Accurate analytic matrix elements for anharmonic oscillators using quantum mechanical commutator relations and sum rules

1973 ◽  
Vol 59 (12) ◽  
pp. 6443-6449 ◽  
Author(s):  
R. H. Tipping
Keyword(s):  
Sum Rules ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Anharmonic Oscillators ◽  
Analytic Matrix

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.

Energy and Regge residues in quantum-mechanical ‘‘QCD’’ sum rules

1986 ◽  
Vol 33 (11) ◽  
pp. 3441-3448
Author(s):  
Bernice Durand ◽  
Loyal Durand
Keyword(s):  
Sum Rules ◽  
Quantum Mechanical ◽  
Qcd Sum Rules

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

scholarly journals Parton-hadron duality in QCD sum rules: Quantum-mechanical examples

1998 ◽  
Vol 57 (5) ◽  
pp. 2676-2690 ◽  
Author(s):  
B. Blok ◽  
M. Lublinsky
Keyword(s):  
Sum Rules ◽  
Quantum Mechanical ◽  
Qcd Sum Rules ◽  
Hadron Duality

scholarly journals Quantum mechanical sum rules for two model systems

2008 ◽  
Vol 76 (9) ◽  
pp. 798-806 ◽  
Author(s):  
M. Belloni ◽  
R. W. Robinett
Keyword(s):  
Sum Rules ◽  
Model Systems ◽  
Quantum Mechanical
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