Point-Particle Effective Field Theory III: Relativistic Fermions and the Dirac Equation

We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei.Comment: 29 pages plus appendices, 3 figure

Failure of Perturbation Theory Near Horizons: the Rindler Example

Persistent puzzles to do with information loss for black holes have stimulated critical reassessment of the domain of validity of semiclassical EFT reasoning in curved spacetimes, particularly in the presence of horizons. We argue here that perturbative predictions about evolution for very long times near a horizon are subject to problems of secular growth - i.e. powers of small couplings come systematically together with growing functions of time. Such growth signals a breakdown of naive perturbative calculations of late-time behaviour, regardless of how small ambient curvatures might be. Similar issues of secular growth also arise in cosmology, and we build evidence for the case that such effects should be generic for gravitational fields. In particular, inferences using free fields coupled only to background metrics can be misleading at very late times due to the implicit assumption they make of perturbation theory when neglecting other interactions. Using the Rindler horizon as an example we show how this secular growth parallels similar phenomena for thermal systems, and how it can be resummed to allow late-time inferences to be drawn more robustly. Some comments are made about the appearance of an IR/UV interplay in this calculation, as well as on the possible relevance of our calculations to predictions near black-hole horizons.Comment: LaTeX, 17 pages plus appendix; added references and subsection on back-reactio

A 3.55 keV Photon Line and its Morphology from a 3.55 keV ALP Line

Galaxy clusters can efficiently convert axion-like particles (ALPs) to photons. We propose that the recently claimed detection of a 3.55--3.57 keV line in the stacked spectra of a large number of galaxy clusters and the Andromeda galaxy may originate from the decay of either a scalar or fermionic $7.1$ keV dark matter species into an axion-like particle (ALP) of mass $m_{a} \lesssim 6\cdot 10^{-11}~{\rm eV}$, which subsequently converts to a photon in the cluster magnetic field. In contrast to models in which the photon line arises directly from dark matter decay or annihilation, this can explain the anomalous line strength in the Perseus cluster. As axion-photon conversion scales as $B^2$ and cool core clusters have high central magnetic fields, this model can also explains the observed peaking of the line emission in the cool cores of the Perseus, Ophiuchus and Centaurus clusters, as opposed to the much larger dark matter halos. We describe distinctive predictions of this scenario for future observations.Comment: 6 page

Point-Particle Effective Field Theory II: Relativistic Effects and Coulomb/Inverse-Square Competition

We apply point-particle effective field theory (PPEFT) to compute the leading shifts due to finite-size source effects in the Coulomb bound energy levels of a relativistic spinless charged particle. This is the analogue for spinless electrons of the contribution of the charge-radius of the source to these levels, and we disagree with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size. One is the standard charge-radius contribution, while the other is a contact interaction whose leading contribution to $\delta E$ arises linearly in the small length scale, $\epsilon$, characterizing the finite-size effects, and is suppressed by $(Z\alpha)^5$. We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting particle's mass. Its contribution turns out to be crucial if the charge radius satisfies $\epsilon \lesssim (Z\alpha)^2 a_B$, with $a_B$ the Bohr radius, since then relativistic effects become important. We show how the problem is equivalent to solving the Schr\"odinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts. We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, and the possible relevance to catalysis of reactions through scattering with monopoles.Comment: LaTeX, 22 pages plus appendices, v3: revised appendices, made more precise and concise discussion about proton radius for mesonic system

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The detection of tightly closed flaws by nondestructive testing (NDT) methods

Liquid penetrant, ultrasonic, eddy current and X-radiographic techniques were optimized and applied to the evaluation of 2219-T87 aluminum alloy test specimens in integrally stiffened panel, and weld panel configurations. Fatigue cracks in integrally stiffened panels, lack-of-fusion in weld panels, and fatigue cracks in weld panels were the flaw types used for evaluation. A 2319 aluminum alloy weld filler rod was used for all welding to produce the test specimens. Forty seven integrally stiffened panels containing a total of 146 fatigue cracks, ninety three lack-of-penetration (LOP) specimens containing a total of 239 LOP flaws, and one-hundred seventeen welded specimens containing a total of 293 fatigue cracks were evaluated. Nondestructive test detection reliability enhancement was evaluated during separate inspection sequences in the specimens in the 'as-machined or as-welded', post etched and post proof loaded conditions. Results of the nondestructive test evaluations were compared to the actual flaw size obtained by measurement of the fracture specimens after completing all inspection sequences. Inspection data were then analyzed to provide a statistical basis for determining the flaw detection reliability