Recently released Planck data imply a smaller Hubble constant $H_0$ than that from the Hubble Space Telescope project (HST) and a larger percentage of the matter components ${\mathrm{\Omega }}_m$ compared to the Supernova Legacy Survey (SNLS) in the $\mathrm{\Lambda }$ cold dark matter (CDM) model. In this paper we found that even though the tension on $H_0$ between Planck and HST can be relaxed if the dark radiation is introduced [$\mathrm{\Delta }{N}_{\text{eff}}=0.536_{-0.224}^{+0.229}$ at 68% CL from the data sets of $\text{Planck}+\mathrm{WMAP}$ polarization $\left(\mathrm{WP}\right)+\text{baryon}$ acoustic oscillation $\left(\mathrm{BAO}\right)+\text{the}$ combination of supernova Union2.1 compilation of 580 Supernovae $\left(\text{Union}2.1\right)+\mathrm{HST}$], ${\mathrm{\Omega }}_m$ from Planck is still not nicely compatible with that from SNLS. The tensions between Planck and other astrophysical data sets can be significantly relaxed in the $w\mathrm{CDM}$ model, and the combination of these data sets prefers a phantomlike dark energy at more than 95% CL: $w=-1.15\pm 0.07$ and $w=-1.16\pm 0.06$ at 68% CL from $\text{Planck}+\mathrm{WP}+\mathrm{BAO}+\text{Union}2.1+\mathrm{HST}$ and $\text{Planck}+\mathrm{WP}+\mathrm{BAO}+\mathrm{SNLS}+\mathrm{HST}$, respectively. From the statistical point of view, there is no evidence for a time-evolving equation of state ($\mathrm{\Delta }{\chi }^2=-0.3$ compared to a constant equation of state for the combination of $\text{Planck}+\mathrm{WP}+\mathrm{BAO}+\mathrm{SNLS}+\mathrm{HST}$).

The $\eta$ and ${\eta }^{\prime }$ transition form factors in the spacelike region are analyzed at low and intermediate energies in a model-independent way through the use of rational approximants. The slope and curvature parameters of the form factors as well as their values at zero and infinity are extracted from experimental data. The impact of these results on the mixing parameters of the $\eta$-${\eta }^{\prime }$ system and the pseudoscalar-exchange contributions to the hadronic light-by-light scattering part of the anomalous magnetic moment $a_{\mu }$ are also discussed.

We study transition form factors for decays of $D$ mesons. That is, we consider matrix elements of the weak left-handed quark current for the transitions $D\to P$ and $D\to V$, where $P$ and, $V$ are light pseudoscalar or vector mesons, respectively. Our motivation to perform the present study of these form factors is future calculations of nonleptonic decay amplitudes. We consider the transition form factors within a class of chiral quark models. Especially, we study how the large energy effective theory limit works for $D$-meson decays. In this paper, we extend previous work on the case $B\to \pi$ to the case $D\to P=\pi$, $K$. Further, we extend our previous model based on the large energy effective theory to the entirely new case $D\to V=\rho ,K^{*},\dots$ To determine some of the parameters in our model, we use existing data and results based on some other methods like lattice calculations, light-cone sum rules, and heavy-light chiral perturbation theory. We also obtain some new predictions for relations between form factors.

Lepton flavor-violating processes offer interesting possibilities to probe new physics at multi-TeV scale. We discuss those in the framework of effective field theory, emphasizing the role of gluonic operators. Those operators are obtained by integrating out heavy quarks that are kinematically inaccessible at the scale where low-energy experiments take place and make those experiments sensitive to the couplings of lepton flavor-changing neutral currents to heavy quarks. We discuss constraints on the Wilson coefficients of those operators from the muon conversion ${\mu }^{-}+(A,Z)\to e^{-}+(A,Z)$ and from lepton flavor-violating tau decays with one or two hadrons in the final state, e.g., $\tau \to \ell {\eta }^{(\prime )}$ and $\tau \to \ell {\pi }^{+}{\pi }^{-}$ with $\ell =\mu ,e$. To illustrate the results we discuss explicit examples of constraining parameters of leptoquark models.

By eschewing fine-tuning from the electroweak and QCD sectors of supersymmetry (natural supersymmetry or SUSY), and by invoking the Kim-Nilles solution to the SUSY $\mu$ problem, one is lead to models wherein the dark matter is comprised of a mixture of axions and Higgsino-like WIMPs. Over a large range of Peccei-Quinn breaking scale $f_a\sim {10}^9–{10}^{12}\mathrm{GeV}$, one then expects about 90%–95% axion dark matter. In such a scenario, both axion and WIMP direct detection may be expected.

