Showing papers on "Big Bang nucleosynthesis published in 2008"

Big-bang nucleosynthesis and gravitinos

Abstract: We derive big-bang nucleosynthesis (BBN) constraints on both unstable and stable gravitino taking account of recent progress in theoretical study of the BBN processes as well as observations of primordial light-element abundances In the case of unstable gravitino, we set the upper limit on the reheating temperature assuming that the primordial gravitinos are mainly produced by the scattering processes of thermal particles For stable gravitino, we consider B-ino, stau, and sneutrino as the next-to-the-lightest supersymmetric particle and obtain constraints on their properties Compared with the previous works, we improved the following points: (i) we use the most recent observational data, (ii) for gravitino production, we include contribution of the longitudinal component, and (iii) for the case with unstable long-lived stau, we estimate the bound-state effect of stau accurately by solving the Boltzmann equation

An update on the big bang nucleosynthesis prediction for 7Li: The problem worsens

Abstract: The lithium problem arises from the significant discrepancy between the primordial 7Li abundance as predicted by big bang nucleosynthesis (BBN) theory and the Wilkinson Microwave Anisotropy Probe (WMAP) baryon density, and the pre-Galactic lithium abundance inferred from observations of metal-poor (Population II) stars. This problem has loomed for the past decade, with a persistent discrepancy of a factor of 2–3 in 7Li/H. Recent developments have sharpened all aspects of the Li problem. Namely: (1) BBN theory predictions have sharpened due to new nuclear data; in particular, the uncertainty on the reaction rate for3He(α,γ)7Be has reduced to 7.4%, nearly a factor of 2 tighter than previous determinations. (2) The WMAP five-year data set now yields a cosmic baryon density with an uncertainty reduced to 2.7%. (3) Observations of metal-poor stars have tested for systematic effects. With these, we now find that the BBN+WMAP predicts7Li/H = (5.24−0.67+0.71) × 10−10. The central value represents an increase by 23%, most of which is due to the upward shift in the3He(α,γ)7Be rate. More significant is the reduction in the7Li/H uncertainty by almost a factor of 2, tracking the reduction in the3He(α,γ)7Be error bar. These changes exacerbate the Li problem; the discrepancy is now a factor 2.4 or 4.2σ (from globular cluster stars) to 4.3 or 5.3σ (from halo field stars). Possible resolutions to the lithium problem are briefly reviewed, and key experimental and astronomical measurements highlighted.

Thermal relics in hidden sectors

Abstract: Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models (WIMP: weakly interacting massive particles) with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter's thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from big bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated. A flavour-free version of the standard model is allowed if the hidden sector is just 30% colder than the observable sector after reheating. Alternatively, if the hidden sector contains a one-generation version of the standard model with characteristic mass scale below 1 MeV, even identical reheating temperatures are allowed. We then analyse hidden sector freeze-out in detail for a concrete model, solving the Boltzmann equation numerically and explaining the results from both observable and hidden sector points of view. We find that WIMPless dark matter does indeed obtain the correct relic density for masses in the range . The upper bound results from the requirement of perturbativity, and the lower bound assumes that the observable and hidden sectors reheat to the same temperature, and is raised to the MeV scale if the hidden sector is ten times colder. WIMPless dark matter therefore generalizes the WIMP paradigm to the largest mass range possible for viable thermal relics and provides a unified framework for exploring dark matter signals across nine orders of magnitude in dark matter mass.

Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: implications for the early universe

