scholarly journals SU(3) analysis of four-quark operators: K → ππ and vacuum matrix elements

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. Pich ◽  
A. Rodríguez-Sánchez
Keyword(s):  
Dispersion Relations ◽  
Matrix Elements ◽  
Lattice Data ◽  
Kaon Decays ◽  
Spectral Functions ◽  
Penguin Contribution ◽  
Electroweak Penguin ◽  
Dynamical Parameters ◽  
Analytical Approaches ◽  
Dynamical Origin

Abstract Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in τ-decay analyses. Using an SU(3)L ⊗ SU(3)R decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio ε′/ε, using the measured hadronic spectral functions in τ decay. Second, we fit our SU(3) dynamical parameters to the most recent lattice data on K → ππ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the ∆I = $$ \frac{1}{2} $$ 1 2 enhancement, confirming old suggestions about its underlying dynamical origin.

scholarly journals EXTENDED ANALYSIS OF THE “PENGUIN” PART OF THE K→ππ AMPLITUDE

1995 ◽  
Vol 10 (28) ◽  
pp. 4065-4086 ◽  
Author(s):  
A.A. PENIN ◽  
A.A. PIVOVAROV
Keyword(s):  
Theoretical Description ◽  
Effective Theory ◽  
Interaction Matrix ◽  
Matrix Elements ◽  
Kaon Decays ◽  
Penguin Contribution ◽  
The Standard Model ◽  
Penguin Operator ◽  
Extended Analysis

We make an attempt to clarify the role of the annihilation or “penguin” mode in the description of the K→ππ decay within the Standard Model. Attention is centered on new operators in the effective ΔS=1 Hamiltonian and the violation of factorization for mesonic matrix elements of the local four-quark operators. We propose a regular method to evaluate the mesonic matrix elements of K→ππ transitions based on the study of three-point correlators via QCD sum rules using the chiral effective theory as an underlying low energy model for strong interaction. Matrix elements of the QCD penguin operator are calculated within this approach. The total “penguin” contribution is found to be relatively large, which improves the theoretical description of the ΔI=1/2 rule in nonleptonic kaon decays.

Bc → J/ψ tensor form factors at large momentum recoil

2021 ◽  
pp. 2150135
Author(s):  
Dandan Shen ◽  
Huimin Ren ◽  
Fan Wu ◽  
Ruilin Zhu
Keyword(s):  
Form Factors ◽  
Distance Matrix ◽  
Relativistic Correction ◽  
Large Momentum ◽  
Matrix Elements ◽  
Leading Order ◽  
Lattice Data ◽  
Tensor Form ◽  
Long Distance ◽  
Current Form

We present a next-to-leading order (NLO) relativistic correction to [Formula: see text] tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears [Formula: see text] with [Formula: see text] matrices [Formula: see text] in the [Formula: see text] transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for [Formula: see text] meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil.

scholarly journals On the determination of nonleptonic kaon decays from K→π matrix elements

2000 ◽  
Vol 2000 (08) ◽  
pp. 023-023 ◽  
Author(s):  
Maarten Golterman ◽  
Elisabetta Pallante
Keyword(s):  
Matrix Elements ◽  
Kaon Decays

Causal amplitudes and the Yang-Feldman formalism

1957 ◽  
Vol 53 (4) ◽  
pp. 843-847 ◽  
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Field Theory ◽  
Green’S Functions ◽  
Free Field ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
Field Equations ◽  
Commutation Relations ◽  
The Matrix ◽  
Free Fields ◽  
Set Up

ABSTRACTThe Yang-Feldman formalism vising the Feynman-like Green's functions is set up. The corresponding free fields have non-trivial commutation relations and contain information about the scattering. S-matrix elements are simply the matrix elements of anti-normal products of the field φF′(x). These are evaluated, and they give directly expressions used in the theory of causality and dispersion relations. It is possible to formulate field theory in a form in which the fields obey free field equations and the effects of interaction are contained in their commutation relations.

Some QCD/gravity intersections

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645032
Author(s):  
O. V. Teryaev
Keyword(s):  
Equivalence Principle ◽  
Energy Momentum Tensor ◽  
Form Factors ◽  
Momentum Tensor ◽  
Matrix Elements ◽  
Lattice Data ◽  
Hadron Structure ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Quark Transverse Momentum

Gravitational form factors are the matrix elements of the Belinfante energy momentum tensor (EMT) which naturally incorporate the hadron structure and the equivalence principle. The relocalization property allowing to transform EMT to the Belinfante form provides the “kinematical” counterpart of the famous [Formula: see text] problem. The equivalence principle may be approximately valid for quarks and gluons separately in non-perturbative (NP)QCD, and this conjecture is supported by the experimental and lattice data. The extra-dimensional gravity leading to holographic AdS/QCD is supporting the relation of quark transverse momentum to the Regge slope, discovered by V.N. Gribov.

scholarly journals Two-current correlations in the pion in the Nambu and Jona-Lasinio model

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Aurore Courtoy ◽  
Santiago Noguera ◽  
Sergio Scopetta
Keyword(s):  
High Energy ◽  
Low Energy ◽  
Matrix Elements ◽  
Lattice Data ◽  
Energy Matrix ◽  
Parton Distributions ◽  
Factorization Approximation ◽  
Lattice Result ◽  
Villars Regularization ◽  
Current Correlations

AbstractWe present an analysis of two-current correlations for the pion in the Nambu–Jona-Lasinio model, with Pauli–Villars regularization. We provide explicit expressions in momentum space for two-current correlations corresponding to the zeroth component of the vector Dirac bilinear in the quark vertices, which has been evaluated on the lattice, thinking to applications in a high energy framework, as a step towards the calculation of pion double parton distributions. The numerical results show a remarkable qualitative agreement with recent lattice data. The factorization approximation into one-body currents is discussed based on previous evaluation of the relevant low energy matrix elements in the Nambu–Jona-Lasinio model, confirming the lattice result.

scholarly journals BELLE B PHYSICS RESULTS

2002 ◽  
Vol 17 (22) ◽  
pp. 2967-2981 ◽  
Author(s):  
◽  
H. TAJIMA
Keyword(s):  
B Physics ◽  
Rare Decay ◽  
Matrix Elements ◽  
Decay Modes ◽  
Electroweak Penguin ◽  
Belle Experiment

B physics results from the Belle experiment are reviewed. Precise measurements of Cabbibo-Kobayashi-Maskawa matrix elements are made. Several decay modes are observed which will enable us to measure the CP angles ϕi in channels other than B0 → ψK0 modes. New rare decay modes are observed in many channels. Particular attention is paid to the first observation of the electroweak penguin-mediated decay.

Mass Radius of the Nucleon

1972 ◽  
Vol 50 (11) ◽  
pp. 1163-1168 ◽  
Author(s):  
M. G. Hare ◽  
G. Papini
Keyword(s):  
Mass Distribution ◽  
Intermediate State ◽  
Energy Momentum Tensor ◽  
Form Factors ◽  
Momentum Tensor ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
State Expansion ◽  
The Matrix ◽  
The Mean

The mean radius of the mass distribution of the nucleon is determined to be [Formula: see text]. The calculation makes use of sidewise, unsubtracted, threshold dominated dispersion relations for the form factors appearing in the matrix elements of the contracted energy–momentum tensor. It uses a π meson–nucleon intermediate state expansion.

Sign in / Sign up

Export Citation Format

Share Document