scholarly journals Operator Product Expansion, Heavy Quarks, QCD Duality and Its Violations

1997 ◽  
Vol 12 (11) ◽  
pp. 2075-2133 ◽  
Author(s):  
B. Chibisov ◽  
R. D. Dikeman ◽  
M. Shifman ◽  
N. G. Uraltsev
Keyword(s):  
Operator Product Expansion ◽  
Background Field ◽  
Decay Rates ◽  
Operator Product ◽  
Theoretical Treatment ◽  
Heavy Flavor ◽  
Wide Range ◽  
Euclidean Domain ◽  
Inclusive Processes ◽  
Hadron Duality

The quark(gluon)–hadron duality constitutes a basis for the theoretical treatment of a wide range of inclusive processes — from hadronic τ decays and Re+e- to semileptonic and nonleptonic decay rates of heavy flavor hadrons. A theoretical analysis of these processes is carried out by using the operator product expansion in the Euclidean domain, with subsequent analytic continuation to the Minkowski domain. We formulate the notion of the quark(gluon)–hadron duality in quantitative terms, then classify various contributions leading to violations of duality. A prominent role in the violations of duality seems to belong to the so-called exponential terms which, conceptually, may represent the (truncated) tail of the power series. A qualitative model, relying on an instanton background field, is developed, allowing one to get an estimate of the exponential terms. We then discuss a number of applications, mostly from heavy quark physics.

scholarly journals Using Factorization to Estimate the Charmed Meson Decays

2016 ◽  
Vol 32 (3) ◽  
Author(s):  
Nguyen Thu Huong ◽  
Ha Huy Bang
Keyword(s):  
Operator Product Expansion ◽  
Factorization Method ◽  
Branching Ratios ◽  
Decay Rates ◽  
Operator Product ◽  
Charmed Meson ◽  
Meson Decays ◽  
Light Mesons

Abstract: Study of the charmed meson decays is mentioned in the articles [1, 2]. These researches help to improve the results of light mesons decays. In this paper, applying the factorization method, we try to estimate the branching ratios of charmed meson decays, namely . This can be an effective method for computing the decay rates of new channels. Keywords: Factorization, charmed meson decays, operator product expansion.

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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