# Presentation: 720957

## Second Berkeley School on Collective Dynamics, May 21-25, 2007

- Tetsuo Hatsuda, Univ. Tokyo

## Lattice QCD Basics

## QCD partition function  

-  Zero temperature   :   1/T   ~   L
-  Finite temperature  :   1/T <<  L

## Important limits  and theory-guides

*L**-1* 0  (thermodynamics limit)   : finite size scaling
*a*   0 (continuum limit)              : asymptotic freedom
*m*  0  (chiral limit)                     : chiral pert. theory

## Example of improvement:

- 76

- 31

- 5  0.05

- Number of floating-point operations
- To collect 100 config. on 2LxL3 lattice
- with DDHMC algorithm:

- 1 year = 3 x 107 sec

- HNCDDHMC

- Del debbio, Giusti, Luscher, Petronzio, Tantalo, hep-lat/0610059

## To collect 1000 indep. gauge conf.

- on 243x40, a=0.08 fm lattice (T=0)

- Clark, hep-lat/0610048.

## Slide 7

## Slide 8

## Examples in quenched QCD

*Examples in quenched QCD*

## Examples in full QCD

*Examples in full QCD*

## Slide 11

## Nuclear Force

-  Why the nuclear force important now?
-  How to extract the nuclear force from QCD ?

- nucleus

## Modern Nuclear Force from NN scatt. data

*Modern Nuclear Force from NN scatt. data*

## High precision NN potentials

- Machleidt and Entem, nucl-th/0503025

*High precision NN potentials*

- Maximum mass of neutron stars

*Nuclear repulsive core*

- Origin of RC is not known ....
- But, it is intimately related to

- 1.Nuclear saturation

- Ignition of Type II supernovae

## Nuclear Equation of State   

*Nuclear Equation of State**   *

## Mass-Radius relation of neutron star in Akmal-Pandharipande-Ravenhall EoS   

*Mass-Radius relation of neutron star **in **A**kmal-**P**andharipande-**R**avenhall EoS**   *

**(ρ****max****  ****~  ****6ρ****0****)  **

## How to extract (bare) NN force in QCD ?   

*How to extract (bare) NN force in QCD ?**   *

-   unrealistic
-   fundamental difficulty

- (i) Born-Oppenheimer potential

- r

- Takahashi, Doi & Suganuma, hep-lat/0601006

## Equal time BS amplitude (r) 

*Equal time BS amplitude ****(****r****)** *

- cf: for π-πscattering,
- Lin, Martinelli, Sachradja & Testa, NP **B169** (2001)
- CP-PACS Coll, Phys. Rev.  **D71** (2005)

##  asymptotic form of (r) (= the phase shift)

-  asymptotic form of **(*r*)** (= the phase shift)
-       determined by elastic pole
-       interpolating operator independent
-  inelastic contribution:
-        interpolating operator dependent
-        exponentially localized in space
-        magnitude suppressed by Ep/Eth

## Slide 21

## Measurement of (r) (s-wave) 

*Measurement of ****(****r****)** **(s-wave)** *

- + all possible
-    combinations

## Simulation details   

*Simulation details**   *

-  324 lattice
-  Quenched QCD
-  Plaquette gauge action
-  Wilson fermion
-  Periodic (Dirichlet) B.C.
-   for spatial (temporal) direction

| m(GeV) |   0.37 |   0.53 |   0.73 |   0.99 |
| --- | --- | --- | --- | --- |
|  Nconf |  1093 |  1900 |  1000 |  1000 |

-     as of today

## 2s+1LJ

*BS amplitude ****(****r****)  for m****=0.53 GeV*

***2s+1******L******J***

- Ishii, Aoki & Hatsuda, hep-lat/0611096

## 2s+1LJ

*NN central potential V*c*(r) for m****=0.53 GeV**   *

***2s+1******L******J***

- Ishii, Aoki & Hatsuda, hep-lat/0611096

## 2s+1LJ

*NN central potential V*c*(r) for m****=0.53 GeV**   *

***2s+1******L******J***

- Ishii, Aoki & Hatsuda, hep-lat/0611096

## Slide 27

## Quark mass dependence (preliminary)   

*Quark mass dependence (preliminary)**   *

- Ishii, Aoki & Hatsuda, in preparation

## Remarks    

- 4. Hyperons ?    to be announced in two weeks (INPC2007)

- 3. Different Interpolating operators ?
-      same phase shift but  different V(r) at short distances

- 2. Tensor force ?     coupled channel  3S1-3D1

##  Nuclear force : bridge between one and many 

* **Nuclear force : bridge between one and many *