Abstract: gw 0 (f1) and gw 0 (f2). Here r is the so-called “tensor-to-scalar ratio,” which is constrained by cosmic-microwave-background (CMB) experiments; and gw (f) is the energy spectrum of primordial gravitational-waves, which is constrained e.g. by pulsar-timing (PT) measurements, laser-interferometer (LI) experiments, and the standard Big Bang Nucleosynthesis (BBN) bound. Differentiating the master equation yields a new expression for the tilt dln gw (f)/dlnf of the present-day gravitational-wave spectrum. The relationship between r and gw (f) depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities: ˆ w(f) and ˆ nt(f), where ˆ nt(f) is a certain logarithmic average over nt(k) (the primordial tensor spectral index); and ˆ w(f) is a certain logarithmic average over ˜ w(a) (the effective equation-of-state parameter in the early universe, after horizon re-entry). Here the effective equation-of-state parameter ˜ w(a) is a combination of the ordinary equation-of-state parameter w(a) and the bulk viscosity �(a). Thus, by comparing observational constraints on r and gw (f), one obtains (remarkably tight) constraints in the { ˆ w(f), ˆ nt(f)} plane. In particular, this is the best way to constrain (or detect) the presence of a “stiff” energy component (with w > 1/3) in the early universe, prior to BBN. (The discovery of such a component would be no more surprising than the discovery of a tiny cosmological constant at late times!) Finally, although most of our analysis does not assume inflation, we point out that if CMB experiments detect a non-zero value for r, then we will immediately obtain (as a free by-product) a new upper bound ˆ w < 0.55 on the logarithmically averaged effective equation-of-state parameter during

Signatures of a hidden cosmic microwave background.

Abstract: If there is a light Abelian gauge boson gamma' in the hidden sector its kinetic mixing with the photon can produce a hidden cosmic microwave background (HCMB). For meV masses, resonant oscillations gamma gamma' happen after big bang nucleosynthesis (BBN) but before CMB decoupling, increasing the effective number of neutrinos Nnu(eff) and the baryon to photon ratio, and distorting the CMB blackbody spectrum. The agreement between BBN and CMB data provides new constraints. However, including Lyman-alpha data, Nnu(eff) > 3 is preferred. It is tempting to attribute this effect to the HCMB. The interesting parameter range will be tested in upcoming laboratory experiments.

Compulsory Deep Mixing of 3He and CNO Isotopes in the Envelopes of Low-Mass Red Giants

Abstract: Three-dimensional stellar modeling has enabled us to identify a deep-mixing mechanism that must operate in all low-mass giants. This mixing process is not optional, and is driven by a molecular weight inversion created by the 3He(3He,2p)4He reaction. In this paper we characterize the behavior of this mixing, and study its impact on the envelope abundances. It not only eliminates the problem of 3He overproduction, reconciling stellar and big bang nucleosynthesis with observations, but solves the discrepancy between observed and calculated CNO isotope ratios in low-mass giants, a problem of more than three decades standing. This mixing mechanism, which we call "δ μ mixing," operates rapidly (relative to the nuclear timescale of overall evolution, ~108 yr) once the hydrogen-burning shell approaches the material homogenized by the surface convection zone. In agreement with observations, Population I stars between 0.8 and 2.0 M☉ develop 12C/13C ratios of 14.5 ± 1.5, while Population II stars process the carbon to ratios of 4.0 ± 0.5. In stars less than 1.25 M☉, this mechanism also destroys 90%-95% of the 3He produced on the main sequence.

Antimatter signatures of gravitino dark matter decay

Abstract: The scenario of gravitino dark matter with broken R-parity naturally reconciles three paradigms that, albeit very well motivated separately, seem to be in mutual conflict: supersymmetric dark matter, thermal leptogenesis and standard big bang nucleosynthesis. Interestingly, the products of the gravitino decay could be observed, opening the possibility of indirect detection of gravitino dark matter. In this paper, we compute the positron and the antiproton fluxes from gravitino decay. We find that a gravitino with a mass of m3/2~150 GeV and a lifetime of τ3/2~1026 s could simultaneously explain the EGRET anomaly in the extragalactic diffuse gamma ray background and the HEAT excess in the positron fraction. However, the predicted antiproton flux tends to be too large, although the prediction suffers from large uncertainties and might be compatible with present observations for certain choices of propagation parameters.

Probing the reheating temperature of the universe with a gravitational wave background

Abstract: The thermal history of the universe after big bang nucleosynthesis (BBN) is well understood both theoretically and observationally, and recent cosmological observations also begin to reveal the inflationary dynamics. However, the epoch between inflation and BBN is scarcely known. In this paper we show that the detection of the stochastic gravitational wave background around 1 Hz provides useful information about thermal history well before BBN. In particular, the reheating temperature of the universe may be determined by future space-based laser interferometer experiments such as DECIGO and/or BBO if it is around 106−9 GeV, depending on the tensor-to-scalar ratio r and dilution factor F.

