International Journal of Modern Physics A

This paper describes the work pursued in the years 2008–2013 on improving the Standard Model prediction of selected flavor-physics observables. The latter includes: (1) ${𝜖}_K$, that quantifies indirect CP violation in the $K^0-{\bar{K}}^0$ system and (2) the very rare decay $B_s\to \mu \mu$, recently measured at the LHC. Concerning point (1), the paper describes our reappraisal of the long-distance contributions to ${𝜖}_K$,${}^{1\text{–}3}$ that have permitted to unveil a potential tension between CP violation in the $K^0$- and $B_d$-system. Concerning point (2), the paper gives a detailed account of various systematic effects pointed out in Ref. 4 and affecting the Standard Model $B_s\to \mu \mu$ decay rate at the level of 10% — hence large enough to be potentially misinterpreted as nonstandard physics, if not properly included. The paper further describes the multifaceted importance of the $B_{d,s}\to \mu \mu$ decays as new physics probes, for instance how they compare with $Z$-peak observables at LEP, following the effective-theory approach of Ref. 5. Both cases (1) and (2) offer clear examples in which the pursuit of precision in Standard Model predictions offered potential avenues to discovery. Finally, this paper describes the impact of the above results on the literature, and what is the further progress to be expected on these and related observables.

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger–Keldysh formalism is used in AdS/CFT instead of conventional Feynman–Witten diagrams technique, permits to calculate values of conformal dimensions in the $O(N)$ symmetric model with conformal or composite Habbard–Stratonovich field.

The idea of a muon collider has been developed since the 70s. In these projects, muons are produced at targets at low or intermediate energies. Then, after reducing the emittance, they should accelerate very quickly, since the lifetime is very short (${\tau }_{\mu }=2\mu$s in the rest frame). Here, we want to propose the option of the collider, where the muons can be obtained on the hadron collider at high energy using a focusing bent crystals.

In this paper, we restudy the ground state mass spectrum of the diquark–diquark–antiquark-type $uudc\bar{c}$ pentaquark states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 13 in a consistent way. The predicted masses support assigning the $P_c(4312)$ to be the hidden-charm pentaquark state with $J^P={\frac{1}{2}}^{-}$, assigning the $P_c(4440)$ to be the hidden-charm pentaquark state with $J^P={\frac{1}{2}}^{-}$, ${\frac{3}{2}}^{-}$ or ${\frac{5}{2}}^{-}$, assigning the $P_c(4457)$ to be the hidden-charm pentaquark state with $J^P={\frac{1}{2}}^{-}$ or ${\frac{3}{2}}^{-}$.

Unitarity of the $3\times 3$ lepton flavor mixing matrix $V$ is unavoidably violated in a seesaw mechanism if its new heavy degrees of freedom are slightly mixed with the active neutrino flavors. We propose to use the atomic transition process $|\mathrm{\text{e}}〉\to |\mathrm{\text{g}}〉+\gamma +{\nu }_i^{}+{\bar{\nu }}_j^{}$ (for $i$, $j=1,2,3$), where $|\mathrm{\text{e}}〉$ and $|\mathrm{\text{g}}〉$ stand, respectively for the excited and ground levels of an atomic system, to probe or constrain the unitarity-violating effects of $V$. We find that the photon spectrum of this transition will be distorted by the effects of $V{V}^{†}\ne 1$ and $V^{†}V\ne 1$ as compared with the $V{V}^{†}=V^{†}V=1$ case. We locate certain frequencies in the photon spectrum to minimize the degeneracy of effects of the unitarity violation and uncertainties of the flavor mixing parameters themselves. The requirements of a nominal experimental setup to test the unitarity of $V$ are briefly discussed.

