Order In Effective Field Theory Research Articles

Lee-Yang-inspired functional including contributions to fourth order in effective field theory

In the last years, a new family of energy density functionals directly inspired by effective field theory (EFT) has been developed, among which the ELYO (extended Lee-Yang Orsay) functional. In this paper, a new extension of ELYO that includes the recently calculated fourth-order EFT terms is presented. Compared to the previous version, the description of neutron-drop energies slightly degrades for a harmonic trap ħω = 10 MeV—yet remaining reasonable—, but improves for ħω = 5 MeV. Furthermore, the obtained neutron effective mass agrees significantly better with ab-initio estimates.

Vanishing of Black Hole Tidal Love Numbers from Scattering Amplitudes.

We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory and in general relativity. We point out that the general relativity amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational nonlinearities in the wave region, whose proper treatment requires higher order effective field theory loop calculations. In particular, the elastic scattering in the near field approximation is produced exclusively by tidal effects. We find this contribution to vanish identically, which implies that the static Love numbers of Kerr BHs are zero for all types of perturbations. We also reproduce the known behavior of scalar Love numbers for higher-dimensional BHs. Our results are manifestly gauge invariant and coordinate independent, thereby providing a valuable consistency check for the commonly used off-shell methods.

Dilute Fermi gas at fourth order in effective field theory

Using effective field theory methods, we calculate for the first time the complete fourth-order term in the Fermi-momentum or kFas expansion for the ground-state energy of a dilute Fermi gas. The convergence behavior of the expansion is examined for the case of spin one-half fermions and compared against quantum Monte-Carlo results, showing that the Fermi-momentum expansion is well-converged at this order for |kFas|≲0.5.

Inflationary perturbation spectra at next-to-leading slow-roll order in effective field theory of inflation

The effective field theory (EFT) of inflation provides an essential picture to explore the effects of the unknown high energy physics in the single scalar field inflation models. For a generic EFT of inflation, possible high energy corrections to simple slow-roll inflation can modify both the propagating speed and dispersion relations of the cosmological scalar and tensor perturbations. With the arrival of the era of precision cosmology, it is expected that these high energy corrections become more important and have to be taken into account in the analysis with future precise observational data. In this paper we study the observational predictions of the EFT of inflation by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble flow parameters and the flow of four new slow-roll parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. The flow of the four new slow-roll parameters, which arise from the four new operators introduced in the action of the EFT of inflation, can affect the primordial perturbation spectra at the leading-order and the corresponding spectral indices at the next-to-leading order.

Three-body repulsive forces among identical bosons in one dimension

I consider non-relativistic bosons interacting via pairwise potentials with infinite scattering length and supporting no two-body bound states. To lowest order in effective field theory, these conditions lead to non-interacting bosons, since the coupling constant of the Lieb-Liniger model vanishes identically in this limit. Since any realistic pairwise interaction is not a mere delta function, the non-interacting picture is an idealisation indicating that the effect of interactions is weaker than in the case of off-resonant potentials. I show that the leading order correction to the ground state energy for more than two bosons is accurately described by the lowest order three-body force in effective field theory that arises due to the off-shell structure of the two-body interaction. For natural two-body interactions with a short-distance repulsive core and an attractive tail, the emergent three-body interaction is repulsive and, therefore, three bosons do not form any bound states. This situation is analogous to the two-dimensional repulsive Bose gas, when treated using the lowest-order contact interaction, where the scattering amplitude exhibits an unphysical Landau pole. The avoidance of this state in the three-boson problem proceeds in a way that parallels the two-dimensional case. These results pave the way for the experimental realisation of one-dimensional Bose gases with pure three-body interactions using ultracold atomic gases.

Study of decuplet baryon resonances from lattice QCD

A lattice QCD study of the strong decay width and coupling constant of decuplet baryons to an octet baryon - pion state is presented. The transfer matrix method is used to obtain the overlap of lattice states with decuplet baryon quantum numbers on the one hand and octet baryon-pion quantum numbers on the other as an approximation to the matrix element of the corresponding transition. By making use of leading order effective field theory, the coupling constants, as well as the widths for the various decay channels are determined. The transitions studied are $ \Delta \to \pi \,N$, $\Sigma^* \to \Lambda\,\pi$, $\Sigma^* \to \Sigma\,\pi$ and $\Xi^* \to \Xi\,\pi$. We obtain results for two ensembles of $N_f=2+1$ dynamical fermion configurations, one using domain wall valence quarks on a staggered sea at a pion mass of $350\,\mathrm{MeV}$ and a box size of $3.4\,\mathrm{fm}$ and a second one using domain wall sea and valence quarks at pion mass $180\,\mathrm{MeV}$ and box size $4.5\,\mathrm{fm}$.

Next-to-leading order effective field theory ΛN → NN potential in coordinate space

The potential in coordinate space for the ΛN→NN weak transition, which drives the weak decay of most hypernuclei, is derived within the effective field theory formalism up to next-to-leading order. This coordinate space potential allows us to discuss how the different contributions to the potential add up at the different scales. Explicit expressions are given for each two-pion-exchange diagram contributing to the interaction. The potential is also reorganized into spin and isospin operators, and the coefficient for each operator is given in analytical form and represented in coordinate space. The relevance of explicitly including the mass differences among the baryons appearing in the two-pion-exchange diagrams is also discussed in detail.