Constraining the early-Universe baryon density and expansion rate

Abstract: We explore the constraints on those extensions to the standard models of cosmology and particle physics which modify the early-Universe, radiation dominated, expansion rate (parameterized by the effective number of neutrinos Nν). The constraints on S(Nν) and the baryon density parameter , derived from big bang nucleosynthesis (BBN, t~20 min), are compared with those inferred from the cosmic microwave background anisotropy spectrum (CMB, t~400 kyr) and large scale structure (LSS, t~14 Gyr). At present, BBN provides the strongest constraint on Nν (Nν = 2.4 ± 0.4 at 68% confidence), but a weaker constraint on the baryon density. In contrast, while the CMB/LSS data best constrain the baryon density (η10 = 6.1−0.1+0.2 at 68% confidence), independent of Nν, at present they provide a relatively weak constraint on Nν which is, however, consistent with the standard value of Nν = 3. When the best fit values and the allowed ranges of these CMB/LSS-derived parameters are used to calculate the BBN-predicted primordial abundances, there is excellent agreement with the observationally inferred abundance of deuterium and good agreement with 4He, confirming the consistency between the BBN and CMB/LSS results. However, the BBN-predicted abundance of 7Li is high, by a factor of 3 or more, if its observed value is uncorrected for possible dilution, depletion, or gravitational settling. We comment on the relation between the value of Nν and a possible anomaly in the matter power spectrum inferred from observations of the Ly-α forest. Comparing our BBN and CMB/LSS results permits us to constrain any post-BBN entropy production as well as the production of any non-thermalized relativistic particles. The good agreement between our BBN and CMB/LSS results for Nν and ηB permits us to combine our constraints finding, at 95% confidence, 1.8

Using big bang nucleosynthesis in cosmological parameter extraction from the cosmic microwave background: a forecast for PLANCK

Abstract: Data from future high precision cosmic microwave background measurements will be sensitive to the primordial helium abundance Yp. At the same time, this parameter can be predicted from big bang nucleosynthesis (BBN) as a function of the baryon and radiation densities, as well as a neutrino chemical potential. We suggest using this information to impose a self-consistent BBN prior on Yp and determining its impact on parameter inference from simulated planck data. We find that this approach can significantly improve bounds on cosmological parameters compared to an analysis which treats Yp as a free parameter, if the neutrino chemical potential is taken to vanish. We demonstrate that fixing the helium fraction at an arbitrary value can seriously bias parameter estimates. Under the assumption of degenerate BBN (i.e., letting the neutrino chemical potential ξ vary), the BBN prior's constraining power is somewhat weakened, but nevertheless allows us to constrain ξ with an accuracy that rivals that for bounds inferred from present data on light element abundances.

Bounds on long-lived charged massive particles from Big Bang nucleosynthesis

Abstract: The Big Bang nucleosynthesis (BBN) process in the presence of charged massive particles (CHAMPs) is studied in detail. All currently known effects due to the existence of bound states between CHAMPs and nuclei, including possible late-time destruction of 6Li and 7Li, are included. The study sets conservative bounds on CHAMP abundances in the decay time range . It is stressed that the production of 6Li at early times T~10 keV is overestimated by a factor ~10 when the approximation of the Saha equation for the 4He bound state fraction is utilized. To obtain conservative limits on the abundance of CHAMPs, a Monte Carlo analysis with ~3 × 106 independent BBN runs, varying the reaction rates of 19 different reactions, is performed. The analysis yields the surprising result that, except for small areas in the particle parameter space, conservative constraints on the abundance of decaying charged particles are currently very close to those of neutral particles. It is shown that, in the case that the rates of a number of heretofore unconsidered reactions may be determined reliably in the future, it is conceivable that the limit on CHAMPs in the early Universe could be tightened by orders of magnitude.

