The anthropic principle and the mass scale of the Standard Model

In theories in which different regions of the universe can have different values of the the physical parameters, we would naturally find ourselves in a region which has parameters favorable for life. We explore the range of anthropically allowed values of the mass parameter in the Higgs potential, $\mu^2$. For $\mu^2<0$, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value $v$ must have a magnitude less than 5 times its observed value. For $\mu^2>0$, baryon stability requires that $|\mu|<<M_P$, the Planck Mass. Smaller values of $|\mu^2|$ may or may not be allowed depending on issues of element synthesis and stellar evolution. We conclude that the observed value of $\mu^2$ is reasonably typical of the anthropically allowed range, and that anthropic arguments provide a plausible explanation for the closeness of the QCD scale and the weak scale.Comment: 28 pages, LaTeX. No changes from version originally submitted to archive, except that problem with figure file has been correcte

Baryon Masses in Chiral Perturbation Theory with Infrared Regularization

The baryon masses are examined in SU(3) chiral perturbation theory to third order using the recently proposed infrared regularization scheme. Fourth order is estimated by evaluating the dominant diagram. With this regularization the magnitude of the loop integrals is reduced so that the convergence of the series appears to be better than in the heavy baryon approach.Comment: The original third order calculation is supplemented by an estimate of fourth order using just the dominant diagram. The convergence still appears to be better than in the heavy baryon approach. To be published in Phys. Rev. C. 15 pages latex, 2 postscript figure

Radiative Neutron Capture on Carbon-14 in Effective Field Theory

The cross section for radiative capture of neutron on carbon-14 is calculated using the model-independent formalism of halo effective field theory. The dominant contribution from E1 transition is considered, and the cross section is expressed in terms of elastic scattering parameters of the effective range expansion. Contributions from both resonant and non-resonant interaction are calculated. Significant interference between these leads to a capture contribution that deviates from simple Breit-Wigner resonance form.Comment: 14 pages, 6 figure

Dimension-eight operators in the weak OPE

We argue that there is a potential flaw in the standard treatment of weak decay amplitudes, including that of ǫ′/ǫ. We show that (contrary to conventional wisdom) dimension-eight operators do contribute to weak amplitudes, at order GFαs and without 1/M2W suppression. We demonstrate the existence of these operators through the use of a simple weak hamiltonian. Their contribution appears in different places depending on which scheme is adopted in performing the OPE. If one performs a complete separation of short and long distance physics within a cutoff scheme, dimension-eight operators occur in the weak hamiltonian at order GFαs/μ2, μ being the separating scale. However, in an MS renormalization scheme for the OPE the dimension-eight operators do not appear explicitly in the hamiltonian at order GFαs. In this case, matrix elements must include physics above the scale μ, and it is here that dimension eight effects enter. The use of a cutoff scheme (especially quark model methods) for the calculation of the matrix elements of dimension-six operators is inconsistent with MS unless there is careful matching including dimension-eight operators. The contribution of dimension-eight operators can be minimized by working at large enough values of the scale μ. We find from sum rule methods that the contribution of dimension-eight operators to the dimension-six operator Q(6) 7 is at the 100% level for μ = 1.5 GeV. This suggests that presently available values of μ are too low to justify the neglect of these effects. Finally, we display the dimension-eight operators which appear within the Standard Model at one loop

K -\u3epi pi phenomenology in the presence of electromagnetism

We describe the influence of electromagnetism on the phenomenology of $K \to \pi\pi$ decays. This is required because the present data were analyzed without inclusion of electromagnetic radiative corrections, and hence contain several ambiguities and uncertainties which we describe in detail. Our presentation includes a full description of the infrared effects needed for a new experimental analysis. It also describes the general treatment of final state interaction phases, needed because Watson\u27s theorem is no longer valid in the presence of electromagnetism. The phase of the isospin-two amplitude ${\cal A}_2$ may be modified by $50 \to 100\%$. We provide a tentative analysis using present data in order to illustrate the sensitivity to electromagnetic effects, and also discuss how the standard treatment of $\epsilon\u27 /\epsilon$ is modified

Non-isotropy in the CMB power spectrum in single field inflation

Contaldi et al. [1] have suggested that an initial period of kinetic energy domination in single field inflation may explain the lack of CMB power at large angular scales. We note that in this situation it is natural that there also be a spatial gradient in the initial value of the inflaton field, and that this can provide a spatial asymmetry in the observed CMB power spectrum, manifest at low multipoles. We investigate the nature of this asymmetry and comment on its relation to possible anomalies at low multipoles.Comment: 25 pages, 12 figures. In this revised version, we include the Integrated Sachs-Wolfe effect, which was missing from the original. This modifies some results in the low multipoles. The comparison with experiment is slightly better but the change is not statistically significan

Electromagnetic corrections to K -\u3epi pi. I. Chiral perturbation theory

An analysis of electromagnetic corrections to the (dominant) octet K → ππ hamiltonian using chiral perturbation theory is carried out. Relative shifts in amplitudes at the several per cent level are found

Electromagnetic corrections to K -\u3epi pi. II. Dispersive matching

We express the leading electromagnetic corrections in K → ππ as integrals over the virtual photon squared-momentum Q2. The high Q2 behavior is obtained via the operator product expansion. The low Q2 behavior is calculated using chiral perturbation theory. We model the intermediate Q2 region using resonance contributions in order to enforce the matching of these two regimes. Our results confirm our previous estimates that the electromagnetic corrections provide a reasonably small shift in the I = 3/2 amplitude