0}\bar{K}^{*0}\) decays. The fitted results indicate that the endpoint parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless \(B\rightarrow PP\) and PV (where P stands for a light pseudo-scalar meson) decays observed in previous work. Moreover, the abnormal polarization fractions \(f_{L,\bot }(\bar{B}_{s}\rightarrow K^{*0}\bar{K}^{*0})=(20.1\pm 7.0)\%,(58.4\pm 8.5)\%\) measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of \(\bar{B}_{s}\rightarrow \phi K^{*0}\) decay exhibits a tension between the data and theoretical result, which dominates the contributions to \(\chi _\mathrm{min}^2\) in the fits. Using the fitted endpoint parameters, we update the theoretical results for the charmless \(B_s\rightarrow VV\) decays, which will be further tested by the LHCb and Belle-II experiments in the near future.     

The strong decays of <Emphasis Type="Italic">X</Emphasis>(3940) and <Emphasis Type="Italic">X</Emphasis>(4160)

The new mesons X(3940) and X(4160) have been found by Belle Collaboration in the processes \(e^+e^-\rightarrow J/\psi D^{(*)}{\bar{D}}^{(*)}\). Considering X(3940) and X(4160) as \(\eta _c(3S)\) and \(\eta _c(4S)\) states, the two-body open charm OZI-allowed strong decay of \(\eta _c(3S)\) and \(\eta _c(4S)\) are studied by the improved Bethe–Salpeter method combined with the \(^3P_0\) model. The strong decay width of \(\eta _c(3S)\) is \(\Gamma _{\eta _c(3S)}=(33.5^{+18.4}_{-15.3})\) MeV, which is close to the result of X(3940); therefore, \(\eta _c(3S)\) is a good candidate of X(3940). The strong decay width of \(\eta _c(4S)\) is \(\Gamma _{\eta _c(4S)}=(69.9^{+22.4}_{-21.1})\) MeV, considering the errors of the results, it is close to the lower limit of X(4160). But the ratio of the decay width \(\frac{\Gamma (D{\bar{D}}^*)}{\Gamma (D^*{\bar{D}}^*)}\) of \(\eta _c(4S)\) is larger than the experimental data of X(4160). According to the above analysis, \(\eta _c(4S)\) is not the candidate of X(4160), and more investigations of X(4160) is needed.     

$$f_0(500)$$, $$f_0(980)$$f0(980), and $$a_0(980)$$a0(980) production in the $$\chi _{c1} \rightarrow \eta \pi ^+\pi ^-$$χc1→ηπ+π- reaction

We study the \(\chi _{c1} \rightarrow \eta \pi ^+ \pi ^-\) decay, paying attention to the production of \(f_0(500)\), \(f_0(980)\), and \(a_0(980)\) from the final state interaction of pairs of mesons that can lead to these three mesons in the final state, which is implemented using the chiral unitary approach. Very clean and strong signals are obtained for the \(a_0(980)\) excitation in the \(\eta \pi \) invariant mass distribution and for the \(f_0(500)\) in the \(\pi ^+ \pi ^-\) mass distribution. A smaller, but also clear signal for the \(f_0(980)\) excitation is obtained. The results are contrasted with experimental data and the agreement found is good, providing yet one more test in support of the picture where these resonances are dynamically generated from the meson–meson interaction.     

Thermodynamic implications of the gravitationally induced particle creation scenario

A rigorous thermodynamic analysis has been done as regards the apparent horizon of a spatially flat Friedmann–Lemaitre–Robertson–Walker universe for the gravitationally induced particle creation scenario with constant specific entropy and an arbitrary particle creation rate \(\Gamma \). Assuming a perfect fluid equation of state \(p=(\gamma -1)\rho \) with \(\frac{2}{3} \le \gamma \le 2\), the first law, the generalized second law (GSL), and thermodynamic equilibrium have been studied, and an expression for the total entropy (i.e., horizon entropy plus fluid entropy) has been obtained which does not contain \(\Gamma \) explicitly. Moreover, a lower bound for the fluid temperature \(T_f\) has also been found which is given by \(T_f \ge 8\left( \frac{\frac{3\gamma }{2}-1}{\frac{2}{\gamma }-1}\right) H^2\). It has been shown that the GSL is satisfied for \(\frac{\Gamma }{3H} \le 1\). Further, when \(\Gamma \) is constant, thermodynamic equilibrium is always possible for \(\frac{1}{2}<\frac{\Gamma }{3H} < 1\), while for \(\frac{\Gamma }{3H} \le \text {min}\left\{ \frac{1}{2},\frac{2\gamma -2}{3\gamma -2} \right\} \) and \(\frac{\Gamma }{3H} \ge 1\), equilibrium can never be attained. Thermodynamic arguments also lead us to believe that during the radiation phase, \(\Gamma \le H\). When \(\Gamma \) is not a constant, thermodynamic equilibrium holds if \(\ddot{H} \ge \frac{27}{4}\gamma ^2 H^3 \left( 1-\frac{\Gamma }{3H}\right) ^2\), however, such a condition is by no means necessary for the attainment of equilibrium.     

