In this paper, we propose a new algorithm to systematically determine the missing boundary contributions, when one uses the BCFW on-shell recursion relation to calculate tree amplitudes for general quantum field theories. After an instruction of the algorithm, we will use several examples to demonstrate its application, including amplitudes of color-ordered φ 4 theory, Yang-Mills theory, Einstein-Maxwell theory and color-ordered Yukawa theory with φ 4 interaction.

We report constraints on the dark photon effective kinetic mixing parameter (κ) with data taken from two p-type point-contact germanium detectors of the CDEX-10 experiment at the China Jinping Underground Laboratory. The 90% confidence level upper limits on κ of solar dark photon from 205.4 kg-day exposure are derived, probing new parameter space with masses (m V) from 10 to 300 eV=c 2 in direct detection experiments. Considering dark photon as the cosmological dark matter, limits at 90% confidence level with m V from 0.1 to 4.0 keV=c 2 are set from 449.6 kg-day data, with a minimum of κ ¼ 1.3 × 10 −15 at m V ¼ 200 eV=c 2 .

We present improved constraints on couplings of solar axions and more generic bosonic dark matter particles using 737.1 kg-days of data from the CDEX-1B experiment. The CDEX-1B experiment, located at the China Jinping Underground Laboratory, primarily aims at the direct detection of WIMPs using a p-type point-contact germanium detector. We develop the profile likelihood ratio method for analysis of data in the presence of backgrounds. The background modeling is compatible with the data and no excess signals are observed. An energy threshold of 160 eV was achieved. This significantly improve the sensitivity for the bosonic dark matter below 0.8 keV. Limits are also placed on the coupling gAe < 2.26 × 10 −11 from Compton, bremsstrahlung, atomic-recombination and deexcitation channels and g ef f AN × gAe < 4.14 × 10 −17 from a 57 Fe M1 transition at 90% confidence level. All the constrains improve over our previous results.

To find boundary contributions is a rather difficult problem when applying the BCFW recursion relation. In this paper, we propose an approach to bypass this problem by calculating general tree amplitudes that contain no polynomial using factorization limits. More explicitly, we construct an expression iteratively, which produces the correct factorization limits for all physical poles, and does not contain other poles, then it should be the correct amplitude. To some extent, this approach can be considered as an alternative way to find boundary contributions. To demonstrate our approach, we present several examples: φ 4 theory, pure gauge theory, Einstein-Maxwell theory, and Yukawa theory. While the amplitude allows the existence of polynomials which satisfy the correct mass dimension and helicities, this approach is not applicable to determining the full amplitude.