A phenomenological analysis on isospin-violating decay of X(3872)

In a molecular scenario, we investigate the isospin-breaking hidden charm decay processes of X(3872), i.e., $$X(3872) \rightarrow \pi ^+ \pi ^- J/\psi $$ X ( 3872 ) → π + π - J / ψ , $$X(3872) \rightarrow \pi ^+ \pi ^- \pi ^0 J/\psi $$ X ( 3872 ) → π + π - π 0 J / ψ , and $$X(3872)\rightarrow \pi ^0\chi _{cJ}$$ X ( 3872 ) → π 0 χ cJ . We assume that the source of the strong isospin violation comes from the different coupling strengths of X(3872) to its charged components $$D^{*+} D^-$$ D ∗ + D - and neutral components $$D^{*0 } {\bar{D}}^0$$ D ∗ 0 D ¯ 0 as well as the interference between the charged meson loops and neutral meson loops. The former effect could fix our parameters by using the measurement of the ratio $$\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- \pi ^0 J/\psi ]/\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- J/\psi ]$$ Γ [ X ( 3872 ) → π + π - π 0 J / ψ ] / Γ [ X ( 3872 ) → π + π - J / ψ ] . With the determined parameter range, we find that the estimated ratio $$\Gamma [X(3872) \rightarrow \pi ^0 \chi _{c1}/\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- J/\psi ]$$ Γ [ X ( 3872 ) → π 0 χ c 1 / Γ [ X ( 3872 ) → π + π - J / ψ ] is well consistent with the experimental measurement from the BESIII collaboration. Moreover, the partial width ratio of $$\pi ^0 \chi _{cJ}$$ π 0 χ cJ for $$J=0,1,2$$ J = 0 , 1 , 2 is estimated to be $$1.77{-}1.65:1:1.09{-}1.43$$ 1.77 - 1.65 : 1 : 1.09 - 1.43 , which could be tested by further precise measurements of BESIII and Belle II.

New results on energy and momentum conservation in meson production for A+A collisions at SPS energies

We review our recent findings on electromagnetic (EM) effects in Ar+Sc and Pb+Pb collisions at CERN SPS energies, and discuss them in the context of our earlier results on the EM splitting of π+/π- meson directed flow. A specific space-time picture emerges, on the basis of which we construct a simple model of the collision. Starting from local energy and momentum conservation, we nicely describe the centrality dependence of π meson rapidity distributions in Pb+Pb collisions at $\rad{}{s_{NN} } = 17.3\,{\rm{GeV}}$. We discuss the resulting implications on the role of energy and momentum conservation for the dynamics of meson production in A+A collisions. We present our conclusions on the link between the initial stages of the nuclear collision and the final state observables connected to strong and electromagnetic phenomena in charged meson emission. We also discuss the possibility to use the latter EM phenomena to obtain new insight into the spectator space-time evolution and excitation energy.

New baryonic and mesonic observables from NA61/SHINE

One of the main objectives of the NA61/SHINE experiment at the CERN SPS is to study properties of strongly interacting matter. This paper presents new results on observables relevant for this part of the NA61/SHINE programme. These include the first ever measurements of ϕ meson production in p+p collisions at 40 and 80 GeV, and most detailed ever experimental data at 158 GeV. This contribution demonstrates the superior accuracy of the present dataset with respect to existing measurements. The comparison of p+p to Pb+Pb collisions shows a non-trivial system size dependence of the longitudinal evolution of hidden strangeness production, contrasting with that of other mesons. Furthermore, proton density fluctuations are investigated as a possible order parameter of the second order phase transition in the neighbourhood of the critical point (CP) of strongly interacting matter. An intermittency analysis is performed of the proton second scaled factorial moments in transverse momentum space. A previous analysis of this sort revealed significant power-law fluctuations for the “Si”+Si system at 158A GeV measured by the NA49 experiment. The fitted power-law exponent was consistent within errors with the theoretically expected critical value, a result suggesting a baryochemical potential in the vicinity of the CP of about 250MeV [24]. The analysis will now be extended to NA61/SHINE systems of similar size, Be+Be and Ar+Sc, at 150A GeV. Finally, spectator-induced electromagnetic (EM) effects on charged meson production are being studied and bring information on the space-time position of the pion formation zone, which appears to be much closer to the spectator system for faster pions than for slower ones. On that basis, we demonstrate that the longitudinal evolution of the system at CERN SPS energies may be interpreted as a pure consequence of local energymomentum conservation.

MASS RELATIONS OF NUCLEONS AND MESONS UNDER SU(2) SYMMETRY BREAKING IN A GAUGED LINEAR SIGMA MODEL

We evaluate mass differences between a neutron and a proton, and between a charged and a neutral meson by using a gauged linear sigma model retaining the chiral SU (2) L × SU (2) R × U (1)V symmetry. Masses of nucleons and relevant mesons are generated through the spontaneous and the explicit chiral symmetry breaking. Since our Lagrangian includes explicitly SU(2) isospin symmetry breaking term, it enables us to simultaneously consider the mass differences of a neutron and a proton, and a charged meson and a neutral one. Their reciprocal relations of the mass differences are also derived, where radiative corrections due to electromagnetic interactions are deliberately taken into account to exactly obtain the isospin symmetry breaking effect in the particle mass differences.