Heavy Particle Effective Theories Research Articles

The sub-leading scattering waveform from amplitudes

We compute the next-to-leading order term in the scattering waveform of uncharged black holes in classical general relativity and of half-BPS black holes in mathcal{N} = 8 supergravity. We propose criteria, generalizing explicit calculations at next-to-leading order, for determining the terms in amplitudes that contribute to local observables. For general relativity, we construct the relevant classical integrand through generalized unitarity in two distinct ways, (1) in a heavy-particle effective theory and (2) in general relativity minimally-coupled to scalar fields. With a suitable prescription for the matter propagator in the former, we find agreement between the two methods, thus demonstrating the absence of interference of quantum and classically-singular contributions. The classical mathcal{N} = 8 integrand for massive scalar fields is constructed through dimensional reduction of the known five-point one-loop integrand. Our calculation exhibits novel features compared to conservative calculations and inclusive observables, such as the appearance of master integrals with intersecting matter lines and the appearance of a classical infrared divergence whose absence from classical observables requires a suitable definition of the retarded time.

On-shell heavy particle effective theories

We introduce on-shell variables for Heavy Particle Effective Theories (HPETs) with the goal of extending Heavy Black Hole Effective Theory to higher spins and of facilitating its application to higher post-Minkowskian orders. These variables inherit the separation of spinless and spin-inclusive effects from the HPET fields, resulting in an explicit spin-multipole expansion of the three-point amplitude for any spin. By matching amplitudes expressed using the on-shell HPET variables to those derived from the one-particle effective action, we find that the spin-multipole expansion of a heavy spin-s particle corresponds exactly to the multipole expansion (up to order 2s) of a Kerr black hole, that is, without needing to take the infinite spin limit. Finally, we show that tree-level radiative processes with same-helicity bosons emitted from a heavy spin-s particle exhibit a spin-multipole universality.

Reparameterization invariant operator basis for NRQED and HQET

We provide a self-contained discussion of how reparameterization invariance connects a rotationally-invariant heavy particle effective theory with a single heavy fermion to a Lorentz-invariant theory. Furthermore, using Hilbert-series methods, a Lorentz- invariant operator basis is tabulated, up to and including operators of order 1/M4, when the fermion couples to an external U(1) or SU(3) gauge interaction.

Bino variations: Effective field theory methods for dark matter direct detection

We apply effective field theory methods to compute bino-nucleon scattering, in the case where tree-level interactions are suppressed and the leading contribution is at loop order via heavy flavor squarks or sleptons. We find that leading log corrections to fixed-order calculations can increase the bino mass reach of direct detection experiments by a factor of two in some models. These effects are particularly large for the bino-sbottom coannihilation region, where bino dark matter as heavy as 5-10 TeV may be detected by near future experiments. For the case of stop- and selectron-loop mediated scattering, an experiment reaching the neutrino background will probe thermal binos as heavy as 500 and 300 GeV, respectively. We present three key examples that illustrate in detail the framework for determining weak scale coefficients, and for mapping onto a low energy theory at hadronic scales, through a sequence of effective theories and renormalization group evolution. For the case of a squark degenerate with the bino, we extend the framework to include a squark degree of freedom at low energies using heavy particle effective theory, thus accounting for large logarithms through a "heavy-light current." Benchmark predictions for scattering cross sections are evaluated, including complete leading order matching onto quark and gluon operators, and a systematic treatment of perturbative and hadronic uncertainties.

Lorentz invariance in heavy particle effective theories

Employing induced representations of the Lorentz group (Wigner's little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the $S$ matrix are derived. The relationship between Lorentz invariance and reparametrization invariance is established and it is shown why a standard ansatz for implementing reparametrization invariance in heavy fermion effective Lagrangians breaks down at order $1/{M}^{4}$. Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extension to effective theories of massless fields is discussed.

Universal behavior in the scattering of heavy, weakly interacting dark matter on nuclear targets

Particles that are heavy compared to the electroweak scale (M≫mW), and that are charged under electroweak SU(2) gauge interactions display universal properties such as a characteristic fine structure in the mass spectrum induced by electroweak symmetry breaking, and an approximately universal cross section for scattering on nuclear targets. The heavy particle effective theory framework is developed to compute these properties. As illustration, the spin independent cross section for low-velocity scattering on a nucleon is evaluated in the limit M≫mW, including complete leading-order matching onto quark and gluon operators, renormalization analysis, and systematic treatment of perturbative and hadronic-input uncertainties.

Fat gravitons, the cosmological constant and submillimeter tests

We revisit the proposal that the resolution of the Cosmological Constant Problem involves a sub-millimeter breakdown of the point-particle approximation for gravitons. No fundamental description of such a breakdown, which simultaneously preserves the point-particle nature of matter particles, is yet known. However, basic aspects of the self-consistency of the idea, such as preservation of the macroscopic Equivalence Principle while satisfying quantum naturalness of the cosmological constant, are addressed in this paper within a Soft Graviton Effective Theory. It builds on Weinberg's analysis of soft graviton couplings and standard heavy particle effective theory, and minimally encompasses the experimental regime of soft gravity coupled to hard matter. A qualitatively distinct signature for short-distance tests of gravity is discussed, bounded by naturalness to appear above approximately 20 microns.

One-loop vertex integrals in heavy-particle effective theories

We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.

Three- and two-point one-loop integrals in heavy particle effective theories

We give a complete analytical computation of three- and two-point loop integrals occurring in heavy particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.

Three- and two-point one-loop integrals in heavy particle effective theories

We give a complete analytical computation of three- and two-point loop integrals occurring in heavy particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.

Nonrealitivistic chiral expansion and nonleptonic decays of octet and decuplet baryons

We discuss the chiral lagrangian for J P = 1 2 + octet and J P = 3 2 + decuplet baryons in the language of the heavy particle effective theory. We show that the effective theory qualitatively reproduces the Pauli amplitudes for the nonleptonic hyperon decays, calculated recently by Trofimenkoff. We discuss the relation of our results to nonrelativistic SU(6). We argue that we can consistently classify the meson-baryon interaction terms in lowest order in the momentum expansion according to their transformation properties under nonrelativistic SU(6). Nevertheless, the theory as a whole remains explicitly Lorentz invariant. We explain why this does not run afoul of the theorems concerning interacting relativistic SU(6) theories. We use this SU(6) classification to discuss the relation between the nonleptonic Ω − decays and the nonleptonic decays of the octet baryons. We find that the Ω − decays cannot be explained by any interaction term transforming simply under SU(6) because the nonleptonic Ω − decays do not display the pronounced ΔI = 1 2 enhancement seen in the octet hyperon decays. Any explanation of the Ω − decays requires a fine tuning of the parameters in the effective theory. We speculate that this problem may point to a flow in the basic assumption that ΔI = 1 2 four-quark operators, universally enhanced by QCD, are the dominant mechanism behind the ΔS = 1 nonleptonic decays.