# Presentation: 209352

## Thermal unpairing transitionsaffected by charge neutrality constraints and chiral dynamics

*Hiroaki Abuki*
*in collaboration with*
*Teiji Kunihiro*
*(Yukawa Institute of Kyoto Univ., JAPAN)*
*Based on **arXiv:hep-ph/0509172 *

## Color superconductivity

*Color superconductivity*

***d******s****** ******         ******u******s****** ******         ******u******d******    ******     ****J**P*=0+
***d******s****** ******         ******u******s****** ******   ****** ******   ******    ******u******d***

**	****Possible States****	****	****# of gapped quasi-quarks**
**CFL (9)**     	            **9**** ****(all quarks)**
**2SC (4)**	 ( *ud* pair ) 	      	 **4**
**dSC (6)?****	**** **( without *ds* pair )	 **6**

*Rich variety of phase candidates*

- Alford-Rajagopal-Wilczek (’98)

- Bailin-Love (84), Iwasaki-Iwado (’95)

- Iida-Matsuura-Tachiabana-Hatsuda (’04)

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

**Notes:**
Phases with different colored condensate

## Various BCS and non-BCS states

*Various BCS and non-BCS states*

*Gapless (quasi-)quarks*

-        *fully* *gapped* BCS state:*Qtilde-*insulator
- 		    		     ***u******s*************	******	******    ******d******s**********
***            ******s******	******	******	******   ******u****** ******s******	******	******  ******d****** ******s***
-      ***d******u************* ******s****** ***	     ***d******u*************	******   ******u****** ******s******	******	******  ******d****** ******s***
***	******s******u************* ***	         ***	******   ******u****** ******s******	***
***	******s******u************* ***	         ***	******   ******u****** ******s******	******          ******d******s**********

***	******      ******u ******d****** ******s******	******     ******u****** ******d******	******     ******u****** ******s******	******    ******d****** ******s***
*** ******Qtilde *****= (****)****	****    (****) ****	****    (****)****	****    (****)**

-  CFL (9) :
- gCFL (7) :
- 2SC (4) :
- g2SC (2) :
- dSC (6) :
- gdSC (5) :
- etc...

- Alford-Kouvaris-Rajagopal (’03)

- Shovkovy-Huang, PLB564, 205 (’03)

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

**Notes:**
Three red quarks and three blue quarks
Partially ungapped

## 1st order CFL  2SC

**CFL(9)**

**2SC(4)**

**Unpaired(0)**

- high density                             low density

-   Alford-Berges-Rajagopal, ’99
-   Schaefer-Wilczek, ’99

- Alford-Kouvaris-Rajagopal, ’03

- Alford-Rajagopal, ’02

**Only direct effect of **
**strange quark mass**

- 1st order CFL  2SC

- Continuous CFL  gCFL
- 1st order gCFL  UQ

**Effective potential for ****T = 0,**
**Diquark coupling **[MeV]

## Dynamical effects?

*Chiral dynamics in scalar qqbar channel*
*Strong coupling effects beyond MFA*

-   Just neglect this effect in this talk;
- BCS-BEC crossover scenario
-   Nishida-Abuki, arXiv:hep-ph/0504083  poster
- Precursory fluctuation
-   Kitazawa-Koide-Nemoto-Kunihiro, PRD65, 091504 (2002)

- Strange quark mass is NOT an external parameter
- like magnetic field applied to metallic superconductor!
- Ms is dynamical variable and is phase-dependent
-   Abuki-Kitazawa-Kunihiro, PLB615, 102 (2005)
-   Ruster et al.,PRD72, 034004 (2005)
-   Blaschke et al., PRD72, 065020 (2005)
-   Abuki-Kunihiro, arXiv:hep-ph/0509172
- Interplay between the *dynamical* and *kinetic* effects

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## A four-Fermi model

**Condensate ansatz**

*A four-Fermi model*

## Phase diagram for various Gd

*Phase diagram for various G**d*

- Extremely
- weak coupling
-                 uSC
-                  
- gCFL  CFL

- Weak coupling
-                 uSC
-               
- UQM  CFL

- Moderate coupling
-                 uSC
-              
- 2SC  CFL

**Notes:**
uSCとは?

## Why dSC phase does not appear?

*This seemingly contradicts the claim **by*
*But consistent with the results in*
*Where this discrepancy comes from?? *

