# Implication of the running mass of the {rho}{sup 0} meson for the dilepton mass spectrum and the {mu}{sup +}{mu}{sup {minus}}/e{sup +}e{sup {minus}} ratio in K{sup +}{r_arrow}{pi}{sup +}l{sup +}l{sup {minus}} decays

## Abstract

We make an attempt to resolve the discrepancy of the observed e{sup +}e{sup {minus}} mass spectrum in the K{sup +}{r_arrow}{pi}{sup +}e{sup +}e{sup {minus}} decay with that predicted by meson dominance. To this end we investigate the properties of the {rho}{sup 0} propagator. We use dispersion relations to evaluate the running mass m{sub {rho}}{sup 2}(t) of the {rho}{sup 0} resonance without adjustable parameters. To improve the convergence of the dispersion integral, the momentum dependence of strong vertices is taken from the flux-tube-breaking model of Kokoski and Isgur. The obtained behavior of m{sub {rho}}{sup 2}(t) at small momentum squared {ital t} makes the K{sup +}{r_arrow}{pi}{sup +}e{sup +}e{sup {minus}} form factor rise faster with increasing {ital t} than in the original meson dominance calculation and more in agreement with the published data. As a consequence, the meson dominance prediction of the {mu}{sup +}{mu}{sup {minus}}/e{sup +}e{sup {minus}} ratio changes slightly, from 0.224 to 0.236. We do not see any possibility to accommodate into the meson dominance approach an even steeper e{sup +}e{sup {minus}} spectrum, indicated by the preliminary data of the E865 Collaboration at BNL AGS. {copyright} {ital 1999} {ital The American Physical Society}

- Authors:

- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)|[Institute of Physics, Silesian University, 746-01 Opava (Czech Republic)

- Publication Date:

- OSTI Identifier:
- 362722

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D

- Additional Journal Information:
- Journal Volume: 60; Journal Issue: 5; Other Information: PBD: Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; KAONS PLUS; LEPTONIC DECAY; PIONS PLUS; ELECTRONS; POSITRONS; MUONS PLUS; MUONS MINUS; MASS SPECTRA; VECTOR DOMINANCE MODEL; DISPERSION RELATIONS

### Citation Formats

```
Lichard, P.
```*Implication of the running mass of the {rho}{sup 0} meson for the dilepton mass spectrum and the {mu}{sup +}{mu}{sup {minus}}/e{sup +}e{sup {minus}} ratio in K{sup +}{r_arrow}{pi}{sup +}l{sup +}l{sup {minus}} decays*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevD.60.053007.

```
Lichard, P.
```*Implication of the running mass of the {rho}{sup 0} meson for the dilepton mass spectrum and the {mu}{sup +}{mu}{sup {minus}}/e{sup +}e{sup {minus}} ratio in K{sup +}{r_arrow}{pi}{sup +}l{sup +}l{sup {minus}} decays*. United States. doi:10.1103/PhysRevD.60.053007.

```
Lichard, P. Wed .
"Implication of the running mass of the {rho}{sup 0} meson for the dilepton mass spectrum and the {mu}{sup +}{mu}{sup {minus}}/e{sup +}e{sup {minus}} ratio in K{sup +}{r_arrow}{pi}{sup +}l{sup +}l{sup {minus}} decays". United States. doi:10.1103/PhysRevD.60.053007.
```

```
@article{osti_362722,
```

title = {Implication of the running mass of the {rho}{sup 0} meson for the dilepton mass spectrum and the {mu}{sup +}{mu}{sup {minus}}/e{sup +}e{sup {minus}} ratio in K{sup +}{r_arrow}{pi}{sup +}l{sup +}l{sup {minus}} decays},

author = {Lichard, P.},

abstractNote = {We make an attempt to resolve the discrepancy of the observed e{sup +}e{sup {minus}} mass spectrum in the K{sup +}{r_arrow}{pi}{sup +}e{sup +}e{sup {minus}} decay with that predicted by meson dominance. To this end we investigate the properties of the {rho}{sup 0} propagator. We use dispersion relations to evaluate the running mass m{sub {rho}}{sup 2}(t) of the {rho}{sup 0} resonance without adjustable parameters. To improve the convergence of the dispersion integral, the momentum dependence of strong vertices is taken from the flux-tube-breaking model of Kokoski and Isgur. The obtained behavior of m{sub {rho}}{sup 2}(t) at small momentum squared {ital t} makes the K{sup +}{r_arrow}{pi}{sup +}e{sup +}e{sup {minus}} form factor rise faster with increasing {ital t} than in the original meson dominance calculation and more in agreement with the published data. As a consequence, the meson dominance prediction of the {mu}{sup +}{mu}{sup {minus}}/e{sup +}e{sup {minus}} ratio changes slightly, from 0.224 to 0.236. We do not see any possibility to accommodate into the meson dominance approach an even steeper e{sup +}e{sup {minus}} spectrum, indicated by the preliminary data of the E865 Collaboration at BNL AGS. {copyright} {ital 1999} {ital The American Physical Society}},

doi = {10.1103/PhysRevD.60.053007},

journal = {Physical Review, D},

number = 5,

volume = 60,

place = {United States},

year = {1999},

month = {9}

}