Improved action for contact effective field theory

We present an improved action for renormalizable effective field theories (EFTs) of systems near the two-body unitarity limit. The ordering of EFT interactions is constrained, but not entirely fixed, by the renormalization group. The remaining freedom can be used to improve the theory's convergence, to simplify its applications, and to connect it to phenomenological models. We exemplify the method on a contact theory applied to systems of up to five $^4$He atoms. We solve the EFT at LO including a subleading interaction that accounts for part of the two-body effective range. We show that the effects of such fake range can be compensated in perturbation theory at NLO, as long as the fake range is smaller or comparable to the experimental effective range. These results open the possibility of using similar improved actions for other many-body systems.Comment: 15 pages, 8 figure

Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory

An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two- and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For $m_\pi=510~$MeV we obtain, respectively, $^4a_{\rm nD}=2.3\pm 1.3~$fm, $^2a_{\rm nD}=2.2\pm 2.1~$fm, and $B_{\alpha}^{}=35\pm 22~$MeV, while for $m_\pi=805~$MeV $^4a_{\rm nD}=1.6\pm 1.3~$fm, $^2a_{\rm nD}=0.62\pm 1.0~$fm, and $B_{\alpha}^{}=94\pm 45~$MeV are found. Phillips- and Tjon-like correlations to the triton binding energy are established. Higher-order effects on the respective correlation bands are found insensitive to the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.Comment: 19 pages, 8 figures, 4 tables, submitted to PR

Effective Field Theory for the Bound States and Scattering of a Heavy Charged Particle and a Neutral Atom

We show the system of a heavy charged particle and a neutral atom can be described by a low-energy effective field theory where the attractive $1/r^4$ induced dipole potential determines the long-distance/low-energy wave functions. The $1/r^4$ interaction is renormalized by a contact interaction at leading order. Derivative corrections to that contact interaction give rise to higher-order terms. We show that this ``Induced-dipole EFT'' (ID-EFT) reproduces the $\pi^+$-hydrogen phase shifts of a more microscopic potential, the Temkin-Lamkin potential, over a wide range of energies. Already at leading order it also describes the highest-lying excited bound states of the pionic-hydrogen ion. Lower-lying bound states receive substantial corrections at next-to-leading order, with the size of the correction proportional to their distance from the scattering threshold. Our next-to-leading order calculation shows that the three highest-lying bound states of the Temkin-Lamkin potential are well-described in ID-EFT

Effective Field Theory for Few-Nucleon Systems

We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact interactions allows a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behavior. Manifestly model-independent calculations can be carried out to high orders, leading to high precision. At higher energies, an EFT that includes pion fields justifies and extends the traditional framework of phenomenological potentials. The correct treatment of QCD symmetries ensures a connection with lattice QCD. Several tests and prospects of these EFTs are discussed.Comment: 55 pages, 18 figures, to appear in Ann. Rev. Nucl. Part. Sci. 52 (2002

