We revisit the calculation of a heavy-quark potential in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at finite temperature using the AdS/CFT correspondence. As is widely known, the potential calculated in the pioneering works of Rey et al. [Nucl. Phys. B527, 171 (1998)] and Brandhuber et al. [Phys. Lett. B 434, 36 (1998)] is zero for separation distances $r$ between the quark and the antiquark above a certain critical separation, at which the potential has a kink. We point out that by analytically continuing the string configurations into the complex plane, and using a slightly different renormalization subtraction, one obtains a smooth nonzero (negative definite) potential without a kink. The obtained potential also has a nonzero imaginary (absorptive) part for separations $r>r_c=0.870/\pi T$. Most importantly, at large separations $r$ the real part of the potential does not exhibit the exponential Debye falloff expected from perturbation theory and instead falls off as a power law, proportional to $1/r^4$ for $r>r_0=2.702/\pi T$.

Flavor symmetry has been widely studied for figuring out the masses and mixing angles of standard model fermions. In this paper we present a framework for handling flavor symmetry breaking where the symmetry breaking is triggered by boundary conditions of scalar fields in extra-dimensional space. The alignment of scalar expectation values is achieved without referring to any details of scalar potential and its minimization procedure. As applications to non-Abelian discrete flavor symmetries, illustrative lepton mass models are constructed where the $S_3$ and $A_4$ flavor symmetries are broken down to the directions leading to the tribimaximal form of lepton mixing and realistic mass patterns.

We have studied the interaction of vector mesons within the hidden gauge formalism and applied it to the particular case of the $\rho \rho$ interaction. We find a strong attraction in the isospin, spin channels $I$, $S=0$, 0 and 0, 2, which is enough to bind the $\rho \rho$ system. We also find that the attraction in the $I$, $S=0$, 2 channel is much stronger than in the 0, 0 case. The states develop a width when the $\rho$ mass distribution is considered, and particularly when the $\pi \pi$ decay channel is turned on. Using a regularization scheme with cutoffs of natural size, we obtain results in fair agreement with the mass and the width of the $f_0(1370)$ and $f_2(1270)$ meson states, providing a natural explanation of why the tensor state is more bound than the scalar and offering a new picture for these states, which would be dynamically generated from the $\rho \rho$ interaction or, in simpler words, $\rho \rho$ molecular states.

We consider $B\to PS$ decays where $P$ stands for pseudoscalar and $S$ for a heavy (1500 MeV) scalar meson. We achieve agreement with available experimental data, which includes two orders of magnitude hierarchy, assuming the scalars mesons are two quark states. The contribution of the dipolar penguin operator ${\mathcal{O}}_{11}$ is quantified.

Details of a recent calculation of $\mathcal{O}({\alpha }_s^2)$ corrections to the decay $b\to c\ell {\nu }_l$, taking into account the $c$-quark mass, are described. Construction of the expansion in the mass ratio $m_c/m_b$ as well as the evaluation of new four-loop master integrals are presented. The same techniques are applicable to the muon decay, $\mu \to e{\nu }_{\mu }{\overline{\nu }}_e$. Analytical results are presented, for the physical cases as well as for a model with purely-vector couplings.

We present a study of hadronic transitions between $\mathit{{\rm Y}}(mS)$ ($m=4$, 3, 2) and $\mathit{{\rm Y}}(nS)$ ($n=2$, 1) resonances based on $347.5{\mathrm{fb}}^{-1}$ of data taken with the BABAR detector at the PEP-II storage rings. We report the first observation of $\mathit{{\rm Y}}(4S)\to \eta \mathit{{\rm Y}}(1S)$ decay with a branching fraction $\mathcal{B}(\mathit{{\rm Y}}(4S)\to \eta \mathit{{\rm Y}}(1S))=(1.96\pm {0.06}_{\mathrm{stat}}\pm {0.09}_{\mathrm{syst}})\times {10}^{-4}$ and measure the ratio of partial widths $\Gamma (\mathit{{\rm Y}}(4S)\to \eta \mathit{{\rm Y}}(1S))/\Gamma (\mathit{{\rm Y}}(4S)\to {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(1S))=2.41\pm {0.40}_{\mathrm{stat}}\pm {0.12}_{\mathrm{syst}}$. We set 90% CL upper limits on the ratios $\Gamma (\mathit{{\rm Y}}(2S)\to \eta \mathit{{\rm Y}}(1S))/\Gamma (\mathit{{\rm Y}}(2S)\to {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(1S))<5.2\times {10}^{-3}$ and $\Gamma (\mathit{{\rm Y}}(3S)\to \eta \mathit{{\rm Y}}(1S))/\Gamma (\mathit{{\rm Y}}(3S)\to {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(1S))<1.9\times {10}^{-2}$. We also present new measurements of the ratios $\Gamma (\mathit{{\rm Y}}(4S)\to {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(2S))/\Gamma (\mathit{{\rm Y}}(4S)\to {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(1S))=1.16\pm {0.16}_{\mathrm{stat}}\pm {0.14}_{\mathrm{syst}}$ and $\Gamma (\mathit{{\rm Y}}(3S)\to {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(2S))/\Gamma (\mathit{{\rm Y}}(3S)\to {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(1S))=0.577\pm {0.026}_{\mathrm{stat}}\pm {0.060}_{\mathrm{syst}}$.

