The removal of unphysical singularities in the perturbatively calculable part of the pion form factor—a classic example of a three-point function in QCD—is discussed. Different analytization procedures in the sense of Shirkov and Solovtsov are examined in comparison with standard QCD perturbation theory. We show that demanding the analyticity of the partonic amplitude as a whole, as proposed before by Karanikas and Stefanis, one can make infrared finite not only the strong running coupling and its powers, but also cure potentially large logarithms (that first appear at next-to-leading order) containing the factorization scale and modifying the discontinuity across the cut along the negative real axis. The scheme used here generalizes the analytic perturbation theory of Shirkov and Solovtsov to noninteger powers of the strong coupling and diminishes the dependence of QCD hadronic quantities on all perturbative scheme and scale-setting parameters, including the factorization scale.

We propose a new generalized version of the QCD analytic perturbation theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes. We construct nonpower series expansions for the analytic images of the running coupling and its powers for any fractional (real) power and complete the linear space of these solutions by constructing the index derivative. Using the Laplace transformation in conjunction with dispersion relations, we are able to derive at the one-loop order closed-form expressions for the analytic images in terms of the Lerch function. At the two-loop order we provide approximate analytic images of products of powers of the running coupling and logarithms—typical in higher-order perturbative calculations and when including evolution effects. Moreover, we supply explicit expressions for the two-loop analytic coupling and the analytic images of its powers in terms of one-loop quantities that can strongly simplify two-loop calculations. We also show how to resum powers of the running coupling while maintaining analyticity, a procedure that captures the generic features of Sudakov resummation. The algorithmic rules to obtain analytic-coupling expressions within the proposed fractional analytic perturbation theory from the standard QCD power-series expansion are supplied ready for phenomenological applications and numerical comparisons are given for illustration.

In this paper, we extend the study of Drell-Yan processes with antiproton beams already presented in a previous work. We consider the fully polarized ${\overline{p}}^{\uparrow }{p}^{\uparrow }\to {\mu }^{+}{\mu }^{-}X$ process, because this is the simplest scenario for extracting the transverse spin distribution of quarks, or transversity, which is the missing piece to complete the knowledge of the nucleon spin structure at leading twist. We perform Monte Carlo simulations for transversely polarized antiproton and proton beams colliding at a center-of-mass energy of interest for the future HESR at GSI. The goal is to possibly establish feasibility conditions for an unambiguous extraction of the transversity from data on double spin asymmetries.

We perform a QCD sum-rule study of the open-charmed $D_s(2317)$ as a four-quark state. Using the diquark-antidiquark picture for the four-quark state, we consider four possible interpolating fields for $D_s(2317)$, namely, scalar-scalar, pseudoscalar-pseudoscalar, vector-vector, and axial-vector–axial-vector types. We test all four currents by constructing four separate sum rules. The sum-rule with the scalar-scalar current gives a stable value for the $D_s$ mass which qualitatively agrees with the experimental value, and the result is not sensitive to the continuum threshold. The vector-vector sum rule also gives a stable result with small sensitivity to the continuum threshold and the extracted mass is somewhat lower than the scalar-scalar current value. On the other hand, the two sum rules in the pseudoscalar and axial-vector channels are found to yield the mass highly sensitive to the continuum threshold, which implies that a four-quark state with the combination of pseudoscalar-pseudoscalar or axial-vector–axial-vector type would be disfavored. These results would indicate that $D_s(2317)$ is a bound state of scalar-diquark and scalar-antidiquark and/or vector-diquark and vector-antidiquark.

We determine the weak mixing angle in the $\overline{\mathrm{MS}}$ scheme, ${sin}^2{\widehat{\theta }}_W(\mu )$, at energy scales $\mu$ relevant for present and future low-energy electroweak measurements. We relate the renormalization group evolution of ${sin}^2{\widehat{\theta }}_W(\mu )$ to the corresponding evolution of $\widehat{\alpha }(\mu )$ and include higher-order terms in ${\alpha }_s$ and $\alpha$ that had not been treated in previous analyses. We also update the analysis of nonperturbative, hadronic contributions and argue that the associated uncertainty is small compared to anticipated experimental errors. The resulting value of the low-energy $\overline{\mathrm{MS}}$ weak mixing angle is ${sin}^2{\widehat{\theta }}_W(0)=0.23867\pm 0.00016$.

