Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet-Singlet and Singlet-Triplet Excitation Energies

<div> <div> <div> <p>Following the work on spin-component and spin-opposite scaled (SCS/SOS) global double hybrids for singlet-singlet excitations by Schwabe and Goerigk [J. Chem. Theory Comput. 2017, 13, 4307-4323] and our own works on new long-range corrected (LC) double hybrids for singlet-singlet and singlet-triplet excitations [J. Chem. Theory Comput. 2019, 15, 4735- 4744; J. Chem. Phys. 2020, 153, 064106], we present new LC double hybrids with SCS/SOS that demonstrate further improvement over previously published results and methods. We introduce new unscaled and scaled versions of different global and LC double hybrids based on Becke88 or PBE exchange combined with LYP, PBE or P86 correlation. For singlet-singlet excitations, we cross-validate them on six benchmark sets that cover small to medium-sized chromophores with different excitation types (local valence, Rydberg, and charge transfer). For singlet-triplet excitations, we perform the cross-validation on three different benchmark sets following the same analysis as in our previous work in 2020. In total, 203 unique excitations are analyzed. Our results confirm and extend those of Schwabe and Goerigk regarding the superior performance of SCS and SOS variants compared to their unscaled parents by decreasing mean absolute deviations, root-mean-square deviations or error spans by more than half and bringing absolute mean deviations closer to zero. Our SCS/SOS variants show to be highly efficient and robust for the computation of vertical excitation energies, which even outperform specialized double hybrids that also contain an LC in their perturbative part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86 functional are four of the most accurate and robust methods tested in this work and we fully recommend them for future applications. However, if the relevant SCS and SOS algorithms are not available to the user, we suggest ωB88PP86 as the best unscaled method in this work. </p> </div> </div> </div>

Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet-Singlet and Singlet-Triplet Excitation Energies

<div> <div> <div> <p>Following the work on spin-component and spin-opposite scaled (SCS/SOS) global double hybrids for singlet-singlet excitations by Schwabe and Goerigk [J. Chem. Theory Comput. 2017, 13, 4307-4323] and our own works on new long-range corrected (LC) double hybrids for singlet-singlet and singlet-triplet excitations [J. Chem. Theory Comput. 2019, 15, 4735- 4744; J. Chem. Phys. 2020, 153, 064106], we present new LC double hybrids with SCS/SOS that demonstrate further improvement over previously published results and methods. We introduce new unscaled and scaled versions of different global and LC double hybrids based on Becke88 or PBE exchange combined with LYP, PBE or P86 correlation. For singlet-singlet excitations, we cross-validate them on six benchmark sets that cover small to medium-sized chromophores with different excitation types (local valence, Rydberg, and charge transfer). For singlet-triplet excitations, we perform the cross-validation on three different benchmark sets following the same analysis as in our previous work in 2020. In total, 203 unique excitations are analyzed. Our results confirm and extend those of Schwabe and Goerigk regarding the superior performance of SCS and SOS variants compared to their unscaled parents by decreasing mean absolute deviations, root-mean-square deviations or error spans by more than half and bringing absolute mean deviations closer to zero. Our SCS/SOS variants show to be highly efficient and robust for the computation of vertical excitation energies, which even outperform specialized double hybrids that also contain an LC in their perturbative part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86 functional are four of the most accurate and robust methods tested in this work and we fully recommend them for future applications. However, if the relevant SCS and SOS algorithms are not available to the user, we suggest ωB88PP86 as the best unscaled method in this work. </p> </div> </div> </div>

Black hole evolution in quantum-gravitational framework

We found black hole evolution on a quantum-gravitational scattering framework with an aim to tackle the black hole information paradox. With this setup, various pieces of the system information are explicit from the start and unitary evolution is manifest throughout. The scattering amplitudes factorize into the perturbative part and nonperturbative part. The nonperturbative part is dominated by an instanton-type contribution, i.e., a black hole analogue of the Coleman-De Luccia’s bounce solution, and we propose that the Hawking radiation be identified with the particles generated by the vacuum decay. Our results indicate that the black hole degrees of freedom are entangled not only with the Hawking modes but also with the pre-Hawking modes. The Wald’s entropy charge measures their entanglement. The full quantum-gravitational entropy is defined as the vev of the Wald entropy charge. With this definition a shifted Page-like curve is generically generated and its quantum extension is readily defined.

