Using chiral perturbation theory to extract the neutron-neutron scattering length from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>π</mml:mi><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant="italic">nn</mml:mi><mml:mi>γ</mml:mi></mml:mrow></mml:math>

Gårdestig, Anders; Phillips, Daniel R.

doi:10.1103/physrevc.73.014002

Cited by 50 publications

(78 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Notice that the resulting current operator A µ ( x) = A H µ ( x, x 0 = 0) satisfies the usual, non-modified continuity equation 51) where, similar to the axial-vector current, we have introduced the corresponding modified version of the pseudoscalar current …”

Section: E Relation To the S-matrixmentioning

confidence: 99%

Nuclear axial current operators to fourth order in chiral effective field theory

2017

View full text Add to dashboard Cite

We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant onebody contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two-and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.

show abstract

Section: E Relation To the S-matrixmentioning

confidence: 99%

Nuclear axial current operators to fourth order in chiral effective field theory

2017

View full text Add to dashboard Cite

show abstract

“…[14,35], the LECs which appear in the two-di-baryon-axial-current or fournucleon-axial-current contact interactions, denoted by l 1A in the pionless EFT with dibaryon fields, L 1A in the pionless EFT without di-baryon fields, andd R in HBχPT, are universal. In other words, those LECs are shared by the processes, such as, the pp fusion process (pp → de + ν e ) [12,13,14,16,17], nn fusion process (nn → de −ν e ) [21], neutrino deuteron reactions (ν e d → ppe − , ν e d → npν e ) [36,37], muon capture on the deuteron (µ − d → nnν µ ) [38,39], radiative pion capture on the deuteron (π − d → nnγ [40] and its crossed partner γd → nnπ + [41]), tritium beta decay [14], and hep process (p 3 He → 4 He e + ν e ) [14]. If these LECs are determined by using the experimental data from one of the processes, the lattice simulation [42], or the renormalization group method [43], then we can predict the other processes in each of the formalisms without any unknown parameters.…”

Section: Discussionmentioning

confidence: 99%

Proton–proton fusion in pionless effective theory

et al. 2008

View full text Add to dashboard Cite

The proton-proton fusion reaction, pp → de + ν, is studied in pionless effective field theory (EFT) with di-baryon fields up to next-to leading order. With the aid of the di-baryon fields, the effective range corrections are naturally resummed up to the infinite order and thus the calculation is greatly simplified. Furthermore, the low-energy constant which appears in the axial-current-di-baryon-di-baryon contact vertex is fixed through the ratio of two-and one-body matrix elements which reproduces the tritium lifetime very precisely. As a result we can perform a parameter free calculation for the process. We compare our numerical result with those from the accurate potential model and previous pionless EFT calculations, and find a good agreement within the accuracy better than 1%. PACS IntroductionThe proton-proton fusion process, pp → de + ν e , is a fundamental reaction for the nuclear astrophysics, especially important for the understanding of the star evolutions [1] and solar neutrinos [2,3,4]. However, the process has never been studied experimentally because the event is extremely unlikely to take place in the laboratory at the proton energies in the sun. The calculation of the transition rate and its uncertainty has naturally become a challenge to nuclear theory. The first calculation of the process was carried out by Bethe and Critchfield [5] in 1938. This estimation was improved by Salpeter [6] 2 in 1952. Later, small corrections, such as the electromagnetic radiative corrections, were considered by Bahcall and his collaborators [8,9] in the framework of effective range theory. Recently, accurate phenomenological potential models were employed to study the process [10,11]. Furthermore, in Ref.[12] the two-nucleon current operators were calculated from heavybaryon chiral perturbation theory (HBχPT) up to next-to-next-to-next-to leading order (N 3 LO), and Park et al. obtained quite an accurate estimation (∼ 0.3% uncertaity) for the process by fixing an unknown parameter, so-called low energy constant (LEC), which appears in the two-nucleon-axial-current contact interaction in terms of the tritium lifetime [13,14].The kinetic energy relevant to the pp fusion process at the core of the sun is quite low, kT c ≃ 1.18 keV, where T c is the core temperature of the sun, T c ≃ 13.7 × 10 6 K, and k is the Boltzmann constant. The proton momentum at the core, p c ≃ 2m p kT c ≃ 1.5 MeV, where m p is the proton mass, is still significantly small compared to the pion mass, m π ≃ 140 MeV. Therefore, we may regard the pion as a heavy degree of freedom for the pp fusion process. It may be convenient and suitable to employ a pionless effective field theory (EFT) [15], in which the pions are integrated out of the effective Lagrangian for the process in question. The pp fusion process in the pionless theory has been studied by Kong and Ravndal [16] up to next-to leading order (NLO) and by Butler and Chen [17] up to fifth order (N 4 LO). Thanks to the perturbative scheme in EFT, the accuracy of the N 4 LO calculation w...

show abstract

“…A calculation of b nn using low energy effective field theories of QCD would seem to be out of reach at present since there are so few constraints on the nature of charge symmetry breaking in the strong interaction from other systems. EFT analyses to extract b nn from neutron-neutron final state effects in few body reactions are possible, and an EFT analysis of the π − d → nnγ reaction to extract b nn has recently appeared [357]. It is interesting that both the n-d and n-3 He scattering lengths are now of interest as input for few body calculations in other systems.…”

Section: Precision Scattering Length Measurements Using Interferometrmentioning

confidence: 99%

Fundamental Neutron Physics

Nico

Snow

2005

Annu. Rev. Nucl. Part. Sci.

View full text Add to dashboard Cite

▪ Abstract Experiments using slow neutrons address a growing range of scientific issues spanning nuclear physics, particle physics, astrophysics, and cosmology. The field of fundamental physics using neutrons has experienced a significant increase in activity over the last two decades. This review summarizes some of the recent developments in the field and outlines some of the prospects for future research.

show abstract

Using chiral perturbation theory to extract the neutron-neutron scattering length fromπ−d→nnγ

Cited by 50 publications

References 62 publications

Nuclear axial current operators to fourth order in chiral effective field theory

Nuclear axial current operators to fourth order in chiral effective field theory

Proton–proton fusion in pionless effective theory

Fundamental Neutron Physics

Contact Info

Product

Resources

About