OPERATOR PRODUCT EXPANSIONS, SLAVNOV-TAYLOR IDENTITIES AND d=4 CONDENSATES

1990 ◽  
Vol 05 (09) ◽  
pp. 653-660 ◽  
Author(s):  
V.P. SPIRIDONOV
Keyword(s):  
Operator Product Expansion ◽  
Gluon Propagator ◽  
Gluon Condensate ◽  
Tree Level ◽  
Operator Product ◽  
Gluon Condensates ◽  
Slavnov Taylor Identities

Operator product expansion (OPE) for the gluon propagator and the corresponding Slavnov-Taylor identities are discussed. Tree-level contribution of the d=4 quark and bilinear in the gluon fields condensates is calculated. It is transverse without any connection between ghost and gluon condensates. Drawbacks of the previous calculations are uncovered. It is found that there is non-zero contribution of the gauge non-invariant quark-gluon condensate.

scholarly journals Renormalon-free definition of the gluon condensate within the large-$\beta_0$ approximation

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Hiroshi Suzuki ◽  
Hiromasa Takaura
Keyword(s):  
Operator Product Expansion ◽  
Density Operator ◽  
Gradient Flow ◽  
Gluon Condensate ◽  
Operator Product ◽  
Clear Definition ◽  
Lattice Data ◽  
Perturbative Calculation ◽  
Yang Mills ◽  
Definition Of

Abstract We propose a clear definition of the gluon condensate within the large-$\beta_0$ approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of $\mathcal{O}(\Lambda^4)$, which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang–Mills gradient flow.

Effective Field Theories for Heavy Quarks: Heavy Quark Effective Theory and Heavy Quark Expansion

2020 ◽  
pp. 560-615
Author(s):  
Thomas Mannel
Keyword(s):  
Heavy Quark ◽  
Particle Physics ◽  
Operator Product Expansion ◽  
Effective Field ◽  
Field Theories ◽  
Effective Theory ◽  
Tree Level ◽  
Operator Product ◽  
Heavy Quark Effective Theory ◽  
Inclusive Decays

The heavy quark effective theory (HQET) and the heavy quark expansion (HQE) have developed into the standard tools in heavy-flavour physics. The lectures in this chapter introduce the basics of the approach and illustrates the methods by discussing some of their phenomenological applications. The chapter covers construction of the HQET Lagrangian, symmetries of HQET, HQET at one loop, and HQET applications to phenomenology. It also discusses HQE inclusive decays, operator product expansion (OPE), tree-level results, HQE parameters, QCD corrections, and end-point regions. It concludes by reiterating the enormous impact that both HQET and the HQE have had on particle physics phenomenology.

scholarly journals Celestial operator products of gluons and gravitons

2021 ◽  
pp. 2140003
Author(s):  
Monica Pate ◽  
Ana-Maria Raclariu ◽  
Andrew Strominger ◽  
Ellis Ye Yuan
Keyword(s):  
Operator Product Expansion ◽  
Beta Function ◽  
Tree Level ◽  
Operator Product ◽  
Recursion Relations ◽  
Yang Mills ◽  
Euler Beta Function ◽  
Celestial Sphere ◽  
Asymptotic Symmetries

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.

scholarly journals Analysis of the triply heavy baryon states with the QCD sum rules

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Zhi-Gang Wang
Keyword(s):  
Mass Spectrum ◽  
Ground State ◽  
Operator Product Expansion ◽  
Sum Rules ◽  
Heavy Baryon ◽  
Operator Product ◽  
Qcd Sum Rules ◽  
Gluon Condensates ◽  
First Time ◽  
Vacuum Condensates

AbstractIn this article, we reexamine the mass spectrum of the ground state triply heavy baryon states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 6 in a consistent way and preforming a novel analysis. It is for the first time to take into account the three-gluon condensates in the QCD sum rules for the triply heavy baryon states.

scholarly journals Operator product expansion of the non-local gluon condensate

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
V. M. Braun ◽  
K. G. Chetyrkin ◽  
B. A. Kniehl
Keyword(s):  
Operator Product Expansion ◽  
Wilson Line ◽  
Gluon Condensate ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Distribution Functions ◽  
Operator Product ◽  
Nonlocal Operator ◽  
Expectation Value ◽  
Qcd Vacuum

Abstract We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study [1], we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.

scholarly journals High-energy operator product expansion at sub-eikonal level

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Giovanni Antonio Chirilli
Keyword(s):  
Operator Product Expansion ◽  
Evolution Equations ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Distribution Functions ◽  
Impact Factors ◽  
Operator Product ◽  
The Impact ◽  
New Distribution

Abstract The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.

scholarly journals Conformal Regge theory at finite boost

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Simon Caron-Huot ◽  
Joshua Sandor
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Exact Results ◽  
Double Integral ◽  
Regge Theory ◽  
Conformal Field ◽  
Regge Trajectories ◽  
Continuous Spins ◽  
Regge Limit

Abstract The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid even away from Regge limit. The representation extends convergence of the OPE by rewriting it as a double integral over continuous spins and dimensions, and features a novel “Regge block”. We test the formula in the conformal fishnet theory, where exact results involving nontrivial Regge trajectories are available.

Operator product expansion in the minimal subtraction scheme

1982 ◽  
Vol 119 (4-6) ◽  
pp. 407-411 ◽  
Author(s):  
K.G. Chetyrkin ◽  
S.G. Gorishny ◽  
F.V. Tkachov
Keyword(s):  
Operator Product Expansion ◽  
Operator Product ◽  
Minimal Subtraction ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme

scholarly journals OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

1999 ◽  
Vol 14 (30) ◽  
pp. 4819-4840
Author(s):  
JAN FISCHER ◽  
IVO VRKOČ
Keyword(s):  
Operator Product Expansion ◽  
Deflection Angle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Operator Product ◽  
Coupling Constant ◽  
Expectation Value ◽  
Euclidean Region ◽  
The Deflection Angle ◽  
Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

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