Starting from a new zeroth order basis for quark mixing (CKM) matrix based on the quark-lepton complementarity and the tribimaximal pattern of lepton mixing, we derive a triminimal parametrization of a CKM matrix with three small angles and a $CP$-violating phase as its parameters. This new triminimal parametrization has the merits of fast convergence and simplicity in application. With the quark-lepton complementary relations, we derive relations between the two unified triminimal parametrizations for quark mixing obtained in this work and for lepton mixing obtained by Pakvasa-Rodejohann-Weiler. Parametrization deviating from quark-lepton complementarity is also discussed.

We study the quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions. Our main objective, based upon experimental and observational evidence, is to construct an effective theory which is a genuine perturbation of QED, such that setting the Lorentz invariance violation parameters to zero will reproduce it. To this end we provide a physically motivated prescription, based on the effective character of the model, regarding the way in which the model should be constructed and how the QED limit should be approached. This amounts to the introduction of an additional coarse-graining physical energy scale $M$, under which we can trust the effective field theory formulation. The prescription is successfully tested in the calculation of the Lorentz invariance violating contributions arising from the electron self-energy. Such radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters and no fine-tuning problems are found. Microcausality violations are highly suppressed and occur only in a spacelike region extremely close to the light cone. The stability of the model is guaranteed by restricting to concordant frames satisfying $1-|{\mathbf{v}}_{\max }|>6.5\times {10}^{-11}$.

We investigate the $1/N$ expansion proposed recently as a strategy to include quantum fluctuation effects in the nonrelativistic, attractive Fermi gas at and near unitarity. We extend the previous results by calculating the next-to-leading order corrections to the critical temperature along the whole crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation. We demonstrate explicitly that the extrapolation from the mean-field approximation, based on the $1/N$ expansion, provides a useful approximation scheme only on the BCS side of the crossover. We then apply the technique to the study of strongly interacting relativistic many-fermion systems. Having in mind the application to color superconductivity in cold dense quark matter, we develop, within a simple model, a formalism suitable to compare the effects of order parameter fluctuations in phases with different pairing patterns. Our main conclusion is that the relative correction to the critical temperature is to a good accuracy proportional to the mean-field ratio of the critical temperature and the chemical potential. As a consequence, it is significant even rather deep in the BCS regime, where phenomenologically interesting values of the quark–quark coupling are expected. Possible impact on the phase diagram of color-superconducting quark matter is discussed.

A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the $\theta$ expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in $\theta$ for the Plebański action is explicitly obtained.

Mirror matter is a promising self-collisional dark matter candidate. Here we study the evolution of thermodynamical quantities in the early Universe for temperatures below $\sim 100\mathrm{MeV}$ in presence of a hidden mirror sector with unbroken parity symmetry and only with gravitational interactions. This range of temperatures is interesting for primordial nucleosynthesis analyses, therefore we focus on the temporal evolution of number of degrees of freedom in both sectors. Numerically solving the equations, we obtain the interesting prediction that the effective number of extra-neutrino families raises for decreasing temperatures before and after big bang nucleosynthesis; this could help solving the discrepancy in this number computed at nucleosynthesis and cosmic microwave background formation epochs.

Taking into account the gluon condensate contributions, the form factors of the semileptonic $B_c^{-}\to D^{*0}\ell \nu$ transition with $l=\tau$, $e$ are calculated in the framework of the three-point QCD sum rules. The heavy quark effective theory limit of the form factors is also computed. The relevant total decay width as well as the branching ratio are evaluated and compared with the predictions of the other nonperturbative approaches.

Pion condensation is studied at one-loop level and nonzero baryochemical potential in the framework of the two-flavor constituent quark model using the one-loop level optimized perturbation theory for the resummation of the perturbative series. A Landau-type of analysis is presented for the investigation of the phase boundary between the pion condensed/noncondensed phases. The statement that the condensation starts at ${\mu }_I=m_{\pi }$ is slightly modified by one-loop corrections. The second order critical surface is determined and analyzed in the ${\mu }_I-{\mu }_B-T$ space. The ${\mu }_I$ dependence of the one-loop level charged pion pole masses is also studied.

The parton distribution function for a $b$ quark in the $B$ meson (called the shape function) plays an important role in the analysis of the $B\to X_s\gamma$ and $B\to X_u\ell \overline{\nu }$ data, and gives one of the dominant uncertainties in the determination of $|V_{ub}|$. We introduce a new framework to treat the shape function, which consistently incorporates its renormalization group evolution and all constraints on its shape and moments in any short distance mass scheme. At the same time it allows a reliable treatment of the uncertainties. We develop an expansion in a suitable complete set of orthonormal basis functions, which provides a procedure for systematically controlling the uncertainties due to the unknown functional form of the shape function. This is a significant improvement over fits to model functions. Given any model for the shape function, our construction gives an orthonormal basis in which the model occurs as the first term, and corrections to it can be studied. We introduce a new short distance scheme, the “invisible scheme,” for the kinetic energy matrix element ${\lambda }_1$. We obtain closed form results for the differential rates that incorporate perturbative corrections and a summation of logarithms at any order in perturbation theory, and present results using known next-to-next-to-leading order expressions. The experimental implementation of our framework is straightforward.

