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The Alpha Constant from Relativistic Groups  [PDF]
Gustavo R. Gonzalez-Martin
Physics , 2000,
Abstract: The value of the alpha constant, known to be equal to an algebraic expression in terms of pi and entire numbers related to certain group volumes, is derived from the relativistic structure group of a geometric unified theory, its subgroups and corresponding symmetric space quotients.
On the factor alpha in Peyre's constant  [PDF]
Ulrich Derenthal,Andreas-Stephan Elsenhans,J?rg Jahnel
Mathematics , 2012,
Abstract: For an arbitrary del Pezzo surface S, we compute alpha(S), which is the volume of a certain polytope in the dual of the effective cone of S, using Magma and Polymake. The constant alpha(S) appears in Peyre's conjecture for the leading term in the asymptotic formula for the number of rational points of bounded height on S over number fields.
Comment on the cosmological constant and a gravitational alpha  [PDF]
Ronald J. Adler
Physics , 2011,
Abstract: We call attention to a simple analogy between atomic physics and cosmology. Both have two characteristic length scales. In atomic physics the lengths are the Compton wavelength of the electron and the Bohr radius; the ratio of these two lengths is the fine structure constant, $\alpha=7.30\times10^{-3}$. In cosmology we take the lengths to be the Planck length and the de Sitter radius divided by $\sqrt 3$; the ratio of these two lengths is about $\alpha_g=1.91\times10^{-61}$, which we suggest should be called the gravitational fine structure constant. There is also a basic energy ratio in atomic physics, the ratio of the hydrogen atom binding energy to the electron rest energy, which is equal to ${\alpha^2}/2$. The analogous energy ratio in cosmology is the ratio of the dark energy density (described in terms of the cosmological constant) to the Planck energy density, which is equal to $(1/8\pi)\alpha_g^2$. The long-standing problem of the nature of the dark energy and its small density is obviously equivalent to understanding the extraordinarily small value of $\alpha_g$. We further emphasize that our observational knowledge of dark energy, which is consistent with the cosmological constant interpretation, is entirely on the cosmological scale, so we know essentially nothing about the nature of dark energy on a smaller and presumably more fundamental scale.
Calibration issues in estimating variability of the fine structure constant (alpha) with cosmic time  [PDF]
Miriam Centurión,Paolo Molaro,Sergei Levshakov
Physics , 2009,
Abstract: Laser Comb Wavelength calibration shows that the ThAr one is locally unreliable with possible deviations of up to 100 m/s within one order range, while delivering an overall 1 m/s accuracy (Wilken et al 2009). Such deviation corresponds to delta alpha/alpha ~ 7E-6 for a FeII-MgII pair. Comparison of line shifts among the 5 FeII lines, with almost identical sensitivity to fine structure constant changes, offers a clean way to directly test the presence of possible local wavelength calibration errors of whatever origin. We analyzed 5 absorption systems, with zabs ranging from 1.15 to 2.19 towards 3 bright QSOs. The results show that while some lines are aligned within 20 m/s, others reveal large deviations reaching 200 m/s or higher and corresponding to a delta alpha/alpha > 1E-5 level. The origin of these deviations is not clearly identified but could be related to the adaptation of wavelength calibration to CCD manufacturing irregularities. These results suggest that to draw conclusions from delta alpha/alpha analysis based on one or only few lines must be done with extreme care.
The running fine structure constant alpha(E) via the Adler function
Jegerlehner, F.
High Energy Physics - Phenomenology , 2008, DOI: 10.1016/j.nuclphysbps.2008.09.010
Abstract: We present an up-to-date analysis for a precise determination of the effective fine structure constant and discuss the prospects for future improvements. We advocate to use a determination monitored by the Adler function which allows us to exploit perturbative QCD in an optimal well controlled way. Together with a long term program of hadronic cross section measurements at energies up to a few GeV, a determination of alpha(M_Z) at a precision comparable to the one of the Z mass M_Z should be feasible. Presently alpha(E) at E>1 GeV is the least precisely known of the fundamental parameters of the SM. Since, in spite of substantial progress due to new BaBar exclusive data, the region 1.4 to 2.4 GeV remains the most problematic one a major step in the reduction of the uncertainties are expected from VEPP-2000 and from a possible ``high-energy'' option DAFNE-2 at Frascati. The up-to-date evaluation reads Delta alpha^{(5)}_{had}(M_Z^2) = 0.027515 +/- 0.000149 or alpha^{-1}(M_Z)=128.957 +/- 0.020.
Does the fine structure constant vary? A third quasar absorption sample consistent with varying alpha  [PDF]
J. K. Webb,M. T. Murphy,V. V. Flambaum,S. J. Curran
Physics , 2002, DOI: 10.1023/A:1022518515530
Abstract: We report preliminary results from a third sample of quasar absorption line spectra from the Keck telescope which has been studied to search for any possible variation of the fine structure constant, alpha. This third sample, which is larger than the sum of the two previously published samples, shows the same effect, and also gives, as do the previous two samples, a significant result. The combined sample yields a highly significant effect, da/a = (alpha_z - alpha_0)/alpha_0 = -0.57 +/- 0.10 x 10^{-5}, averaged over the redshift range 0.2 < z < 3.7. We include a brief discussion of small-scale kinematic structure in quasar absorbing clouds. However, kinematics are unlikely to impact significantly on the averaged non-zero da/a above, and we have so far been unable to identify any systematic effect which can explain it. New measurements of quasar spectra obtained using independent instrumentation and telescopes are required to properly check the Keck results.
