Note on Higgs Decay into Two Photons H→γγH\to \gamma\gamma

The Higgs decay $H\to \gamma\gamma$ duo to the virtual $W$-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method, which is realized in the four dimensional space-time without changing original theory. Though the one-loop amplitude of $H\to \gamma\gamma$ is finite as the Higgs boson in the standard model has no direct interaction with the massless photons at tree level, while it involves both tensor-type and scalar-type divergent integrals which can in general destroy the gauge invariance without imposing a proper regularization scheme to make them well-defined. As the loop regularization scheme can ensure the consistency conditions between the regularized tensor-type and scalar-type divergent irreducible loop integrals to preserve gauge invariance, we explicitly show the absence of decoupling in the limit $M_W/M_H\to0$ and obtain a result agreed exactly with the earlier one in the literature. We then clarify the discrepancy between the earlier result and the recent one obtained by R. Gastmans, S.L. Wu and T.T. Wu. The advantage of calculation in the unitary gauge becomes manifest that the non-decoupling arises from the longitudinal contribution of the $W$ gauge boson.Comment: 13 pages, 2 figures, references added, advantage of loop regularization method with the concept of irreduciable loop integral is emphasized, published versio

Controlling the second-harmonic in a phase matched negative-index metamaterial

Nonlinear metamaterials (NLMMs) have been predicted to support new and exciting domains in the manipulation of light, including novel phase matching schemes for wave mixing. Most notable is the so-called nonlinear-optical mirror, in which a nonlinear negative-index medium emits the generated frequency towards the source of the pump. For the first time, we experimentally demonstrate the nonlinear-optical mirror effect in a bulk negative-index NLMM, along with two other novel phase matching configurations, utilizing periodic poling to switch between the three phase matching domains.Comment: 5 pages, 7 figure

Stochastic Gravitational Waves from Inflaton Decays

Due to the universality of gravitational interactions, it is generally expected that a stochastic gravitational wave (GW) background could form during the reheating period when the inflaton perturbatively decays with the emission of gravitons. Previously, only models in which the inflaton dominantly decays into a pair of light scalar and/or fermion particles were considered in the literature. In the present paper, we focus on the cases with a vector particle pair in the final decay product. The differential decay rates for the three-body gravitational inflaton decays are presented for two typical couplings between the inflaton and vector fields, from which we predict their respective GW frequency spectra. It turns out that, similar to the scalar and fermion cases, the obtained GW spectra is too high in frequency to be observed by the current and near-future GW detection experiments and calls for a new design of high-frequency GW detectors.Comment: 15 pages, 4 figure

CP Violation in Predictive Neutrino Mass Structures

We study the CP violation effects from two types of neutrino mass matrices with (i) $(M_\nu)_{ee}=0$, and (ii) $(M_\nu)_{ee}=(M_\nu)_{e\mu}=0$, which can be realized by the high dimensional lepton number violating operators $\bar \ell_R^c\gamma^\mu L_L (D_\mu \Phi)\Phi^2$ and $\bar \ell_R^c l_R (D_\mu{\Phi})^2\Phi^2$, respectively. In (i), the neutrino mass spectrum is in the normal ordering with the lightest neutrino mass within the range $0.002\,{\rm eV}\lesssim m_0\lesssim 0.007\,{\rm eV}$. Furthermore, for a given value of $m_0$, there are two solutions for the two Majorana phases $\alpha_{21}$ and $\alpha_{31}$, whereas the Dirac phase $\delta$ is arbitrary. For (ii), the parameters of $m_0$, $\delta$, $\alpha_{21}$, and $\alpha_{31}$ can be completely determined. We calculate the CP violating asymmetries in neutrino-antineutrino oscillations for both mass textures of (i) and (ii), which are closely related to the CP violating Majorana phases.Comment: 17 pages, 4 figures, revised version accepted by EPJ

X-ray Line from the Dark Transition Electric Dipole

We study a two-component dark matter (DM) model in which the two Majorana fermionic DM components with nearly degenerate masses are stabilized by an $Z_2$ symmetry and interact with the right-handed muon and tau only via real Yukawa couplings, together with an additional $Z_2$-odd singly-charged scalar. In this setup, the decay from the heavy DM to the lighter one via the transition electric dipole yields the 3.55 keV X-ray signal observed recently. The Yukawa couplings in the dark sector are assumed to be hierarchical, so that the observed DM relic abundance can be achieved with the leading s-wave amplitudes without a fine-tuning. We also consider the constraints from flavor physics, DM direct detections and collider searches, respectively.Comment: 16 pages, 4 figures, revised version accepted for publication in JHE

Consistency of Loop Regularization Method and Divergence Structure of QFTs Beyond One-Loop Order

We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the general procedure. In the processes, we find a new divergence structure: the regulated result for each two-loop diagram contains a gauge-violating quadratic harmful divergent term even combined with their corresponding counterterm insertion diagrams. Only when we sum up over all the relevant diagrams do these quadratic harmful divergences cancel, recovering the gauge invariance and locality.Comment: 33 pages, 5 figures, Sub-section IIIE removed, to be published in EPJ

Superconducting pairing in Sr2_2RuO4_4 from weak to intermediate coupling

The unconventional superconductivity in Sr$_2$RuO$_4$ continues to attract considerable interest. While many measurements can be interpreted on the basis of chiral $p$-wave pairing with intriguing topological character, a number of exceptions hinder an unambiguous verification of such pairing. The pairing mechanism also remains under debate. In this paper, with effects of the sizable spin-orbit coupling accounted for, we reexamine the superconducting instabilities in Sr$_2$RuO$_4$ through systematic microscopic analysis within random phase approximation. Our calculations show that the odd-parity $p$-wave pairing is favored in the regime of extremely weak interactions, but that highly anisotropic even-parity pairings become most leading over a broad range of stronger interactions. These results could shed light on the nature of the enigmatic superconductivity in Sr$_2$RuO$_4$.Comment: 5.5 pages + supplemental materials. Minor edits. Published versio

Connecting Neutrino Masses and Dark Matter by High-dimensional Lepton Number Violation Operator

We propose a new model with the Majorana neutrino masses generated at two-loop level, in which the lepton number violation (LNV) processes, such as neutrinoless double beta decays, are mainly induced by the dimension-7 LNV effective operator O_7=\bar l_R^c \gamma^\mu L_L(D_mu \Phi) \Phi \Phi. Note that it is necessary to impose an Z_2 symmetry in order that O_7 dominates over the conventional dimension-5 Weinberg operator, which naturally results in a stable Z_2-odd neutral particle to be the cold dark matter candidate. More interestingly, due to the non-trivial dependence of the charged lepton masses, the model predicts the neutrino mass matrix to be in the form of the normal hierarchy. We also focus on a specific parameter region of great phenomenological interests, such as electroweak precision tests, dark matter direct searches along with its relic abundance, and lepton flavor violation processes.Comment: 19 pages, 5 figure