A method for calculating coefficient functions of the operator product expansion, which was previously derived for the nonsinglet case, is generalized for the singlet coefficient functions. The resulting formula defines coefficient functions entirely in terms of corresponding singlet composite operators without applying to elementary (quark and gluon) fields. Both “diagonal” and “nondiagonal” gluon coefficient functions in the product expansion of two electromagnetic currents are calculated in QCD. Their renormalization properties are studied.

By requiring the correct Regge behavior in both meson and nucleon sectors, we determine the infrared asymptotic behavior of various background fields in the soft-wall anti-de Sitter/QCD model, including the dilaton, the warp factor, and the scalar vacuum expectation value. We then use a simple parametrization which smoothly connects these IR limits and their usual UV limits. The resulting spectrum is compared with experimental data, and the agreement between them is good.

This paper reports the tenth-order QED contribution to the lepton $g-2$ from the gauge-invariant set, called Set III(c), which consists of 390 Feynman vertex diagrams containing an internal fourth-order light-by-light-scattering subdiagram. The mass-independent contribution of Set III(c) to the electron $g-2$ ($a_e$) is 4.9210 (103) in units of $(\alpha /\pi {)}^5$. The mass-dependent contributions to $a_e$ from diagrams containing a muon loop is 0.00370 (37) $(\alpha /\pi {)}^5$. The tau-lepton loop contribution is negligible at present. Altogether the contribution of Set III(c) to $a_e$ is 4.9247 (104) $(\alpha /\pi {)}^5$. We have also evaluated the contribution of the closed electron loop to the muon $g-2$ ($a_{\mu }$). The result is 7.435 (134) $(\alpha /\pi {)}^5$. The contribution of the tau-lepton loop to $a_{\mu }$ is 0.1999 (28) $(\alpha /\pi {)}^5$. The total contribution of various leptonic loops (electron, muon, and tau-lepton) of Set III(c) to $a_{\mu }$ is 12.556 (135)$(\alpha /\pi {)}^5$.

We discuss the accuracy of the usual procedure for neutrino energy reconstruction which is based on the quasielastic kinematics. Our results are described in terms of a probability distribution for a real neutrino energy value. Several factors are responsible for the deviations from the reconstructed value. The main one is the multinucleon component of the neutrino interaction which in the case of Cherenkov detectors enters as a quasielastic cross section, increasing the mean neutrino energy which can differ appreciably from the reconstructed value. As an application we derive, for excess electron events attributed to the conversion of muon neutrinos, the true neutrino energy distribution based on the experimental one which is given in terms of the reconstructed value. The result is a reshaping effect. For MiniBooNE the low energy peak is suppressed and shifted at higher energies, which may influence the interpretation in terms of oscillation. For T2K at the Super Kamiokande far detector the reshaping translates into a narrowing of the energy distribution.

The TWIST Collaboration has completed its measurement of the three muon decay parameters $\rho$, $\delta$, and $P_{\mu }\xi$. This paper describes our determination of $\rho$, which governs the shape of the overall momentum spectrum, and $\delta$, which controls the momentum dependence of the parity-violating decay asymmetry. The results are $\rho =0.74977\pm 0.00012(\mathrm{stat})\pm 0.00023(\mathrm{syst})$ and $\delta =0.75049\pm 0.00021(\mathrm{stat})\pm 0.00027(\mathrm{syst})$. These are consistent with the value of $3/4$ given for both parameters in the standard model, and each is over a factor of 10 more precise than the measurements published prior to TWIST. Our final results on $\rho$, $\delta$, and $P_{\mu }\xi$ have been incorporated into a new global analysis of all available muon decay data, resulting in improved model-independent constraints on the possible weak interactions of right-handed particles.

We introduce analytical quantum gravity modifications of the production cross section for terascale black holes by employing an effective ultraviolet cutoff $l$. We find the new cross sections approach the usual “black-disk” form at high-energy, while they differ significantly near the fundamental scale from the standard increase with respect to $s$. We show that the heretofore discontinuous step function used to represent the cross section threshold can realistically be modeled by two functions representing the incoming and final parton states in a high-energy collision. The growth of the cross section with collision energy is thus a unique signature of $l$ and number of spatial dimensions $d$. Contrary to the classical black-disk result, our cross section is able to explain why black holes might not be observable in LHC experiments while they could be still within the reach of ultra-high-energy cosmic ray events.

We explore string and $M$-theory constructions of holographic theories with Lifshitz scaling exponent $z$ and hyperscaling violation exponent $\theta$, finding a range of $z$, $\theta$ values. Some of these arise as effective metrics from dimensional reduction of certain kinds of null deformations of AdS spacetimes appearing in the near-horizon geometries of extremal D3-, M2-, and M5-brane theories. The ${\mathrm{AdS}}_5$ solution, in particular, gives rise to $\theta =1$ in $d=2$ (boundary) space dimensions. Other solutions arise as the IIA D2- and D4-brane solutions with appropriate null deformations, and we discuss the phase structure of these systems.