We calculate the single transverse-spin asymmetry for open charm production in $pp$ collisions within the QCD collinear factorization approach. We include contributions from both twist-three quark-gluon and trigluon correlation functions. We find that the quark-gluon correlation functions alone generate only a very small asymmetry for open charm production in the kinematic region of current interest at RHIC, so that the observation of any significant single-spin asymmetry would be a clear indication of the presence of trigluon correlations inside a polarized proton. We furthermore demonstrate that the trigluon contribution could be very different for the production of $D$ and $\overline{D}$ mesons. These features make the single-spin asymmetry in open charm production in polarized $pp$ collisions at RHIC an excellent probe of trigluon correlation functions.

We study the static potential between external quark-antiquark pairs in a strongly coupled gauge theory with a large number of colors and massive dynamical flavors, using a dual string description. When the constituent mass of the dynamical quarks is set below a certain critical value, we find a first-order phase transition between a linear and a Coulomb-like regime. Above the critical mass the two phases are smoothly connected. We also study the dependence on the theory parameters of the quark-antiquark separation at which the static configuration decays into specific static-dynamical mesons.

We investigate the effects of nonstandard four-fermion neutrino-neutrino interactions on the flavor evolution of dense neutrino gases. We find that in the regions where the neutrino-neutrino refractive index leads to collective flavor oscillations, the presence of new neutrino interactions can produce flavor equilibration in both normal and inverted neutrino mass hierarchy. In realistic supernova environments, these effects are significant if the nonstandard neutrino-neutrino interaction strength is comparable to the one expected in the standard case, dominating the ordinary matter potential. However, very small nonstandard neutrino-neutrino couplings are enough to trigger the usual collective neutrino flavor transformations in the inverted neutrino mass hierarchy, even if the mixing angle vanishes exactly.

Using isospin relations, we predict the standard model correlation between $S_{{\pi }^0{K}_{\mathrm{S}}}\equiv (\sin 2\beta {)}_{{\pi }^0{K}_{\mathrm{S}}}$ and $A_{{\pi }^0{K}_{\mathrm{S}}}$, the mixing-induced and direct $CP$ asymmetries of $B^0\to {\pi }^0{K}_{\mathrm{S}}$. The calculation uses flavor $SU(3)$ only to fix the isospin-$3/2$ amplitude through the $B^{\pm }\to {\pi }^{\pm }{\pi }^0$ branching ratio, and thus has a small irreducible theoretical error. It can reach percent level precision thanks to expected future lattice-QCD progress for the calculation of the relevant $SU(3)$-breaking form-factor ratio, and serves as a benchmark for new-physics searches. We obtain an interesting picture in the $A_{{\pi }^0{K}_{\mathrm{S}}}–S_{{\pi }^0{K}_{\mathrm{S}}}$ plane, where the current experimental data show a discrepancy with the standard model, and comment on the direct $CP$ asymmetries of $B^0\to {\pi }^{-}{K}^{+}$ and $B^{+}\to {\pi }^0{K}^{+}$. A modified electroweak penguin with a large new $CP$-violating phase can explain the discrepancy and allows us to accommodate also the corresponding data for other $b\to s$ penguin-dominated decays.

It is generally believed that neutrino mass hierarchy can be determined at a long baseline experiment, often using accelerator neutrino beams. Reactor neutrino experiments at an intermediate baseline have the capability to distinguish normal or inverted hierarchy. Recently, it has been demonstrated that the mass hierarchy could possibly be identified using Fourier transform to the $L/E$ spectrum if the mixing angle ${sin}^2(2{\theta }_{13})>0.02$. In this study, a more sensitive Fourier analysis is introduced. We found that an ideal detector at an intermediate baseline ($\sim 60\mathrm{km}$) could identify the mass hierarchy for a mixing angle ${sin}^2(2{\theta }_{13})>0.005$, without requirements on accurate information of reactor neutrino spectra and the value of $\Delta m_{32}^2$.

In this work, exact solutions of static and spherically symmetric space-times are analyzed in $f(R)$ modified theories of gravity coupled to nonlinear electrodynamics. First, we restrict the metric fields to one degree of freedom, considering the specific case of $g_{tt}{g}_{rr}=-1$. Using the dual $P$ formalism of nonlinear electrodynamics, an exact general solution is deduced in terms of the structural function $H_P$. In particular, specific exact solutions to the gravitational field equations are found, confirming previous results and new pure electric field solutions are found. Second, motivated by the existence of regular electric fields at the center, and allowing for the case of $g_{tt}{g}_{rr}\ne -1$, new specific solutions are found. Finally, we outline alternative approaches by considering the specific case of constant curvature, followed by the analysis of a specific form for $f(R)$.