Wave-packet effects: a solution for isospin anomalies in vector-meson decay

Kenzo Ishikawa (Department of Physics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan; Natural Science Center, Keio University, Yokohama, 223-8521, Japan) ; Osamu Jinnouchi (Department of Physics, Faculty of Science, Tokyo Institute of Technology, Tokyo, 152-8550, Japan) ; Kenji Nishiwaki (Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, 201314, India) ; Kin-ya Oda (Department of Mathematics, Tokyo Woman’s Christian University, Tokyo, 167-8585, Japan)

There is a long-standing anomaly in the ratio of the decay width for $$\psi (3770)\rightarrow D^0\overline{D^0}$$ ψ ( 3770 ) D 0 D 0 ¯ to that for $$\psi (3770)\rightarrow D^+D^-$$ ψ ( 3770 ) D + D - at the level of $$9.5\,\sigma $$ 9.5 σ . A similar anomaly exists for the ratio of $$\phi (1020)\rightarrow K_\text {L}^0K_\text {S}^0$$ ϕ ( 1020 ) K L 0 K S 0 to $$\phi (1020)\rightarrow K^+K^-$$ ϕ ( 1020 ) K + K - at $$2.1\,\sigma $$ 2.1 σ . In this study, we reassess the anomaly through the lens of a Gaussian wave-packet formalism. Our comprehensive calculations include the localization of the overlap of the wave packets near the mass thresholds and the composite nature of the initial-state vector mesons. The results align within a $$\sim 1 \sigma $$ 1 σ confidence level with the Particle Data Group’s central values for a physically reasonable value of the form-factor parameter, indicating a resolution to these anomalies. We also check the deviation of a wave-packet resonance from the Briet–Wigner shape and find that wide ranges of the wave-packet size are consistent with the experimental data.

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      "source": "Springer", 
      "value": "There is a long-standing anomaly in the ratio of the decay width for  $$\\psi (3770)\\rightarrow D^0\\overline{D^0}$$  <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> <mo>\u2192</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> <mover> <msup> <mi>D</mi> <mn>0</mn> </msup> <mo>\u00af</mo> </mover> </mrow> </math>   to that for  $$\\psi (3770)\\rightarrow D^+D^-$$  <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> <mo>\u2192</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math>   at the level of  $$9.5\\,\\sigma $$  <math> <mrow> <mn>9.5</mn> <mspace width=\"0.166667em\"></mspace> <mi>\u03c3</mi> </mrow> </math>  . A similar anomaly exists for the ratio of  $$\\phi (1020)\\rightarrow K_\\text {L}^0K_\\text {S}^0$$  <math> <mrow> <mi>\u03d5</mi> <mrow> <mo>(</mo> <mn>1020</mn> <mo>)</mo> </mrow> <mo>\u2192</mo> <msubsup> <mi>K</mi> <mtext>L</mtext> <mn>0</mn> </msubsup> <msubsup> <mi>K</mi> <mtext>S</mtext> <mn>0</mn> </msubsup> </mrow> </math>   to  $$\\phi (1020)\\rightarrow K^+K^-$$  <math> <mrow> <mi>\u03d5</mi> <mrow> <mo>(</mo> <mn>1020</mn> <mo>)</mo> </mrow> <mo>\u2192</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>K</mi> <mo>-</mo> </msup> </mrow> </math>   at  $$2.1\\,\\sigma $$  <math> <mrow> <mn>2.1</mn> <mspace width=\"0.166667em\"></mspace> <mi>\u03c3</mi> </mrow> </math>  . In this study, we reassess the anomaly through the lens of a Gaussian wave-packet formalism. Our comprehensive calculations include the localization of the overlap of the wave packets near the mass thresholds and the composite nature of the initial-state vector mesons. The results align within a  $$\\sim 1 \\sigma $$  <math> <mrow> <mo>\u223c</mo> <mn>1</mn> <mi>\u03c3</mi> </mrow> </math>   confidence level with the Particle Data Group\u2019s central values for a physically reasonable value of the form-factor parameter, indicating a resolution to these anomalies. We also check the deviation of a wave-packet resonance from the Briet\u2013Wigner shape and find that wide ranges of the wave-packet size are consistent with the experimental data."
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Published on:
30 October 2023
Publisher:
Springer
Published in:
European Physical Journal C , Volume 83 (2023)
Issue 10
Pages 1-32
DOI:
https://doi.org/10.1140/epjc/s10052-023-12077-7
arXiv:
2308.09933
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: