scholarly journals Radiative decays and the SU(6) Lie algebra

2019 ◽  
Vol 34 (21) ◽  
pp. 1950108
Author(s):  
Milton Dean Slaughter
Keyword(s):  
Lie Algebra ◽  
Radiative Decay ◽  
Radiative Decays ◽  
Electromagnetic Current ◽  
Quark System ◽  
Positive Roots ◽  
Quark Structure ◽  
Predicted Values ◽  
Equal Time Commutation ◽  
Vector Formula

We present research on radiative decays of vector [Formula: see text] to pseudoscalar [Formula: see text] particles ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] quark system) using broken symmetry techniques in the infinite-momentum frame and equal-time commutation relations and the [Formula: see text] Lie algebra, and conducted without ascribing any specific form to meson quark structure or intra-quark interactions. We utilize the physical electromagnetic current [Formula: see text] including its singlet [Formula: see text] term and focus on the [Formula: see text] 35-plet. We derive new relations involving the electromagnetic current (including its singlet — proportional to the [Formula: see text] singlet). Remarkably, we find that the electromagnetic current singlet plays an intrinsic role in understanding the physics of radiative decays and that the charged and neutral [Formula: see text] meson radiative decays into [Formula: see text] are due entirely to the singlet term in [Formula: see text]. Although there is insufficient radiative decay experimental data available at this time, parametrization of possible predicted values of [Formula: see text] is made. For conciseness and self-containment, we compute all [Formula: see text] Lie algebra simple roots, positive roots, weights and fundamental weights which allow the construction of all [Formula: see text] representations. We also derive all nonzero [Formula: see text] generator commutators and anticommutators — useful for further research on grand unified theories.

AUTOMORPHISMS OF CERTAIN NILPOTENT LIE ALGEBRAS OVER COMMUTATIVE RINGS

2007 ◽  
Vol 17 (03) ◽  
pp. 527-555 ◽  
Author(s):  
YOU'AN CAO ◽  
DEZHI JIANG ◽  
JUNYING WANG
Keyword(s):  
Automorphism Group ◽  
Commutative Ring ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Commutative Rings ◽  
Nilpotent Lie Algebras ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Positive Roots ◽  
Nilpotent Subalgebra

Let L be a finite-dimensional complex simple Lie algebra, Lℤ be the ℤ-span of a Chevalley basis of L and LR = R⊗ℤLℤ be a Chevalley algebra of type L over a commutative ring R. Let [Formula: see text] be the nilpotent subalgebra of LR spanned by the root vectors associated with positive roots. The aim of this paper is to determine the automorphism group of [Formula: see text].

scholarly journals Photophysical Properties of Spirobifluorene-Based o-Carboranyl Compounds Altered by Structurally Rotating the Carborane Cages

Molecules ◽  
2019 ◽  
Vol 24 (22) ◽  
pp. 4135
Author(s):  
Seonah Kim ◽  
Hyunhee So ◽  
Ji Hye Lee ◽  
Hyonseok Hwang ◽  
Hyoshik Kwon ◽  
...  
Keyword(s):  
Radiative Decay ◽  
Photophysical Properties ◽  
High Energy ◽  
Low Energy ◽  
Radiative Decays ◽  
Absorption Bands ◽  
Molecular Features ◽  
Td Dft ◽  
Structural Fluctuations ◽  
Energy Emissions

9,9′-Spirobifluorene-based o-carboranyl compounds C1 and C2 were prepared and fully characterized by multinuclear nuclear magnetic resonance (NMR) spectroscopy and elemental analysis. The solid-state structure of C1 was also determined by single-crystal X-ray diffractometry. The two carboranyl compounds display major absorption bands that are assigned to π−π* transitions involving their spirobifluorene groups, as well as weak intramolecular charge-transfer (ICT) transitions between the o-carboranes and their spirobifluorene groups. While C1 only exhibited high-energy emissions (λem = ca. 350 nm) in THF at 298 K due to locally excited (LE) states assignable to π−π* transitions involving the spirobifluorene group alone, a remarkable emission in the low-energy region was observed in the rigid state, such as in THF at 77 K or the film state. Furthermore, C2 displays intense dual emissive patterns in both high- and low-energy regions in all states. Electronic transitions that were calculated by time-dependent-DFT (TD-DFT) for each compound based on ground (S0) and first-excited (S1) state optimized structures clearly verify that the low-energy emissions are due to ICT-based radiative decays. Calculated energy barriers that are based on the relative energies associated with changes in the dihedral angle around the o-carborane cages in C1 and C2 clearly reveal that the o-carborane cage in C1 rotates more freely than that in C2. All of the molecular features indicate that ICT-based radiative decay is only available to the rigid state in the absence of structural fluctuations, in particular the free-rotation of the o-carborane cage.