- Ginzburg-Landau analysis with Ms as a parameter
-      Iida-Matsuura-Tachibana-Hatsuda, PRL93, 132001 (2004)
- NJL numerical anslysis with Ms as a dynamical variable
-     Ruster et al., PRD72, 034004 (2005)
-     Blaschke et al., PRD72, 065020 (2005)
- The answer is given by our recent work:
-     **Abuki-Kunihiro, arXiv:hep-ph/0509172**** **
- aimed at the unified description of  thermal transitions

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## Ginzburg-Landau re-analysis

- By solving min.{****1****0, one gets
- the critical temperature for CFL  *non-*CFL

*Ginzburg-Landau re-analysis*

- Effect of strange quark mass and neutrality condition

- Free fermi gas part

- Usual GL part

- Iida-Baym (’01)

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

**Notes:**
Implicit dependence on Delta’s

## Ginzburg-Landau re-analysis

- CFL

- 2SC

**dSC**

- uQM

- 2SC

- dSC

- uQM

**uSC**

*Ginzburg-Landau re-analysis*

- dSC as second coldest phase : *Iida* et al (2003)
- Growing window for dSC at high density

**Notes:**
Quartec terms takes com

## Ginzburg-Landau re-analysis

- In the weak coupling perturbative regime

- If (*M**s*<<0), then the dSC will be realized
- If (*M**s*>>0), then the uSC will be realized

* **M**s *is a *decreasing* function of 
-  is an *increasing* function of 

*M**s * *m**s**** *100MeV
- while 0>100MeV only for **********10****11**** MeV**

- c.f. Schaefer-Wilczek, PRD60, 114033 (1999)

**Notes:**
Quartec terms takes com

## Summary

*Extensive analysis of the phase diagram*
*The second densest phase depends **	**         on the strength of the (qq)-coupling*
*The second coldest phase depends**	**         on quark density*
*Analytic nature of the DCP was clarified*

- Please see Abuki-Kunihiro, arxiv:hep-ph/0509172
- for more details

- Interplay with chiral dynamics; gCFL, uQM, g2SC or 2SC?
- Abuki-Kitazawa-Kunihiro, PLB615, 102 (2005)

- dSC at high density, or uSC at low density

- dSC is realized at extremely high density in QCD

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## Future issues

*Instability in the gapless phases?*
*Seek for astrophysical consequences*

- Crystalline ordered phase??
-     Alford-Bowers-Rajagopal, PRD63, 074016 (2001)
-     Casalbuoni et al., arXiv:hep-ph/0507247, ...etc.
- Gluonic phase??
-     Gorbar-Hashimoto-Miransky, arXiv:hep-ph/0507303.
- Anything other??
- Bulk structure of NS
- Neutrino transport property and NS Cooling
- Viscosity and R-mode instability
- etc.

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## LOFF phase?

- From Casalbuoni et al., arXiv:hep-ph/0507247
- LOFF line was calculated within the Ginzburg-Landau approach
- We still have a wide unstable region! Needs something further

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## Backup slides

*Ginzburg-Landau potential up to quartic order*
*Why the gCFL is taken over at strong coupling?*
*Phase diagram for even stronger coupling*
*Phases for extremely weak coupling*
*Cutting phase diagram for T=0*
*Cutting phase diagram for finite T*
*Phases for Weak coupling*
*Cutting phase diagram at finite T*
*Why the g2SC phase at finite T?*
*Phases for Intermediate coupling*
*Cutting phase diagram at finite T*
*Why the g2SC phase at finite T?*
*Baryon number density vs. ***

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## Second densest phase and Gd

*Why the gCFL ceases to be second phase?*

- 

- UQM without **<qqbar>**

## Ginzburg-Landau re-analysis

*Ginzburg-Landau re-analysis*

**Notes:**
Quartec terms takes com

## Effective potential from a model

*Effective potential from a model*

- high density                               low density

**Only direct effect of **
**strange quark mass**

- 1st order
- unlocking
- CFL  2SC

-   Alford-Berges-Rajagopal, ’99
-   Schaefer-Wilczek, ’99

**CFL(9)**

**2SC(4)**

**Unpaired(0)**

- Alford-Kouvaris-Rajagopal, ’03

- Alford-Rajagopal, ’02

- continuous
- transition
- CFL  gCFL
- 1st order
- gCFL  UQ

## Even stronger coupling

*Even stronger coupling*

- Extremely
- weak coupling
-                 uSC
-                  
- 2SC  CFL

## Extremely weak coupling

## Cutting phase diagram

- Gap parameters
- and chemical
- potentials

- Gaps in quark spectra:
- SU(2)C+V symmetry
- CFL / gCFL  Kaon cond.