We carry out the $N=1$ supersymmetrization of a physical non-Abelian tensor with nontrivial consistent couplings in four dimensions. Our system has three multiplets: (i) The usual non-Abelian vector multiplet $(A_{\mu }{}^I,{\lambda }^I)$, (ii) A non-Abelian tensor multiplet (TM) $(B_{\mu \nu }{}^I,{\chi }^I,{\phi }^I)$, and (iii) A compensator vector multiplet (CVM) $(C_{\mu }{}^I,{\rho }^I)$. All of these multiplets are in the adjoint representation of a non-Abelian group $G$. Unlike topological theory, all of our fields are propagating with kinetic terms. The $C_{\mu }{}^I$-field plays the role of a Stueckelberg compensator absorbed into the longitudinal component of $B_{\mu \nu }{}^I$. We give not only the component Lagrangian, but also a corresponding superspace reformulation, reconfirming the total consistency of the system. The adjoint representation of the TM and CVM is further generalized to an arbitrary real representation of general $SO(N)$ gauge group. We also couple the globally $N=1$ supersymmetric system to supergravity, as an additional nontrivial confirmation.

We present an explicit and exact boost of a relativistic bound state defined at equal time of the constituents in the Born approximation (lowest order in $\hslash$). To this end, we construct the Poincaré generators of QED and QCD in $D=1+1$ dimensions, using Gauss’ law to express $A^0$ in terms of the fermion fields in $A^1=0$ gauge. We determine the fermion-antifermion bound states in the Born approximation as eigenstates of the time and space translation generators $P^0$ and $P^1$. The boost operator is combined with a gauge transformation so as to maintain the gauge condition $A^1=0$ in the new frame. We verify that the boosted state remains an eigenstate of $P^0$ and $P^1$ with appropriately transformed eigenvalues and determine the transformation law of the equal-time, relativistic wave function. The shape of the wave function is independent of the center-of-mass momentum when expressed in terms of a variable which is quadratically related to the distance $x$ between the fermions. As a consequence, the Lorentz contraction of the wave function is $\propto 1/(E-V(x))$ and thus depends on $x$ via the linear potential $V(x)$.

Scattering of two baryons in the large-$N$ Gross-Neveu model via the time-dependent Dirac-Hartree-Fock approach has recently been solved in closed analytical form. Here, we generalize this result to scattering processes involving any number and complexity of the scatterers. The result is extrapolated from the solution of few baryon problems, found via a joint ansatz for the scalar mean field and the Dirac spinors, and presented in analytical form. It has been verified numerically for up to 8-baryon problems so far, but a full mathematical proof is still missing. Examples shown include the analogue of proton-nucleus and nucleus-nucleus scattering in this toy model. All the parameters of the general result can be fixed by 1- and 2-baryon input only. We take this finding as evidence for factorized scattering, but on the level of composite multifermion states rather than elementary fermions.

Kempf et al. in Ref. [A. Kempf, G. Mangano, and R. B. Mann, Phys. Rev. D 52, 1108 (1995).] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles’ momentum cannot be arbitrarily imprecise and therefore there is an upper bound for momentum fluctuations. Taking this achievement into account, we generalize the seminal work of Kempf et al. to the case that there is also a maximal particles’ momentum. Existence of an upper bound for the test particles’ momentum provides several novel and interesting features, some of which are studied in this paper.

The ekpyrotic scenario is studied in the context of some extensions of Hořava-Lifshitz gravity. Some particular solutions that lead to cyclic Hubble parameters are analyzed, where the corresponding gravitational actions are reconstructed by using several techniques and auxiliary fields. Its comparison with standard $F(R)$ gravity is performed. In addition, the so-called little rip, a stage of the universe evolution when some bounded systems may be dissolute, is also studied in this frame of theories.

Supersymmetry plays a fundamental role in the radiative stability of many inflationary models. Spontaneous breaking of the symmetry inevitably leads to fields with masses of order the Hubble scale during inflation. When these fields couple to the inflaton, they produce a unique signature in the squeezed limit of the three-point function of primordial curvature perturbations. In this paper, we make this connection between naturalness, supersymmetry, Hubble-mass degrees of freedom, and the squeezed limit precise. To study the physics in a model-insensitive way, we develop a supersymmetric effective theory of inflation. We use the effective theory to classify all possible interactions between the inflaton and the additional fields, and determine which ones naturally allow large non-Gaussianities when protected by supersymmetry. Finally, we discuss the tantalizing prospect of using cosmological observations as a probe of supersymmetry.