RADIATIVE DECAYS OF BARYONS IN A FIELD THEORETIC QUARK MODEL

1996 ◽  
Vol 11 (32) ◽  
pp. 5685-5700 ◽  
Author(s):  
A.R. PANDA ◽  
R.K. SAHOO
Keyword(s):  
Quark Model ◽  
Radiative Decay ◽  
Constituent Quark ◽  
Theoretical Calculations ◽  
Wave Functions ◽  
Radiative Decays ◽  
Quark Field ◽  
Decay Widths ◽  
Helicity Amplitudes ◽  
Decays Of Baryons

Radiative decays of baryons are considered in a field theoretic quark model of composite hadrons where the translationally invariant SU (6) hadron states are described by constituent quark field operators and harmonic oscillator wave functions. The constituent quark field operators of the model satisfying the equal time algebra are also Lorentz-boosted through a spin rotation to describe hadrons in motion. The model, like its earlier success in describing the different hadronic phenomena, in the present investigation without any free parameters, obtains the radiative decay widths and helicity amplitudes in reasonable agreement with other theoretical calculations as well as with the available experimental measurements.

On basic Cycles of An, Bn, Cn and Dn

1985 ◽  
Vol 37 (1) ◽  
pp. 122-140 ◽  
Author(s):  
D. J. Britten ◽  
F. W. Lemire
Keyword(s):  
Lie Algebra ◽  
Dual Space ◽  
Cartan Subalgebra ◽  
Closed Field ◽  
Generating Set ◽  
Enveloping Algebra ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Positive Roots

In this paper, we investigate a conjecture of Dixmier [2] on the structure of basic cycles. Our interest in basic cycles arises primarily from the fact that the irreducible modules of a simple Lie algebra L having a weight space decomposition are completely determined by the irreducible modules of the cycle subalgebra of L. The basic cycles form a generating set for the cycle subalgebra.First some notation: F denotes an algebraically closed field of characteristic 0, L a finite dimensional simple Lie algebra of rank n over F, H a fixed Cartan subalgebra, U(L) the universal enveloping algebra of L, C(L) the centralizer of H in U(L), Φ the set of nonzero roots in H*, the dual space of H, Δ = {α1, …, αn} a base of Φ, and Φ+ = {β1, …, βm} the positive roots corresponding to Δ.

Weyl ǵroups and finite Chevalley ǵroups

1970 ◽  
Vol 67 (2) ◽  
pp. 269-276 ◽  
Author(s):  
R. W. Carter
Keyword(s):  
Finite Group ◽  
Finite Field ◽  
Lie Algebra ◽  
Weyl Groups ◽  
Chevalley Groups ◽  
Simple Lie Algebra ◽  
Positive Roots ◽  
Image Position ◽  
A Finite Group ◽  
Fundamental Paper

In his fundamental paper (1) Chevalley showed how to associate with each complex simple Lie algebra L and each field K a group G = L(K) which is (in all but four exceptional cases) simple. If K is a finite field GF(q), G is a finite group of orderwhere l is the rank of L, m is the number of positive roots of L and d is a certain integer determined by L and K. The integers m1, m2,…,m1 are determined by L only and satisfy the condition

scholarly journals ANALYSIS OF THE RADIATIVE DECAYS AMONG THE BOTTOMONIUM STATES

2012 ◽  
Vol 27 (34) ◽  
pp. 1250197 ◽  
Author(s):  
ZHI-GANG WANG
Keyword(s):  
Experimental Data ◽  
Systematic Study ◽  
Radiative Decay ◽  
Radiative Decays ◽  
Heavy Quarkonium ◽  
Radiative Transitions ◽  
Decay Widths ◽  
The Future

In this paper, we perform an systematic study of the radiative transitions among the bottomonium states using the heavy quarkonium effective Lagrangians, and make predictions for the ratios among the radiative decay widths of a special multiplet to another multiplet. The predictions can be confronted with the experimental data in the future.

