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.

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.

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.

An Operator Product Expansion for Form Factors II. Born level

Form factors in planar $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in [1]. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.

Causality, crossing and analyticity in conformal field theories

Analyticity and crossing properties of four-point function are investigated in conformal field theories in the frameworks of Wightman axioms. A Hermitian scalar conformal field, satisfying the Wightman axioms, is considered. The crucial role of microcausality in deriving analyticity domains is discussed and domains of analyticity are presented. A pair of permuted Wightman functions are envisaged. The crossing property is derived by appealing to the technique of analytic completion for the pair of permuted Wightman functions. The operator product expansion of a pair of scalar fields is studied and analyticity property of the matrix elements of composite fields, appearing in the operator product expansion, is investigated. An integral representation is presented for the commutator of composite fields where microcausality is a key ingredient. Three fundamental theorems of axiomatic local field theories; namely, PCT theorem, the theorem proving equivalence between PCT theorem and weak local commutativity and the edge-of-the-wedge theorem are invoked to derive a conformal bootstrap equation rigorously.

Hexagon bootstrap in the double scaling limit

We study the six-particle amplitude in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory in the double scaling (DS) limit, the only nontrivial codimension-one boundary of its positive kinematic region. We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation. Expanding the latter in the collinear boundary of the DS limit, and using the Pentagon Operator Product Expansion, we compute the non-divergent coefficient of a certain component of the Next-to-Maximally-Helicity-Violating amplitude through weight 12 and eight loops. We also specialize our results to the overlapping origin limit, observing a general pattern for its leading divergences.

Celestial operator products of gluons and gravitons

The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein–Yang–Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.