We investigate the possibility that the observed flatness of the rotation curves of spiral galaxies is not evidence for the existence of dark matter haloes, but rather a signal of the breakdown of General Relativity. To this aim, we consider power-law fourth-order theories of gravity obtained by replacing the scalar curvature R with f(R) =f 0 R n in the gravity Lagrangian. We show that, in the low energy limit, the gravitational potential generated by a point-like source may be written as Φ(r) ∝ r -1 [1 + (r/r c ) β ] with β a function of the slope n of the gravity Lagrangian and r c a scalelength depending on the gravitating system properties. In order to apply the model to realistic systems, we compute the modified potential and the rotation curve for spherically symmetric and for thin disc mass distributions. It turns out that the potential is still asymptotically decreasing, but the corrected rotation curve, although not flat, is higher than the Newtonian one, thus offering the possibility to fit rotation curves without dark matter. To test the viability of the model, we consider a sample of 15 low surface brightness galaxies with combined H [I and Ha measurements of the rotation curve extending in the putative dark matter dominated region. We find a very good agreement between the theoretical rotation curve and the data using only stellar disc and interstellar gas when the slope n of the gravity Lagrangian is set to the value n = 3.5 (giving β = 0.817) obtained by fitting the Type Ia supernova Hubble diagram with the assumed power-law f(R) model and no dark matter. The excellent agreement between theoretical and observed rotation curves and the values of the stellar mass-to-light ratios in agreement with the predictions of population synthesis models make us confident that R n gravity may represent a good candidate to solve both the dark energy problem on cosmological scales and the dark matter one on galactic scales with the same value of the slope n of the higher-order gravity Lagrangian.

Low surface brightness galaxy rotation curves in the low energy limit of Rn gravity: no need for dark matter?

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether symmetry approach. A general formalism in the metric framework is developed considering a point-like f(R) Lagrangian where spherical symmetry is required. Examples of exact solutions are given.

Spherically symmetric solutions in f(R) gravity via the Noether symmetry approach

The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleon-nucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: $f_0(500)$. We then provide a rather conservative average of the most recent and advanced dispersive determinations of its pole position $\sqrt{s_\sigma}=449^{+22}_{-16}-i(275\pm12)$. 
In addition, after comprehensive introductions, we will review within the modern perspective of effective theories and dispersion theory, its relation to chiral symmetry, unitarization techniques, its quark mass dependence, popular models, as well as the recent strong evidence, obtained from the QCD $1/N_c$ expansion or Regge theory, for its non ordinary nature in terms of quarks and gluons.

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From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance

About 120 baryons and baryon resonances are known, from the abundant nucleon with $u$ and $d$ light-quark constituents up to the recently discovered $\Omega_b^-=bss$, and the $\Xi_b^-=bsd$ which contains one quark of each generation In spite of this impressively large number of states, the underlying mechanisms leading to the excitation spectrum are not yet understood Heavy-quark baryons suffer from a lack of known spin-parities In the light-quark sector, quark-model calculations have met with considerable success in explaining the low-mass excitations spectrum but some important aspects like the mass degeneracy of positive-parity and negative-parity baryon excitations are not yet satisfactorily understood At high masses, above 18 GeV, quark models predict a very high density of resonances per mass interval which is not observed In this review, issues are identified discriminating between different views of the resonance spectrum; prospects are discussed how open questions in baryon spectroscopy may find answers from photo- and electro-production experiments which are presently carried out in various laboratories

Baryon spectroscopy

Properties of nucleon and Δ resonances are derived from a multichannel partial wave analysis of pion and photo-induced reactions off protons. This paper summarizes the latest results on masses, widths, and decay properties of nucleon and Δ resonances.

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Properties of baryon resonances from a multichannel partial wave analysis

The reactions pi /sup +/ + p yields pi /sup +/ + pi /sup 0/ + p and pi /sup +/ + p yields pi/sup +/ + pi /sup +/ + n are studied at 910, 1090, and 1260 Mev, in an attempt to detect a pi - pi resonance. For the outgoing pi / sup +/ pi /sup 0/ pair, peaks in the Q-values lead to a di-pion resonance with a mass of 5.0 to 5.5 pion masses and 1= 1 or 2. No resonance is observed in the outgoing pi + pi + (I = 2) pair, leading to the conclusion that the pi pi resonance is a 1 = 1 state. (T.F.H.)