We have investigated the electromagnetic moments of the tau lepton in $e^{+}{e}^{-}\to e^{+}{\gamma }^{*}{\gamma }^{*}{e}^{-}\to e^{+}\tau \overline{\tau }{e}^{-}$ process at the CLIC. We have obtained 95% confidence level bounds on the anomalous magnetic and electric dipole moments for various values of the integrated luminosity and the center of mass energy. We have shown that the $e^{+}{e}^{-}\to e^{+}{\gamma }^{*}{\gamma }^{*}{e}^{-}\to e^{+}\tau \overline{\tau }{e}^{-}$ process at the CLIC leads to a remarkable improvement in the existing experimental bounds on the anomalous magnetic and electric dipole moments.

We construct a comprehensive list of nonsupersymmetric standard model extensions with a low-scale left-right (LR)-symmetric intermediate stage that may be obtained as simple low-energy effective theories within a class of renormalizable $SO(10)$ grand unified theories. Unlike the traditional “minimal” LR models many of our example settings support a perfect gauge coupling unification even if the LR scale is in the LHC domain at a price of only (a few copies of) one or two types of extra fields pulled down to the TeV-scale ballpark. We discuss the main aspects of a potentially realistic model building conforming the basic constraints from the quark and lepton sector flavor structure, proton decay limits, etc. We pay special attention to the theoretical uncertainties related to the limited information about the underlying unified framework in the bottom-up approach, in particular, to their role in the possible extraction of the LR-breaking scale. We observe a general tendency for the models without new colored states in the TeV domain to be on the verge of incompatibility with the proton stability constraints.

The magnetic and transition magnetic moments of the ground-state baryons are computed in heavy baryon chiral perturbation theory in the large-$N_c$ limit, where $N_c$ is the number of colors. SU(3) symmetry breaking is systematically studied twofold: On the one hand, one-loop nonanalytic corrections of orders $m_q^{1/2}$ and $m_q\ln m_q$ are included, with contributions of baryon intermediate states from both flavor octet and flavor decuplet multiplets, assuming degeneracy between baryon states within a given flavor multiplet but nondegeneracy between baryons of different multiplets. On the other hand, perturbative SU(3) symmetry breaking is also analyzed by including all relevant leading-order operators that explicitly break SU(3) at linear order. The resultant expressions are compared with the available experimental data and with other determinations in the context of conventional heavy baryon chiral perturbation theory for three flavors of light quarks and at the physical value $N_c=3$. The agreement reached is quite impressive.

In this paper, we study the $B_c$-meson exclusive decays to S-wave charmonia and light pseudoscalar or vector mesons, i.e., $\pi$, $K$, $\rho$, and $K^{*}$ at the next-to-leading order (NLO) in the QCD coupling. The nonfactorizable contribution is included, which is absent in traditional naive factorization. Numerical results show that NLO QCD corrections markedly enhance the branching ratio with a $K$ factor of 1.75 for $B_c^{\pm }\to {\eta }_c{\pi }^{\pm }$ and 1.31 for $B_c^{\pm }\to J/\psi {\pi }^{\pm }$ using certain input parameters. And the theoretical uncertainties for their branching ratios are reduced compared with that of direct tree-level calculation. In order to investigate the asymptotic behavior, the analytic form is obtained in the heavy quark limit, i.e., $m_b\to \infty$. We note that annihilation topologies contribute trivia in this limit, and the corrections at leading order in $z=m_c/m_b$ expansion come from form factors and hard spectator interactions. At last, some related phenomenologies are also discussed.

The results of our new QCD analysis of helicity parton distributions of the nucleon at full next-to-leading order accuracy in the fixed-flavor number scheme are presented. Performing a combined QCD fit on the global sets of latest inclusive and the semi-inclusive polarized deep inelastic scattering data, we are able to extract new polarized parton distribution functions (PPDFs) at the input scale $Q_0^2=1{\mathrm{GeV}}^2$. Particularly, we calculate PPDFs considering light sea-quark decomposition, and the results are compared with the experimental data and the most precise theoretical models obtained by recent analyses. The latest COMPASS2010 SIDIS data, which were not used in the combined analyses before 2010, are employed in the current analysis, and the effect of COMPASS SIDIS data is studied in detail. Also, the uncertainties of PPDFs are determined using the standard Hessian technique.

