Harald W. Griesshammer

The dynamics of scattering on light nuclei is numerically expensive using standard methods. Fortunately, recent developments allow one to factor the relevant quantities for a given probe into a convolution of an $n$-body Transition Density Amplitude (TDA) and the interaction kernel for a given probe. These TDAs depend only on the target, and not the probe; they are calculated once for each set of kinematics and can be used for different interactions.\ % in the same kinematics. The kernels depend only on the probe, and not on the target; they can be reused for different targets and different kinematics. The calculation of TDAs becomes numerically difficult for more than four nucleons, but we discuss a new solution through the use of a Similarity Renormalization Group transformation, and a subsequent back-transformation. This technique allows for extending the TDA method to heavier nuclei such as ${}^6\mathrm{Li}$. We present preliminary results for Compton scattering on ${}^6\mathrm{Li}$ and compare with available data, anticipating an upcoming, more thorough study. We also discuss ongoing extensions to pion-photoproduction and other reactions on light nuclei.

Theorists love nontrivial fixed points. In the Unitarity Limit, the NN 𝑆-wave binding energies are zero, the scattering lengths infinite, Physics is universal, i.e. insensitive to details of the interactions, and observables display richer symmetries, namely invariance under both scaling and Wigner’s combined SU(4) transformation of spin and isospin. In “Pionless” EFT, both are explicitly but weakly broken and hence perturbative in the Unitarity Window (phase shifts $45^\circ \lesssim \delta(𝑘) \lesssim 135^\circ$ , i.e. momenta $𝑘 \approx 𝑚 \pi $). This Unitarity Expansion provides strong hints that Nuclear Physics resides indeed in a sweet spot: bound weakly enough to be insensitive to the details of the nuclear interaction; and therefore interacting strongly enough that the NN scattering lengths are perturbatively close to the Unitarity Limit. In this paradigm change, NN details are less important than NNN interactions to explain the complexity and patterns of the nuclear chart. This presentation is a digest of the first quantitative exploration of corrections to this picture when pions are included [1] (see there for a more comprehensive list of references). Since the pion mass and decay constant introduce dimensionful scales in the NN system, they explicitly break the symmetries of the Unitarity fixed point. In $\chi EFT$, these symmetries must therefore be hidden and instead be classified as emergent. This text focuses on the $\chi EFT$ variant with Perturbative (“KSW”) Pions at next-to-next-to leading order ($N^2LO$). In the $^1S_0$ channel up to cm momenta $\lesssim 300 MeV$, the results are clearly converged order-by-order and agree very well with phase shift analyses. Apparent large discrepancies in the $^3 S_1 $channel even at 𝑘 ≈ 100 MeV are remedied by taking only the central part of the pion’s $N^2LO$ contribution. In contradistinction to the tensor part, it does not mix the different Wigner-SU(4) multiplets and hence is identical in $^1 S_0$ and $^3 S_1$ . With this formulation, pionic effects are small in both channels even for 𝑘 $\gtrsim 𝑚_\pi$ , i.e. where both Unitarity and pion effects are expected to be relevant. This leads to the Hypothesis that both scale invariance and Wigner-SU(4) symmetry in the Unitarity Expansion show persistence, i.e. the footprint of both combined dominates even for 𝑘 $\gtrsim 𝑚_\pi$ and is more relevant than chiral symmetry, so that the tensor/Wigner-SU(4) symmetry-breaking part of OPE is suppressed and does not enter before N3 LO. Included are also ideas about underlying mechanisms and LO results of $\chi EFT$ with Nonperturbative Pions in the expansion about Unitarity.

Resummed-Range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio $ξ:=2r_0/a$ once $|r_0|$ is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion [1]. At leading order, no three-body interaction is needed. A ground state exists only in the range $0.366\ldots\geξ\ge-8.72\ldots$, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero $r_0$.

"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 $ξ:=2r_0/a$, 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 $ξ$. We investigate three identical bosons at leading order for a two-body system with one bound and one virtual state ($ξ\le0$), or with two virtual states ($0\leξ<1$). 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 $0.366\ldots\geξ\ge-8.72\ldots$. Three-body excitations appear for even smaller ranges of $ξ$ around the ``quasi-unitarity point'' $ξ=0$ ($|r_0|\ll|a|\to\infty$) and obey discrete scaling relations. We explore in detail the ground state and the lowest three excitations and parametrise their trajectories as function of $ξ$ and of the binding momentum $κ_2^-$ 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 $Λ_*$ 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.