Short-distance constraints for HLbL in muon g-2

Model-independent short-distance constraints allow for a reduction of theoretical uncertainties associated to the analytic evaluation of Hadronic Light-by-Light contributions to the muon g-2. In this talk we focus on the region where the three loop virtualities are large. Even when the fourth photon leg is soft, we show how a precise Operator Product Expansion can be applied in that region. The leading contribution is found to be given by the quark loop, while the evaluation of both gluonic and power corrections show how the expansion is well behaved at relatively low energies, where significant contributions to the muon g-2 remain. Numerical values for them are also presented.

Does vacuum saturation work for the higher-dimensional vacuum condensates in the QCD sum rules?

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the [Formula: see text]-type and [Formula: see text]-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter [Formula: see text] to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the [Formula: see text] leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.

A model-independent analysis of $$b{\rightarrow }s\mu ^{+}\mu ^{-}$$transitions with GAMBIT ’s FlavBit

The search for flavour-changing neutral current effects in B-meson decays is a powerful probe of physics beyond the Standard Model. Deviations from SM behaviour are often quantified by extracting the preferred values of the Wilson coefficients of an operator product expansion. We use the module of the package to perform a simultaneous global fit of the Wilson coefficients $$C_7$$ C 7 , $$C_9$$ C 9 , and $$C_{10}$$ C 10 using a combination of all current data on $$b{\rightarrow }s\mu ^{+}\mu ^{-}$$ b → s μ + μ - transitions. We further extend previous analyses by accounting for the correlated theoretical uncertainties at each point in the Wilson coefficient parameter space, rather than deriving the uncertainties from a Standard Model calculation. We find that the best fit deviates from the SM value with a significance of 6.6$$\sigma $$ σ . The largest deviation is associated with a vector coupling of muons to b and s quarks.

Vacuum correlators at short distances from lattice QCD

Non-perturbatively computing the hadronic vacuum polarization at large photon virtualities and making contact with perturbation theory enables a precision determination of the electromagnetic coupling at the Z pole, which enters global electroweak fits. In order to achieve this goal ab initio using lattice QCD, one faces the challenge that, at the short distances which dominate the observable, discretization errors are hard to control. Here we address challenges of this type with the help of static screening correlators in the high-temperature phase of QCD, yet without incurring any bias. The idea is motivated by the observations that (a) the cost of high-temperature simulations is typically much lower than their vacuum counterpart, and (b) at distances x3 far below the inverse temperature 1/T, the operator-product expansion guarantees the thermal correlator of two local currents to deviate from the vacuum correlator by a relative amount that is power-suppressed in (x3T). The method is first investigated in lattice perturbation theory, where we point out the appearance of an O(a2 log(1/a)) lattice artifact in the vacuum polarization with a prefactor that we calculate. It is then applied to non-perturbative lattice QCD data with two dynamical flavors of quarks. Our lattice spacings range down to 0.049 fm for the vacuum simulations and down to 0.033 fm for the simulations performed at a temperature of 250 MeV.

Efficient rules for all conformal blocks

We formulate a set of general rules for computing d-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism [1]. With these rules, the procedure for determining any conformal block of interest is reduced to (1) identifying the relevant projection operators and tensor structures and (2) applying the conformal rules to obtain the blocks. To facilitate the bookkeeping of contributing terms, we introduce a convenient diagrammatic notation. We present several concrete examples to illustrate the general procedure as well as to demonstrate and test the explicit application of the rules. In particular, we consider four-point functions involving scalars S and some specific irreducible representations R, namely 〈SSSS〉, 〈SSSR〉, 〈SRSR〉 and 〈SSRR〉 (where, when allowed, R is a vector or a fermion), and determine the corresponding blocks for all possible exchanged representations.

The AdS3 × S1 chiral ring

We study AdS3× S1× Y supersymmetric string theory backgrounds with Neveu-Schwarz-Neveu-Schwarz flux that are dual to $$ \mathcal{N} $$ N = 2 superconformal theories on the boundary. We classify all worldsheet vertex operators that correspond to space-time chiral primaries. We compute space-time chiral ring structure constants for operators in the zero spectral flow sector using the operator product expansion in the worldsheet theory. We find that the structure constants take a universal form that depends only on the topological data of the $$ \mathcal{N} $$ N = 2 superconformal theory on Y.

A 3d disordered superconformal fixed point

We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a $$ \mathcal{N} $$ N = 2 large N Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large N spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.

The ground states and the first radially excited states of D-wave vector ρ and ϕ mesons

In this paper, we first derive two QCD sum rules QCDSR I and QCDSR II which are, respectively, used to extract observable quantities of the ground states and the first radially excited states of the D-wave vector [Formula: see text] and [Formula: see text] mesons. In our calculations, we consider the contributions of vacuum condensates up to dimension-7 in the operator product expansion. The predicted masses for [Formula: see text] [Formula: see text] meson and [Formula: see text] [Formula: see text] meson are consistent well with the experimental data of [Formula: see text]([Formula: see text]) and [Formula: see text]([Formula: see text]), respectively. Besides, our analysis indicates that it is reliable to assign the recent reported [Formula: see text]([Formula: see text]) state as the [Formula: see text] [Formula: see text] meson. Finally, we obtain the decay constants of these states with QCDSR I and QCDSR II. These predictions are helpful not only to reveal the structure of the newly observed [Formula: see text]([Formula: see text]) state, but also to establish [Formula: see text] meson and [Formula: see text] meson families.

Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $$\tau $$ τ -decay data. The determination involves the double-pinched Borel–Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the $${\overline{\mathrm{MS}}}$$ MS ¯ coupling is $$\alpha _s(m_{\tau }^2) = 0.3116 \pm 0.0073$$ α s ( m τ 2 ) = 0.3116 ± 0.0073 [$$\alpha _s(M_Z^2)=0.1176 \pm 0.0010$$ α s ( M Z 2 ) = 0.1176 ± 0.0010 ] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, $$\alpha _s(m_{\tau }^2) = 0.3194 \pm 0.0167$$ α s ( m τ 2 ) = 0.3194 ± 0.0167 [$$\alpha _s(M_Z^2)=0.1186 \pm 0.0021$$ α s ( M Z 2 ) = 0.1186 ± 0.0021 ].