Dynamical system approach to scalar–vector–tensor cosmology

Using scalar–vector–tensor Brans Dicke (VBD) gravity (Ghaffarnejad in Gen Relativ Gravit 40:2229, 2008; Gen Relativ Gravit 41:2941, 2009) in presence of self interaction BD potential \(V(\phi )\) and perfect fluid matter field action we solve corresponding field equations via dynamical system approach for flat Friedmann Robertson Walker metric (FRW). We obtained three type critical points for \(\Lambda CDM\) vacuum de Sitter era where stability of our solutions are depended to choose particular values of BD parameter \(\omega \). One of these fixed points is supported by a constant potential which is stable for \(\omega <0\) and behaves as saddle (quasi stable) for \(\omega \ge 0\). Two other ones are supported by a linear potential \(V(\phi )\sim \phi \) which one of them is stable for \(\omega =0.27647\). For a fixed value of \(\omega \) there is at least 2 out of 3 critical points reaching to a unique critical point. Namely for \(\omega =-0.16856(-0.56038)\) the second (third) critical point become unique with the first critical point. In dust and radiation eras we obtained one critical point which never become unique fixed point. In the latter case coordinates of fixed points are also depended to \(\omega \). To determine stability of our solutions we calculate eigenvalues of Jacobi matrix of 4D phase space dynamical field equations for de Sitter, dust and radiation eras. We should point also potentials which support dust and radiation eras must be similar to \(V(\phi )\sim \phi ^{-\frac{1}{2}}\) and \(V(\phi )\sim \phi ^{-1}\) respectively. In short our study predicts that radiation and dust eras of our VBD–FRW cosmology transmit to stable de Sitter state via non-constant potential (effective variable cosmological parameter) by choosing \(\omega =0.27647\).     

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (Nof the average translocation time \(\ensuremath \langle\tau\rangle\) , the average velocity of the center of mass \(\ensuremath \langle v_{{\rm CM}}\rangle\) , and the effective radius of gyration \(\ensuremath \langle {R}_g\rangle\) during the translocation process defined as \(\ensuremath \langle\tau\rangle \sim N^{\alpha}\) , \(\ensuremath \langle v_{{\rm CM}} \rangle \sim N^{-\delta}\) , and \(\ensuremath {R}_g \sim N^{\bar{\nu}}\) respectively, and the exponent of the translocation coordinate (s -coordinate) as a function of the translocation time \(\ensuremath \langle s^2(t)\rangle\sim t^{\beta}\) . We find \(\ensuremath \alpha=1.36 \pm 0.01\) , \(\ensuremath \beta=1.60 \pm 0.01\) for \(\ensuremath \langle s^2(t)\rangle\sim \tau^{\beta}\) and \(\ensuremath \bar{\beta}=1.44 \pm 0.02\) for \(\ensuremath \langle\Delta s^2(t)\rangle\sim\tau^{\bar{\beta}}\) , \(\ensuremath \delta=0.81 \pm 0.04\) , and \(\ensuremath \bar{\nu}\simeq\nu=0.59 \pm 0.01\) , where \( \nu\) is the equilibrium Flory exponent in 3D. Therefore, we find that \(\ensuremath \langle\tau\rangle\sim N^{1.36}\) is consistent with the estimate of \(\ensuremath \langle\tau\rangle\sim\langle R_g \rangle/\langle v_{{\rm CM}} \rangle\) . However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent α = 1.36 ± 0.01 < 1 + ν. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the “cis” and “trans” parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.     