Simple $SO(10)$ Higgs models with the adjoint representation triggering the grand unified symmetry breaking, discarded long ago due to inherent tree-level tachyonic instabilities in the physically interesting scenarios, have been recently brought back to life by quantum effects. In this work we focus on the variant with ${45}_H\oplus {126}_H$ in the Higgs sector and show that there are several regions in the parameter space of this model that can support stable unifying configurations with the $B-L$-breaking scale as high as ${10}^{14}\mathrm{GeV}$, well above the previous generic estimates based on the minimal survival hypothesis. This admits for a renormalizable implementation of the canonical seesaw and makes the simplest potentially realistic scenario of this kind a good candidate for a minimal $SO(10)$ grand unification. Last, but not least, this setting is likely to be extensively testable at future large-volume facilities such as Hyper-Kamiokande.

The interplay of deconfinement and chiral symmetry restoration are considered in terms of effective theories. We generalize the earlier model studies by considering fermions in higher representations, and study the finite temperature phase diagrams of SU(2) and SU(3) gauge theories with two fermion flavors in fundamental, adjoint, or two-index symmetric representations. We discuss our results in relation to recent lattice simulations on these theories and outline possible applications in the context of dynamical electroweak symmetry breaking.

We study the four-body semileptonic baryonic decay of $B^{-}\to \Lambda \overline{p}\nu \overline{\nu }$ in the standard model. We find that the decay branching ratio is $(7.9\pm 1.9)\times {10}^{-7}$. Similar to the rare decays of $B^{-}\to K^{(*)-}\nu \overline{\nu }$, this baryonic decay of $B^{-}\to \Lambda \overline{p}\nu \overline{\nu }$ is also sensitive to new physics and accessible to the future $B$ factories.

We revisit the extraction of ${\alpha }_s(M_{\tau }^2)$ from the QCD perturbative corrections to the hadronic $\tau$ branching ratio, using an improved fixed-order perturbation theory based on the explicit summation of all renormalization-group accessible logarithms, proposed some time ago in the literature. In this approach, the powers of the coupling in the expansion of the QCD Adler function are multiplied by a set of functions $D_n$, which depend themselves on the coupling and can be written in a closed form by iteratively solving a sequence of differential equations. We find that the new expansion has an improved behavior in the complex energy plane compared to that of the standard fixed-order perturbation theory (FOPT), and is similar but not identical to the contour-improved perturbation theory (CIPT). With five terms in the perturbative expansion we obtain in the $\overline{\mathrm{MS}}$ scheme ${\alpha }_s(M_{\tau }^2)=0.338\pm 0.010$, using as input a precise value for the perturbative contribution to the hadronic width of the $\tau$ lepton reported recently in the literature.

We study the $N\overline{D}$ system by means of a chiral constituent quark model. This model, tuned in the description of the baryon and meson spectra as well as the $NN$ interaction, provides parameter-free predictions for the charm $-1$ two-hadron systems. The presence of a heavy antiquark makes the interaction rather simple. We have found sharp quark-Pauli effects in some particular channels, generating repulsion, due to lacking degrees of freedom to accommodate the light quarks. Our results point to the existence of an attractive state, the $\Delta {\overline{D}}^{*}$ with $(T,S)=(1,5/2)$, presenting a resonance close to threshold. It would show up in the scattering of $\overline{D}$ mesons on nucleons as a $D$ wave state with quantum numbers $(T)J^P=(1)5/2^{-}$. This resonance resembles our findings in the $\Delta \Delta$ system, that offered a plausible explanation to the cross section of double-pionic fusion reactions through the so-called Abashian-Booth-Crowe effect. The study of the interaction of $D$ mesons with nucleons is a goal of the $\overline{\mathrm{P}}$ANDA collaboration at the European facility FAIR and, thus, the present theoretical study is a challenge to be tested at the future experiments.

The $U_L(2)\underset{}{\overset{}{⨂}}{U}_R(2)$ gauge model for the unified theory of the electromagnetic and weak interactions which is free from the auxiliary self-interaction scalar field is developed. Because of breaking the initial symmetry, the $S{U}_L(2)\underset{}{\overset{}{⨂}}{U}_R(1)$ Lagrangian is derived. The obtained $S{U}_L(2)\underset{}{\overset{}{⨂}}{U}_R(1)$ Lagrangian contains all the terms corresponding to the free boson and fermion fields as well as to interactions between them, as they take place in the standard model consideration. All boson fields, including the Higgs one, directly arise due to breaking the initial symmetry, and are generated by the initial gauge fields. The Higgs fields are studied in detail. We show that there is a wide spectrum of states of the Higgs bosons. The Higgs particle masses in such states are calculated.