scholarly journals Operator Product Expansion, Renormalization Group and Weak Decays

2000 ◽  
pp. 65-85 ◽  
Author(s):  
Andrzej J. Buras
Keyword(s):  
Renormalization Group ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Weak Decays

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 Nonperturbative Expansion, Renormalons and τ-Decay

1997 ◽  
Vol 12 (19) ◽  
pp. 1361-1368 ◽  
Author(s):  
H. F. Jones ◽  
A. Ritz ◽  
I. L. Solovtsov
Keyword(s):  
Renormalization Group ◽  
Physical Quantity ◽  
Operator Product Expansion ◽  
Spectral Representation ◽  
Infrared Region ◽  
Operator Product ◽  
Effective Coupling ◽  
Power Corrections

We analyze inclusive τ-decay using a modified version of the a expansion, a nonperturbative technique in which the effective coupling is analytic in the infrared region. The modification involves renormalization group improvement of the integrand in a spectral representation for the D-function prior to implementing the a expansion. The advantage of this approach is that it enables us to monitor the structure of the induced power corrections and to ensure that these are consistent with the operator product expansion. Numerically the method agrees well with experiment: the comparison is made with the physical quantity RZ using Rτ as input.

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.

SYMMETRIES OF THE RENORMALIZATION GROUP EQUATIONS AND THE SCALING LAW REVISITED

1993 ◽  
Vol 08 (32) ◽  
pp. 3017-3023
Author(s):  
P. K. JHA ◽  
K. C. TRIPATHY
Keyword(s):  
Renormalization Group ◽  
Operator Product Expansion ◽  
Scaling Laws ◽  
Scaling Law ◽  
Renormalization Group Equation ◽  
Operator Product ◽  
Electromagnetic Current ◽  
Group Equation ◽  
Infinite Dimensional ◽  
Renormalization Group Equations

The symmetry associated with the renormalization group equation satisfied by the Wilson coefficients in the operator product expansion of the electromagnetic current in deep inelastic scattering is re-examined using Blueman-Cole-Obsiannikov-Olver program. It is shown that the system exhibits infinite-dimensional symmetry. From the characteristics, we derive the detailed solutions of the renormalization group equation and the scaling laws for Wilson moments.

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