Light Cone Singularities and the Asymptotic Behavior of Matrix Elements of Operator Products in Momentum Space

1973 ◽  
Vol 21 (5) ◽  
pp. 205-263 ◽  
Author(s):  
Fritz Schwarz
Keyword(s):  
Asymptotic Behavior ◽  
Momentum Space ◽  
Light Cone ◽  
Matrix Elements

scholarly journals Light-cone sum rules for proton decay

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ulrich Haisch ◽  
Amando Hala
Keyword(s):  
Lattice Qcd ◽  
Light Cone ◽  
Sum Rules ◽  
State Of The Art ◽  
Form Factors ◽  
Baryon Number ◽  
Proton Decay ◽  
Matrix Elements ◽  
Decay Channels ◽  
Systematic Uncertainties

Abstract We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.

scholarly journals COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 3387-3420 ◽  
Author(s):  
G. LONGHI ◽  
M. MATERASSI
Keyword(s):  
General Relativity ◽  
Asymptotic Behavior ◽  
Harmonic Analysis ◽  
Momentum Space ◽  
Conserved Quantities ◽  
Canonical Transformations ◽  
Collective Variables ◽  
Klein Gordon ◽  
Definition Of

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9

scholarly journals Wave-packet propagation in momentum space: Calculation of sharp-energyS-matrix elements

1992 ◽  
Vol 46 (5) ◽  
pp. 2304-2316 ◽  
Author(s):  
Zeki C. Kuruoğlu ◽  
F. S. Levin
Keyword(s):  
Wave Packet ◽  
Momentum Space ◽  
Matrix Elements

Light-Cone Singularities and Asymptotic Domains of Momentum Space

1973 ◽  
Vol 7 (10) ◽  
pp. 3091-3104 ◽  
Author(s):  
Patrizio Vinciarelli ◽  
Peter Weisz
Keyword(s):  
Momentum Space ◽  
Light Cone

scholarly journals Exact light-cone wavefunction representation of matrix elements of electroweak currents

1999 ◽  
Vol 543 (1-2) ◽  
pp. 239-252 ◽  
Author(s):  
Stanley J. Brodsky ◽  
Dae Sung Hwang
Keyword(s):  
Light Cone ◽  
Matrix Elements

scholarly journals One-loop structure of parton distribution for the gluon condensate and “zero modes”

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Anatoly Radyushkin ◽  
Shuai Zhao
Keyword(s):  
Gauge Invariance ◽  
Parton Distribution ◽  
Light Cone ◽  
Zero Mode ◽  
Gluon Condensate ◽  
Loop Structure ◽  
Matrix Elements ◽  
Zero Modes ◽  
Strict Compliance ◽  
Evolution Kernel

Abstract We present results for one-loop corrections to the recently introduced “gluon condensate” PDF F(x). In particular, we give expression for the gg-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No “zero mode” δ(x) terms were found for the twist-4 gluon PDF F(x). However a q2δ(x) term was found for the ξ = 0 GPD F(x, q2) at nonzero momentum transfer q. Overall, our results do not agree with the original attempt of one-loop calculations of F(x) for gluon states, which sets alarm warning for calculations that use matrix elements with virtual external gluons and for lattice renormalization procedures based on their results.

DOMINANCE OF LONG DISTANCE EFFECTS IN THE KL-KS MASS DIFFERENCE

1990 ◽  
Vol 05 (19) ◽  
pp. 1477-1483 ◽  
Author(s):  
K. TERASAKI ◽  
S. ONEDA
Keyword(s):  
Asymptotic Behavior ◽  
Vector Meson ◽  
Ground State ◽  
Mass Shell ◽  
Mass Difference ◽  
Matrix Elements ◽  
Long Distance ◽  
Distance Effects ◽  
Intermediate States ◽  
The Matrix

It is argued that the asymptotic behavior of the matrix elements of Hw involving on-mass-shell ground-state mesons with infinite momenta, which were instrumental in explaining the |ΔI|=1/2 rule in the K→ππ decays, actually implies [Formula: see text]. The long distance effects (contributions of PS and vector meson poles and ππ intermediate states) may reproduce the observed KL−Ks mass difference, consistent with the |ΔI|=1/2 rule. Its estimate is however sensitive to the η-η′-… mixing.

scholarly journals Momentum space CFT correlators for Hamiltonian truncation

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Nikhil Anand ◽  
Zuhair U. Khandker ◽  
Matthew T. Walters
Keyword(s):  
Momentum Space ◽  
Hypergeometric Functions ◽  
Arbitrary Spin ◽  
Direct Application ◽  
Hamiltonian Matrix ◽  
Infinite Volume ◽  
Matrix Elements ◽  
Hamiltonian Density ◽  
Strongly Coupled ◽  
Finite Sums

Abstract We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding to a Hamiltonian density) carries zero spatial momentum, but otherwise allowing operators to have arbitrary spin. A direct application of our formulas is the computation of Hamiltonian matrix elements within the framework of conformal truncation, a recently proposed method for numerically studying strongly-coupled QFTs in real time and infinite volume. Our momentum space formulas take the form of finite sums over 2F1 hypergeometric functions, allowing for efficient numerical evaluation. As a concrete application, we work out matrix elements for 3d ϕ4-theory, thus providing the seed ingredients for future truncation studies.

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