Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type

Recently was shown that standard odd and even-dimensional General Relativity can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld Lagrangian invariant under a subalgebra $\cal{L}^{B_{2n+1}}$ respectively. Very Recently, it was shown that the generalized In\"on\"u-Wigner contraction of the generalized AdS-Maxwell algebras provides Maxwell algebras types $\cal{M}_{m}$ which correspond to the so called $B_{m}$ Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional General Relativity may emerge as a weak coupling constant limit of a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the Maxwell algebra type $\cal{M}_{2m+1}$, if and only if $m\geq p$. Similarly, we show that standard even-dimensional General Relativity emerges as a weak coupling constant limit of a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under a subalgebra $\cal{L}^{\cal{M}_{2m}}$ of the Maxwell algebra type, if and only if $m\geq p$. It is shown that when $m<p$ this is not possible for a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the $\cal{M}_{2m+1}$ and for a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under $\cal{L}^{\cal{M}_{2m}}$ algebra.Comment: 30 pages, accepted for publication in Eur.Phys.J.C. arXiv admin note: text overlap with arXiv:1309.006

Generalized Poincare algebras and Lovelock-Cartan gravity theory

We show that the Lagrangian for Lovelock-Cartan gravity theory can be re-formulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory invariant under the generalized Poincar\'{e} algebra $\mathfrak{B}_{2n+1},$ while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant under a subalgebra of the $\mathfrak{B}_{2n+1}$ algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern-Pontryagin character for the $B_{2n+1}$ group.Comment: v2: 18 pages, minor modification in the title, some clarifications in the abstract, introduction and section 2, section 4 has been rewritten, typos corrected, references added. Accepted for publication in Physic letters

The scale dependent nuclear effects in parton distributions for practical applications

The scale dependence of the ratios of parton distributions in a proton of a nucleus $A$ and in the free proton, $R_i^A(x,Q^2)=f_{i/A}(x,Q^2)/f_i(x,Q^2)$, is studied within the framework of the lowest order leading-twist DGLAP evolution. By evolving the initial nuclear distributions obtained with the GRV-LO and CTEQ4L sets at a scale $Q_0^2$, we show that the ratios $R_i^A(x,Q^2)$ are only moderately sensitive to the choice of a specific modern set of free parton distributions. We propose that to a good first approximation, this parton distribution set-dependence of the nuclear ratios $R_i^A(x,Q^2)$ can be neglected in practical applications. With this result, we offer a numerical parametrization of $R_i^A(x,Q^2)$ for all parton flavours $i$ in any $A>2$, and at any $10^{-6}\le x \le 1$ and any $Q^2\ge 2.25$ GeV$^2$ for computing cross sections of hard processes in nuclear collisions.Comment: 14 pages, including 4 eps-figure

Constraints for nuclear gluon shadowing from DIS data

The $Q^2$ dependence of the ratios of the cross sections of deep inelastic lepton--nucleus scattering is studied in the framework of leading twist, lowest order perturbative QCD. The $\log Q^2$ slope of the ratio $F_2^{\rm Sn}/F_2^{\rm C}$ is computed by using the DGLAP evolution equations, and shown to be sensitive to the nuclear gluon distribution functions. Four different parametrizations for the nuclear effects of parton distributions are studied. We show that the NMC data on the $Q^2$ dependence of $F_2^{\rm Sn}/F_2^{\rm C}$ rule out the case where nuclear shadowing (suppression) of gluons at $x\sim 0.01$ is much larger than the shadowing observed in the ratio $F_2^A/F_2^{\rm D}$. We also show that the possible nonlinear correction terms due to gluon fusion in the evolution equations do not change this conclusion. Some consequences for computation of RHIC multiplicities, which probe the region x\gsim0.01, are also discussed.Comment: 11 pages, 3 eps figure

Constraints for nuclear gluon densities from DIS data

The $Q^2$ dependence of the ratios of nuclear structure functions $F_2^A$ is studied by performing QCD evolution of nuclear parton distribution functions. The log $Q^2$ slope of these ratios is very sensitive to the nuclear gluon distribution function. Taking different parametrizations, we show that the NMC data on the $Q^2$ dependence of $F_2^{\rm Sn}/F_2^{\rm C}$ rule out the case where nuclear shadowing (suppression) of gluons at $x\sim 0.01$ is much larger than the shadowing observed in the ratio $F_2^A/F_2^{\rm D}$. We also take into account modifications to the DGLAP evolution by including gluon fusion terms and see that the effect is small at present energies, and, in any case, a strong gluon shadowing is not favored. The region studied ($x \sim 0.01$) is the most relevant for RHIC multiplicities.Comment: 4 pages, 3 postscript figures. Contributed to 37th Rencontres de Moriond on QCD and Hadronic Interactions, Les Arcs, France, 16-23 Mar 200

Global DGLAP fit analyses of the nPDF: EKS98 and HKM

The DGLAP analyses of the nuclear parton distribution functions (nPDF) based on the global fits to the data are reviewed, and the results from EKS98 and HKM are compared. The usefulness of measuring hard probes in $pA$ collisions, at the LHC in particular, is demonstrated.Comment: 10 pages, 3 figures. Contribution to CERN Yellow Report on Hard Probes in Heavy Ion Collisions at the LH