International Journal of Modern Physics A

Our 2003 “Cicerone” had discussed charm dynamics with different directions and levels.¹ Here we focus on two items, where the “landscape” has changed sizably. (a) The lifetimes and semileptonic decays of charm hadrons show the impact of nonperturbative QCD and to which degree one can apply heavy quark expansion (HQE) for charm hadrons. It is more complex as we have learnt from 2019/20 data. (b) CP asymmetry has been established in 2019:² $\mathrm{\Delta }{A}_{CP}\equiv A_{CP}(D^0\to K^{+}{K}^{-})-A_{CP}(D^0\to {\pi }^{+}{\pi }^{-})=-(1.54\pm 0.29)\cdot 10^{-3}$ is quite an achievement by the LHCb collaboration! Our community is at the beginning of a long travel for fundamental dynamics. Can the SM account for these? We discuss the assumptions that were made up to 2018 data and new conclusions from 2019/20 ones. We need more data; however, one has to discuss correlations between different transitions. We give an Appendix, what we have learnt for large CP asymmetry in $K_L\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$.

The moduli space of the maximally supersymmetric heterotic string in $d$-dimensional Minkowski space contains various components characterized by the rank of the gauge symmetries of the vacua they parametrize. We develop an approach for describing in a unified way continuous Wilson lines which parametrize a component of the moduli space, together with discrete deformations responsible for the switch from one component to the other. Applied to a component that contains vacua with $SO(2n+1)$ gauge-symmetry factors, our approach yields a description of all backgrounds of the component in terms of free-orbifold models. The orbifold generators turn out to act symmetrically or asymmetrically on the internal space, with or without discrete torsion. Our derivations use extensively affine characters of $SO(2n+1)$. As a by-product, we find a peculiar orbifold description of the heterotic string in 10 dimensions, where all gauge degrees of freedom arise as twisted states, while the untwisted sector reduces to the gravitational degrees of freedom.

In this article, we study the $Z_c(3900)$ with the QCD sum rules in details by including the two-particle scattering state contributions and nonlocal effects between the diquark and antidiquark constituents. The two-particle scattering state contributions cannot saturate the QCD sum rules at the hadron side, the contribution of the $Z_c(3900)$ plays an unsubstitutable role, we can saturate the QCD sum rules with or without the two-particle scattering state contributions. If there exists a repulsive barrier or spatial distance between the diquark and antidiquark constituents, the Feynman diagrams can be divided into the factorizable and nonfactorizable diagrams. The factorizable diagrams consist of two-colored clusters and lead to a stable tetraquark state. The nonfactorizable Feynman diagrams correspond to the tunneling effects, which play a minor important role in the QCD sum rules, and are consistent with the small width of the $Z_c(3900)$. It is feasible to apply the QCD sum rules to study the tetraquark states, which begin to receive contributions at the order ${𝒪}({\alpha }_s^0)$, not at the order ${𝒪}({\alpha }_s^2)$.

Kaluza–Klein fields characterizing, from a four-dimensional viewpoint, the presence of compact universal extra dimensions would alter low-energy observables through effects determined by some compactification scale, $R^{-1}$, since the one-loop level, thus being particularly relevant for physical phenomena forbidden at tree level by the Standard Model. This paper explores, for the case of one universal extra dimension, such new-physics contributions to Higgs decays $h^{(0)}\to q_{\alpha }^{(0)}{q}_{\beta }^{(0)}$, into pairs of quarks with different flavors, a sort of decay process which, in the Standard Model, strictly occurs at the loop level. Finite results, decoupling as $R^{-1}\to \infty$, are calculated. Approximate short expressions, valid for large compactification scales, are provided. We estimate that Kaluza–Klein contributions lie below predictions from the Standard Model, being about 2 to 3 orders of magnitude smaller for compactification scales within $1.4\mathrm{\text{TeV}}<R^{-1}<10\mathrm{\text{TeV}}$.

Numerically estimating the integral of functions in high dimensional spaces is a nontrivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present an Adaptive Harmonic Mean Integration (AHMI) algorithm. Given samples drawn according to a probability distribution proportional to the function, the algorithm will estimate the integral of the function and the uncertainty of the estimate by applying a harmonic mean estimator to adaptively chosen regions of the parameter space. We describe the algorithm and its mathematical properties, and report the results using it on multiple test cases.

We study the integrability from the spectral form factor in the Chern–Simons formulation. The effective action in the higher spin sector was not derived so far. Therefore, we begin from the SL(3) Chern–Simons higher spin theory. Then the dimensional reduction in this Chern–Simons theory gives the SL(3) reparametrization invariant Schwarzian theory, which is the boundary theory of an interacting theory between the spin-2 and spin-3 fields at the infrared or massless limit. We show that the Lorentzian SL(3) Schwarzian theory is dual to the integrable model, SL(3) open Toda chain theory. Finally, we demonstrate the application of open Toda chain theory from the SL(2) case. The numerical result shows that the spectral form factor loses the dip-ramp-plateau behavior, consistent with integrability. The spectrum is not a Gaussian random matrix spectrum. We also give an exact solution of the spectral form factor for the SL(3) theory. This solution provides a similar form to the SL(2) case for $\beta \ne 0$. Hence the SL(3) theory should also do not have a Gaussian random matrix spectrum.

We observe a new puzzling physical phenomenon in F-theory on the multisection geometry, wherein a model without a gauge group transitions to another model with a discrete ${\mathbb{Z}}_n$ gauge group via Higgsing. This phenomenon may suggest an unknown aspect of F-theory compactification on multisection geometry lacking a global section. A possible interpretation of this puzzling physical phenomenon is proposed in this note. We also propose a possible interpretation of another unnatural physical phenomenon observed for F-theory on four-section geometry, wherein a discrete ${\mathbb{Z}}_2$ gauge group transitions to a discrete ${\mathbb{Z}}_4$ gauge group via Higgsing as described in the previous literature.

In this paper we describe RooFitUnfold, an extension of the RooFit statistical software package to treat unfolding problems, and which includes most of the unfolding methods that commonly used in particle physics. The package provides a common interface to these algorithms as well as common uniform methods to evaluate their performance in terms of bias, variance and coverage. In this paper we exploit this common interface of RooFitUnfold to compare the performance of unfolding with the Richardson–Lucy, Iterative Dynamically Stabilized, Tikhonov, Gaussian Process, bin-by-bin and inversion methods on several example problems.

In our recent publications, the partition function of the Gross–Witten–Wadia unitary matrix model with the logarithmic term has been identified with the $\tau$ function of a certain Painlevé system, and the double scaling limit of the associated discrete Painlevé equation to the critical point provides us with the Painlevé II equation. This limit captures the critical behavior of the $su(2)$, $N_f=2$, ${𝒩}=2$ supersymmetric gauge theory around its Argyres–Douglas 4D superconformal point. Here, we consider further extension of the model that contains the $k$th multicritical point and that is to be identified with ${Â}_{2k,2k}$ theory. In the $k=2$ case, we derive a system of two ODEs for the scaling functions to the free energy, the time variable being the scaled total mass and make a consistency check on the spectral curve on this matrix model.