Constraints on supersymmetric models from catalytic primordial nucleosynthesis of beryllium

Abstract: The catalysis of nuclear reactions by negatively charged relics leads to increased outputs of primordial 6Li and 9Be. In combination with observational constraints on the primordial fractions of 6Li and 9Be, this imposes strong restrictions on the primordial abundance and the lifetime of charged relics. We analyze the constraints from the catalysis of 9Be on supersymmetric models in which the gravitino is the lightest supersymmetric particle and a charged slepton—such as the lighter stau—the next-to-lightest supersymmetric particle (NLSP). Barring the special cases in which the primordial fraction of the slepton NLSP is significantly depleted, we find that the 9Be data require a slepton NLSP lifetime of less than 6 × 103 s. We also address the issue of the catalytic destruction of 6Li and 9Be by late-forming bound states of protons with negatively charged relics, finding that it does not lead to any significant modification of the limit on the slepton lifetime.

Constraints on Supersymmetric Models from Catalytic Primordial Nucleosynthesis of Beryllium

Abstract: The catalysis of nuclear reactions by negatively charged relics leads to increased outputs of primordial ^6Li and ^9Be In combination with observational constraints on the primordial fractions of ^6Li and ^9Be, this imposes strong restrictions on the primordial abundance and the lifetime of charged relics We analyze the constraints from the catalysis of ^9Be on supersymmetric models in which the gravitino is the lightest supersymmetric particle and a charged slepton--such as the lighter stau--the next-to-lightest supersymmetric particle (NLSP) Barring the special cases in which the primordial fraction of the slepton NLSP is significantly depleted, we find that the ^9Be data require a slepton NLSP lifetime of less than 6x10^3 seconds We also address the issue of the catalytic destruction of ^6Li and ^9Be by late forming bound states of protons with negatively charged relics finding that it does not lead to any significant modification of the limit on the slepton lifetime

Evaluation of Modern 3He(alpha,gamma)7Be Data

Abstract: In both the Sun and the early universe, the 3He(alpha,gamma)7Be reaction plays a key role. The rate of this reaction is the least certain nuclear input needed to calculate both the primordial 7Li abundance in big bang nucleosynthesis (BBN) and the solar neutrino flux. Taking advantage of several recent highly precise experiments, we analyse modern 3He(alpha,gamma)7Be data using a robust and minimally model dependent approach capable of handling discrepant data sets dominated by systematic rather than statistical errors. We find S34(0)=0.580 pm 0.043(0.054) keV b at the 68.3(95.4)% confidence level.

Cosmic microwave anisotropies from BPS semilocal strings

Abstract: We present the first ever calculation of cosmic microwave background (CMB) anisotropy power spectra from semilocal cosmic strings, obtained via simulations of a classical field theory. Semilocal strings are a type of non-topological defect arising in some models of inflation motivated by fundamental physics, and are thought to relax the constraints on the symmetry breaking scale as compared to models with (topological) cosmic strings. We derive constraints on the model parameters, including the string tension parameter mu, from fits to cosmological data, and find that in this regard Bogomol'nyi-Prasad -Sommerfield (BPS) semilocal strings resemble global textures more than topological strings. The observed microwave anisotropy at l = 10 is reproduced if mu = 5.3 x 10(-6) (G is Newton's constant). However as with other defects the spectral shape does not match observations, and in models with inflationary perturbations plus semilocal strings the 95% confidence level upper bound is G mu < 2.0 x 10(-6) when CMB, Hubble key project and big bang nucleosynthesis data are used (cf G mu < 0.9 x 10(-6) for cosmic strings). We additionally carry out a Bayesian model comparison of several models with and without defects, showing that models with defects are neither conclusively favoured nor disfavoured at present.

Probing the effective number of neutrino species with the cosmic microwave background

Abstract: We discuss how much we can probe the effective number of neutrino species ${N}_{\ensuremath{ u}}$ with the cosmic microwave background alone. Using the data of the WMAP, ACBAR, CBI, and BOOMERANG experiments, we obtain a constraint on the effective number of neutrino species as $0.96l{N}_{\ensuremath{ u}}l7.94$ at 95% C.L. for a power-law $\ensuremath{\Lambda}\mathrm{CDM}$ flat universe model. The limit is improved to be $1.39l{N}_{\ensuremath{ u}}l6.38$ at 95% C.L. if we assume that the baryon density, ${N}_{\ensuremath{ u}}$, and the helium abundance are related by the big bang nucleosynthesis theory. We also provide a forecast for the Planck experiment using a Markov chain Monte Carlo approach. In addition to constraining ${N}_{\ensuremath{ u}}$, we investigate how the big bang nucleosynthesis relation affects the estimation for these parameters and other cosmological parameters.