Effective Theories Of The Strong Interaction

This is the final report corresponding to the full funding period (08/01-07/04) in the Department of Energy Outstanding Junior Investigator Grant DE-FG03-01ER41196. The development of an understanding of the interplay between perturbative and non-perturbative effects in strong-interacting systems forms the broad context of this research. The main thrust is the application of effective theories to QCD. Topics included a new power counting in the pionful effective theory, low-energy Compton scattering, charge-symmetry breaking in pion production and in the two-nucleon potential, parity violation, coupled-channel scattering, shallow resonances and halo nuclei, chiral symmetry in the baryon spectrum, existence of a tetraquark state, and molecular meson states. DOE grant DE-FG03-01ER41196 was used to partially support in the period 08/01-07/04 the research activities of the Principal Investigator, Dr. Ubirajara van Kolck, one post-doctoral research associate, Dr. Boris A. Gelman, and one graduate student, Mr. Will Hockings. During the grant period the PI was first Assistant then Associate Professor of Physics at the University of Arizona (UA), and a RHIC Physics Fellow at the RIKEN-BNL Research Center (RBRC). The association with RBRC ended in the Summer of 2004. Since September of 2002 the PI has also been partially supported by a Sloan Research Fellowship. Dr. Boris Gelman was supported by the grant from September 2002 to May 2004. He joined the UA after receiving a Ph.D. from the University of Maryland in the Summer of 2002. He left to take a research associate position in the nuclear theory group of the State University of New York at Stony Brook. The support of a post-doctoral researcher on this grant for two years was only possible by carrying over first- and second-year funds to later years. In addition, Mr. William Hockings started doing research under the PI's guidance. Mr. Hockings took Independent Study courses with the PI, while working as a teaching assistant in the UA Department of Physics. He learned the basic ideas of non-relativistic effective field theories, such as ''reparametrization'' invariance, and studied a simple application of effective field theory to Compton scattering on the nucleon at energies well below the pion mass. Mr. Hockings has passed the qualifying exam (called ''comprehensive'' at UA) with a solid performance, and is now pursuing a Ph.D. in nuclear physics, supported by the grant. Grant activities are described in Sect. 2. They included the publication of research papers, the delivery of seminars and lectures, and the organization of scientific meetings and (together with UA colleagues) of a series of local seminars, as listed in the Appendix

Weinberg’s Compositeness †

International audienceNearly 60 years ago, Weinberg suggested a criterion for particle “compositeness”, which has acquired a new life with the discovery of new, exotic hadrons. His idea resonates with model-based intuition. I discuss the role it plays in the context of another of Weinberg’s creations, the model-independent framework of effective field theories

Universality of Three Identical Bosons with Large, Negative Effective Range

International audience"Resummed-Range Effective Field Theory'' is a consistent nonrelativistic effective field theory of contact interactions with large scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is non-perturbative. Its observables are universal, i.e.~they depend only on the dimensionless ratio $\xi:=2r_0/a$, with the overall distance scale set by $|r_0|$. In the two-body sector, the position of the two shallow $S$-wave poles in the complex plane is determined by $\xi$. We investigate three identical bosons at leading order for a two-body system with one bound and one virtual state ($\xi\le0$), or with two virtual states ($0\le\xi<1$). Such conditions might, for example, be found in systems of heavy mesons. We find that no three-body interaction is needed to renormalise (and stabilise) Resummed-Range EFT at LO. A well-defined ground state exists for $0.366\ldots\le\xi\le-8.72\ldots$. Three-body excitations appear for even smaller ranges of $\xi$ around the ``quasi-unitarity point''$\xi=0$ ($|r_0|\ll|a|\to\infty$) and obey discrete scaling relations. We explore in detail the ground state and the lowest three excitations and parametrise their trajectories as function of $\xi$ and of the binding momentum $\kappa_2^-$ of the shallowest \twoB state from where three-body and two-body binding energies are identical to zero three-body binding. As $|r_0|\ll|a|$ becomes perturbative, this version turns into the ``Short-Range EFT'' which needs a stabilising three-body interaction and exhibits Efimov's Discrete Scale Invariance. By interpreting that EFT as a low-energy version of Resummed-Range EFT, we match spectra to determine Efimov's scale-breaking parameter $\Lambda_*$ in a renormalisation scheme with a ``hard'' cutoff. Finally, we compare phase shifts for scattering a boson on the two-boson bound state with that of the equivalent Efimov system

Improved action for contact effective field theory

International audienceWe present an improved action for renormalizable effective field theories (EFTs) of systems near the two-body unitarity limit. The ordering of EFT interactions is constrained, but not entirely fixed, by the renormalization group. The remaining freedom can be used to improve the theory's convergence, to simplify its applications, and to connect it to phenomenological models. We exemplify the method on a contact theory applied to systems of up to five $^4$He atoms. We solve the EFT at LO including a subleading interaction that accounts for part of the two-body effective range. We show that the effects of such fake range can be compensated in perturbation theory at NLO, as long as the fake range is smaller or comparable to the experimental effective range. These results open the possibility of using similar improved actions for other many-body systems