We report a Dalitz-plot analysis of the charmless hadronic decays of charged $B$ mesons to the final state $K^{\pm }{\pi }^{\mp }{\pi }^{\pm }$. Using a sample of $226.0\pm 2.5$ million $B\overline{B}$ pairs collected by the BABAR detector, we measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for both charge-conjugate decays. We present measurements of the corresponding branching fractions and their charge asymmetries that supersede those of previous BABAR analyses. We find the charge asymmetries to be consistent with zero.

In this paper, we discuss the properties of one-parameter sequences that arise when solving the Hamiltonian constraint in Bianchi I loop quantum cosmology using a separation of variables method. In particular, we focus on finding an expression for the sequence for all real values of the parameter, and discuss the preclassicality of this function. We find that the behavior of these preclassical sequences imply time asymmetry on either side of the classical singularity in Bianchi I cosmology.

We disprove the Vafa-Witten theorem on the impossibility of spontaneously breaking parity in vectorlike gauge field theories, identifying a mechanism driven by quantum fluctuations. With the introduction of a meromorphic lattice formulation, defined over 5 dimensions, we demonstrate that the minima of the free energy can be distinct from the maxima of the partition function. By identifying and evaluating a suitable contour for the partition function the asymptotic behavior of the complex action is shown to be nonoscillatory.

The models based on $\mathrm{SU}(3{)}_C\otimes \mathrm{SU}(3{)}_L\otimes \mathrm{U}(1{)}_X$ gauge group (3-3-1) contain new Higgs bosons and one of them is the standard model (SM)-like Higgs boson $h$. Production of this Higgs boson at $pp$ colliders in the framework of 3-3-1 model with right-handed neutrinos is calculated. We found that the contribution of the real $Z^{\prime }$ to the process $pp\to hZ$ is nearly 60 fb if $M_{Z^{\prime }}$ is about 1 TeV. The decay width and the branching ratios of the $Z^{\prime }$ extra neutral gauge boson are systematically discussed.

In the event that the Higgs mass is large or that the electroweak interactions are strongly interacting at high energy, top-quark couplings to longitudinal components of the weak gauge bosons could offer important clues to the underlying dynamics. It has been suggested that precision measurements of $W_L{W}_L\to t\overline{t}$ and $Z_L{Z}_L\to t\overline{t}$ might provide hints of new physics. In this paper we present results for $\mathcal{O}({\alpha }_s)$ QCD corrections to $V_L{V}_L\to t\overline{t}$ scattering at the International Linear Collider (ILC). We find that corrections to cross sections can be as large as 30% and must be accounted for in any precision measurement of $VV\to t\overline{t}$.

We present a very general argument that the analogue of a heavy pentaquark (a state with the quantum numbers of a baryon combined with an additional light quark and a heavy antiquark $\overline{Q}$) must exist as a particle stable under strong interactions in the combined heavy quark and large $N_c$ limits of QCD. Moreover, in the combined limit these heavy pentaquark states fill multiplets of $\mathrm{SU}(4)\times \mathrm{O}(8)\times \mathrm{SU}(2)$. We explore the question of whether corrections in the combined $1/N_c$ and $1/m_Q$ expansions are sufficiently small to maintain this qualitative result. Since no model-independent way is known to answer this question, we use a class of realistic hadronic models in which a pentaquark can be formed via nucleon-heavy-meson binding through a pion-exchange potential. These models have the virtue that they necessarily yield the correct behavior in the combined limit, and the long-distance parts of the interactions are model independent. If the long-distance attraction in these models were to predict bound states in a robust way (i.e., largely insensitive to the details of the short-range interaction), then one could safely conclude that heavy pentaquarks do exist. However, in practice the binding does depend very strongly on the details of the short-distance physics, suggesting that the real world is not sufficiently near the combined large $N_c$, $m_Q$ limit to use it as a reliable guide. Whether stable heavy pentaquarks exist remains an open question.

