Low energy proton-proton scattering in effective field theory

Abstract

Low energy proton-proton scattering is studied in pionless effective field theory. Employing the dimensional regularization and MS and power divergence subtraction schemes for loop calculation, we calculate the scattering amplitude in 1 S 0 channel up to nextto-next-to leading order and fix low-energy constants that appear in the amplitude by effective range parameters. We study regularization scheme and scale dependence in separation of Coulomb interaction from the scattering length and effective range for the S-wave proton-proton scattering.PACS(s): 11.10.Gh, 13.75.Cs.1 mailto:sando@color.skku.ac.kr 1 IntroductionEffective field theories (EFTs), which provide us a systematic perturbative scheme and a model-independent calculation method, have become a popular method to study hadronic reactions with and without external probes at low and intermediate energies.(See, e.g., Refs. [1, 2, 3, 4, 5] for reviews.) At very low energies, the Coulomb interaction becomes essential for the study of reactions involving charged particles. The first consideration of the Coulomb interaction in a pionless EFT was done by Kong and Ravndal (KR) for low energy S-wave proton-proton (pp) scattering [6,7]. They calculated the pp scattering amplitude up to next-to leading order (NLO). For loop calculations, they employed dimensional regularization with minimum subtraction (MS) scheme and so called power divergence subtraction (PDS) scheme suggested by Kaplan, Savage and Wise [8,9]. Then KR estimated a scattering length a(µ) for the pp scattering after separating off the Coulomb correction where µ is the scale for dimensional regularization. The leading order (LO) result of a(µ) was almost infinite at µ = m π where m π is the pion mass [6]. In addition, the LO a(µ) was highly dependent on the value of µ. Including the NLO correction, they obtained a(µ = m π ) = −29.9 fm [7] which is comparable to the value of the scattering length a np in the np channel, a np = −23.748 ± 0.009 fm 2 . The value of a(µ) deduced after separating the Coulomb and strong interactions is particularly important in the study of isospin breaking effects in S-wave NN interaction [11,12]. The accurate value of a np is well known as quoted above, while the values of the scattering length in the nn channel (a nn ) and in the pp channel (a pp ) still have considerable uncertainties.There exists no direct nn scattering experiment because of the lack of free neutron target. The values of a nn have been deduced from the experimental data of π − d → nnγ and nd → nnp reactions. Recent publications suggest a nn = −18.50 ± 0.05(stat.) ± 0.44(syst.) ± 0.30(th.) fm from the π − d → nnγ process [13] and a nn = −18.7 ± 0.6 fm [14], −16.06 ± 0.35 fm [15] and −16.5 ± 0.9 fm [16] from the nd → nnp process. As seen, the values of a nn have significant errors compared to that of a np , and the center values do not seem to converge yet.

Elastic $\alpha$ - 12C scattering at low energies in cluster effective field theory

“…For derivation of the amplitudes from the diagrams in detail the reader may referee to, e.g., Refs. [26,27] and we do not repeat the detailed calculation.…”

He3andpdscattering to next-to-leading order in pionless effective field theory

“…This theory, pionless effective field theory (EFT π ), has a simple and manifest power counting [8][9][10][11][12]. In the two-nucleon sector EFT π has been used successfully to calculate nucleon-nucleon (N N ) scattering [13][14][15][16], electromagnetic form factors of the deuteron [17], and the neutron-proton capture process [18,19].…”

Triton charge radius to next-to-next-to-leading order in pionless effective field theory

“…Ref. [7] for a review) has been used with great success in the two-body sector calculating deuteron electromagnetic form factors [8,9], NN scattering [8,10,11], neutron-proton (np) capture [8,9,12] to (<∼1%) [13], proton-proton fusion [14][15][16], and neutrino deuteron scattering [17]. Progress has also been made in the three-body sector with calculations of nd scattering [6,[18][19][20][21][22][23], pd scattering [24][25][26], nd capture [27][28][29], and the energy difference between 3 H and 3 He [25,30,31].…”