Revision 1

Accepted · first revision · record

Title: A renormalizable power counting for chiral nuclear forces
Plain: Chiral effective field theory builds nuclear forces as a series ordered by powers of small momenta divided by roughly 600 MeV. The standard ordering gives results that depend on an arbitrary cutoff in some channels, and no consistent alternative has been agreed upon.
Precise: For the NN interaction in chiral EFT with one-pion exchange treated nonperturbatively, find a power counting under which amplitudes at each order are independent of the momentum cutoff $\Lambda$ for $\Lambda$ well above the breakdown scale (about 600 MeV) in all partial waves, including singular attractive tensor channels such as $3P0$ and $3P2-3F2$, and which converges for observables at physical $m_{\pi}$. Answer: the scheme with a demonstration of order-by-order renormalization and convergence, or a proof that none exists.
Settled by: A scheme shown to give cutoff-independent, order-by-order convergent NN phase shifts and light-nucleus binding energies, accepted after independent checks.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: contested
Status note: Weinberg counting fails cutoff independence in attractive triplet channels (Nogga, Timmermans and van Kolck, 2005); several modified schemes exist but none was generally adopted as of 2026.
Posed since: 2005