scholarly journals Colour?Spin Matrix Elements for Multiquark Systems

1980 ◽  
Vol 33 (6) ◽  
pp. 951 ◽  
Author(s):  
RP Bickerstaff ◽  
BG Wybourne
Keyword(s):  
Classification Scheme ◽  
Spin Operator ◽  
Tensor Operator ◽  
Matrix Elements ◽  
S Wave ◽  
Strange Quarks ◽  
Colour Singlet ◽  
Singlet States ◽  
The Matrix ◽  
Relevant Interaction

Tensor operator methods have been developed for calculating the matrix elements of the two-particle colour-spin operator that arises in the calculation of the quark-gluon interaction in the MIT bagmodel treatment of the S-wave colour singlet states of multiquark hadrons. A group classification scheme for multi quark states which distinguishes the nonstrange and strange quarks, and thus avoids the occurrence of hidden strangeness ss pairs, is constructed. This scheme has the added advantage of avoiding any need to approximate the strangeness dependence of the relevant interaction integrals. The colour-spin matrix elements for all the q4 if colour singlet states and for the strangeness - 2 states of q6 are given by way of examples. A number of checking procedures have been developed to ensure the correctness of the calculated matrix elements.

New relativistic crystalline electric field effective operators

1989 ◽  
Vol 67 (6) ◽  
pp. 632-633 ◽  
Author(s):  
R. Chatterjee ◽  
H. A. Buckmaster
Keyword(s):  
Electric Field ◽  
Tensor Operator ◽  
Operator Technique ◽  
Matrix Elements ◽  
Effective Operator ◽  
Crystalline Electric Field ◽  
The Matrix ◽  
Definition Of ◽  
Effective Operators

This paper shows that the use of the Landau and Lifshitz definition of the Hermitian adjoint of a tensor operator combined with the triangular rule leads to new terms in the relativistic "effective operator technique" formulation of a crystalline electric field, and that the matrix elements of these terms are significant for S-state ions.

Zero-field splitting calculations. Part II. Tabulation of the reduced matrix elements of the irreducible double tensor operators

1976 ◽  
Vol 54 (12) ◽  
pp. 1228-1233 ◽  
Author(s):  
R. Chatterjee ◽  
M. R. Smith ◽  
H. A. Buckmaster
Keyword(s):  
The Other ◽  
Tensor Operator ◽  
Zero Field ◽  
Matrix Elements ◽  
Zero Field Splitting ◽  
Field Splitting ◽  
The Matrix ◽  
The Many ◽  
Relationship Of ◽  
The Relationship

The many-electron reduced matrix elements of the double tensor operator [Formula: see text] are tabulated for the pn, dn and fn configurations. These tables have been calculated from the Racah formalism and form an extension of the tabulations given by Nielson and Koster for K2 = 1. The relationship of this tensor with the other double tensors and the calculation of the matrix elements is summarized. See Chatterjee et al for an application.

scholarly journals S-wave Colour Singlet States of Multiquark Configurations

1978 ◽  
Vol 31 (2) ◽  
pp. 117 ◽  
Author(s):  
BG Wybourne
Keyword(s):  
Mass Spectra ◽  
S Wave ◽  
Bag Model ◽  
Colour Singlet ◽  
Singlet States ◽  
Mit Bag Model ◽  
The Masses

Simple methods for determining and systematically labelling the S-wave colour singlet states of multiquark configurations are developed and results are given for the quark configurations QN (N = 0 (mod 3)) and for the quark-antiquark configurations Q2Q2, Q4Q and Q3Q3. The masses of the colour singlet states associated with the Q6 and Q9 configurations are calculated using the MIT bag model and a number of conclusions concerning these mass spectra are drawn.

scholarly journals Improving the theoretical prediction for the Bs - B̅s width difference: matrix elements of next-to-leading order ΔB = 2 operators

2018 ◽  
Vol 175 ◽  
pp. 13023 ◽  
Author(s):  
Christine Davies ◽  
Judd Harrison ◽  
G Peter Lepage ◽  
Christopher Monahan ◽  
Junko Shigemitsu ◽  
...  
Keyword(s):  
Standard Model Prediction ◽  
Bottom Quarks ◽  
Matrix Elements ◽  
Leading Order ◽  
Physical Point ◽  
Difference Matrix ◽  
Strange Quarks ◽  
Width Difference ◽  
The Standard Model ◽  
The Matrix

We present lattice QCD results for the matrix elements of R2 and other dimension-7, ΔB = 2 operators relevant for calculations of Δs, the Bs - B̅s width difference. We have computed correlation functions using 5 ensembles of the MILC Collaboration’s 2+1 + 1-flavour gauge field configurations, spanning 3 lattice spacings and light sea quarks masses down to the physical point. The HISQ action is used for the valence strange quarks, and the NRQCD action is used for the bottom quarks. Once our analysis is complete, the theoretical uncertainty in the Standard Model prediction for ΔΓs will be substantially reduced.

Parity, time, charge and Hermitian conjugations of Racah tensor operators

1983 ◽  
Vol 61 (12) ◽  
pp. 1613-1617 ◽  
Author(s):  
R. Chatterjee ◽  
J. A. Tuszyński ◽  
H. A. Buckmaster
Keyword(s):  
Magnetic Properties ◽  
Electric Properties ◽  
Tensor Operator ◽  
Matrix Elements ◽  
Selection Rules ◽  
Angular Momenta ◽  
The Matrix ◽  
Polar Tensor ◽  
The Relationship ◽  
Tensor Operators

The relationship between the parity P, time θ, charge C, and Hermitian h conjugation operators and the irreducible Racah tensor operators is reexamined. Polar tensor operators (describing electric properties) are distinguished from axial tensor operators (describing magnetic properties and angular momenta) on the basis of their individual parity and time conjugation properties. However, the effect of the Pθ product conjugation is identical for both classes and for even rank is equivalent to the Racah definition for the Hermitian conjugation of a tensor operator. It is shown that this property separates the Racah tensor operators from other vector quantities like linear momentum which cannot be represented by such operators. The selection rules due to parity and time conjugation and Hermitian conjugation that arise in the calculation of the matrix elements of the tensor operators and their products are then obtained self-consistently using the Wigner–Eckart theorem.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

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