A note on the primordial abundance of stau NLSPs

Abstract: In scenarios with gravitino lightest supersymmetric particles, there exist strong big bang nucleosynthesis constraints on the abundance of possible stau next-to-lightest supersymmetric particles. We find that in settings with substantial left-right mixing of the stau mass eigenstates these constraints can be evaded even for very long-lived staus.

Ultra-cold WIMPs: relics of non-standard pre-BBN cosmologies

Abstract: Weakly interacting massive particles (WIMPs) are one of very few probes of cosmology before Big Bang nucleosynthesis (BBN). We point out that in scenarios in which the Universe evolves in a non-standard manner during and after WIMP kinetic decoupling, the horizon mass scale at decoupling can be smaller and the dark matter WIMPs can be colder than in standard cosmology. This would lead to much smaller first objects in hierarchical structure formation. In low reheating temperature scenarios the effect may be large enough as to noticeably enhance indirect detection signals in GLAST and other detectors, by up to two orders of magnitude.

Nucleosynthesis in O-Ne-Mg Supernovae

Abstract: We have studied detailed nucleosynthesis in the shocked surface layers of an oxygen-neon-magnesium core collapse supernova with an eye to determining whether the conditions are suitable for r-process nucleosynthesis. We find no such conditions in an unmodified model, but do find overproduction of N=50 nuclei (previously seen in early neutron-rich neutrino winds) in amounts that, if ejected, would pose serious problems for Galactic chemical evolution.

Ultra-cold weakly interacting massive particles: relics of non-standard pre-big-bang-nucleosynthesis cosmologies

Abstract: Weakly interacting massive particles (WIMPs) constitute one of very few probes of cosmology before big bang nucleosynthesis (BBN). We point out that in scenarios in which the Universe evolves in a non-standard manner during and after WIMP kinetic decoupling, the horizon mass scale at decoupling can be smaller and the dark matter WIMPs can be colder than in standard cosmology. This would lead to much smaller first objects in hierarchical structure formation. In low reheating temperature scenarios the effect may be large enough to noticeably enhance indirect detection signals in GLAST and other detectors, by up to two orders of magnitude.

Hunting the lightest lightest neutralinos

Abstract: The lightest neutralino in the minimal supersymmetric extension of the standard model can be, in principle, massless. If superlight neutralinos are the dark matter, structure formation constrains their mass to be above a few keV. I show that relaxing the assumption of radiation domination and entropy conservation prior to big bang nucleosynthesis, the relic abundance of very light neutralinos can be consistent with the inferred cold dark matter density. I study how one can hunt for light neutralino dark matter, with a mass at or below a GeV, focusing on both direct and indirect searches. I argue that the two most promising channels are spin-dependent direct detection and the search for monochromatic gamma rays from the prompt pair-annihilation of neutralinos into photons with GLAST. My study indicates that the lightest lightest neutralinos can be detected as long as their mass is above a few tenth of a GeV, a mass range where a future linear collider could provide important information on the details of the particle dark matter model.

Constraining the universal lepton asymmetry

Abstract: The relic cosmic background neutrinos accompanying the cosmic microwave background (CMB) photons may hide a universal lepton asymmetry orders of magnitude larger than the universal baryon asymmetry. At present, the only direct way to probe such an asymmetry is through its effect on the abundances of the light elements produced during primordial nucleosynthesis. The relic light element abundances also depend on the baryon asymmetry, parameterized by the baryon density parameter () and on the early-universe expansion rate, parameterized by the expansion rate factor () or, equivalently, by the effective number of neutrinos (). We use data from the CMB (and large scale structure: LSS) along with the observationally inferred relic abundances of deuterium and helium-4 to provide new bounds on the universal lepton asymmetry, finding for ηL, the analog of ηB,0.072 ± 0.053 if it is assumed that Nν = 3 and, 0.115 ± 0.095 along with Nν = 3.3−0.6+0.7, if Nν is free to vary.

