Covariant Bardeen Perturbation Formalism

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem. Using our mixed and pure tensors approach, we were able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hyper-surface dependence inherent to the covariant approach. Finally, through the use of this map, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $\Phi$, $\Psi$ and $\Xi$, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hyper-surface invariant variables at any order.Comment: 15 pages, no figures, revtex4-1, accepted for publication in PRD, typos fixed, improved discussion about higher order gauge and foliation invarianc

Modified Gravity Away from a Λ\LambdaCDM Background

Within the effective field theory approach to cosmic acceleration, the background expansion can be specified separately from the gravitational modifications. We explore the impact of modified gravity in a background different from a cosmological constant plus cold dark matter ($\Lambda$CDM) on the stability and cosmological observables, including covariance between gravity and expansion parameters. In No Slip Gravity the more general background allows more gravitational freedom, including both positive and negative Planck mass running. We examine the effects on cosmic structure growth, as well as showing that a viable positive integrated Sachs-Wolfe effect crosscorrelation easily arises from this modified gravity theory. Using current data we constrain parameters with a Monte Carlo analysis, finding a maximum running $|\alpha_M|\lesssim 0.03$. We provide the modified {\tt hi\_class} code publicly on GitHub, now enabling computation and inclusion of the redshift space distortion observable $f\sigma_8$ as well as the No Slip Gravity modifications.Comment: 14 pages, 13 figures. Matches published version in JCAP, LCDM discussion adde

Lorentz invariance relations and Wandzura-Wilczek approximation

A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.Comment: 10 pages; Proceedings of the workshop "Recent Advances in Perturbative QCD and Hadronic Physics", July 20-24, 2009, at ECT*, Trento (Italy), in honor of Anatoli V. Efremov on the occasion of his 75th birthday; to appear in Mod. Phys. Lett.

Q^2 dependence of azimuthal asymmetries in semi-inclusive deep inelastic scattering and in Drell-Yan

We study several azimuthal asymmetries in semi-inclusive deep inelastic scattering and in Drell-Yan, interpreting them in the framework of the formalism of the quark correlator, with a particular reference to T-odd functions. The correlator contains an undetermined energy scale, which we fix on the basis of a simple and rather general argument. We find a different value than the one assumed in previous treatments of T-odd functions. This implies different predictions on the Q^2 dependence of the above mentioned asymmetries. Our result about the azimuthal asymmetry of unpolarized Drell-Yan agrees with presently available data, contrary to the alternative assumption on the scale. Predictions on other azimuthal asymmetries could be tested against data of planned experiments on Drell-Yan and semi-inclusive deep inelastic scattering.Comment: 37 pages, 7 figure

Monte-Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions

The complete knowledge of the nucleon spin structure at leading twist requires also addressing the transverse spin distribution of quarks, or transversity, which is yet unexplored because of its chiral-odd nature. Transversity can be best extracted from single-spin asymmetries in fully polarized Drell-Yan processes with antiprotons, where valence contributions are involved anyway. Alternatively, in single-polarized Drell-Yan the transversity happens convoluted with another chiral-odd function, which is likely to be responsible for the well known (and yet unexplained) violation of the Lam-Tung sum rule in the corresponding unpolarized cross section. We present Monte-Carlo simulations for the unpolarized and single-polarized Drell-Yan $\bar{p} p^{(\uparrow)} \to \mu^+ \mu^- X$ at different center-of-mass energies in both configurations where the antiproton beam hits a fixed proton target or it collides on another proton beam. The goal is to estimate the minimum number of events needed to extract the above chiral-odd distributions from future measurements at the HESR ring at GSI. It is important to study the feasibility of such experiments at HESR in order to demonstrate that interesting spin physics can be explored already using unpolarized antiprotons.Comment: Deeply revised text with improved discussion of kinematics and results; added one table; 12 figures. Accepted for publication in Phys. Rev.

