On a Neutrino Electroweak Radius

We study a combination of amplitudes for neutrino scattering that can isolate a (gauge-invariant) difference of chirality-preserving neutrino electroweak radii for $\nu_\mu$ and $\nu_\tau$. This involves both photon and $Z_\mu$ exchange contributions. It is shown that the construction singles out the contributions of the hypercharge gauge field $B_{\mu}$ in the standard model. We comment on how gauge-dependent terms from the charge radii cancel with other terms in the relative electroweak radii defined.Comment: 16 pages, revtex with embedded figure

Stability and renormalization of Yang-Mills theory with Background Field Method: a regularization independent proof

In this paper the stability and the renormalizability of Yang-Mills theory in the Background Field Gauge are studied. By means of Ward Identities of Background gauge invariance and Slavnov-Taylor Identities the stability of the classical model is proved and, in a regularization independent way, its renormalizability is verified. A prescription on how to build the counterterms is given and the possible anomalies which may appear for Ward Identities and for Slavnov-Taylor Identities are shown.Comment: 25 pages, Latex 2.09, no figure

The Two-Loop Pinch Technique in the Electroweak Sector

The generalization of the two-loop Pinch Technique to the Electroweak Sector of the Standard Model is presented. We restrict ourselves to the case of conserved external currents, and provide a detailed analysis of both the charged and neutral sectors. The crucial ingredient for this construction is the identification of the parts discarded during the pinching procedure with well-defined contributions to the Slavnov-Taylor identity satisfied by the off-shell one-loop gauge-boson vertices; the latter are nested inside the conventional two-loop self-energies. It is shown by resorting to a set of powerful identities that the two-loop effective Pinch Technique self-energies coincide with the corresponding ones computed in the Background Feynman gauge. The aforementioned identities are derived in the context of the Batalin-Vilkovisky formalism, a fact which enables the individual treatment of the self-energies of the photon and the $Z$-boson. Some possible phenomenological applications are briefly discussed.Comment: 50 pages, uses axodra

Pinch Technique and the Batalin-Vilkovisky formalism

In this paper we take the first step towards a non-diagrammatic formulation of the Pinch Technique. In particular we proceed into a systematic identification of the parts of the one-loop and two-loop Feynman diagrams that are exchanged during the pinching process in terms of unphysical ghost Green's functions; the latter appear in the standard Slavnov-Taylor identity satisfied by the tree-level and one-loop three-gluon vertex. This identification allows for the consistent generalization of the intrinsic pinch technique to two loops, through the collective treatment of entire sets of diagrams, instead of the laborious algebraic manipulation of individual graphs, and sets up the stage for the generalization of the method to all orders. We show that the task of comparing the effective Green's functions obtained by the Pinch Technique with those computed in the background field method Feynman gauge is significantly facilitated when employing the powerful quantization framework of Batalin and Vilkovisky. This formalism allows for the derivation of a set of useful non-linear identities, which express the Background Field Method Green's functions in terms of the conventional (quantum) ones and auxiliary Green's functions involving the background source and the gluonic anti-field; these latter Green's functions are subsequently related by means of a Schwinger-Dyson type of equation to the ghost Green's functions appearing in the aforementioned Slavnov-Taylor identity.Comment: 45 pages, uses axodraw; typos corrected, one figure changed, final version to appear in Phys.Rev.

Enhancing gravitational wave astronomy with galaxy catalogues

Joint gravitational wave (GW) and electromagnetic (EM) observations, as a key research direction in multi-messenger astronomy, will provide deep insight into the astrophysics of a vast range of astronomical phenomena. Uncertainties in the source sky location estimate from gravitational wave observations mean follow-up observatories must scan large portions of the sky for a potential companion signal. A general frame of joint GW-EM observations is presented by a multi-messenger observational triangle. Using a Bayesian approach to multi-messenger astronomy, we investigate the use of galaxy catalogue and host galaxy information to reduce the sky region over which follow-up observatories must scan, as well as study its use for improving the inclination angle estimates for coalescing binary compact objects. We demonstrate our method using a simulated neutron stars inspiral signal injected into simulated Advanced detectors noise and estimate the injected signal sky location and inclination angle using the Gravitational Wave Galaxy Catalogue. In this case study, the top three candidates in rank have $72\%$, $15\%$ and $8\%$ posterior probability of being the host galaxy, receptively. The standard deviation of cosine inclination angle (0.001) of the neutron stars binary using gravitational wave-galaxy information is much smaller than that (0.02) using only gravitational wave posterior samples.Comment: Proceedings of the Sant Cugat Forum on Astrophysics. 2014 Session on 'Gravitational Wave Astrophysics

Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model

We present a lattice QCD calculation of the ΔI=1/2, K→ππ decay amplitude A0 and ϵ′, the measure of direct CP violation in K→ππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 323×64 lattice with an inverse lattice spacing of a-1=1.3784(68)  GeV. However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the ππ ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re(A0)=2.99(0.32)(0.59)×10-7  GeV and Im(A0)=-6.98(0.62)(1.44)×10-11  GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re(A0)=3.3201(18)×10-7  GeV. These results for A0 can be combined with our earlier lattice calculation of A2 [2] to obtain Re(ϵ′/ϵ)=21.7(2.6)(6.2)(5.0)×10-4, where the third error represents omitted isospin breaking effects, and Re(A0)/Re(A2)=19.9(2.3)(4.4). The first agrees well with the experimental result of Re(ϵ′/ϵ)=16.6(2.3)×10-4. A comparison of the second with the observed ratio Re(A0)/Re(A2)=22.45(6), demonstrates the standard model origin of this “ΔI=1/2 rule” enhancement.We present a lattice QCD calculation of the $\Delta I=1/2$, $K\to\pi\pi$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to\pi\pi$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $\pi\pi$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$\Delta I = 1/2$ rule" enhancement

Determination of the Jet Energy Scale at the Collider Detector at Fermilab

A precise determination of the energy scale of jets at the Collider Detector at Fermilab at the Tevatron $p\bar{p}$ collider is described. Jets are used in many analyses to estimate the energies of partons resulting from the underlying physics process. Several correction factors are developed to estimate the original parton energy from the observed jet energy in the calorimeter. The jet energy response is compared between data and Monte Carlo simulation for various physics processes, and systematic uncertainties on the jet energy scale are determined. For jets with transverse momenta above 50 GeV the jet energy scale is determined with a 3% systematic uncertainty

Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3

We review the duality and integrability of N=6 superconformal Chern-Simons theory in three dimensions and IIA superstring theory on the background AdS4xCP3. We introduce both of these models and describe how their degrees of freedom are mapped to excitations of a long-range integrable spin-chain. Finally, we discuss the properties of the Bethe equations, the S-matrix and the algebraic curve that are special to this correspondence and differ from the case of N=4 SYM theory and strings on AdS5xS5.Comment: 22 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3: references added, v4: brief discussion of giant magnons added, further minor changes, published version, v5: union of v3 and v4 because changes made in v3 were accidentally lost in v