We present results of unitary triangle fits based on the scan method. This frequentist approach employs Gaussian uncertainties for experimental quantities, but avoids assumptions about the distribution of theoretical errors. Instead, we perform a large number of fits, scanning over regions of plausible theory errors for each quantity. We retain those fits meeting a specific confidence level criterion, thereby constructing a region in the $\overline{\rho }-\overline{\eta }$ plane using the “standard” measurements (Cabibbo-Kobayashi-Maskawa matrix elements, $\sin 2\beta$, $B_{d,s}^0$ mixing, ${\epsilon }_K$). In addition we use branching fraction and $CP$ asymmetry measurements of $B$ decays to pseudoscalar pseudoscalar, pseudoscalar vector, vector vector, and $a_1$ pseudoscalar final states to determine $\alpha$, $D^{(*)}{K}^{(*)}$ modes to determine $\gamma$, and $D^{(*)}\pi$ and $D\rho$ modes to determine $2\beta +\gamma$. We parametrize individual decay amplitudes in terms of color-allowed tree, color-suppressed tree, penguin, singlet penguin, electroweak penguin, as well as $W$-exchange and $W$-annihilation amplitudes. With this parametrization, we obtain a good fit to the measured branching fractions and $CP$ asymmetries within the standard model ansatz, with no new physics contributions. This simultaneous fit allows us to determine, for the first time in a global fit, the correlation between $\alpha$ and $\beta$, as well as between $\gamma$ and $\beta$.

We present a model where Majorana neutrino mass terms are forbidden by the flavor symmetry group $\mathrm{\Delta }(27)$. Neutrinos are Dirac fermions and their masses arise in the same way as those of the charged fermions, due to very small Yukawa couplings. The model fits current neutrino oscillation data and correlates the octant of the atmospheric angle ${\theta }_{23}$ with the magnitude of the lightest neutrino mass, with maximal mixing excluded for any neutrino mass hierarchy.

We investigate the background field method with the Batalin-Vilkovisky formalism, to generalize known results, study the parametric completeness of general gauge theories and achieve a better understanding of several properties. In particular, we study renormalization and gauge dependence to all orders. Switching between the background field approach and the usual approach by means of canonical transformations, we prove parametric completeness without making use of cohomological theorems; namely we show that if the starting classical action is sufficiently general all divergences can be subtracted by means of parameter redefinitions and canonical transformations. Our approach applies to renormalizable and nonrenormalizable theories that are manifestly free of gauge anomalies and satisfy the following assumptions: the gauge algebra is irreducible and closes off shell, the gauge transformations are linear functions of the fields, and closure is field independent. Yang-Mills theories and quantum gravity in arbitrary dimensions are included, as well as effective and higher-derivative versions of them, but several other theories, such as supergravity, are left out.

In this paper, we analyze the quasinormal mode spectrum of realistic neutron stars by studying the polar modes. In particular, we calculate the fundamental mode (f mode), the fundamental pressure mode (p mode), and the fundamental curvature mode (wI mode) for 15 different equations of state satisfying the $2{\mathrm{M}}_{\odot }$ constraint, most of them containing exotic matter. Since f and p modes couple to matter perturbations, the influence of the presence of hyperons and quarks in the core of the neutron stars is more significant than for the axial component. We present phenomenological relations, which are compatible with previous results, for the frequency and damping time with the compactness of the neutron star. We also consider new phenomenological relations between the frequency and damping time of the wI mode and the f mode. These new relations are independent of the equation of state and could be used to estimate the central pressure, mass, or radius and eventually constrain the equation-of-state of neutron stars. To obtain these results, we have developed a new method based on the exterior complex scaling technique with a variable angle.

We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $\mathrm{\Omega }(\tilde{\mu })$ with complex chemical potential $\tilde{\mu }$. The result is given in terms of a single sum, the coefficients of which are analytical functions of $\tilde{\mu }$ consisting of polynomials and polygamma functions, decoupled from the physical expansion parameter $\beta m$. The analytic structure of the coefficients permits us to explicitly calculate the thermodynamic potential for the imaginary chemical potential and analytically continue the domain to the complex $\tilde{\mu }$ plane. Furthermore, our representation of $\mathrm{\Omega }(\tilde{\mu })$ is particularly well suited for the Landau-Ginzburg type of phase transition analysis. This fact, along with the possibility of interpreting the imaginary chemical potential as an effective generalized-statistics phase, allows us to investigate the singular origin of the $m^3$ term appearing only in the bosonic thermodynamic potential.