Primordial Nucleosynthesis: from precision cosmology to fundamental physics

Abstract: We present an up-to-date review of Big Bang Nucleosynthesis (BBN). We discuss the main improvements which have been achieved in the past two decades on the overall theoretical framework, summarize the impact of new experimental results on nuclear reaction rates, and critically re-examine the astrophysical determinations of light nuclei abundances. We report then on how BBN can be used as a powerful test of new physics, constraining a wide range of ideas and theoretical models of fundamental interactions beyond the standard model of strong and electroweak forces and Einstein's general relativity.

Constraining The Universal Lepton Asymmetry

Abstract: The relic cosmic background neutrinos accompanying the cosmic microwave background (CMB) photons may hide a universal lepton asymmetry orders of magnitude larger than the universal baryon asymmetry. At present, the only direct way to probe such an asymmetry is through its effect on the abundances of the light elements produced during primordial nucleosynthesis. The relic light element abundances also depend on the baryon asymmetry, parameterized by the baryon density parameter (eta_B = n_B/n_gamma = 10^(-10)*eta_10), and on the early-universe expansion rate, parameterized by the expansion rate factor (S = H'/H) or, equivalently by the effective number of neutrinos (N_nu = 3 + 43(S^2 - 1)/7). We use data from the CMB (and Large Scale Structure: LSS) along with the observationally-inferred relic abundances of deuterium and helium-4 to provide new bounds on the universal lepton asymmetry, finding for eta_L, the analog of eta_B, 0.072 +/- 0.053 if it is assumed that N_nu = 3 and, 0.115 +/- 0.095 along with N_nu = 3.3^{+0.7}_{-0.6}, if N_nu is free to vary.

Big-bang nucleosynthesis and the relic abundance of dark matter in a stau-neutralino coannihilation scenario

Abstract: A scenario of the big-bang nucleosynthesis is analyzed within the minimal supersymmetric standard model, which is consistent with a stau-neutralino coannihilation scenario to explain the relic abundance of dark matter. We find that we can account for the possible discrepancy of the abundance of $^{7}\mathrm{Li}$ between the observation and the prediction of the big-bang nucleosynthesis by taking the mass of the neutralino as 300 GeV and the mass difference between the stau and the neutralino as $(100--120)\text{ }\text{ }\mathrm{MeV}$. We can therefore simultaneously explain the abundance of the dark matter and that of $^{7}\mathrm{Li}$ by these values of parameters. The lifetime of staus in this scenario is predicted to be $O(100--1000)\text{ }\text{ }\mathrm{sec}$.

Thermal Relics in Hidden Sectors

Abstract: Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter's thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from Big Bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated. A flavour-free version of the standard model is allowed if the hidden sector is just 30% colder than the observable sector after reheating. Alternatively, if the hidden sector contains a 1-generation version of the standard model with characteristic mass scale below 1 MeV, even identical reheating temperatures are allowed. We then analyze hidden sector freezeout in detail for a concrete model, solving the Boltzmann equation numerically and understanding the results from both observable and hidden sector points of view. We find that WIMPless dark matter indeed obtains the correct relic density for masses in the range keV < m_X < TeV. The upper bound results from the requirement of perturbativity, and the lower bound assumes that the observable and hidden sectors reheat to the same temperature and is raised to the MeV scale if the hidden sector is 10 times colder. WIMPless dark matter therefore generalizes the WIMP paradigm to the largest mass range possible for viable thermal relics and provides a unified framework for exploring dark matter signals across nine orders of magnitude in dark matter mass.

Early universe constraints on time variation of fundamental constants

Abstract: We study the time variation of fundamental constants in the early Universe. Using data from primordial light nuclei abundances, cosmic microwave background, and the 2dFGRS power spectrum, we put constraints on the time variation of the fine structure constant {alpha} and the Higgs vacuum expectation value without assuming any theoretical framework. A variation in leads to a variation in the electron mass, among other effects. Along the same line, we study the variation of {alpha} and the electron mass m{sub e}. In a purely phenomenological fashion, we derive a relationship between both variations.