We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate. Theoretical error estimates of this low-energy process is important for a reliable interpretation of forthcoming experimental results by the MuSun collaboration. Specifically, we estimate the three dominant sources of uncertainties that impact theoretical calculations of this rate: those resulting from uncertainties in the pool of fit data used to constrain the coupling constants in the nuclear interaction, those due to the truncation of the effective field theory, and those due to uncertainties in the axial radius of the nucleon. For the capture rate into the ${}^1S_0$ channel, we find an uncertainty of approximately $4.6~s^{-1}$ due to the truncation in the effective field theory and an uncertainty of $3.9~s^{-1}$ due to the uncertainty in the axial radius of the nucleon, both of which are similar in size to the targeted experimental precision.
The muon capture reaction $μ^- + d \rightarrow n + n + ν_μ$ in the doublet hyperfine state is studied using nuclear potentials and consistent currents derived in chiral effective field theory, which are local and expressed in coordinate-space (the so-called Norfolk models). Only the largest contribution due to the $^1S_0$ $nn$ scattering state is considered. Particular attention is given to the estimate of the theoretical uncertainty, for which four sources have been identified: (i) the model dependence, (ii) the chiral order convergence for the weak nuclear current, (iii) the uncertainty in t…
We present a study of the two-photon-exchange ($2γ$-exchange) corrections to the $S$-levels in muonic ($μ$D) and ordinary (D) deuterium within the pionless effective field theory (pionless EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the pionless EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope sh…
We calculate the longitudinal structure function of the deuteron up through next-to-next-to-leading order in the framework of pionless effective field theory. We use these results to compute the two-photon polarizability contribution to Lamb shift in muonic deuterium, which can be utilized to extract the nuclear charge radius of the deuteron. We present analytical expressions order-by-order for the relevant transition matrix elements and the longitudinal structure function, and we give numerical results for the corresponding contributions to the Lamb shift. We also discuss the impact of relati…
We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order (NLO) for the transverse amplitude. The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO. We also study the lowest spin-independent generalised polarisabilitie…
Neutron-proton radiative capture, photo-magnetic and anti-neutrino disintegration of the deuteron in the relativistic field theory model of the deuteron
在相对论性氘核场论模型（RFMD）下计算了氘核的M1俘获n + p -> D + γ、光磁衰变和反中微子衰变截面.通过考虑手征单介子环修正和Delta（1232）共振的贡献，计算了M1俘获的截面.通过考虑自旋单重态S波中核子对的末态相互作用，计算了氘核光磁衰变和反中微子衰变的截面。根据S波散射长度和有效作用距离，得到了低能弹性np和nn散射的振幅。这大大放宽了Bahcall和Kamionkowski（Nucl.Phys.A625（1997）893）的陈述，即RFMD不能描述低能弹性核子-核子散射的非零有效范围。在反中微子能谱上平均得到的氘核反中微子衰变的截面与实验值符合得很好。
We calculate the muon capture rate on the deuteron to next-to-next-to-leading order in the pionless effective field theory. The result can be used to constrain the two-nucleon isovector axial coupling L_{1,A} to +/- 2 fm^3 if the muon capture rate is measured to 2% level. From this, one can determine the neutrino-deuteron break up reactions and the pp-fusion cross section in the sun to a same level of accuracy.
The isotope $ {}^{99} \rm{Mo} $, the generator of $ {}^{99m} \rm{Tc} $ used for diagnostic imaging, is supplied by extracting from fission fragments of highly enriched uranium in reactors. However, a reactor-free production method of $ {}^{99} \rm{Mo} $ is searched over the world from the point of view of nuclear proliferation. Recently, $ {}^{99} \rm{Mo} $ production through a muon capture reaction was proposed and it was found that about $ 50 \, \% $ of $ {}^{100} \rm{Mo} $ turned into $ {}^{99} \rm{Mo} $ through $ {}^{100} \rm{Mo} \left( μ^-, n \right) $ reaction [arXiv:1908.08166]. However…
Trinucleon Photo Reactions with $Δ$-Isobar Excitation: Radiative Nucleon-Deuteron Capture and Two-Body Photo Disintegration of the Three-Nucleon Bound State
本文从势模型和树近似下的弱二体介子交换流出发，从有效场论出发，研究了氘中负μ介子俘获率的模型依赖性.从$N Δπρωa_1$系统的硬π手征拉格朗日量导出了树单玻色子交换流。如果与单玻色子交换势一起构建，则可以一致地计算捕获率。另一方面，在重子手征微扰理论中构造的有效场论电流包含一个低能常数$\hat d ^R$，它不能从单粒子水平的数据中提取，也不能从第一原理中确定。通过对双峰跃迁速率结果的比较分析，我们可以提取出常数$\hat d ^R$。
The Quasiparticle Random Phase Approximation (QRPA) is used in evaluation of the total muon capture ratesfor the final nuclei participating in double-beta decay. Several variants of the method are used, depending on the size of the single particle model space used, or treatment of the initial bound muon wave function. The resulting capture rates are all reasonably close to each other. In particular, the variant that appears to be most realistic, results in rates in good agreement with the experimental values. There is no necessity for an empirical quenching of the axial current coupling consta…
