scholarly journals Operator product expansion and the short distance behavior of 3-flavor baryon potentials

2010 ◽  
Vol 2010 (9) ◽  
Author(s):  
Sinya Aoki ◽  
Janos Balog ◽  
Peter Weisz
Keyword(s):  
Operator Product Expansion ◽  
Short Distance ◽  
Operator Product ◽  
Distance Behavior

scholarly journals SHORT DISTANCE REPULSION AMONG BARYONS

2013 ◽  
Vol 22 (05) ◽  
pp. 1330012 ◽  
Author(s):  
SINYA AOKI ◽  
JANOS BALOG ◽  
TAKUMI DOI ◽  
TAKASHI INOUE ◽  
PETER WEISZ
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Lattice Qcd ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Results ◽  
Wave Functions ◽  
Operator Product ◽  
Distance Behavior

We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu–Bethe–Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distance behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion (OPE) and a renormalization group (RG) analysis in the perturbation theory (PT) of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.

scholarly journals NEW INSIGHTS CONCERNING DIMENSION EIGHT EFFECTS IN WEAK DECAYS

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1228-1230
Author(s):  
JOHN F. DONOGHUE
Keyword(s):  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Estimate ◽  
Dimensional Regularization ◽  
Operator Product ◽  
Higher Dimension ◽  
Matrix Elements ◽  
Weak Decays ◽  
The Matrix ◽  
Weak Operator

Most past work on weak nonleptonic decays has mixed dimensional regularization in the weak operator product expansion with some form of a cutoff regularization in the evaluation of the matrix elements. Even with the usual technique of matching the two schemes, this combination misses physics at short distance which can be described by dimension eight (and higher dimension) operators. I describe some recent work with V. Cirigliano and E. Golowich which clarifies these effects and provides a numerical estimate suggesting that they are important.

scholarly journals The two-loop perturbative correction to the (g − 2)μ HLbL at short distances

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Johan Bijnens ◽  
Nils Hermansson-Truedsson ◽  
Laetitia Laub ◽  
Antonio Rodríguez-Sánchez
Keyword(s):  
Electromagnetic Field ◽  
Perturbative Qcd ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Operator Product ◽  
Quark Loop ◽  
Perturbative Correction ◽  
Massless Quark ◽  
Leading Term ◽  
Perturbative Corrections

Abstract The short-distance behaviour of the hadronic light-by-light (HLbL) contribution to (g − 2)μ has recently been studied by means of an operator product expansion in a background electromagnetic field. The leading term in this expansion has been shown to be given by the massless quark loop, and the non-perturbative corrections are numerically very suppressed. Here, we calculate the perturbative QCD correction to the massless quark loop. The correction is found to be fairly small compared to the quark loop as far as we study energy scales where the perturbative running for the QCD coupling is well-defined, i.e. for scales μ ≳ 1 GeV. This should allow to reduce the large systematic uncertainty associated to high-multiplicity hadronic states.

scholarly journals Short-distance constraints for HLbL in muon g-2

2022 ◽  
Vol 258 ◽  
pp. 06005
Author(s):  
Johan Bijnens ◽  
Nils Hermansson-Truedsson ◽  
Antonio Rodríguez-Sánchez
Keyword(s):  
Operator Product Expansion ◽  
Short Distance ◽  
Operator Product ◽  
Quark Loop ◽  
Distance Constraints ◽  
Analytic Evaluation ◽  
Power Corrections ◽  
Low Energies ◽  
Model Independent

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.

scholarly journals Implications of tau data for CP violation in K decays

2019 ◽  
Author(s):  
Antonio Rodríguez Sánchez
Keyword(s):  
Cp Violation ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Chiral Limit ◽  
Operator Product ◽  
Distance Constraint ◽  
Matrix Elements ◽  
Kaon Decays ◽  
The Matrix

The \bm{D=6}𝐃=6 contribution of the Operator Product Expansion (OPE) of the \bm{\mathrm{VV-AA}}VV−AA correlator of quark currents can be related to hadronic matrix elements associated to CP violation in non-leptonic kaon decays. We use those relations to find an updated value for \bm{\langle(\pi\pi)_{I=2}|\mathcal{Q}_{8}|K\rangle}⟨(𝛑𝛑)𝐈=2|𝒬8|𝐊⟩ in the chiral limit using the updated ALEPH spectral function. Taking instead values of the matrix elements from the lattice to obtain the \bm{D=6}𝐃=6 vacuum elements provides a new short-distance constraint that allows for an inclusive determination of \bm{f_{\pi}}𝐟𝛑 and an updated value for the \bm{D=8}𝐃=8 condensate.

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.

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