We generalize the Jacob-Wick helicity formalism, which applies to sequential decays, to effective field theories of rare decays of the type $B\to K_{J_K}(\to K\pi ){\overline{\ell }}_1{\ell }_2$. This is achieved by reinterpreting local interaction vertices $\overline{b}{\mathrm{\Gamma }}_{{\mu }_1\dots {\mu }_n}^{\prime }s\overline{\ell }{\mathrm{\Gamma }}^{{\mu }_1\dots {\mu }_n}\ell$ as a coherent sum of $1\to 2$ processes mediated by particles whose spin ranges between zero and $n$. We illustrate the framework by deriving the full angular distributions for $\overline{B}\to \overline{K}{\ell }_1{\overline{\ell }}_2$ and $\overline{B}\to {\overline{K}}^{*}(\to \overline{K}\pi ){\ell }_1{\overline{\ell }}_2$ for the complete dimension-six effective Hamiltonian for nonequal lepton masses. Amplitudes and decay rates are expressed in terms of Wigner rotation matrices, leading naturally to the method of moments in various forms. We discuss how higher-spin operators and QED corrections alter the standard angular distribution used throughout the literature, potentially leading to differences between the method of moments and the likelihood fits. We propose to diagnose these effects by assessing higher angular moments. These could be relevant in investigating the nature of the current LHCb anomalies in $R_K=\mathcal{B}(B\to K{\mu }^{+}{\mu }^{-})/\mathcal{B}(B\to K{e}^{+}{e}^{-})$ as well as angular observables in $B\to K^{*}{\mu }^{+}{\mu }^{-}$.

We revisit the theory of Cherenkov radiation in uniaxial crystals. Historically, a number of flawed attempts have been made at explaining this radiation phenomenon, and a consistent error-free description is nowhere available. We apply our calculation to a large modern day telescope—IceCube. Located in Antarctica, this detector makes use of the naturally occurring ice as a medium to generate Cherenkov radiation. However, due to the high pressure at the depth of the detector site, large volumes of hexagonal ice crystals are formed. We calculate how this affects the Cherenkov radiation yield and angular dependence. We conclude that the effect is small, at most about a percent, and would only be relevant in future high-precision instruments like e.g. Precision IceCube Next Generation Upgrade (PINGU). For radio-Cherenkov experiments which use the presence of a clear Cherenkov cone to determine the arrival direction, any variation in emission angle will directly and linearly translate into a change in apparent neutrino direction. In closing, we also describe a simple experiment to test this formalism and calculate the impact of anisotropy on light yields from lead tungstate crystals as used, for example, in the CMS calorimeter at the CERN LHC.

Nonperturbative studies of Schwinger-Dyson equations require their infinite, coupled tower to be truncated in order to reduce them to a practically solvable set. In this connection, a physically acceptable Ansatz for the three point vertex is the most favorite choice. Scalar quantum electrodynamics (sQED) provides a simple and neat platform to address this problem. The most general form of the three point scalar-photon vertex can be expressed in terms of only two independent form factors, a longitudinal and a transverse one. Ball and Chiu have demonstrated that the longitudinal vertex is fixed by requiring the Ward-Fradkin-Green-Takahashi identity while the transverse vertex remains undetermined. In massless quenched sQED, we construct the transverse part of the nonperturbative scalar-photon vertex. This construction (i) ensures multiplicative renormalizability of the scalar propagator in keeping with the Landau-Khalatnikov-Fradkin transformations, (ii) has the same transformation properties as the bare vertex under charge conjugation, parity and time reversal, (iii) has no kinematic singularities and (iv) reproduces the one-loop asymptotic result in the weak coupling regime of the theory.

Schwinger’s formalism in quantum field theory can be easily implemented in the case of scalar theories in $D$ dimension with exponential interactions, such as ${\mu }^D\exp (\alpha \varphi )$. In particular, we use the relation $\exp (\alpha \frac{\delta }{\delta J(x)})\exp (-Z_0[J])=\exp (-Z_0[J+{\alpha }_x])$ with $J$ the external source, and ${\alpha }_x(y)=\alpha \delta (y-x)$. Such a shift is strictly related to the normal ordering of $\exp (\alpha \varphi )$ and to a scaling relation which follows by renormalizing $\mu$. Next, we derive a new formulation of perturbation theory for the potentials $V(\varphi )=\frac{\lambda }{n!}:{\varphi }^n:$, using the generating functional associated to $:\exp (\alpha \varphi ):$. The $\mathrm{\Delta }(0)$-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to $J$ to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.

In this paper, we discuss the gluon propagator in the linear covariant gauges in $D=2$, 3, 4 Euclidean dimensions. Nonperturbative effects are taken into account via the so-called refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for $D=3$, 4, the gluon propagator displays a massive (decoupling) behavior, while for $D=2$, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced nonperturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our nonperturbative definition of the linear covariant gauge.