A possible explanation for the discrepancy between electronic and muonic hydrogen measurements of the proton charge radius are new, lepton universality violating interactions. Several new couplings and particles have been suggested that account for this discrepancy. At present, these explanations are poorly constrained. Experiments such as the upcoming kaon decay experiment at the Japan Proton Accelerator Research Complex may constrain or eliminate some explanations by measuring the decay channel $K^{+}\to {\mu }^{+}+\nu +e^{-}+e^{+}$. We calculate the predicted contributions of the various explanations to this channel. The predicted signals, if present, should be large enough to be resolved in the experiment.

We derive some exact bounds on the free energy $W(J)$ in an $SU(N)$ gauge theory, where $J_{\mu }^b$ is a source for the gluon field $A_{\mu }^b$ in the minimal Landau gauge, and $W(J)$ is the generating functional of connected correlators, $\exp W(J)=⟨\exp (J,A)⟩$. We also provide asymptotic expressions for the free energy $W(J)$ at large $J$ and for the quantum effective action $\mathrm{\Gamma }(A)$ at large $A$. We specialize to a source $J(x)=h\cos (k·x)$ of definite momentum $k$ and source strength $h$, and study the gluon propagator $D(k,h)$ in the presence of this source. Among other relations, we prove ${\int }_0^{\infty }dhD(k,h)\le \sqrt{2}k$, which implies $\underset{k\to 0}{\lim }D(k,h)=0$, for all positive $h>0$. Thus the system does not respond to a static color probe, no matter how strong. Recent lattice data in minimal Landau gauge in $d=3$ and 4 dimensions at $h=0$ indicate that the gluon propagator in the minimum Landau gauge is finite, ${\lim }_{k\to 0}D(k,0)>0$. Thus these lattice data imply a jump in the value of $D(k,h)$ at $h=0$ and $k=0$, and the value of $D(k,h)$ at this point depends on the order of limits. We also present numerical evaluations of the free energy $W(k,h)$ and the gluon propagator $D(k,h)$ for the case of $SU(2)$ Yang-Mills theory in various dimensions which support all of these findings.

We present a method to obtain spectral functions at finite temperature and density from the functional renormalization group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically continued frequency components in the originally Euclidean external momenta. For the uniqueness of this continuation at finite temperature we furthermore implement the physical Baym-Mermin boundary conditions. We demonstrate the feasibility of the method by calculating the mesonic spectral functions in the quark-meson model along the temperature axis of the phase diagram, and at finite quark chemical potential along the fixed-temperature line that crosses the critical end point of the model.

The latest LHC monojet searches place stringent bounds on the $pp\to \overline{\chi }\chi$ cross section of dark matter. Further properties such as the dark matter mass or the precise structure of the interactions between dark matter and the standard model, however, cannot be determined in this manner. We point out that measurements of the azimuthal angle correlations between the two jets in $2j+\overline{\chi }\chi$ events may be used to disentangle whether dark matter pair production proceeds dominantly through tree or loop diagrams. Our general observation is illustrated by considering theories in which dark matter interacts predominantly with the top quark. We show explicitly that in this case the jet-jet azimuthal angle difference is a gold-plated observable to probe the Lorentz structure of the couplings of dark matter to top quarks, thus testing the $CP$ nature of the particle mediating these interactions.

We propose a particle physics explanation of the nonobservation of muon neutrino events at IceCube coincident with gamma ray bursts (GRBs) at the rates predicted by the standard Bahcall-Waxman model, in terms of neutrino oscillations. Our model is based on assuming that (a) all neutrinos are pseudo-Dirac particles and (b) there exists a mirror world interacting gravitationally with the observed world. This scenario has three sterile neutrinos associated with each flavor of ordinary neutrinos. Very tiny mass splitting between these neutrinos is assumed to arise from lepton number violating dimension-five Planck scale suppressed operators. We show that if a mass splitting of $10^{-15}{\mathrm{eV}}^2$ is induced between the four mass eigenstates of a given species, then its flux will be suppressed at IceCube energies by a factor of 4 compared to GRB model predictions. Hierarchies in mass splitting among different flavors may result in different amounts of suppression of each flavor, and based on this we predict a difference in the flavor ratios of the observed neutrinos that is significantly different compared to the standard three-flavor prediction of $1:1:1$, which could serve as a test for this model.