Explanation of IceCube spectrum with ν→3ν\nu\rightarrow 3 \nu neutrino splitting in a ν\nu2HDM model

A single power law flux spectrum of high energy neutrinos does not adequately explain the entire 60 TeV to 10 PeV event spectrum observed at IceCube, specially the excess of PeV events and the lack of Glashow resonance events expected at 6.3 PeV cannot be simultaneously explained by a single power law source neutrino flux. Here we consider a model of neutrino splitting $\nu\rightarrow 3 \nu$ over cosmological distances. Starting from a single power-law spectrum expected from the astrophysical sources, we show that by adjusting the decay length and spectral index one can give a better fit to the observed IceCube events over the entire 1 TeV -6 PeV, compared to that from a single power spectrum. For $\nu\rightarrow 3\nu$ neutrino splitting, the flavor ratios of the daughter neutrinos are different from the standard oscillation or invisible decay cases and can be used as a test of this scenario. We propose a $\nu$2HDM where a light Higgs ($\sim 0.1$~eV) mediates neutrino splitting via a one-loop box diagram. The split in the masses of the scalars in the doublet gives a large contribution to the oblique T parameter which is severely constrained. This constraint from the S,T,U oblique parameters can be evaded by the introduction of an extra vector lepton doublet and with mass $\sim 200$ GeV.Comment: 19 pages, 8 figures, Journal version to appear in JHE

Spinning strings and minimal surfaces in AdS3AdS_3 with mixed 3-form fluxes

Motivated by the recent proposal for the S-matrix in $AdS_3\times S^3$ with mixed three form fluxes, we study classical folded string spinning in $AdS_3$ with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux $b$. We show that dispersion relation for the spinning strings with large spin ${\cal S}$ acquires a term given by $-\frac{\sqrt{\lambda}}{2\pi} b^2\log^2 {\cal S}$ in addition to the usual $\frac{\sqrt\lambda}{\pi} \log {\cal S}$ term where $\sqrt{\lambda}$ is proportional to the square of the radius of $AdS_3$. Using SO(2,2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in $AdS_3$ with Neveu-Schwarz flux $b$. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the $b^2 \log^2 {\cal S}$ term in the dispersion relation of the spinning string. This result indicates that the coefficient of $b^2 \log^2 {\cal S}$ has a property similar to the coefficient of the $\log {\cal S}$ term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling $\lambda$ using the recent proposal for the S-matrix.Comment: 34 pages, Accepted for publication in JHE

Does Regionalism Hinder Multilateralism: A Case Study of India.

Today many developing countries fear that regional movements in other parts of the world will adversely impact their trade as regionalism overtakes multilateralism. The response has been that most of them are trying to get into one regional bloc or the other via regional trade arrangements (RTAs). In this paper we have investigated how India as a non-member country is affected by formation of RTAs like ASEAN, EU, NAFTA, and MERCOSUR..Controlling for non-RTA factors that influence exports, we find thatIndia?s exports to these RTAs seem to be affected not by the formation of these RTAs pese but by demand side factors.