We present a study of $U(1)$ gauged modification of the $2+1$-dimensional planar Skyrme model with a particular choice of the symmetry breaking potential term which combines a short-range repulsion and a long-range attraction. In the absence of the gauge interaction, the multisolitons of the model are aloof, as they consist of the individual constituents which are well separated. A peculiar feature of the model is that there are usually several different stable static multisoliton solutions of rather similar energy in a topological sector of given degree. We investigate the pattern of the solutions and find new previously unknown local minima. It is shown that coupling of the aloof planar multi-Skyrmions to the magnetic field strongly affects the pattern of interaction between the constituents. We analyze the dependency of the structure of the solutions, their energies, and magnetic fluxes on the strength of the gauge coupling. It is found that, generically, in the strong coupling limit, the coupling to the gauge field results in effective recovery of the rotational invariance of the configuration.

We study the behavior of two-dimensional supersymmetric connections of $n$ copies of $O(N)$ models with an $\mathcal{N}=(0,1)$ heterotic deformation generated by a right-moving fermion. We develop the model in analogy with the connected $\mathcal{N}=(0,2)$ $CP(N-1)$ models for the case of a single connecting fermionic superfield. We calculate the effective potential in the large-$N$ limit and determine the vacuum field configurations. Similarly to other supersymmetry (SUSY) connected models we find that SUSY is unbroken under certain conditions despite the vanishing of the Witten index. Specifically, this preservation of SUSY occurs when we have an even number $n$ of $O(N)$ families. As in previous cases we show that this result follows from a $Z_n$ symmetry under a particular exchange of the $O(N)$ families. This leads to a definition of a modified Witten index, which guarantees the preservation of SUSY in this case.

We study the application of the rules of thermofield dynamics (TFD) to the covariant formulation of open-string field theory. We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended Becchi, Rouet, Stora and Tyutin (BRST) charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement, and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it of which the results at tree level agree with those of the conventional theory.

The Fock-space Hamiltonian truncation method is developed further, paying particular attention to the treatment of the scalar field zero mode. This is applied to the two-dimensional ${\varphi }^4$ theory in the phase where the ${\mathbb{Z}}_2$-symmetry is spontaneously broken, complementing our earlier study of the ${\mathbb{Z}}_2$-invariant phase and of the critical point. We also check numerically the weak/strong duality of this theory discussed long ago by Chang.

We study asymptotically free $\mathrm{SU}(N_c)$ gauge theories with $\mathcal{N}=1$ supersymmetry, including the purely gluonic theory and theories with $N_f$ copies of a pair of massless chiral superfields in the respective representations $R$ and $\overline{R}$ of $\mathrm{SU}(N_c)$. The cases in which $R$ is the fundamental representation and the symmetric and antisymmetric rank-2 tensor representation are considered. We calculate Padé approximants to the beta functions for these theories in the $\overline{\mathrm{DR}}$ scheme up to four-loop order for the gluonic theory and up to three-loop order for the theories with matter superfields and compare results for IR zeros and poles with results from the NSVZ beta function. Our calculations provide a quantitative measure, for these theories, of how well finite-order perturbative results calculated in one scheme reproduce properties of a known beta function calculated in a different scheme.

We investigate the impact of modified theories of gravity on the kinetic Sunyaev-Zel’dovich (kSZ) effect of the cosmic microwave background. We focus on a specific class of $f(R)$ models of gravity and compare their predictions for the kSZ power spectrum to that of the $\mathrm{\Lambda }\mathrm{CDM}$ model. We use a publicly available modified version of Halofit to properly include the nonlinear matter power spectrum of $f(R)$ in the modeling of the kSZ signal. We find that the well-known modifications of the growth rate of structure in $f(R)$ can indeed induce sizable changes in the kSZ signal, which are more significant than the changes induced by modifications of the expansion history. We discuss prospects of using the kSZ signal as a complementary probe of modified gravity, giving an overview of assumptions and possible caveats in the modeling.

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2), and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, we find that matter which couples to the generators of special conformal transformations reproduces Newton’s inverse square law. Conversely, matter which couples to generators of translations induces a constant and possibly repulsive force far from the source, which may be relevant for explaining the late-time acceleration of the Universe. The coupling constant of the theory is dimensionless, which means that it is potentially renormalizable.

We develop a description of tidal effects in astrophysical systems using effective field theory techniques. While our approach is equally capable of describing objects in the Newtonian regime (e.g. moons, rocky planets, main sequence stars, etc.) as well as relativistic objects (e.g. neutron stars and black holes), in this paper we focus special attention on the Newtonian regime. In this limit, we recover the dynamical equations for the “weak friction model” with additional corrections due to tidal and rotational deformations.

Compact binaries in our galaxy are expected to be one of the main sources of gravitational waves for the future eLISA mission. During the mission lifetime, many thousands of galactic binaries should be individually resolved. However, the identification of the sources and the extraction of the signal parameters in a noisy environment are real challenges for data analysis. So far, stochastic searches have proven to be the most successful for this problem. In this work, we present the first application of a swarm-based algorithm combining Particle Swarm Optimization and Differential Evolution. These algorithms have been shown to converge faster to global solutions on complicated likelihood surfaces than other stochastic methods. We first demonstrate the effectiveness of the algorithm for the case of a single binary in a 1-mHz search bandwidth. This interesting problem gave the algorithm plenty of opportunity to fail, as it can be easier to find a strong noise peak rather than the signal itself. After a successful detection of a fictitious low-frequency source, as well as the verification binary $\mathrm{RXJ}0806.3+1527$, we then applied the algorithm to the detection of multiple binaries, over different search bandwidths, in the cases of low and mild source confusion. In all cases, we show that we can successfully identify the sources and recover the true parameters within a 99% credible interval.

In this paper we study geodesic motion around a distorted Schwarzschild black hole. We consider both timelike and null geodesics which are confined to the black hole’s equatorial plane. Such geodesics generically exist if the distortion field has only even interior multipole moments, and so the field is symmetric with respect to the equatorial plane. We specialize to the case of distortions defined by a quadrupole Weyl moment. An analysis of the effective potential for equatorial timelike geodesics shows that finite stable orbits outside the black hole are possible only for $q\in (q_{\min },q_{\max }]$, where $q_{\min }\approx -0.0210$ and $q_{\max }\approx 2.7086\times {10}^{-4}$, while for null equatorial geodesics a finite stable orbit outside the black hole is possible only for $q\in [q_{\min },0)$. Moreover, the innermost stable circular orbits are closer to the distorted black hole horizon than those of an undistorted Schwarzschild black hole for $q\in (q_{\min },0)$, and a null innermost stable circular orbit exists for $q=q_{\min }$. These results show that an external distortion of a negative and sufficiently small quadrupole moment tends to stabilize the motion of massive particles and light.

We reconsider the problem of $f(R)$ theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric spacetime, we find solutions which reduce to their Reissner-Nordström counterparts at large distances but undergo important nonperturbative modifications close to the center. Our new analysis reveals that the pointlike singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thus nonsingular spacetime, despite the existence of curvature divergences at the wormhole throat. Implications of these results, in particular for the cosmic censorship conjecture, are discussed.

Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.

Continuing the work [Phys. Rev. Lett. 115, 161304 (2015)], we discuss various aspects of three-dimensional quantum gravity partition function in anti–de Sitter spacetime in the semiclassical limit. The partition function is holomorphic and is the one which we obtained by using the localization technique of Chern-Simons theory in Phys. Rev. Lett. 115, 161304 (2015). We obtain a good expression for it in the summation form over Virasoro characters for the vacuum and primaries. A key ingredient for that is an interpretation of boundary-localized fermion. We also check that the coefficients in the summation form over Virasoro characters of the partition function are positive integers and satisfy the Cardy formula. These give a physical interpretation that these coefficients represent the number of primary fields in the dual conformal field theory in the large $k$ limit.

Wei et al. [Phys. Rev. D 88, 043510 (2013)] have proposed the existence of a cosmological degeneracy between warm dark matter (WDM), modified gravity and coupled cold dark matter (CDM) cosmologies at both the background expansion and the growth of density perturbation levels; i.e., corresponding cosmological data would not be able to differentiate such scenarios. Here, we will focus on the specific indistinguishability between warm dark matter plus cosmological constant ($\mathrm{\Lambda }$) and coupled scalar field CDM scenarios. Although the statement of Wei et al. is true for very specific conditions we present a more complete discussion on this issue and show in more detail that these models are indeed distinguishable. We show that the degeneracy breaks down since coupled models leave a specific signature in the redshift space distortion data which is absent in the uncoupled warm dark matter cosmologies. Furthermore, we complement our claim by providing the reasons which suggest that even at nonlinear level a breaking of such apparent equivalence is also expected.

We obtain the angular distribution of the cosmic rays reaching an observer from an individual source and after propagation through a turbulent magnetic field, for different ratios between the source distance and the diffusion length. We study both the high-energy quasirectilinear regime as well as the transition towards the diffusive regime at lower energies where the deflections become large. We consider the impact of energy losses, showing that they tend to enhance the anisotropy of the source at a given energy. We also discuss lensing effects, in particular, those that could result from the regular Galactic magnetic field component and show that the effect of the turbulent extragalactic magnetic fields can smooth out the divergent magnification peaks that will result for pointlike sources in the limit of no turbulent deflections.