The Problem of Renormalization of Chiral Nuclear Forces

Abstract

Ever since quantum field theory was first applied to the derivation of nuclear forces in the mid-twentieth century, the renormalization of pion exchange with realistic couplings has presented a challenge. The implementation of effective field theories (EFTs) in the 1990s promised a solution to this problem but unexpected obstacles were encountered. The response of the nuclear community has been to focus on "chiral potentials" with regulators chosen to produce a good description of data. Meanwhile, a successful EFT without explicit pion exchange-Pionless EFT-has been formulated where renormalization is achieved order by order in a systematic expansion of low-energy nuclear observables. I describe how lessons from Pionless EFT are being applied to the construction of a properly renormalized Chiral EFT.

Two-pion exchange as a leading-order contribution in chiral effective field theory

“…Second, the leading-order description of nucleonnucleon phase shifts in the 1 S 0 partial wave are problematic in the Weinberg power counting [14,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], see Ref. [32] for a recent review. The combination of OPE and a single contact fails qualitatively to capture the pronounced peak at 60 − 70 degrees in the phase shift at about 8 MeV of laboratory scattering energy, see blue dotted line in Fig.…”

Nuclear Structure at the Crossroads

“…The reach of the unitary limit in nuclei is an open question. While its role in light nuclei up to A = 4 is well established and naturally explains universal correlations such as the Phillips and Tjon lines [12], the relevance in heavier systems is under debate [39,40]. Pionless EFT, which is organized as an expansion around the unitary limit, seems to fail binding 16 O at leading order [24,41].…”

Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group

“…Simultaneously, advances in many-body theory and computational resources have enabled ab initio treatment of the medium-mass nuclei which are often relevant for BSM searches [11][12][13][14][15][16][17]. Of course, more work remains to be done, both on the effective field theory side [18][19][20] and on understanding how approximation schemes in ab initio calculations impact the observables in question.…”