We present the features of a model which generalizes Schwarzschild’s homogeneous star by adding a transition zone for the density near the surface. By numerically integrating the modified TOV equations for the  $$f(\mathcal {R})=\mathcal {R}+\lambda \mathcal {R}^2$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>λ</mi> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </mrow> </math>   Palatini theory, it is shown that the ensuing configurations are everywhere finite. Depending on the values of the relevant parameters, objects more, less or as compact as those obtained in GR with the same density profile have been shown to exist. In particular, in some region of the parameter space the compactness is close to that set by the Buchdahl limit.

Brazil

Fernanda Silveira

Rodrigo Maier

Santiago Perez Bergliaffa

A model of compact and ultracompact objects in  $$f(\mathcal {R})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </math>  -Palatini theory

We present an application to cosmological models in $$f({{\mathcal {R}}})$$ <math><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math>  theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given $$f({{\mathcal {R}}})$$ <math><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math> -model. Two particular families of $$f(\mathcal{R})$$ <math><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math> -cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type $$f({{\mathcal {R}}})={{\mathcal {R}}}-\beta /{{\mathcal {R}}}^n$$ <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>=</mo><mi>R</mi><mo>-</mo><mi>β</mi><mo>/</mo><msup><mrow><mi>R</mi></mrow><mi>n</mi></msup></mrow></math> , and (ii) theories of the form $$f({{\mathcal {R}}})={{\mathcal {R}}}+\alpha \ln {{{\mathcal {R}}}} -\beta $$ <math><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mi>α</mi><mo>ln</mo><mi>R</mi><mo>-</mo><mi>β</mi></mrow></math> . The constraints on $$(n,\beta )$$ <math><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></math>  and $$(\alpha ,\beta )$$ <math><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></math> , respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.

Florencia Teppa Pannia

Nivaldo Manske

Cosmography and the redshift drift in Palatini $$f({{\mathcal {R}}})$$ <math><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math>  theories

We use a non-relativistic model to study the spectroscopy of a tetraquark composed of in a diquark-antidiquark configuration. By numerically solving the Schrödinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the diquark-antidiquark system, despite the heavy diquark mass, and also that the diquark has a finite size if treated in the same way as the systems. We find that the lowest S-wave T4c tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs, while orbital and radial excitations would be mostly above the corresponding charmonium pair thresholds. Finally, we repeat the calculations without the confining part of the potential and obtain bound diquarks and bound tetraquarks. This might be relevant to the study of exotic charmonium in the quark-gluon plasma. The T4c states could be investigated in the forthcoming experiments at the LHC and Belle II.

Spain

V.R. Debastiani

France

F.S. Navarra

A non-relativistic model for the tetraquarkThe authors acknowledge the support received from the brazilian funding agencies FAPESP (contract 12/50984-4), CNPq and CAPES. V. R. Debastiani also acknowledges the support from Generalitat Valenciana in the Program Santiago Grisolia (Exp. GRISOLIA/2015/005)

Motivated by the experimental measurements of D0 radiative decay modes, we have proposed a model to study the decay, by establishing a link with (V=ρ0, ω) decays through the vector meson dominance hypothesis. In order to do this properly, we have used the Lagrangians from the local hidden gauge symmetry approach to account for Vγ conversion. As a result, we have found the branching ratio , which is in fair agreement with the experimental values reported by the Belle and BaBar collaborations.

China

J.M. Dias

Ju-Jun Xie

E. Oset

The radiative decay with vector meson dominanceJ. M. Dias would like to thank the Brazilian funding agency FAPESP for the financial support (2016/22561-2), V. R. Debastiani wishes to acknowledge the support from the Programa Santiago Grisolia of Generalitat Valenciana (Exp. GRISOLIA/2015/005). This work is also partly supported by the Spanish Ministerio de Economia y Competitividad and European FEDER funds (FIS2014-57026- REDT, FIS2014-51948-C2-1-P, FIS2014-51948-C2-2-P), and the Generalitat Valenciana in the program Prometeo II-2014/068. This work is partly supported by the National Natural Science Foundation of China (11475227, 11735003) and the Youth Innovation Promotion Association CAS (2016367)