Prediction of the effective Majorana mass for neutrinoless double $\beta$ decay in a simple extension of the standard model ($\nu \mathrm{MSM}$) is given. The model adds three right-handed neutrinos with masses smaller than the electroweak scale and explains dark matter of the Universe. This leads to constraints $1.3<m_{\beta \beta }^{\mathrm{NH}}<3.4\mathrm{meV}$ in normal neutrino mass hierarchy and $13<m_{\beta \beta }^{\mathrm{IH}}<50\mathrm{meV}$ in inverted hierarchy.

We calculate cross sections for mixed stop-sbottom pair production at the LHC, analogous to single-top production, a weak process involving the $W$-${\tilde{t}}_i$-${\tilde{b}}_j$ vertex. While coupling-suppressed relative to QCD same-flavor squark pair production, the signal is distinctive due to heavy-flavor tagging along with a possible same-sign lepton pair in the final state. SUSY backgrounds can often be suppressed many orders of magnitude by taking advantage of distinct kinematic differences from the signal. Measuring the rate of this process would add significant additional information to that gathered from other SUSY processes. If the stop and sbottom mixings can be determined elsewhere, stop-sbottom production would provide for a measurement of the weak squark gauge coupling and super-CKM vertex factor.

We have performed a global analysis of muon decay measurements to establish model-independent limits on the space-time structure of the muon decay matrix element. We find limits on the scalar, vector, and tensor coupling of right- and left-handed muons to right- and left-handed electrons. The limits on those terms that involve the decay of right-handed muons to left-handed electrons are more restrictive than in previous global analyses, while the limits on the other nonstandard model interactions are comparable. The value of the Michel parameter $\eta$ found in the global analysis is $-0.0036\pm 0.0069$, slightly more precise than the value found in a more restrictive analysis of a recent measurement. This has implications for the Fermi coupling constant $G_F$.

We extend the refined $G$-structure classification of supersymmetric solutions of 11 dimensional supergravity. We derive necessary and sufficient conditions for the existence of an arbitrary number of Killing spinors whose common isotropy group contains a compact factor acting irreducibly in eight spatial dimensions and which embeds in $(\mathrm{Spin}(7)⋉{\mathbb{R}}^8)\times \mathbb{R}$. We use these conditions to explicitly derive the general local bosonic solution of the Killing spinor equation admitting an $\mathrm{N}=4$ SU(4) structure embedding in a $(\mathrm{Spin}(7)⋉{\mathbb{R}}^8)\times \mathbb{R}$ structure, up to an eight-manifold of SU(4) holonomy. Subject to very mild assumptions on the form of the metric, we explicitly derive the general local bosonic solutions of the Killing spinor equation for $\mathrm{N}=6\mathrm{Sp}(2)$ structures and $\mathrm{N}=8\mathrm{SU}(2)\times \mathrm{SU}(2)$ structures embedding in a $(\mathrm{Spin}(7)⋉{\mathbb{R}}^8)\times \mathbb{R}$ structure, again up to eight-manifolds of special holonomy. We construct several other classes of explicit solutions, including some for which the preferred local structure group defined by the Killing spinors does not correspond to any holonomy group in 11 dimensions. We also give a detailed geometrical characterization of all supersymmetric spacetimes in 11 dimensions admitting $G$-structures with structure groups of the form $(G⋉{\mathbb{R}}^8)\times \mathbb{R}$.

We study the classical spinning closed string configurations on a logarithmically deformed ${\mathrm{AdS}}_5\times T^{1,1}$ background with the nontrivial Neveu-Schwarz $B$-field in which the IIB string theory is dual to a nonconformal $\mathcal{N}=1$ $\mathrm{SU}(N+M)\times \mathrm{SU}(N)$ gauge theory. The integrability on the original ${\mathrm{AdS}}_5\times T^{1,1}$ background are significantly reduced by the $B$-field. We find several spinning string solutions with two different ansatzs. Solutions for the pointlike strings and few circular strings are explicitly obtained. The folded spinning string solutions along the radial direction are shown to be allowed in this background. These solutions exhibit novel properties and bring some challenges to understand them from dual quantum field theory.

