# Presentation: 880203

##  Meson-Meson and Meson-Baryon Interactionsin Lattice QCD

-  **Meson-Meson and ****Meson-Baryon Interactions****in Lattice QCD**

**Takumi Doi**
- (RIKEN BNL Research Center)

*In collaboration with*

**Toru T. Takahashi** (YITP)
**Hideo Suganuma **(Kyoto U.)

- PANIC2005@SantaFe

- 10/25/2005

## Introduction

_*Hierarchical structure*_* in hadron physics*
**quarks/gluons**
-       **[QCD]**  **hadrons (mesons/baryons)**
-                          **[Nuclear potential]** **nucleus,**
-                                                                **nuclear matter**
- How can we understand the interaction between hadrons from the fundamental theory, QCD ?

*(commonly appear in physics...)*

- Semi-fundamental theory

*(known only phenomenologically)*

- PANIC2005@SantaFe

- 10/25/2005

## We employ lattice QCD
Direct calculation from QCD, no model assumption
Nonperturbative framework
quarks/gluons       hadrons        nucleus

Meson-meson, meson-baryon interactions
What kind of short range interaction appear ? Color-magnetic int. ?
Useful for study of multi quark physics, exotics ?
Nuclear force between baryons  next talk by Takahashi

- Direct calculation from QCD, no model assumption
- Nonperturbative framework
**quarks/gluons   ********    hadrons    ********    nucleus**
- Meson-meson, meson-baryon interactions
- What kind of short range interaction appear ? Color-magnetic int. ?
- Useful for study of multi quark physics, exotics ?
- Nuclear force between baryons  *next talk by Takahashi*

- Introduction

**[QCD]**

**[Nuclear int.]**

*Lattice QCD succeeded !*

**?**

- Short distance QCD

- PANIC2005@SantaFe

- 10/25/2005

## Formalism

**Measure the energy of two hadron states and observe the shift of energy from the potential**
**Focus the energy difference ********M to improve S/N**

- PANIC2005@SantaFe

- 10/25/2005

## Formalism

**Potential:  V(r)**
**How can we define the distance “r”                    between two hadrons ?**
****** ****adopt one static (heavy) quark in each hadron**
**Dynamics of quark propagation can be accessed from other light quarks**

- F.Okiharu, H.Suganuma, T.T.Takahashi PRL94(2005)192001

- C.Michael, P.Pennanen PRD60(1999)054012

- c.f. all quarks are static

- M.S..Cook, H.R.Fiebig  hep-lat/0509025

- PANIC2005@SantaFe

- 10/25/2005

## Operator

If q3=q1(or q2) in flavor space, the correlation function includes exchange diagram

Otherwise, only no-exchange diagram contributes

- If q3=q1(or q2) in flavor space, the correlation function includes exchange diagram
- Otherwise, only no-exchange diagram contributes

- Propagator and Diagrams

**Q: heavy (static) quark**
**q: light quark**

- Note: propagator of static quark can be written by links

- Q

- U+

- PANIC2005@SantaFe

- 10/25/2005

## Lattice QCD parameters

**Gauge Configurations**
- Standard Wilson plaquette action
- =5.7   a-1=1.1GeV
**V=20****3****×24 ** **(3.7fm)****3****×4.4fm**
**Large volume to analyze multi hadrons**
** **#(gauge config) =~ 200 configs
**Fermion action**
- Wilson fermion at the quenched level
- =0.1600, 0.1625, 0.1650  m= 500-700MeV
- Average over 2-4 spacial configurations are taken in order to enhance the statistics

- PANIC2005@SantaFe

- 10/25/2005

## Numerical Results:Effective mass plot of RBM,RMM

- Numerical Results:Effective mass plot of RBM,RMM

**Meson-Meson**

**Baryon-Meson**

- Without exchange diagrams

**Very weak interaction regardless of distance “r”**

- r=0.18fm & 0.78fm

- PANIC2005@SantaFe

- 10/25/2005

## Numerical Results:Effective mass plot of RBM,RMM

- Numerical Results:Effective mass plot of RBM,RMM

**Meson-Meson**

**Baryon-Meson**

**With** exchange diagrams

**Very weak interaction      regardless of distance “r”          even when w/ exchange diagram **

- r=0.18fm & 0.78fm

- PANIC2005@SantaFe

- 10/25/2005

## Potential between two hadrons

***Preliminary***

**Baryon-Meson**

**Meson-Meson**

- Interaction is very weak for both of baryon-meson and meson-meson.

- Dependence on the  quark mass is also weak

- Nontrivial feature of heavy-light hadrons ?

- PANIC2005@SantaFe

- 10/25/2005

## Summary

**We have investigated the meson-meson and meson-baryon interactions from lattice QCD**
- Define the distance between two hadrons adopting heavy (static) quark in each hadron
- Correlators with & w/o exchange diagram have been analyzed
- Large Volume simulation with V=(3.7fm)3 X 4.4fm
**We have not observed significant interaction for both of meson-meson and meson-baryon**
- Including/Excluding the exchange diagram yields very small effects
- Does this feature stem from the adopting the heavy quark ?
- Evaluation of lattice artifact is in progress
- Is this feature specific only meson-meson & meson-baryon ?
-  Analysis for baryon-baryon interaction  *next talk*

- PANIC2005@SantaFe

- 10/25/2005