Quantum Cosmological Perturbations of Generic Fluids in Quantum Universes

In previous works, it was shown that the Lagrangians and Hamiltonians of cosmological linear scalar, vector and tensor perturbations of homogeneous and isotropic space-times with flat spatial sections containing a perfect fluid can be put in a simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In this paper, we generalize this result to general fluids, which includes entropy perturbations, and to arbitrary spacelike hyper-surfaces through a new method together with the Faddeev-Jackiw procedure for the constraint reduction. A simple second order Hamiltonian involving the Mukhanov-Sasaki variable is obtained, again without ever using the background equations of motion.Comment: 19 pages, revtex4-1, submitted to PRD, expanded discussion about our method, fixed typo

Formal analogies between gravitation and electrodynamics

We develop a theoretical framework that allows us to compare electromagnetism and gravitation in a fully covariant way. This new scenario does not rely on any kind of approximation nor associate objects with different operational meaning as it's sometime done in the literature. We construct the electromagnetic analogue to the Riemann and Weyl tensors and develop the equations of motion for these objects. In particular, we are able to identify precisely how and in what conditions gravity can be mapped to electrodynamics. As a consequence, many of the gemometrical tools of General Relativity can be applied to Electromagnetism and vice-versa. We hope our results would shed new light in the nature of electromagnetic and gravitational theories.Comment: 9pages, submitted to General Relativity and Gravitatio

Effects of azimuth-symmetric acceptance cutoffs on the measured asymmetry in unpolarized Drell-Yan fixed target experiments

Fixed-target unpolarized Drell-Yan experiments often feature an acceptance depending on the polar angle of the lepton tracks in the laboratory frame. Typically leptons are detected in a defined angular range, with a dead zone in the forward region. If the cutoffs imposed by the angular acceptance are independent of the azimuth, at first sight they do not appear dangerous for a measurement of the cos(2\phi)-asymmetry, relevant because of its association with the violation of the Lam-Tung rule and with the Boer-Mulders function. On the contrary, direct simulations show that up to 10 percent asymmetries are produced by these cutoffs. These artificial asymmetries present qualitative features that allow them to mimic the physical ones. They introduce some model-dependence in the measurements of the cos(2\phi)-asymmetry, since a precise reconstruction of the acceptance in the Collins-Soper frame requires a Monte Carlo simulation, that in turn requires some detailed physical input to generate event distributions. Although experiments in the eighties seem to have been aware of this problem, the possibility of using the Boer-Mulders function as an input parameter in the extraction of Transversity has much increased the requirements of precision on this measurement. Our simulations show that the safest approach to these measurements is a strong cutoff on the Collins-Soper polar angle. This reduces statistics, but does not necessarily decrease the precision in a measurement of the Boer-Mulders function.Comment: 13 pages, 14 figure

Extraction of the pion distribution amplitude from polarized muon pair production

We consider the production of muon pairs from the scattering of pions on longitudinally polarized protons. We calculate the cross section and the single spin asymmetry for this process, taking into account pion bound state effects. We work in the kinematic region where the photon has a large longitudinal momentum fraction, which allows us to treat the bound state problem perturbatively. Our predictions are directly proportional to the pion distribution amplitude. A measurement of the polarized Drell-Yan cross section thus allows the determination of the shape of the pion distribution amplitude.Comment: 13 pages, using revtex, two figures added separately as one uuencoded Z-compressed fil

Intrinsic transverse momentum and the polarized Drell-Yan process

In this paper we study the cross section at leading order in $1/Q$ for polarized Drell-Yan scattering at measured lepton-pair transverse momentum $Q_T$. We find that for a hadron with spin $1/2$ the quark content at leading order is described by six distribution functions for each flavor, which depend on both the lightcone momentum fraction $x$, and the quark transverse momentum \bbox{k}_T^2. These functions are illustrated for a free-quark ensemble. The cross sections for both longitudinal and transverse polarizations are expressed in terms of convolution integrals over the distribution functions.Comment: 25 pages, REVTEX 3.0 (3 figures included in separate LATEX file using feynman.tex), NIKHEF-94-P1 (Revised version