Precision calculation of the quartet-channel p-d scattering length

König, Sebastian; Hammer, H. -W.

doi:10.48550/arxiv.1312.2573

Cited by 2 publications

(6 citation statements)

References 22 publications

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“…This framework recovers Efimov's universal approach to the three-nucleon problem [21][22][23]. With recent progress, pionless EFT also allows for an elegant and efficient fully perturbative treatment of contributions beyond LO [16,[24][25][26].…”

Section: Introductionmentioning

confidence: 73%

“…Since we do not reorganize the pionless EFT expansion in the NN spin-triplet channel, no changes are needed in the nd and pd spin-quartet channels with respect to Refs. [3,6,11,12,24,25].…”

Section: Three-body Sectormentioning

confidence: 99%

“…A calculation of the Coulomb-modified pd scattering length, with the consistent use of a Yukawa-screened Coulomb potential in momentum space, has been presented in Ref. [25].…”

Section: Introductionmentioning

confidence: 99%

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Effective Theory of 3H and 3He

König,

Grießhammer,

Hammer

et al. 2015

Preprint

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We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1 S 0 scattering lengths converges rapidly. Using a new systematic treatment of the proton-proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the 3 H-3 He binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the leading order is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting (E B ( 3 He) − E B ( 3 H)) NLO = (−0.86 ± 0.17) MeV.

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Section: Introductionmentioning

confidence: 73%

“…Since we do not reorganize the pionless EFT expansion in the NN spin-triplet channel, no changes are needed in the nd and pd spin-quartet channels with respect to Refs. [3,6,11,12,24,25].…”

Section: Three-body Sectormentioning

confidence: 99%

See 1 more Smart Citation

Effective Theory of 3H and 3He

König,

Grießhammer,

Hammer

et al. 2015

Preprint

Self Cite

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“…Recently, a fully perturbative calculation of the quartet-channel scattering length up to N 2 LO has been presented in Ref. [40]. In the future, we plan on analyzing that calculation in more detail and furthermore to extend the approach also to the doublet channel.…”

Section: Discussionmentioning

confidence: 99%

“…[15], using a new approach that greatly reduces the computational cost by not requiring to determine the full off-shell scattering amplitude. The approach can be adapted to also include Coulomb effects [40].…”

Section: A Full Dibaryon Propagatorsmentioning

confidence: 99%

The proton–deuteron system in pionless EFT revisited

König

Grießhammer

Hammer

2015

J. Phys. G: Nucl. Part. Phys.

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We provide a detailed discussion of the low-energy proton-deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the 3 He-3 H binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all O(α) Coulomb diagrams in the doublet channel. Our nonperturbative result agrees well with a calculation that involves the full off-shell Coulomb T-matrix. Carefully examining the cutoff-dependence in the doublet channel, we present numerical evidence for a new three-nucleon counterterm being necessary at next-to-leading order if Coulomb effects are included. Indeed, such a term has recently been identified analytically. We furthermore make a case for a simplified Coulomb power counting that is consistent throughout the bound-state and scattering regimes. Finally, using a "partially screened" full off-shell Coulomb T-matrix, we investigate the importance of higher-order Coulomb corrections in low-energy quartet-channel scattering.Effective field theories are powerful tools that can be used to carry out calculations in a formalism involving directly the relevant degrees of freedom for the physical system under consideration. In particular, in nuclear systems at very low energies and momenta, pionexchange effects cannot be resolved and one can hence use the so-called pionless effective field theory. This approach only includes short-range contact interactions between nucleons [1-3] and is constructed to reproduce the effective range expansion [4] in the two-body system.The applicability of this approach, which recovers Efimov's universal approach to the three-nucleon problem [5,6], stems from the experimental fact that the S-wave nucleonnucleon scattering lengths in both the 3 S 1 (isospin 0) channel, a d ≈ 5.42 fm, and in the 1 S 0 (isospin 1) channel, a t ≈ −23.71 fm, are significantly larger than the range of interaction of about 1.4 fm set by the inverse pion mass. The corresponding effective ranges, on the other hand, have the values 1.75 and 2.73 fm, respectively, and are thus of the expected natural order of magnitude [7,8]. In Refs. [9][10][11][12][13][14], the formalism has been extended to the three-nucleon sector. The situation there is particularly interesting because the triton can be interpreted as an approximate Efimov state. Recently, a fully perturbative calculation of neutron-deuteron scattering up to next-to-next-to-leading order has been carried out by J. Vanasse [15], using a novel technique that circumvents the (numerically expensive) calculation of full off-shell quantities.Since most low-energy nuclear experiments involve more than one charged particle (proton), it is very important to discuss the treatment of Coulomb effects. Although this interaction can be treated as a perturbative correction for intermediate and higher energies, it becomes strong close to threshold and has to be treated nonperturbati...

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Precision calculation of the quartet-channel p-d scattering length

Cited by 2 publications

References 22 publications

Effective Theory of 3H and 3He

Effective Theory of 3H and 3He

The proton–deuteron system in pionless EFT revisited

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