Non-perturbative quantum geometry II

The Nekrasov-Shatashvili limit of β -ensembles with polynomial potential and N = 2 $$\mathcal{N}=2$$ supersymmetric gauge theories in the Ω-background is intimately related to complex one-dimensional quantum mechanics. Multi-instanton corrections in quantum mechanics, inferable from exact quantization conditions, imply additional non-perturbative corrections to the Nekrasov-Shatashvili free energies. Besides filling some of the gaps in previous derivations, we present analytic expressions for such additional non-perturbative corrections in the case of SU(2) gauge theory expanded at strong coupling. In contrast, at weak coupling these additional non-perturbative corrections appear to be negligible

The static quark potential from the gauge independent Abelian decomposition

We investigate the relationship between colour confinement and the gauge independent Cho–Duan–Ge Abelian decomposition. The decomposition is defined in terms of a colour field n ; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential

The static quark potential from the gauge invariant Abelian decomposition

We investigate the relationship between colour confinement and topological structures derived from the gauge invariant Abelian (Cho–Duan–Ge) decomposition. This Abelian decomposition is made imposing an isometry on a colour field n which selects the Abelian direction; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson loop. This allows us to establish an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. By using Stokesʼ theorem, we can relate the Wilson loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by topological structures, which occur when one of the parameters parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these objects will lead to an area law scaling for the Wilson loop and provide a mechanism for quark confinement. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and find that the restricted field strength is dominated by peaks on the lattice. Wilson loops containing these peaks show a stronger area-Law and thus provide the dominant contribution to the string tension

More is different: Reconciling eV sterile neutrinos with cosmological mass bounds

It is generally expected that adding light sterile species would increase the effective number of neutrinos, Neff . In this paper we discuss a scenario that Neff can actually decrease due to the neutrino oscillation effect if sterile neutrinos have self-interactions. We specifically focus on the eV mass range, as suggested by the neutrino anomalies. With large self-interactions, sterile neutrinos are not fully thermalized in the early Universe because of the suppressed effective mixing angle or matter effect. As the Universe cools down, flavor equilibrium between active and sterile species can be reached after big bang nucleosynthesis (BBN) epoch, but leading to a decrease of Neff . In such a scenario, we also show that the conflict with cosmological mass bounds on the additional sterile neutrinos can be relaxed further when more light species are introduced. To be consistent with the latest Planck results, at least 3 sterile species are needed

Witten index and wall crossing

We compute the Witten index of one-dimensional gauged linear sigma models with at least N $$\mathcal{N}$$ = 2 supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied through the phase boundaries. The wall crossing formula is expressed as an integral at infinity of the Coulomb branch. The result is applied to many examples, including quiver quantum mechanics that is relevant for BPS states in d = 4 N $$\mathcal{N}$$ =2 theories

Lepton flavour violating signature in supersymmetric U(1) ′ seesaw models at the LHC

We consider a U(1) ′ supersymmetric seesaw model in which a right-handed sneutrino is a thermal dark matter candidate whose relic density can be in the right range due to its coupling to relatively light Z ˜ ′ $$\tilde{Z}^{\prime }$$ , the superpartner of the extra gauge boson Z ′ . Such light Z ˜ ′ $$\tilde{Z}^{\prime }$$ can be produced at the LHC through cascade decays of colored superparticles, in particular, stops and sbottoms, and then decay to a right-handed neutrino and a sneutrino dark matter, which leads to lepton flavor violating signals of same/opposite-sign dileptons (or multileptons) accompanied by large missing energy. Taking some benchmark points, we analyze the opposite- and same-sign dilepton signatures and the corresponding flavour difference i.e., (2 e − 2 μ ). It is shown that 5 σ signal significance can be reached for some benchmark points with very early data of ∼ 2 fb −1 integrated luminosity. In addition, 3 ℓ and 4 ℓ signatures also look promising to check the consistency in the model prediction, and it is possible to reconstruct the Z ˜ ′ $$\tilde{Z}^{\prime }$$ mass from jjℓ invariant mass distribution

Disentangling Higgs-top couplings in associated production

In the presence of CP violation, the Higgs-top coupling may have both scalar and pseudoscalar components, κ t and ${{\widetilde{\kappa}}_t}$ , which are bounded indirectly but only weakly by the present experimental constraints on the Higgs-gluon-gluon and Higgs-γ-γ couplings, whereas upper limits on electric dipole moments provide strong additional indirect constraints on ${{\widetilde{\kappa}}_t}$ , if the Higgs-electron coupling is similar to that in the Standard Model and there are no cancellations with other contributions. We discuss methods to measure directly the scalar and pseudoscalar Higgs-top couplings by measurements of Higgs production in association with $\overline{t}t$ , single t and single $\overline{t}$ at the LHC. Measurements of the total cross sections are very sensitive to variations in the Higgs-top couplings that are consistent with the present indirect constraints, as are invariant mass distributions in $\overline{t}tH$ , tH and $\overline{t}H$ final states. We also investigate the additional information on κ t and ${{\widetilde{\kappa}}_t}$ that could be obtained from measurements of the longitudinal and transverse t polarization in the different associated production channels, and the $\overline{t}t$ spin correlation in $\overline{t}tH$ events

Bethe states for the two-site Bose–Hubbard model: A binomial approach

We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2) -invariant R -matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n -th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed

Search for B decays to final states with the η c meson

We report a search for B decays to selected final states with the η c meson: B ± → K ± η c π + π − , B ± → K ± η c ω , B ± → K ± η c η and B ± → K ± η c π 0 . The analysis is based on 772 × 10 6 B B ¯ $$B\overline{B}$$ pairs collected at the Υ(4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. We set 90% confidence level upper limits on the branching fractions of the studied B decay modes, independent of intermediate resonances, in the range (0 . 6–5 . 3) × 10 −4 . We also search for molecular-state candidates in the D 0 D ¯ ∗ 0 − D ¯ 0 D ∗ 0 , D 0 D ¯ 0 + D ¯ 0 D 0 $${D}^0{\overline{D}}^{\ast 0}-{\overline{D}}^0{D}^{\ast 0},{D}^0{\overline{D}}^0+{\overline{D}}^0{D}^0$$ and D ∗ 0 D ¯ ∗ 0 + D ¯ ∗ 0 D ∗ 0 $${D}^{\ast 0}{\overline{D}}^{\ast 0}+{\overline{D}}^{\ast 0}{D}^{\ast 0}$$ combinations, neutral partners of the Z (3900) ± and Z (4020) ± , and a poorly understood state X (3915) as possible intermediate states in the decay chain, and set 90% confidence level upper limits on the product of branching fractions to the mentioned intermediate states and decay branching fractions of these states in the range (0 . 6–6 . 9) × 10 −5

Measurement of branching fractions for B J / K decays and search for a narrow resonance in the J / final state

We report an observation of the and decays using pairs collected at the resonance with the Belle detector at the KEKB asymmetric-energy collider. We obtain the branching fractions and . We search for a new narrow charmonium(-like) state in the mass spectrum and find no significant excess. We set upper limits on the product of branching fractions, , at where a -odd partner of may exist, at and assuming their known mass and width, and over a range from 3.8 to . The obtained upper limits at 90 confidence level for , , and are , , and , respectively