arXiv subjects

James M. Hansen

Publications and source records attributed to James M. Hansen.

4 recordsLinked to original sources

arXiv1999

The Predictive Power of Effective Field Theory in NN Scattering: ^3S_1-^3D_1 Mixing at Next-to Next-to Leading Order

The convergence of the Q expansion in the ^3S_1-^3D_1 mixing angle is investigated through the renormalization condition used to fit the free paramteter encountered at NNLO. Although the NNLO calculation describes the data well at momenta much less than 50 MeV, a variation in the renormalization condition results in 100% expected uncertainties at momenta as low as 100 MeV. This uncertainty can be traced to the presence of large cancelations between terms entering at NNLO, which are found to be several times larger than the terms entering at NLO. This implies a fundamental lack of predictive power at this order int he Q expansion of ε_1. Given the small empirical size, this lack of predictive power is easily understood in terms of simple power counting arguments.

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arXiv1999

Testing Low Energy Theorems in Nucleon-Nucleon Scattering

Low energy theorems have been derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading nontrivial order in an expansion based $Q$ counting, a scheme in which both $m_π$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Previous tests of these theorems based on coefficients extracted from scattering data indicate a pattern of gross violations which suggested serious problems for the perturbative treatment of pions implicit in $Q$ counting. We discuss the possibility that uncertainties associated with extracting the coefficients from the scattering data make such tests invalid. Here we show that errors in the s-wave phase shift extractions are sufficiently small to test direct test predictions from $Q$ counting at next to leading order. In particular we show that there exist low energy theorems for the sum of all terms in the effective range expansion beyond the first two which allow for precise tests. These low energy theorems fail badly which suggests that pionic aspects of $Q$ counting are not under control.

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arXiv1998

Low Energy Theorems For Nucleon-Nucleon Scattering

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_π$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the energy dependence $ε$ parameter which describes $^3S_1 - ^3D_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_π$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_π$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.

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arXiv1998

Systematic Power Counting in Cutoff Effective Field Theories for Nucleon-Nucleon Interactions and the Equivalence With PDS

An analytic expression for the ${}^1S_0$ phase shifts in nucleon-nucleon scattering is derived in the context of the Schrödinger equation in configuration space with a short distance cutoff and with a consistent power counting scheme including pionic effects. The scheme treats the pion mass and the inverse scattering length over the intrinsic short distance scale as small parameters. Working at next-to-leading order in this scheme, we show that the expression obtained is identical to one obtained using the recently introduced PDS approach which is based on dimensional regularization with a novel subtraction scheme. This strongly supports the conjecture that the schemes are equivalent provided one works to the same order in the power counting.

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