- Quark densities:
- Enforced neutrality
- in CFL phase

## Extremely weak coupling

## Cutting phase diagram

*Cutting phase diagram*

- Gap parameters
- and chemical
- potentials

- Gaps in quark spectra
- behave in more
- complicated manner!

- metal / insulator
- crossover:
- gCFL8 / CFL

## Weak coupling

*Weak coupling*

## Cutting phase diagram

- and chemical
- potentials

*Cutting phase diagram*

## Why the g2SC phase at finite T?

*Why the g2SC phase at finite T?*

- We needs
- close look at
- the structure
- of the uQM
- solution
- which would
- be unstable
- against
- pair formation
- only at finite T

## Why the g2SC phase at finite T?

- Occupation
- number for
- u and d quarks

*Why the g2SC phase at finite T?*

- Isospin mismatch
- is reduced at finite T
- due to thermal effect

- Instability to
- formation of
- Iso-singlet qq

## Intermediate coupling

*Intermediate coupling*

- Unusual
- 1st order
- 2SC / g2SC
- Transition
- What is
- happening in
- the 2SC sector?

## Cutting phase diagram

*Cutting phase diagram*

- Gap parameters
- and chemical
- Potentials
- in the 2SC sector

- Neutral Isospin density

- Order parameter
- for 2SC/g2SC

*1**st** order*
*2SC / g2SC*
*transition*

## Intermediate coupling

*Intermediate coupling*

## Cutting phase diagram

*Cutting phase diagram*

- Gap parameters
- and chemical
- Potentials
- in the 2SC sector

- Neutral Isospin density

*Smooth crossover*
*2SC / g2SC*

## Baryon number density

*Baryon number density*

- Baryon density
- in the CFL
- Increases
- with coupling
- 

- Minimum
- CFL density
- decreases
- however

- Several jumps
- at 1st order
- transitions

## Dense phase of QCD

- Strange quark mass
- Charge neutrality constraints & -equilibrium condition

*Dense phase of QCD*

*The most prominent candidate of Densest / Coldest phase: Color-Favor Locking (CFL)*
*What’s the ****2******nd**** densest phase?*

-   Alford-Rajagopal-Wilczek, NPB537:443 (1999)
-   Schaefer, NPB575, 269 (2000))

- But only convincing for ** *M**s*

-   Alford-Berges-Rajagopal, NPB558, 219 (1999)
-   Schaefer-Wilczek, PRD60, 074014 (1999)

-   Iida-Baym, PRD63, 074018 (2001)
-   Rajagopal-Wilczek, PRL86, 3492 (2001)
-   Amore-Birse-McGovern-Walet, PRD65, 074005 (2002)
-   Alford-Rajagopal, JHEP0206, 031 (2002)
-   Alford-Kouvaris-Rajagopal, PRL92, 222001 (2004)

**Notes:**
Key ingredients to consider this is the following
Both is the kinetic effects

## Dynamical effects?

*Chiral dynamics in scalar qqbar channel*

- Strange quark mass is NOT an external parameter
-   Abuki-Kitazawa-Kunihiro, PLB615, 102 (2005)
-   Ruster et al.,PRD72, 034004 (2005)
-   Blaschke et al., PRD72, 065020 (2005)
-   Abuki-Kunihiro, arXiv:hep-ph/0509172
- Nonlinear Interplay between *dynamical* and *kinetic* effects

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## Setting model (2)

*Parameter settings*

**Chiral SU(2) limit:**
***	******m******u*****= *****m******d*****= 0, and *****m******u *****= 80 ****MeV**
**(q-qbar) coupling**
***	*****set *****G******s***** ****so that**** *****M******u,d *****=400**** ****MeV at**** **********=0**
**(q-q) coupling**
***	*****treat *****G******d *****simply as a parameter: **
**	*****G******d ****** *****0 ****(one to one correspondence**

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## Ginzburg-Landau analysis

*Ginzburg-Landau analysis*

- Effective potential can be expanded in  near Tc

- For symmetric matter at extremely high density

- c.f. Iida-Baym, PRD63, 074018 (2001)
-       Giannakis-Ren, PRD65, 054017 (2002)

- Three equal temperature: Simultaneous melting at Tc0

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

## Ginzburg-Landau re-analysis

*Ginzburg-Landau re-analysis*

- Effect of strange quark mass and neutrality condition

- Free fermi gas part!

- Usual GL part

- H. Abuki @ PANIC05, Santa Fe

- 25 Oct 2005

**Notes:**
Implicit dependence on Delta’s