In our previous paper I (del Valle–Turbiner, 2019) a formalism was developed to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)=\frac{1}{g^2}\widehat{V}(gr)$. It was based on the Perturbation Theory (PT) in powers of $g$ (weak coupling regime) and in inverse, fractional powers of $g$ (strong coupling regime) in both $r$-space and in $(gr)$-space, respectively. As a result, the Approximant was introduced — a locally-accurate uniform compact approximation of a wave function. If taken as a trial function in variational calculations, it has led to variational energies of unprecedented accuracy for cubic anharmonic oscillator. In this paper, the formalism is applied to both quartic and sextic, spherically-symmetric radial anharmonic oscillators with two term potentials $V(r)=r^2+g^{2(m-1)}{r}^{2m}$, $m=2,3$, respectively. It is shown that a two-parametric Approximant for quartic oscillator and a five-parametric one for sextic oscillator for the first four eigenstates used to calculate the variational energy are accurate in 8–12 figures for any $D=1,2,3,\dots$ and $g\ge 0$, while the relative deviation of the Approximant from the exact eigenfunction is less than $10^{-6}$ for any $r\ge 0$.

In electromagnetism, the Faraday tensor $F_{ab}$ can be constructed from the vector potential $A_a$, it is possible to add term to the Lagrangian depending on $A_a$ but not its derivatives called Chern–Simons terms. In gravitation, the Weyl tensor $C_{abcd}$ can be constructed from the Lanczos potential $H_{abc}$, I pursue the analogy to see if terms of Chern–Simons form can be added to the Lagrangian.

A new tensor $D$ is introduced which is constructed from the Lanczos potential and is of the same form as that of the Weyl tensor $C$ expressed in terms of the Lanczos potential except that covariant differentiation is replaced by transvection with a vector $v$. The new tensor has associated invariants $C\cdot D$ and $D^2$, the first of these can be interpreted as a Chern–Simons term for Weyl $C^2$ gravity. Both invariants allow various tensors to be constructed and some of their properties are investigated by using exact examples.

In $N=1$ supergravity, the scalar potential may have supersymmetric (SUSY) and nonsupersymmetric Minkowski vacua (associated with supersymmetric and physical phases) with vanishing energy density. In the supersymmetric Minkowski (second) phase, some breakdown of SUSY may be induced by nonperturbative effects in the observable sector that give rise to a tiny positive vacuum energy density. Postulating the exact degeneracy of the physical and second vacua as well as assuming that at high energies the couplings in both phases are almost identical, one can estimate the dark energy density in these vacua. It is mostly determined by the SUSY breaking scale $M_S$ in the physical phase. Exploring the two-loop renormalization group (RG) flow of couplings in these vacua, we find that the measured value of the cosmological constant can be reproduced if $M_S$ varies from 20 TeV to 400 TeV. We also argue that this prediction for the SUSY breaking scale is consistent with the upper bound on $M_S$ in the higgsino dark matter scenario.

Holoraumy is a tool being developed for dimensional enhancement (supersymmetry holography) where the goal is to build higher-dimensional supersymmetric multiplets from lower-dimensional supersymmetric multiplets. In this paper, for the first time we investigate holoraumy for on-shell supersymmetry. Specifically, the holoraumy tensors for a number of familiar 4D, ${𝒩}=1$ multiplets are calculated. It is shown in all of these cases of on-shell theories, the holoraumy is of the form of an electromagnetic duality charge multiplying a composite transformation involving an electromagnetic duality rotation through an angle of $\pi /2$ times a space–time translation. The details of our calculations can be found at the HEPTHools Data Repository.

Pedrosa et al.¹ have recently used a ${𝒫}{𝒯}$ symmetric linear invariant to study a unidimensional time-dependent ${𝒫}{𝒯}$ symmetric harmonic oscillator with a complex time-dependent ${𝒫}{𝒯}$ symmetric external force. We show in this comment that the normalization condition of the eigenfunctions of the invariant is not verified as claimed in Ref. 1. In order to obtain the normalization condition, we introduce a novel concept of the pseudoparity-time (pseudo-${𝒫}{𝒯}$) symmetry.