The alpha-dependence of transition frequencies for some ions of Ti, Mn, Na, C, and O, and the search for variation of the fine structure constant  [PDF]
J. C. Berengut,V. A. Dzuba,V. V. Flambaum,M. V. Marchenko
Physics , 2004, DOI: 10.1103/PhysRevA.70.064101
Abstract: We use the relativistic Hartree-Fock method, many-body perturbation theory and configuration-interaction method to calculate the dependence of atomic transition frequencies on the fine structure constant, alpha. The results of these calculations will be used in the search for variation of the fine structure constant in quasar absorption spectra.
$\Lambda\alpha$DM: Observational constraints on unified dark matter with constant speed of sound
Balbi, Amedeo;Bruni, Marco;Quercellini, Claudia
High Energy Physics - Phenomenology , 2007, DOI: 10.1103/PhysRevD.76.103519
Abstract: We consider the hypothesis that dark energy and dark matter are the two faces of a single dark component, a unified dark matter (UDM) that we assume can be modeled by the affine equation of state (EoS) $P= p_0 +\alpha \rho$, resulting in an {\it effective cosmological constant} $\rho_\Lambda=-p_0/(1+\alpha)$. The affine EoS arises from the simple assumption that the speed of sound is constant; it may be seen as an approximation to an unknown barotropic EoS $P=P(\rho)$, and may as well represent the tracking solution for the dynamics of a scalar field with appropriate potential. Furthermore, in principle the affine EoS allows the UDM to be phantom. We constrain the parameters of the model, $\alpha$ and $\Omega_\Lambda$, using data from a suite of different cosmological observations, and perform a comparison with the standard $\Lambda$CDM model, containing both cold dark matter and a cosmological constant. First considering a flat cosmology, we find that the UDM model with affine EoS fits the joint observations very well, better than $\Lambda$CDM, with best fit values $\alpha=0.01 \pm 0.02$ and $\Omega_\Lambda=0.70 \pm 0.04$ (95% confidence intervals). The standard model (best fit $\Omega_\Lambda=0.71\pm 0.04$), having one less parameter, is preferred by a Bayesian model comparison. However, the affine EoS is at least as good as the standard model if a flat curvature is not assumed as a prior for $\Lambda$CDM. For the latter, the best fit values are $\Omega_K=-0.02^{+0.01}_{-0.02} $ and $\Omega_\Lambda=0.71 \pm 0.04$, i.e. a closed model is preferred. A phantom UDM with affine EoS is ruled out well beyond $3\sigma$.
Probing The Cosmological Constant Through The Alcock-Paczynski Test Based on The Lyman-Alpha Forest  [PDF]
Wen-Ching Lin,Michael Norman
Physics , 2002,
Abstract: In recent years, the possibility of measuring the cosmological constant $\Omega_\Lambda$ through the application of the Alcock-Paczynski test to the Lyman Alpha (Ly$\alpha$) forest has been suggested (McDonald et al. 1999; Hui et al. 1999). Despite the theoretical uncertainties due to a few other cosmological parameters, some of the greatest difficulties we encounter concern the huge uncertainties due to cosmic variance and noise. In this paper, we propose a maximum likelihood estimation (MLE) method to deal with cosmic variance and noise using synthetic spectra of quasistellar objects (QSOs) from our cosmological hydrodynamic simulations. We demonstrate that the MLE method can overcome the cosmic variance problem. Applying the MLE method, we find that we have more than 90% probability to determine $\Omega_\Lambda$ within 20% error and approximately of 66% probability to determine $\Omega_\Lambda$ within 10% error by using 30 pairs QSO spectra when other cosmological parameters are assumed. Another important source of error is from noise in the flux spectra, and we have modeled the corresponding effect by studying artificial spectra with different kinds of noise added. We discover that the noise distribution does not have significant effect on the final cross-correlation functions as long as the signal-to-noise ratio (S/N) is fixed. Finally, a preliminary test and discussion about the sensitivities to other cosmological parameters are included in this paper as well.
Deducing the asymptotic normalization constant of the 2+ subthreshold state in 16O from 12C + alpha elastic scattering  [PDF]
Jean-Marc Sparenberg
Physics , 2004, DOI: 10.1016/j.nuclphysa.2004.04.077
Abstract: R-matrix analyses of the 12C + alpha elastic-scattering phase shifts deduced from a recent high-precision measurement of the differential cross sections are performed. The l=0 phase shifts constrain the R-matrix radius a around 5.85 fm, while the l=2 phase shifts lead to a strong constrain neither on a nor on the asymptotic normalization constant C of the 2+ subthreshold state (except for a loose upper limit). This contradicts previous R-matrix analyses of the 12C + alpha elastic scattering and explains the incompatibility between values of C obtained in these analyses.
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