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Register a new userRenormalization Group Effects in Dark Matter Interactions
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We present a renormalization-group (RG) analysis of dark matter interactions with the standard model, where dark matter is allowed to be a component of an electroweak multiplet, and has a mass at or below the electroweak scale. We consider, in addition to the gauge interactions, the complete set of effective operators for dark matter interactions with the standard model above the weak scale, up to and including mass dimension six. We calculate the RG evolution of these operators from the high scale Lambda down to the weak scale, and perform the matching to the tower of effective theories below the weak scale. We also summarize the RG evolution below the weak scale and the matching to the nonrelativistic nuclear interactions. We present several numerical examples and show that in certain cases the dark matter - nucleus scattering rate can change by orders of magnitude when the electroweak running is included.
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The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. Explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the naive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms.
Detectors with low thresholds for electron recoil open a new window to direct searches of sub-GeV dark matter (DM) candidates. In the past decade, many strong limits on DM-electron interactions have been set, but most on the one which is spin-independent (SI) of both dark matter and electron spins. In this work, we study DM-atom scattering through a spin-dependent (SD) interaction at leading order (LO), using well-benchmarked, state-of-the-art atomic many-body calculations. Exclusion limits on the SD DM-electron cross section are derived with data taken from experiments with xenon and germanium detectors at leading sensitivities. In the DM mass range of 0.1 - 10 GeV, the best limits set by the XENON1T experiment: $sigma_e^{textrm{(SD)}}<10^{-41}-10^{-40},textrm{cm}^2$ are comparable to the ones drawn on DM-neutron and DM-proton at slightly bigger DM masses. The detectors responses to the LO SD and SI interactions are analyzed. In nonrelativistic limit, a constant ratio between them leads to an indistinguishability of the SD and SI recoil energy spectra. Relativistic calculations however show the scaling starts to break down at a few hundreds of eV, where spin-orbit effects become sizable. We discuss the prospects of disentangling the SI and SD components in DM-electron interactions via spectral shape measurements, as well as having spin-sensitive experimental signatures without SI background.
We apply the renormalization group optimized perturbation theory (RGOPT) to evaluate the quark contribution to the QCD pressure at finite temperatures and baryonic densities, at next-to-leading order (NLO). Our results are compared to NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a nonperturbative approximation, exhibiting a drastically better remnant renormalization scale dependence than pQCD, thanks to built-in renormalization group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed quark contributions the purely perturbative NLO glue contribution, our results show a remarkable agreement with ab initio lattice simulation data for temperatures $0.25 lesssim T lesssim 1 , {rm GeV}$, with a remnant scale dependence drastically reduced as compared to HTLpt.
We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter $a equiv 2sqrt{2} G^{}_{rm F} N^{}_e E$ to be an arbitrary scale-like variable with $N^{}_e$ being the net electron number density and $E$ being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix $V$ and the effective neutrino masses $widetilde{m}^{}_i$ (for $i = 1, 2, 3$). Given the standard parametrization of $V$, the RGEs for ${widetilde{theta}^{}_{12}, widetilde{theta}^{}_{13}, widetilde{theta}^{}_{23}, widetilde{delta}}$ in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial $mu$-$tau$ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of $V$ are also obtained as a by-product.
Casimir energy is calculated for 5D scalar theory in the {it warped} geometry. A new regularization, called {it sphere lattice regularization}, is taken. The regularized configuration is {it closed-string like}. We numerically evaluate $La$(4D UV-cutoff), $om$(5D bulk curvature, extra space UV-boundary parameter) and $T$(extra space IR-boundary parameter) dependence of Casimir energy. 5D Casimir energy is {it finitely} obtained after the {it proper renormalization procedure.} The {it warp parameter} $om$ suffers from the {it renormalization effect}. Regarding Casimir energy as the main contribution to the cosmological term, we examine the dark energy problem.
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