RADIATIVE DECAY OF HEAVY MESONS IN A RELATIVISTIC QUARK MODEL

1999 ◽  
Vol 14 (11) ◽  
pp. 1759-1768 ◽  
Author(s):  
R. K. DAS ◽  
A. R. PANDA ◽  
R. K. SAHOO
Keyword(s):  
Quark Model ◽  
Radiative Decay ◽  
Constituent Quark ◽  
Theoretical Calculations ◽  
Spin Rotation ◽  
Wave Functions ◽  
Radiative Decays ◽  
Quark Field ◽  
Decay Widths ◽  
Free Parameters

Radiative decays of heavy vector mesons are considered in the lowest order in a field-theoretic quark model of composite hadrons. The translationally invariant hadron states required in such a calculation are described by constituent quark field operators satisfying equal time algebra and harmonic oscillator wave functions. The constituent quark field operators are Lorentz-boosted through a spin rotation to describe hadrons in motion. The model, like its earlier success in describing different hadronic phenomena, in the present investigation without any free parameters also obtains the radiative decay widths and transition moments in reasonable agreement with other theoretical calculations as well as experimental measurements.

scholarly journals Strong coupling constants and radiative decays of the heavy tensor mesons

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Guo-Liang Yu ◽  
Zhi-Gang Wang ◽  
Zhen-Yu Li
Keyword(s):  
Strong Coupling ◽  
Radiative Decay ◽  
Sum Rules ◽  
Form Factors ◽  
Strong Form ◽  
Coupling Constants ◽  
Radiative Decays ◽  
Deep Time ◽  
Analytical Functions ◽  
Frame Work

Abstract In this article, we analyze tensor-vector-pseudoscalar(TVP) type of vertices $$D_{2}^{*+}D^{+}\rho $$D2∗+D+ρ, $$D_{2}^{*0}D^{0}\rho $$D2∗0D0ρ, $$D_{2}^{*+}D^{+}\omega $$D2∗+D+ω, $$D_{2}^{*0}D^{0}\omega $$D2∗0D0ω, $$B_{2}^{*+}B^{+}\rho $$B2∗+B+ρ, $$B_{2}^{*0}B^{0}\rho $$B2∗0B0ρ, $$B_{2}^{*+}B^{+}\omega $$B2∗+B+ω, $$B_{2}^{*0}B^{0}\omega $$B2∗0B0ω, $$B_{s2}^{*}B_{s}\phi $$Bs2∗Bsϕ and $$D_{s2}^{*}D_{s}\phi $$Ds2∗Dsϕ in the frame work of three point QCD sum rules(QCDSR). According to these analysis, we calculate their strong form factors which are used to fit into analytical functions of $$Q^{2}$$Q2. Then, we obtain the strong coupling constants by extrapolating these strong form factors into deep time-like regions. As an application of this work, the coupling constants for radiative decays of these heavy tensor mesons are also calculated at the point of $$Q^{2}=0$$Q2=0. With these coupling constants, we finally obtain the radiative decay widths of these tensor mesons.

On the ‘strange formula’ of Freudenthal and de Vries

1989 ◽  
Vol 105 (2) ◽  
pp. 249-252 ◽  
Author(s):  
H. D. Fegan ◽  
B. Steer
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Weyl Chamber ◽  
Inner Product ◽  
Killing Form ◽  
De Vries ◽  
Positive Roots ◽  
Connected Lie Group

Suppose that G is a semi-simple, compact, connected Lie group. Endow g, its Lie algebra, with the inner product which is the negative of the Killing form. Choose a fundamental Weyl Chamber and let R+ denote the positive roots so determined.

Quark structure and radiative decays of new particles

1976 ◽  
Vol 64 (3) ◽  
pp. 345-347 ◽  
Author(s):  
Ya.I. Azimov ◽  
L.L. Frankfurt ◽  
V.A. Khoze
Keyword(s):  
Radiative Decays ◽  
Quark Structure ◽  
New Particles
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