Proton-proton fusion in leading order of effective field theory

Kong, Xu; Ravndal, F.

doi:10.1016/s0375-9474(99)00314-0

Cited by 63 publications

(93 citation statements)

References 19 publications

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“…This is a good approximation because the difference between the amplitude from the effective range theory, which is almost the same as our LO result, and that from accurate potential model calculations Our result KR(NLO) [16] Table 1: Estimated values of Λ 2 (0). The value in second column is our result.…”

Section: Numerical Resultssupporting

confidence: 67%

“…The value in second column is our result. The values in third, fourth, and fifth column are estimated from the pionless EFT calculation up to NLO by Kong and Ravndal (KR) [16], that up to N 4 LO by Butler and Chen (BC) [17], and an accurate phenomenological potential model calculation [11], respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…[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%

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Proton–proton fusion in pionless effective theory

et al. 2008

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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...

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Section: Numerical Resultssupporting

confidence: 67%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Proton–proton fusion in pionless effective theory

et al. 2008

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“…The relative size of the contribution of an operator to a particular observable can be estimated by the power-counting rules developed in [1][2][3][4][5][6][7]. An array of phenomena have been studied with EFT(π /), such as the radiative capture np → dγ relevant to Big-Bang nucleosynthesis [9,10], elastic and inelastic νd scattering [11,12] relevant to the ongoing efforts to measure the solar-neutrino flux and the cross section for pp → deν [13][14][15][16], the electromagnetic form factors of the deuteron [7,17], and other processes involving electroweak gauge fields (for a detailed review of this subject see Ref. [18]).…”

Section: Introductionmentioning

confidence: 99%

Rearranging pionless effective field theory

2001

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We point out a redundancy in the operator structure of the pionless effective field theory, EFT(π /), which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, np → dγ, and Compton scattering from the deuteron. Unlike EFT(π /), the higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.

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“…In the Standard Solar Model (SSM) [28] the total (or bolometric) luminosity of the Sun L ⊙ = (3.846 ± 0.008) × 10 26 W is normalized to the astrophysical factor S pp (0) for the solar proton burning. The recommended value S pp (0) = 4.00×10 −25 MeVb [29] has been found by averaging over the results obtained in the Potential model approach (PMA) [30,31] and the Effective Field Theory (EFT) approach [32,33]. As has been shown recently in Ref.…”

Section: Introductionmentioning

confidence: 99%