Pion-Pion Interaction in Pion Production by π + − p Collisions

An analysis of 3600 two-pronged events, obtained in p-p interactions at 2 Bev in the BNL 20-in. hydrogen bubble chamber, was made. Cross sections were measured for elastic scattering, for the two modes of single-pion production, p + p yields p + n + pi /sup +/, p + p yields p + p + pi /sup 0/ and for strange particle production. The branching ratio for the two one pion production reactions is sigma (pn pi /+sup 0/) = 4.17 plus or minus 0.25 Momentum distributions and Q values indicate that singlepion production proceeds almost entirely through the of the extended isobar model and also a one-pion exchange model for production. The branching ratio and momentum distributions can be explained by including a small effect from the I = 1/2 resonant state in addition to the dominant I =3/2 resonance. The c.m. angular distribution of the nucleons in single-pion production shows very marked backward-forward peaking indicating a one-pion exchange mechanism. Absolute differential cross sections as a function of laboratory kinetic energy were calculated from Selleri's equation for the pn pi reaction. There is sgreement with the data for low four-momentum transfers ers the theoretical are larger than the experimentalmore » cross sections. (auth)« less

p − p Interactions at 2 Bev. I. Single-Pion Production

A novel method of analysis which eliminates the combinatorial background in searches for states produced in p-barn annihilations and in association with a recoil ..pi../sup -/ is presented. The difference between ..pi../sup -/ and ..pi../sup +/ spectra on p-barn annihilations is the spectrum of the recoiling ..pi../sup -/ or difference spectrum. We applied this analysis to the exclusive channels p-barn..-->..2..pi../sup -/..pi../sup +/, 2..pi../sup -/..pi../sup +/..pi../sup 0/, 3..pi../sup -/2..pi../sup +/. A new prominent state of mass and width approx. =1480 and 100 MeV/c/sup 2/ is present in the first and dominates the third channel. These three channels are interpreted in terms of two-body intermediate states only. The suppression or absence of ''direct'' annihilation is consistent with theoretical models which view the annihilation as a short-range (0.1 fm) phenomenon.

Difference spectra: Dominance of two-body cascades in antiproton-neutron annihilations at rest.

Annihilations of antiprotons from atomic pp and pd states have been extensively examined in search of resonant states in a mass region where the low-lying levels for several anticipated spectroscopies are expect­ ed to be. Spectroscopies based on NN potentials! (quasinuclear states), four-quark composites 2 (bary­ onium), and two-gluon states 3 (glueballs) are some of them. The NN annihilation which is rich in "N-N," quarks, and gluons is expected to couple to these spec­ troscopies. Many searches have been made in the past and more recently at the CERN Low Energy Antipro­ ton Ring (LEAR). 4 All of them have been done in hydrogen and have been sensitive to narrow states, and the results have been negative, or at best incon­ clusive.

Evidence for a new state produced in antiproton annihilations at rest in liquid deuterium.

The photon spectrum from ${K}^{\mathrm{\ensuremath{-}}}$ stopping in liquid hydrogen has been measured with a high-resolution (1.5% FWHM at 300 MeV) NaI(Tl) detector. The branching ratios for ${K}^{\mathrm{\ensuremath{-}}}$p\ensuremath{\rightarrow}\ensuremath{\Lambda}\ensuremath{\gamma} (${E}_{\ensuremath{\gamma}}$=281.4 MeV) and ${K}^{\mathrm{\ensuremath{-}}}$p\ensuremath{\rightarrow}${\ensuremath{\Sigma}}^{0}$\ensuremath{\gamma} (${E}_{\ensuremath{\gamma}}$=219.5 MEV) were obtained. The results are ${\mathit{R}}_{\mathrm{\ensuremath{\Lambda}}\ensuremath{\gamma}}$=(0.86\ifmmode\pm\else\textpm\fi{}0.${07}_{\mathrm{\ensuremath{-}}0.08}^{+0.1}$)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ and ${\mathit{R}}_{\mathrm{\ensuremath{\Sigma}}0\ensuremath{\gamma}}$=(1.44\ifmmode\pm\else\textpm\fi{}0.${20}_{\mathrm{\ensuremath{-}}0.10}^{\ifmmode\pm\else\textpm\fi{}0.12}$)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ where the first error is statistical and the second systematic. These results are not in good agreement with published predictions or with previous \ensuremath{\Lambda}\ensuremath{\gamma} measurements.

William Fickinger

Papers

Pion-Pion Interaction in Pion Production by π + − p Collisions

p − p Interactions at 2 Bev. I. Single-Pion Production

Difference spectra: Dominance of two-body cascades in antiproton-neutron annihilations at rest.

Evidence for a new state produced in antiproton annihilations at rest in liquid deuterium.

Radiative kaon capture at rest in hydrogen