Factorization of e+e− → H X cross section, differential in zh, PT and thrust, in the 2-jet limit

Factorizing the cross section for single hadron production in e+e− annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the e+e−→ H X cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in zh, PT and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (NLL) accuracy. The predictions obtained from our computation, applying the simplest and most natural ansatz to model the non-perturbative part of the TMD, are in exceptional agreement with the experimental measurements of the BELLE Collaboration. The factorization scheme we propose relates the TMD parton densities defined in 1-hadron and 2-hadron processes, restoring the possi- bility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, e+e−→ H1H2X and e+e−→ H X annihilations.

An Extended Speculation Game for the Recovery of Hurst Exponent of Financial Time Series

The speculation game is an agent-based toy model to investigate the dynamics of the financial market. Our model has achieved the reproduction of 10 of the well-known stylized facts for financial time series. However, there is also a divergence from the behavior of real market. The market price of the model tends to be anti-persistent to the initial price, resulting in the quite small value of Hurst exponent of price change. To overcome this problem, we extend the speculation game by introducing a perturbative part to the price change with the consideration of other effects besides pure speculative behaviors.

Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$

In the leading order of the large-$N$ approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ with the $\mathbb{Z}_N$ twisted boundary conditions. In our large-$N$ limit, the combination $\Lambda R$, where $\Lambda$ is the dynamical scale and $R$ is the $S^1$ radius, is kept fixed (we set $\Lambda R\ll1$ so that the perturbative expansion with respect to the coupling constant at the mass scale $1/R$ is meaningful). We extract the perturbative part from the large-$N$ expression of the gluon condensate and obtain the corresponding Borel transform $B(u)$. For $\mathbb{R}\times S^1$, we find that the Borel singularity at $u=2$, which exists in the system on the uncompactified $\mathbb{R}^2$ and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at $u=3/2$ for the compactified space $\mathbb{R}\times S^1$. The semi-classical interpretation of this peculiar singularity is not clear because $u=3/2$ is not dividable by the minimal bion action. It appears that our observation for the system on $\mathbb{R}\times S^1$ prompts reconsideration on the semi-classical bion picture of the infrared renormalon.

Analysis of the strong vertices of ΣcND∗ and ΣbNB∗ in QCD sum rules

The strong coupling constant is an important parameter that can help us understand the strong decay behaviors of baryons. In our previous work, we have analyzed the strong vertices [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in QCD sum rules. Following these works, we further analyze the strong vertices [Formula: see text] and [Formula: see text] using the three-point QCD sum rules under Dirac structures [Formula: see text] and [Formula: see text]. In this work, we first calculate strong form-factors considering contributions of the perturbative part and the condensate terms [Formula: see text], [Formula: see text] and [Formula: see text]. Then, these form-factors are used to fit into analytical functions. According to these functions, we finally determine the values of the strong coupling constants for these two vertices [Formula: see text] and [Formula: see text].

Analysis of the strong vertices of Σc∗ND and Σb∗NB in QCD sum rules

The strong coupling constants not only are important to understand the strong interactions of the heavy baryons, but can also help us reveal the nature and structure of these baryons. Additionally, researchers indeed have made great efforts to calculate some of the strong coupling constants, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], etc. In this paper, we analyze the strong vertices [Formula: see text] and [Formula: see text] using the three-point QCD sum rules under the Dirac structure of [Formula: see text]. We perform our analysis by considering the contributions of the perturbative part and the condensate terms of [Formula: see text] and [Formula: see text]. After the form factors are calculated, they are then fitted into analytical functions which are used to get the strong coupling constants for these two vertices. The final results are [Formula: see text] and [Formula: see text].

Single Spin Asymmetry in Electroproduction of J/ψ and QCD-evolved TMD's

We estimate Sivers asymmetry in low virtuality photoproduction of J/ψ using color evaporation model and taking into account Q2- evolution of transverse momentum dependent PDF's and Sivers function. There is a substantial reduction in asymmetry as compared to our previous analysis wherein the Q2-dependence came only from DGLAP evolution of collinear part of TMDs. The estimates of asymmetry are comparable to our earlier estimates in which we had used analytical solution of only an approximated form of the evolution equations. We have also estimated asymmetry using the latest parametrization by Echevarria et al. which are based on an evolution kernel in which the perturbative part is resummed to NLL accuracy.

ESTIMATING THE SIGN AND SIZE OF THE TRANSVERSE SINGLE TARGET-SPIN ASYMMETRY IN INCLUSIVE DIS

The single-spin asymmetry of unpolarized leptons scattering deep-inelastically off transversely polarized nucleons is discussed. This observable is generated by a two-photon exchange between lepton and nucleon. In a partonic description of the asymmetry the non-perturbative part is given in terms of multiparton correlations: quark-gluon correlation functions and quark-photon correlation functions. Using input from models and data fits for these twist-3 correlation functions, estimates for the single-spin asymmetries for a proton and a neutron are presented.