# Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Light mesons

## Abstract

We continue the investigation of mesons in terms of the spectral integral equation initiated before for the bb-bar and cc-bar systems; we consider the light-quark (u, d, s) mesons with masses M {<=} 3 GeV. The calculations have been performed for the mesons lying on linear trajectories in the (n, M{sup 2}) planes, where n is the radial quantum number. Our consideration relates to the qq-bar states with one component in the flavor space, with the quark and antiquark masses equal to each other, such as {pi}(0{sup -+}), {rho}(1{sup --}), {omega}(1{sup --}), {phi}(1{sup --}), a{sub 0}(0{sup ++}), a{sub 1}(1{sup ++}), a{sub 2}(2{sup ++}), b{sub 1}(1{sup +-}), f{sub 2}(2{sup ++}), {pi}{sub 2}(2{sup -+}), {rho}{sub 3}(3{sup --}), {omega}{sub 3}(3{sup --}), {phi}{sub 3}(3{sup --}), {pi}{sub 4}(4{sup -+}) at n {<=} 6. We obtained the wave functions and mass values of mesons lying on these trajectories. The corresponding trajectories are linear, in agreement with data. We have calculated the two-photon decays {pi}, a{sub 0}(980), a{sub 2}(1320), f{sub 2}(1285), f{sub 2}(1525) and radiative transitions {rho}, {omega} {sup {yields}} {gamma}{pi}, which agree qualitatively with the experiment. On this basis, we extract the singular part of the interaction amplitude, which corresponds to the so-called 'confinement interaction.' Themore »

- Authors:

- Russian Academy of Sciences, Petersburg Nuclear Physics Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21075926

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 70; Journal Issue: 3; Other Information: DOI: 10.1134/S1063778807030040; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; A0-980 MESONS; A2-1320 MESONS; AMPLITUDES; COMPUTER CALCULATIONS; CONFINEMENT; D QUARKS; D S MESONS; FLAVOR MODEL; GEV RANGE 01-10; INTEGRAL EQUATIONS; MASS; OMEGA BARYONS; PHOTONS; QUARK-ANTIQUARK INTERACTIONS; RADIATIVE DECAY; SINGULARITY; T CHANNEL; TRAJECTORIES; U QUARKS; WAVE FUNCTIONS

### Citation Formats

```
Anisovich, V. V., Dakhno, L. G., Matveev, M. A., Nikonov, V. A., and Sarantsev, A. V.
```*Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Light mesons*. United States: N. p., 2007.
Web. doi:10.1134/S1063778807030040.

```
Anisovich, V. V., Dakhno, L. G., Matveev, M. A., Nikonov, V. A., & Sarantsev, A. V.
```*Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Light mesons*. United States. doi:10.1134/S1063778807030040.

```
Anisovich, V. V., Dakhno, L. G., Matveev, M. A., Nikonov, V. A., and Sarantsev, A. V. Thu .
"Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Light mesons". United States.
doi:10.1134/S1063778807030040.
```

```
@article{osti_21075926,
```

title = {Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Light mesons},

author = {Anisovich, V. V. and Dakhno, L. G. and Matveev, M. A. and Nikonov, V. A. and Sarantsev, A. V.},

abstractNote = {We continue the investigation of mesons in terms of the spectral integral equation initiated before for the bb-bar and cc-bar systems; we consider the light-quark (u, d, s) mesons with masses M {<=} 3 GeV. The calculations have been performed for the mesons lying on linear trajectories in the (n, M{sup 2}) planes, where n is the radial quantum number. Our consideration relates to the qq-bar states with one component in the flavor space, with the quark and antiquark masses equal to each other, such as {pi}(0{sup -+}), {rho}(1{sup --}), {omega}(1{sup --}), {phi}(1{sup --}), a{sub 0}(0{sup ++}), a{sub 1}(1{sup ++}), a{sub 2}(2{sup ++}), b{sub 1}(1{sup +-}), f{sub 2}(2{sup ++}), {pi}{sub 2}(2{sup -+}), {rho}{sub 3}(3{sup --}), {omega}{sub 3}(3{sup --}), {phi}{sub 3}(3{sup --}), {pi}{sub 4}(4{sup -+}) at n {<=} 6. We obtained the wave functions and mass values of mesons lying on these trajectories. The corresponding trajectories are linear, in agreement with data. We have calculated the two-photon decays {pi}, a{sub 0}(980), a{sub 2}(1320), f{sub 2}(1285), f{sub 2}(1525) and radiative transitions {rho}, {omega} {sup {yields}} {gamma}{pi}, which agree qualitatively with the experiment. On this basis, we extract the singular part of the interaction amplitude, which corresponds to the so-called 'confinement interaction.' The description of the data requires the presence of the strong t-channel singularities for both scalar and vector exchanges.},

doi = {10.1134/S1063778807030040},

journal = {Physics of Atomic Nuclei},

number = 3,

volume = 70,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}