Light quark masses from scalar sum rules

In this work, the mass of the strange quark is calculated from QCD sum rules for the divergence of the strangeness-changing vector current. The phenomenological scalar spectral function which enters the sum rule is determined from our previous work on strangeness-changing scalar form factors [1]. For the running strange mass in the MS_bar scheme, we find m_s(2 GeV) = 99 +- 16 MeV. Making use of this result and the light-quark mass ratios obtained from chiral perturbation theory, we are also able to extract the masses of the lighter quarks m_u and m_d. We then obtain m_u(2 GeV) = 2.9 +- 0.6 MeV and m_d(2 GeV) = 5.2 +- 0.9 MeV. In addition, we present an updated value for the light quark condensate.Comment: 19 pages, 2 figures, 1 table, text improved, references added, version to be published in Eur. Phys. J

On a variant of Giuga numbers

In this paper, we characterize the odd positive integers $n$ satisfying the congruence $\sum_{j=1} ^ {n-1} j^{\frac{n-1}{2}}\equiv 0 \pmod n$. We show that the set of such positive integers has an asymptotic density which turns out to be slightly larger than 3/8.Comment: 14 page

Meson-Baryon Effective Chiral Lagrangians at O(q^3) Revisited

After our work was published, Frink and Mei{\ss}ner \cite{FM06} pointed out that our {\cal O}(q^3) three-flavour meson-baryon chiral Lagrangian was not minimal. Here, we discuss their findings and revise ours accordingly. We find that eight monomials in our ${\cal O}(q^3)$ Lagrangian are not independent, but in addition, two monomials were wrongly discarded, which, as a result, makes the agreement in the number of independent monomials with \cite{FM06} complete.Comment: 7 pages, 1 table. A mistake was corrected. Our Lagrangian and that of [2] contain the same number of monomial

The existence of a two-solar mass neutron star constrains the gravitational constant G_N at strong field

In General Relativity there is a maximum mass allowed for neutron stars that, if exceeded, entails their collapse into a black hole. Its precise value depends on details of the nuclear matter equation of state about which we are much more certain thanks to recent progress in low-energy effective theories. The discovery of a two-solar mass neutron star, near that maximum mass, when analyzed with modern equations of state, implies that Newton's gravitational constant in the star cannot exceed its value on Earth by more than 8% at 95% confidence level. This is a remarkable leap of ten orders of magnitude in the gravitational field intensity at which the constant has been constrained.Comment: 5 pages including 8 figure