Influence of photon-neutrino processes on the cooling of a magnetar

The influence of a strongly magnetized dense plasma on the photon-neutrino processes γe ^± → e ^±ν\(\bar \nu \), γ → ν\(\bar \nu \), and γγ → ν\(\bar \nu \) is considered; invariant amplitudes of the γe ^± → e ^±ν\(\bar \nu \) and γγ → ν\(\bar \nu \) reactions are calculated. The contributions from these processes to the neutrino luminosity are calculated in the special case of a cold plasma. Under these conditions, the contribution from the process γ → ν\(\bar \nu \) to the neutrino emissivity is shown to be strongly suppressed compared to the contributions from the photoneutrino and photon conversion processes. Since the neutron star cooling curve can be modified through a change of the neutrino luminosity in a strong magnetic field, the magnetic field strength in the outer crust of the magnetar is assumed to be constrained.     

$$\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^-}$$ decay in the aligned two-Higgs-doublet model

In the aligned two-Higgs-doublet model, we perform a complete one-loop computation of the short-distance Wilson coefficients \(C_{7,9,10}^{(\prime )}\), which are the most relevant ones for \(b\rightarrow s\ell ^+\ell ^-\) transitions. It is found that, when the model parameter \(\left| \varsigma _{u}\right| \) is much smaller than \(\left| \varsigma _{d}\right| \), the charged scalar contributes mainly to chirality-flipped \(C_{9,10}^\prime \), with the corresponding effects being proportional to \(\left| \varsigma _{d}\right| ^2\). Numerically, the charged-scalar effects fit into two categories: (A) \(C_{7,9,10}^\mathrm {H^\pm }\) are sizable, but \(C_{9,10}^{\prime \mathrm {H^\pm }}\simeq 0\), corresponding to the (large \(\left| \varsigma _{u}\right| \), small \(\left| \varsigma _{d}\right| \)) region; (B) \(C_7^\mathrm {H^\pm }\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are sizable, but \(C_{9,10}^\mathrm {H^\pm }\simeq 0\), corresponding to the (small \(\left| \varsigma _{u}\right| \), large \(\left| \varsigma _{d}\right| \)) region. Taking into account phenomenological constraints from the inclusive radiative decay \(B\rightarrow X_{s}{\gamma }\), as well as the latest model-independent global analysis of \(b\rightarrow s\ell ^+\ell ^-\) data, we obtain the much restricted parameter space of the model. We then study the impact of the allowed model parameters on the angular observables \(P_2\) and \(P_5'\) of \(B^0\rightarrow K^{*0}\mu ^+\mu ^-\) decay, and we find that \(P_5'\) could be increased significantly to be consistent with the experimental data in case B.     

Dynamical analysis and cosmological viability of varying G and $$\Lambda $$ cosmology

The cosmological viability of varying \(G\left( t\right) \) and \(\Lambda \left( t\right) \) cosmology is discussed by determining the cosmological eras provided by the theory. Such a study is performed with the determination of the critical points while stability analysis is performed. The application of renormalization group in the ADM formalism of general relativity provides a modified second-order theory of gravity where varying \(G\left( t\right) \) plays the role of a minimally coupled field, different from that of scalar–tensor theories, while \(\Lambda \left( t\right) =\Lambda \left( G\left( t\right) \right) \) is a potential term. We find that the theory provides two de Sitter phases and a tracking solution. In the presence of matter source, two new critical points are introduced, where the matter source contributes to the universe. One of those points describes the \(\Lambda \)CDM cosmology and in order for the solution at the point to be cosmologically viable, it has to be unstable. Moreover, the second point, where matter exists, describes a universe where the dark energy parameter for the equation of state has a different value from that of the cosmological constant.     

Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ and $$\pi \pi $$ππ scattering

The \(\eta \,\rightarrow \,3\pi \) decays are a valuable source of information on low energy QCD. Yet they were not used for an extraction of the three flavor chiral symmetry breaking order parameters until now. We use a Bayesian approach in the framework of resummed chiral perturbation theory to obtain constraints on the quark condensate and pseudoscalar decay constant in the chiral limit. We compare our results with recent CHPT and lattice QCD fits and find some tension, as the \(\eta \,\rightarrow \,3\pi \) data seem to prefer a larger ratio of the chiral order parameters. The results also disfavor a very large value of the pseudoscalar decay constant in the chiral limit, which was found by some recent work. In addition, we present results of a combined analysis including \(\eta \,\rightarrow \,3\pi \) decays and \(\pi \pi \) scattering and though the picture does not changed appreciably, we find some tension between the data we use. We also try to extract information on the mass difference of the light quarks, but the uncertainties prove to be large.