Graviton Vertices and the Mapping of Anomalous Correlators to Momentum Space for a General Conformal Field Theory

We investigate the mapping of conformal correlators and of their anomalies from configuration to momentum space for general dimensions, focusing on the anomalous correlators $TOO$, $TVV$ - involving the energy-momentum tensor $(T)$ with a vector $(V)$ or a scalar operator ($O$) - and the 3-graviton vertex $TTT$. We compute the $TOO$, $TVV$ and $TTT$ one-loop vertex functions in dimensional regularization for free field theories involving conformal scalar, fermion and vector fields. Since there are only one or two independent tensor structures solving all the conformal Ward identities for the $TOO$ or $TVV$ vertex functions respectively, and three independent tensor structures for the $TTT$ vertex, and the coefficients of these tensors are known for free fields, it is possible to identify the corresponding tensors in momentum space from the computation of the correlators for free fields. This works in general $d$ dimensions for $TOO$ and $TVV$ correlators, but only in 4 dimensions for $TTT$, since vector fields are conformal only in $d=4$. In this way the general solution of the Ward identities including anomalous ones for these correlators in (Euclidean) position space, found by Osborn and Petkou is mapped to the ordinary diagrammatic one in momentum space. We give simplified expressions of all these correlators in configuration space which are explicitly Fourier integrable and provide a diagrammatic interpretation of all the contact terms arising when two or more of the points coincide. We discuss how the anomalies arise in each approach [...]Comment: 57 pages, 7 figures. Refs adde

Prompt atmospheric neutrino fluxes: perturbative QCD models and nuclear effects

We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, $k_T$ factorization including low-$x$ resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for charm and bottom production and compare with the latest data on forward charm meson production from LHCb at $7$ TeV and at $13$ TeV, finding good agreement with the data. In addition, we investigate the role of nuclear shadowing by including nuclear parton distribution functions (PDF) for the target air nucleus using two different nuclear PDF schemes. Depending on the scheme used, we find the reduction of the flux due to nuclear effects varies from $10\%$ to $50 \%$ at the highest energies. Finally, we compare our results with the IceCube limit on the prompt neutrino flux, which is already providing valuable information about some of the QCD models.Comment: 61 pages, 25 figures, 11 table

General Three-Point Functions in 4D CFT

We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible representations of the Lorentz group. We show how to impose in this formalism constraints due to conservation of bosonic or fermionic currents. The number of independent tensor structures appearing in any three-point function is obtained by a simple counting. Using the Operator Product Expansion (OPE), we can then determine the number of structures appearing in 4-point functions with arbitrary operators. This procedure is independent of the way we take the OPE between pairs of operators, namely it is consistent with crossing symmetry, as it should be. An analytic formula for the number of tensor structures for three-point correlators with two symmetric and an arbitrary bosonic (non-conserved) operators is found, which in turn allows to analytically determine the number of structures in 4-point functions of symmetric traceless tensors

Deconstructing Conformal Blocks in 4D CFT

We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few \u201cseed\u201d correlators, simplifying dramatically the computation needed to bootstrap tensor correlators. \ua9 2015, The Author(s)

Downward-going tau neutrinos as a new prospect of detecting dark matter

Dark matter trapped in the Sun produces a flux of all flavors of neutrinos, which then reach the Earth after propagating out of the Sun and oscillating from the production point to the detector. The typical signal which is looked at refers to the muon neutrino component and consists of a flux of up-going muons in a neutrino detector. We propose instead a novel signature: the possibility of looking at the tau neutrino component of the dark matter signal, which is almost background-free in the downward-going direction, since the tau neutrino amount in atmospheric neutrinos is negligible and in the down-going baseline atmospheric muon-neutrinos have no time to sizably oscillate. We analyze the prospects of studying the downward-going tau neutrinos from dark matter annihilation (or decay) in the Sun in Cherenkov detectors, by looking at hadronic showers produced in the charged-current tau neutrino interactions and subsequent tau decay. We discuss the various sources of background (namely the small tau neutrino component in atmospheric neutrinos, both from direct production and from oscillations; tau neutrinos from solar corona interactions; the galactic tau neutrino component) as well as sources of background due to misidentification of electron and muon events. We find that the downward-going tau neutrinos signal has potentially very good prospects for Mton scale Cherenkov detectors, the main limitation being the level of misidentification of non-tau events, which need to be kept at level of percent. Several tens of events per year (depending on the dark matter mass and annihilation/decay channel) are potentially collectible with a Mton scale detector, and a 5 sigma significance discovery is potentially reachable for dark matter masses in the range from 20 to 300 GeV with a few years of exposure on a Mton detector.Comment: 24 pages, 10 figures. Version published in JHEP. Figures revisited with inclusion of galactic neutrino background. Main results and conclusions unchange

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta