The solution to fine tuning is one of the principal motivations for beyond the standard model (BSM) studies. However constraints on new physics indicate that many of these BSM models are also fine-tuned (although to a much lesser extent). To compare these BSM models it is essential that we have a reliable, quantitative measure of tuning. We review the measures of tuning used in the literature and propose an alternative measure. We apply this measure to several toy models and the minimal supersymmetric standard model.

We show that the anomalous magnetic moment of fermion in the gauge-Higgs unification is finite in any spacetime dimensions, which is a new predictive physical observable similar to the Higgs mass.

The many-parametric fits of the LEP2 data on $e^{+}{e}^{-}\to e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}$, ${\tau }^{+}{\tau }^{-}$ processes are performed with the goal to estimate the signals of the Abelian $Z^{\prime }$ boson. Four independent parameters must be fitted, if the derived already low-energy relations between the $Z^{\prime }$ couplings to the standard model fermions are taken into consideration. No signals are found when the complete LEP2 data set for these processes is treated. In the fit of the backward bins, the hint at the $1.3\sigma$ confidence level is detected. The $Z^{\prime }$ couplings to the vector and axial-vector lepton currents are constrained. The comparisons with the one-parameter fits and with the corresponding LEP1 experiments are fulfilled.

We present a study of the electromagnetic structure of the nucleons with constituent quark models in the framework of relativistic quantum mechanics. In particular, we address the construction of spectator-model currents in the instant and point forms. Corresponding results for the elastic nucleon electromagnetic form factors as well as charge radii and magnetic moments are presented. We also compare results obtained by different realistic nucleon wave functions stemming from alternative constituent quark models. Finally, we discuss the theoretical uncertainties that reside in the construction of spectator-model transition operators.

We study $B\to K^{*}\rho$ modes that are analogues of the much studied $B\to K\pi$ modes with $B$ decaying to two vector mesons instead of pseudoscalar mesons, using topological amplitudes in the quark diagram approach. We show how $B\to K^{*}\rho$ modes can be used to obtain many more observables than those for $B\to K\pi$ modes, even though the quark level subprocesses of both modes are exactly the same. All the theoretical parameters (except for the weak phase $\gamma$), such as the magnitudes of the topological amplitudes and their strong phases, can be determined in terms of the observables without any model-dependent assumption. We demonstrate how $B\to K^{*}\rho$ can also be used to verify if there exist any relations between theoretical parameters, such as the hierarchy relations between the topological amplitudes and possible relations between the strong phases. Conversely, if there exist reliable theoretical estimates of amplitudes and strong phases, the presence of new physics could be probed. We show that if the tree and color-suppressed tree are related to the electroweak penguins and color-suppressed electroweak penguins, it is not only possible to verify the validity of such relations but also to have a clean measurement of new physics parameters. We also present a numerical study to examine which of the observables are more sensitive to new physics.

We calculate the $CP$-averaged branching ratios and $CP$-violating asymmetries of a number of two-body charmless hadronic decays ${\overline{B}}_s^0\to PP$, $PV$, $VV$ in the perturbative QCD (pQCD) approach to leading order in ${\alpha }_s$ (here $P$ and $V$ denote light pseudoscalar and vector mesons, respectively). The mixing-induced $CP$ violation parameters are also calculated for these decays. We also predict the polarization fractions of $B_s\to VV$ decays and find that the transverse polarizations are enhanced in some penguin-dominated decays such as ${\overline{B}}_s^0\to K^{*}{\overline{K}}^{*}$, $K^{*}\rho$. Some of the predictions worked out here can already be confronted with the recently available data from the CDF Collaboration on the branching ratios for the decays ${\overline{B}}_s^0\to K^{+}{\pi }^{-}$, ${\overline{B}}_s^0\to K^{+}{K}^{-}$ and the $CP$ asymmetry in the decay ${\overline{B}}_s^0\to K^{+}{\pi }^{-}$, and are found to be in agreement within the current errors. A large number of predictions for the branching ratios, $CP$ asymmetries, and vector-meson polarizations in ${\overline{B}}_s^0$ decays, presented in this paper and compared with the already existing results in other theoretical frameworks, will be put to stringent experimental tests in forthcoming experiments at Fermilab, CERN LHC, and Super $B$ factories.

Form factors of rare $B\to K_0^{*}(1430){\ell }^{+}{\ell }^{-}$ decay are calculated within three-point QCD sum rules, with $K_0^{*}(1430)$ being the $p$-wave scalar meson. The branching ratios are estimated when only short, as well as short and long distance effects, are taken into account. It is obtained that the $B\to K_0^{*}(1430){\ell }^{+}{\ell }^{-}$ ($\ell =e$, $\mu$) decay is measurable at LHC. Measurement of these branching ratios for the semileptonic rare $B\to K_0^{*}(1430){\ell }^{+}{\ell }^{-}$ can give valuable information about the nature of scalar meson $K_0^{*}(1430)$.

We adopt the vector-meson-dominance approach to investigate $Q^2$-evolution of $NR$-transition form factors ($N$ denotes nucleon and $R$ an excited resonance) in the first and second resonance regions. The developed model is based upon conventional $\gamma NR$-interaction Lagrangians, introducing three form factors for spin-$3/2$ resonances and two form factors for spin-$1/2$ nucleon excitations. Lagrangian form factors are expressed as dispersionlike expansions with four or five poles corresponding to the lowest excitations of the mesons $\rho (770)$ and $\omega (782)$. Correct high-$Q^2$ form-factor behavior predicted by perturbative QCD is due to phenomenological logarithmic renormalization of electromagnetic coupling constants and linear superconvergence relations between the parameters of the meson spectrum. The model is found to be in good agreement with all the experimental data on $Q^2$-dependence of the transitions $N\Delta (1232)$, $NN(1440)$, $NN(1520)$, $NN(1535)$. We present fit results and model predictions for high-energy experiments proposed by JLab. Besides, we make special emphasis on the transition to perturbative domain of $N\Delta (1232)$ form factors.

Production of a sterile species is studied within an effective model of active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum kinetic equations for the distribution functions and coherences are obtained from two independent methods: the effective action and the quantum master equation. The decoherence time scale for active-sterile oscillations is ${\tau }_{\mathrm{dec}}=2/{\Gamma }_{aa}$, but the evolution of the distribution functions is determined by the two different time scales associated with the damping rates of the quasiparticle modes in the medium: ${\Gamma }_1={\Gamma }_{aa}{cos}^2{\theta }_m$; ${\Gamma }_2={\Gamma }_{aa}{sin}^2{\theta }_m$ where ${\Gamma }_{aa}$ is the interaction rate of the active species in the absence of mixing and ${\theta }_m$ the mixing angle in the medium. These two time scales are widely different away from Mikheyev-Smirnov-Wolfenstein resonances and preclude the kinetic description of active-sterile production in terms of a simple rate equation. We give the complete set of quantum kinetic equations for the active and sterile populations and coherences and discuss in detail the various approximations. A generalization of the active-sterile transition probability in a medium is provided via the quantum master equation. We derive explicitly the usual quantum kinetic equations in terms of the “polarization vector” and show their equivalence to those obtained from the quantum master equation and effective action.

We observe that the radial gauge can be consistently imposed on-shell together with the Lorenz gauge in Maxwell theory and with the harmonic traceless gauge in linearized general relativity. This simple observation has relevance for some recent developments in quantum gravity where, as we argue, the radial gauge is implicitly utilized.

After simplifying and improving the non-Gaussian formalism we developed in previous work, we derive a quantitative expression for the three-point correlator (bispectrum) of the curvature perturbation in general multiple-field inflation models. Our result describes the evolution of non-Gaussianity on superhorizon scales caused by the nonlinear influence of isocurvature perturbations on the adiabatic perturbation during inflation. We then study a simple quadratic two-field potential and find that, when slow roll breaks down and the field trajectory changes direction in field space, the non-Gaussianity can become large. However, for the simple models studied to date, the magnitude of this non-Gaussianity decays away after the isocurvature mode is converted into the adiabatic mode.

We will study open and hidden charm scalar meson resonances within two different models. The first one is a direct application of a chiral Lagrangian already used to study flavor symmetry breaking in Skyrme models. In another approach to the problem a $SU(4)$ symmetric Lagrangian is built and the symmetry is broken down to $SU(3)$ by identifying currents where heavy mesons are exchanged and suppressing those. Unitarization in coupled channels leads to dynamical generation of resonances in both models, in particular, a new hidden charm resonance with mass 3.7 GeV is predicted. The small differences between these models and with previous works is discussed. We also perform an error analysis of the results, checking their stability and determining the uncertainties in masses and couplings of the heavy resonances.

We study the Drell-Yan production cross section and structure functions in proton (deuteron)-nucleus collisions using the color glass condensate formalism. The nucleus is treated in the color glass condensate framework which includes both higher twist effects due to the inclusion of multiple scatterings and leading twist pQCD shadowing due to the small $x$ resummation, while the proton (or deuteron) is treated within the DGLAP improved parton model. In particular, the Drell-Yan structure functions are used in order to investigate the Lam-Tung relation at small $x$, which is known to be identically zero at leading twist up to next-to-leading order, and is thus a good playground for studying higher twist effects. In agreement with this, we find that violations of this relation are more important for low momentum and invariant mass of the Drell-Yan pair, and also in the region of rapidity that corresponds to smaller values of $x$ in the nucleus.

It was recently argued that the observed PVLAS anomaly can be explained by chameleon field theories in which large deviations from Newton’s law can be avoided. Here we present the predictions for the dichroism and the birefringence induced in the vacuum by a magnetic field in these models. We show that chameleon particles behave very differently from standard axionlike particles (ALPs). We find that, unlike ALPs, the chameleon particles are confined within the experimental setup. As a consequence, the birefringence is always bigger than the dichroism in PVLAS-type experiments.

It is argued that under a natural hypothesis the fermions inside a black hole formed after the collapse of a neutron star could form a noncompressible fluid (well before reaching the Planck scale) leading to some features of the integer quantum Hall effect. The relations with black hole entropy are analyzed. Insights coming from the quantum Hall effect are used to analyze the coupling with the Einstein equations. Connections with some cosmological scenarios and with the higher dimensional quantum Hall effect are briefly pointed out.

We study the growth of cosmological perturbations in the model of Lorentz-violating massive gravity. The Friedmann equation in this model acquires an unconventional term due to the Lorentz-breaking condensates which have the equation of state $w=-1/(3\gamma )$ with $\gamma$ being a free parameter taking values outside of the range $[0,1/3]$. Apart from the standard contributions, the perturbations above the Friedmann background contain an extra piece which is proportional to an arbitrary function $\vartheta (x^i)$ of the space coordinates. This function appears as an integration constant and corresponds to a nonpropagating scalar mode which may, however, become dynamical with the account of the higher-derivative corrections. For $-1<\gamma <0$ and $\gamma =1$ the anomalous perturbations grow slower than the standard ones and thus the model is compatible with observations. Whether the model is experimentally acceptable at other values of $\gamma$ depends on the value of the function $\vartheta (x^i)$ at the beginning of the radiation-dominated epoch.

Cosmological scenarios with $k$-essence are invoked in order to explain the observed late-time acceleration of the Universe. These scenarios avoid the need for fine-tuned initial conditions (the “coincidence problem”) because of the attractorlike dynamics of the $k$-essence field $\varphi$. It was recently shown that all $k$-essence scenarios with Lagrangians $p=L(X){\varphi }^{-2}$, where $X\equiv \frac{1}{2}{\varphi }_{,\mu }{\varphi }^{,\mu }$, necessarily involve an epoch where perturbations of $\varphi$ propagate faster than light (the “no-go theorem”). We carry out a comprehensive study of attractorlike cosmological solutions (“trackers”) involving a $k$-essence scalar field $\varphi$ and another matter component. The result of this study is a complete classification of $k$-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form $p=K(\varphi )L(X)$. Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous “no-go theorem” still holds for this class of models, indicating the existence of a superluminal epoch. In the context of $k$-essence cosmology, the superluminal epoch does not lead to causality violations. We discuss the implications of superluminal signal propagation for possible causality violations in Lorentz-invariant field theories.

We study the evolution of simple cosmic string loop solutions in an inflationary universe. We show, for the particular case of circular loops, that periodic solutions do exist in a de Sitter universe, below a critical loop radius $R_{c}H=1/2$. On the other hand, larger loops freeze in comoving coordinates, and we explicitly show that they can survive more $e$-foldings of inflation than pointlike objects. We discuss the implications of these findings for the survival of realistic cosmic string loops during inflation and for the general characteristics of post-inflationary cosmic string networks. We also consider the analogous solutions for domain walls, in which case the critical radius is $R_{c}H=2/3$.

We ask whether Cohen and Glashow’s very special relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved space-time with a cosmological constant. We show that its symmetry group ISIM(2) does admit a 2-parameter family of continuous deformations, but none of these give rise to noncommutative translations analogous to those of the de Sitter deformation of the Poincaré group: space-time remains flat. Only a 1-parameter family ${\mathrm{DISIM}}_b(2)$ of deformations of SIM(2) is physically acceptable. Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account. The Lorentz-violating point-particle action invariant under ${\mathrm{DISIM}}_b(2)$ is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive ${\mathrm{DISIM}}_b(2)$-invariant wave equations for particles of spins 0, $\frac{1}{2}$, and 1. The experimental bound, $|b|<{10}^{-26}$, raises the question “Why is the dimensionless constant $b$ so small in very special relativity?”

We study the collider signatures of a $T$-odd gauge boson $W_H$ pair production in the littlest Higgs model with $T$ parity (LHT) at Large Hadron Collider (LHC) and Linear Collider (LC). At the LHC, we search for the $W_H$ boson using its leptonic decay, i.e. $pp\to W_H^{+}{W}_H^{-}\to A_H{A}_H{\ell }^{+}{\nu }_{\ell }{\ell }^{\prime -}{\overline{\nu }}_{{\ell }^{\prime }}$, which gives rise to a collider signature of ${\ell }^{+}{\ell }^{\prime -}+{\mathrm{E̸}}_T$. We demonstrate that the LHC not only has a great potential of discovering the $W_H$ boson in this channel, but also can probe enormous parameter space of the LHT. Because of four missing particles in the final state, one cannot reconstruct the mass of $W_H$ at the LHC. But such a mass measurement can be easily achieved at the LC in the process of $e^{+}{e}^{-}\to W_H^{+}{W}_H^{-}\to A_H{A}_H{W}^{+}{W}^{-}\to A_H{A}_{H}jjjj$. We present an algorithm of measuring the mass and spin of the $W_H$ boson at the LC. Furthermore, we illustrate that the spin correlation between the $W$ boson and its mother particle ($W_H$) can be used to distinguish the LHT from other new physics models.