We work out the one-loop $U(1{)}_A$ anomaly for noncommutative $SU(N)$ gauge theories up to second order in the noncommutative parameter ${\theta }^{\mu \nu }$. We set ${\theta }^{0i}=0$ and conclude that there is no breaking of the classical $U(1{)}_A$ symmetry of the theory coming from the contributions that are either linear or quadratic in ${\theta }^{\mu \nu }$. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in ${\theta }^{\mu \nu }$. We adapt our results to noncommutative gauge theories with $SO(N)$ and $U(1)$ gauge groups.

We have investigated the higher loop diagrams of the fourth Legendre transformation which was proposed to obtain the 4PI effective action for the scalar field theory previously. For this purpose, we introduce a method which enables us to obtain the systematic loop expansion of the fourth Legendre transformation from the loop expansion of the second Legendre transformation which gives 2PI effective action. As a result, we have seen that at four-loop order, the 3PR diagrams of the 2PI effective action vanishes completely as expected but at five-loop order, the 4PR diagram of the 2PI effective action does not vanish completely.

We use action-angle variables to describe the basic physics of coherent scalar field oscillations in the expanding universe. These analytical mechanics methods have some advantages, like the identification of adiabatic invariants. As an application, we show some instances of potentials leading to equations of state with $p<-\rho /3$, thus contributing to the dark energy that causes the observed acceleration of the universe.

A comparative study of two predictive SO(10) models, namely, the BPW model (proposed by Babu, Pati and Wilczek) and the AB model (proposed by Albright and Barr) is done based on their predictions regarding $CP$ and flavor violations. There is a significant difference in the structure of the fermion mass matrices in the two models (which are hierarchical for the BPW case and lopsided for the AB model) which gives rise to different $CP$ and flavor violating effects. We include both standard model (SM) and supersymmetric (SUSY) contributions to these processes. Assuming flavor universality of SUSY-breaking parameters at a messenger scale $M^{*}\gtrsim M_{\mathrm{GUT}}$, it has been shown that renormalization group based post-GUT (grand unified theory) physics gives rise to large $CP$ and flavor violations. While these effects were calculated for the BPW model recently, this is the first time (to our knowledge) that post-GUT contributions have been included for the AB model. The values of $\Delta m_K$, ${ϵ}_K$, $\Delta m_{B_d}$ and $S(B_d\to J/\psi K_S)$ are found, in both models, to be close to SM predictions, in good agreement with data. Both models predict that $S(B_d\to \varphi K_S)$ should lie in the range $+0.65–0.74$, close to the SM prediction and that the electric dipole moment (EDM) of the neutron $\approx (\mathrm{few}\times {10}^{-26})e\mathrm{\text{−}}\mathrm{cm}$, which should be observed in upcoming experiments. The lepton sector brings out marked differences between the two models. It is found that $\mathrm{Br}(\mu \to e\gamma )$ in the AB model is generically much larger than that in the BPW model, being consistent with the experimental limit only with a rather heavy SUSY spectrum with $(m_o,m_{1/2})\sim (1000,1000)\mathrm{GeV}$. The BPW model, on the other hand, is consistent with the SUSY spectrum being as light as $(m_o,m_{1/2})\sim (600,300)\mathrm{GeV}$. Another distinction arises in the prediction for the EDM of the electron. In the AB model $d_e$ should lie in the range ${10}^{-27}–{10}^{-28}e\mathrm{\text{−}}\mathrm{cm}$, and should be observed by forthcoming experiments. The BPW model gives $d_e$ to be typically 100 times lower than that in the AB case. Thus the two models can be distinguished based on their predictions regarding $CP$ and flavor violating processes, and can be tested in future experiments.