Radiation reaction at 3.5 post-Newtonian order in effective field theory

We derive the radiation reaction forces on a compact binary inspiral through 3.5 order in the post-Newtonian expansion using the effective field theory approach. We utilize a recent formulation of Hamilton's variational principle that rigorously extends the usual Lagrangian and Hamiltonian formalisms to dissipative systems, including the inspiral of a compact binary from the emission of gravitational waves. We find agreement with previous results, which thus provides a non-trivial confirmation of the extended variational principle. The results from this work nearly complete the equations of motion for the generic inspiral of a compact binary with spinning constituents through 3.5 post-Newtonian order, as derived entirely with effective field theory, with only the spin-orbit corrections to the potential at 3.5 post-Newtonian remaining.

Mixed meson masses with domain-wall valence and staggered sea fermions

Mixed action lattice calculations allow for an additive lattice-spacing-dependent mass renormalization of mesons composed of one sea and one valence quark, regardless of the type of fermion discretization methods used in the valence and sea sectors. The value of the mass renormalization depends upon the lattice actions used. This mixed meson mass shift is an important lattice artifact to determine for mixed action calculations; because it modifies the pion mass, it plays a central role in the low-energy dynamics of all hadronic correlation functions. We determine the leading order, $\mathcal{O}({a}^{2})$, and next-to-leading order, $\mathcal{O}({a}^{2}{m}_{\ensuremath{\pi}}^{2})$, additive mass shift of valence-sea mesons for a mixed lattice action with domain-wall valence fermions and rooted staggered sea fermions, relevant to the majority of current large scale mixed action lattice efforts. We find that, on the asqtad-improved coarse MILC lattices, this additive mass shift is well parametrized in lattice units by $\ensuremath{\Delta}(am{)}^{2}=0.034(2)\ensuremath{-}0.06(2)(a{m}_{\ensuremath{\pi}}{)}^{2}$, which in physical units, using $a=0.125\text{ }\text{ }\mathrm{fm}$, corresponds to $\ensuremath{\Delta}(m{)}^{2}=(291\ifmmode\pm\else\textpm\fi{}8\text{ }\text{ }\mathrm{MeV}{)}^{2}\ensuremath{-}0.06(2){m}_{\ensuremath{\pi}}^{2}$. In terms of the mixed action effective field theory parameters, the corresponding mass shift is given by ${a}^{2}{\ensuremath{\Delta}}_{\mathrm{Mix}}=(316\ifmmode\pm\else\textpm\fi{}4\text{ }\text{ }\mathrm{MeV}{)}^{2}$ at leading order plus next-to-leading order corrections including the necessary chiral logarithms for this mixed action calculation, determined in this work. Within the precision of our calculation, one cannot distinguish between the full next-to-leading order effective field theory analysis of this additive mixed meson mass shift and the parametrization given above.

Impact of spin-zero particle-photon interactions on light polarization in external magnetic fields

If the recent PVLAS results on polarization changes of a linearly polarized laser beam passing through a magnetic field are interpreted by an axion-like particle, it is almost certain that it is not a standard QCD axion. Considering this, we study the general effective interactions of photons with spin-zero particles without restricting the latter to be a pseudo-scalar or a scalar, i.e., a parity eigenstate. At the lowest order in effective field theory, there are two dimension-5 interactions, each of which has previously been treated separately for a pseudo-scalar or a scalar particle. By following the evolution in an external magnetic field of the system of spin-zero particles and photons, we compute the changes in light polarization and the transition probability for two experimental set-ups: one-way propagation and round-trip propagation. While the first may be relevant for astrophysical sources of spin-zero particles, the second applies to laboratory optical experiments like PVLAS. In the one-way propagation, interesting phenomena can occur for special configurations of polarization where, for instance, transition occurs but light polarization does not change. For the round-trip propagation, however, the standard results of polarization changes for a pseudoscalar or a scalar are only modified by a factor that depends on the relative strength of the two interactions.

Geometry on string lattice

Using the method developed by Callan and Thorlacius, we study the low energy effective geometry on a two-dimensional string lattice by examining the energy-momentum relations of the low energy propagation modes on the lattice. We show that the geometry is identical for both the oscillation modes tangent and transverse to the network plane. We determine the relation between the geometry and the lattice variables. The lowest order effective field theory is given by the dimensional reduction of the ten-dimensional N=1 Maxwell theory. The gauge symmetry is related to a property of a three-string junction but not of a higher order junction. A half of the supersymmetries in the effective field theory should be broken at high energy.

Neutrino-deuteron scattering in effective field theory at next-to-next-to-leading order

We study the four channels associated with neutrino-deuteron breakup reactions at next-to-next to leading order in effective field theory. We find that the total cross-section is indeed converging for neutrino energies up to 20 MeV, and thus our calculations can provide constraints on theoretical uncertainties for the Sudbury Neutrino Observatory. We stress the importance of a direct experimental measurement to high precision in at least one channel, in order to fix an axial two-body counterterm.

Proton-proton fusion in leading order of effective field theory

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate the rate for the fusion process p + p → d + e + + ν e to leading order in the momentum expansion. Coulomb effects are included non-perturbatively in a systematic way. The resulting rate is independent of specific models for the strong interactions at short distances and is in agreement with the standard result in the zero-range approximation.

Nucleon-nucleon scattering and effective field theory: including pions non-perturbatively

Next to leading order effective field theory calculations are performed for 1S 0 NN scattering using subtractive renormalization procedure. One pion exchange and contact interaction potentials are iterated using Lippman-Schwinger equation. Satisfactory fit to the Nijmegen data is obtained for the momenta up to 300 MeV in the centre of mass frame. Phase shifts are also compared with the results of KSW approach where pions are included perturbatively.