THE OPERATOR PRODUCT EXPANSION OF THE QCD PROPAGATORS

1992 ◽  
Vol 07 (39) ◽  
pp. 3617-3630 ◽  
Author(s):  
MARTIN LAVELLE ◽  
MICHAEL OLESZCZUK
Keyword(s):  
Operator Product Expansion ◽  
Arbitrary Dimension ◽  
Light Quark ◽  
Equations Of Motion ◽  
Internal Symmetry ◽  
Operator Product ◽  
General Belief ◽  
Quark Masses ◽  
Acceleration Technique ◽  
The Status

We bring together for the first time the coefficients in covariant gauges of all the condensates of dimension four or less in the operator product expansion (OPE) of the quark, gluon and ghost propagators. It is stressed that contrary to general belief the condensates do not enter the OPE of the propagators in gauge-invariant combinations like [Formula: see text] and 〈G2〉. The results are presented in arbitrary dimension to lowest order in the light quark masses for the SU (Nc) internal symmetry group. All terms which, through the equations of motion, may be viewed as being effectively of order αs are included. The importance of the equations of motion if one is to fulfill the Slavnov-Taylor identities is demonstrated. We briefly consider the equivalent, but less complete, calculations in other gauges and give an overview of the status of the OPE of the QCD vertices. Finally we discuss what these non-perturbative structures tell us about the correct solutions of QCD and point out their significance for the Fourier acceleration technique as applied to lattice QCD.

scholarly journals M5-BRANES AND WILSON SURFACES

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2195-2196
Author(s):  
BIN CHEN
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Equations Of Motion ◽  
Soliton Solutions ◽  
High Dimensional ◽  
Operator Product ◽  
Dimensional Representation ◽  
Superconformal Field Theory ◽  
Higher Dimensional

We investigate the M5-brane description of the Wilson surface operators in six-dimensional (2,0) superconformal field theory from AdS/CFT correspondence. We consider the Wilson surface operators in high-dimensional representation, whose description could be M5-brane string soliton solutions in AdS7 × S4 background. We construct such string soliton solutions from the covariant M5-brane equations of motion and discuss their properties. The supersymmetry analysis shows that these solutions are half-BPS. Furthermore, we discuss the operator product expansion of the Wilson surface operators in higher dimensional representation using their corresponding M5-brane configurations.

scholarly journals HOW PENGUINS STARTED TO FLY

1999 ◽  
Vol 14 (30) ◽  
pp. 4705-4719 ◽  
Author(s):  
ARKADY VAINSHTEIN
Keyword(s):  
Cp Violation ◽  
Heavy Quark ◽  
Operator Product Expansion ◽  
Subsequent Development ◽  
Recent Measurement ◽  
Operator Product ◽  
Quark Masses ◽  
Weak Decays ◽  
Particle Phenomenology ◽  
History Of

A mechanism explaining a strong enhancement of nonleptonic weak decays was suggested in 1975, later to be dubbed the penguin. This mechanism extends Wilson's ideas about the operator product expansion at short distances and reveals an intricate interplay of subtle features of the theory such as heavy quark masses in Glashow–Iliopoulos–Maini cancellation, light quarks shaping the chiral properties of QCD, etc. The penguins have subsequently evolved to play a role in a variety of fields in present-day particle phenomenology. I will describe the history of this idea and review its subsequent development. The recent measurement of direct CP violation in K decays gives a new confirmation of the penguin mechanism.

scholarly journals MATCHING MESON RESONANCES TO OPE IN QCD

2006 ◽  
Vol 21 (04) ◽  
pp. 885-888 ◽  
Author(s):  
A. A. Andrianov ◽  
S. S. Afonin ◽  
D. Espriu ◽  
V. A. Andrianov
Keyword(s):  
Quantum Number ◽  
Operator Product Expansion ◽  
Principal Quantum Number ◽  
Light Quark ◽  
Low Energy ◽  
Operator Product ◽  
Regge Trajectories ◽  
Linear Behavior ◽  
Energy Constants ◽  
Perturbative Corrections

We investigate the possible corrections to the linear Regge trajectories for the light-quark meson sector by matching two-point correlators of quark currents to the Operator Product Expansion. We find that the allowed modifications to the linear behavior must decrease rapidly with the principal quantum number. After fitting the lightest states in each channel and certain low-energy constants the whole spectrum for meson masses and residues is obtained in a satisfactory agreement with phenomenology. The perturbative corrections to our results are discussed.

scholarly journals FLAG Review 2019

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
S. Aoki ◽  
Y. Aoki ◽  
D. Bečirević ◽  
T. Blum ◽  
G. Colangelo ◽  
...  
Keyword(s):  
Heavy Quark ◽  
Particle Physics ◽  
Light Quark ◽  
Form Factors ◽  
Matrix Elements ◽  
Ckm Matrix ◽  
Quark Masses ◽  
The Status ◽  
Ckm Matrix Elements

Abstract We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$f+(0) arising in the semileptonic $$K \rightarrow \pi $$K→π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$fK/fπ and its consequences for the CKM matrix elements $$V_{us}$$Vus and $$V_{ud}$$Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$SU(2)L×SU(2)R and $$SU(3)_L\times SU(3)_R$$SU(3)L×SU(3)R Chiral Perturbation Theory. We review the determination of the $$B_K$$BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$mc and $$m_b$$mb as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$αs. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

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.

scholarly journals DK I = 0, $$ D\overline{K} $$ I = 0, 1 scattering and the $$ {D}_{s0}^{\ast } $$(2317) from lattice QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gavin K. C. Cheung ◽  
◽  
Christopher E. Thomas ◽  
David J. Wilson ◽  
Graham Moir ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Scattering Amplitudes ◽  
Lattice Qcd ◽  
Finite Volume ◽  
Energy Region ◽  
Light Quark ◽  
Bound State ◽  
Vector Resonance ◽  
Quark Masses ◽  
Partial Waves

Abstract Elastic scattering amplitudes for I = 0 DK and I = 0, 1 $$ D\overline{K} $$ D K ¯ are computed in S, P and D partial waves using lattice QCD with light-quark masses corresponding to mπ = 239 MeV and mπ = 391 MeV. The S-waves contain interesting features including a near-threshold JP = 0+ bound state in I = 0 DK, corresponding to the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ (2317), with an effect that is clearly visible above threshold, and suggestions of a 0+ virtual bound state in I = 0 $$ D\overline{K} $$ D K ¯ . The S-wave I = 1 $$ D\overline{K} $$ D K ¯ amplitude is found to be weakly repulsive. The computed finite-volume spectra also contain a deeply-bound D* vector resonance, but negligibly small P -wave DK interactions are observed in the energy region considered; the P and D-wave $$ D\overline{K} $$ D K ¯ amplitudes are also small. There is some evidence of 1+ and 2+ resonances in I = 0 DK at higher energies.

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