# Presentation: 248975

## LGT results in 2+1 flavour QCD 

- MILC Coll., **hep-lat/0405029, hep-lat/0309118, hep-lat/0209079, **
**                     **

- Chiral condensate and susceptibility

-  smooth change of the condensate
-  with tempearture     =>   crossover

- No change with               =>   crossover   ???

- But:

## No change with        =>   crossover ??

- Not necessary: e.g. SU(2) pure gauge theory

-  SU(2) gauge theory
-  exhibits 2-end order
-  phase transition
-  However,
-  no change of
-  with       if

- There is                 scaling
- of physical observables near
- critical region

- J. Engels, F. Karsch & K.R.

## QCD at non-vanishing chemical potential                                     Bielefeld-Swansea approach

- Taylor expansion of                    :

-  ,

- complex  fermion determinant

**C.R. Allton, et al..**

## Change of T_c with chemical potential

**From         dependence ****  **
**of  chira****l ****susceptibilities**

##       Chiral critical point in 3-flavour QCD                                              Ch. Schmitd et al.

-  **Strong**** dependence of the position  of  ****second order**** ****endpoint** **on the  ****quark mass!****                                                                                       **

**N_f=3, m=0.1**
**N_f=3, m=0.005**

**T [MeV]**

**miu [GeV]**

**2-en ord.**

**1-st order**

**crossover transition**

**Pure Gauge**

**0.3**

**0.25**

**0.2**

**0.15**

**0.1**

**0.05**

** ****0**

**0.2**

**0.4**

**0.6**

**0.8**

**1.0**

**1.2**

**0**

**Strong**** dependence of the **
**slope on the quark mass**

**p4 improved action**

## The endpoint of QCD in T-miu_B plane                                                  Fodor & Katz  01, 04

-  Multiparameter reweighting:

-  Lee-Yang zeroes:

-  renormalized
-  physical operator

- Finite  volume V:

- If                   and:

-  phase transition

-  crossover transition

##   Chemical freezeout curve from heavy ion data 

**coincides with freezeout T at RHIC and SPC**

##     space-time evolution -- thermalization

**    ****space-time evolution**** ****-- thermalization**

- Initial conditions, momentum distribution
-           L. McLerran & R. Venugopalan  model
- Thermalization:
- pQCD+kinetics                                                       R. Baier, A.H. Mueller, D.Schiff,  D.T.Son
- At LHC and RHIC:       thermalization occurs
-                                   relatively fast  due to
-                                   emission of  gluons
-  also from  Parton Cascade Model
-  B. Müller,   D.K.Srivastava
- Large elliptic flow at RHIC                       fast    1fm
- thermalization of partonic medium

##        Statistical operator  and mass spectrum

**Only 2-parameters  needed to fix all   particle yield ratios**

**  **** ****+  ****approximate****                 ****    ****by ****experimentally  known mass spectrum**

**       ****Statistical operator  and mass spectrum**

**resonance dominance  (R. Hagedorn)**

**Breit-Wigner res.**

**          ****particle yield****     ****thermal density****             ****BR****    ****thermal density of resonances****      **

##   Chemical freezeout curve from heavy ion data 

**coincides with freezeout T at RHIC and ****SPC**

** ****Cleymans & ****Redlich**

**M. Bleicher et al..**

##          Particle Ratios along freezout curve 

**Nu Xu & K.R 2000**

**SPS**

##          From Meson to Baryon dominance 

**  ****baryon density along freezeout curve****          **P. Braun-Munzinger, et al..,**                                                                         **

- F. Antinori

- explicit           dependence cancelled

##      Heavy Ion 
Phenomenology
through

-      Heavy Ion
- Phenomenology
- through

- Lattice Gauge
- Theory at finite
-       and

- ?

**Based on common work  with**** ****Bielefeld-Swansea LGT Coll.**
**      ****C.R. Allton, M. Doring, S. Ejiri,**
**   ****S.J. Hands,**** O. Kaczmarek, F. Karsch,**
**       ****E. Laermann, K.R.**
** ****& Shinji Ejiri, ****Frithjof Karsch**
**                  **

## Taylor expansion of resonance pressure 

**Factorization of the baryonic pressure****           ****    **

** ****Compare with LGT results:**** **

**Consequences: **

**For fixed                 any ratio of these**
**observables  is T-independent **

**the ratio of the O(2) and O(4) **
**coefficients:**

**baryon mass spectrum**

** ****factorization**** on the Lattice **

##   QCD partition function from LGT and Phenomenology

**check ****T****-dependence **** ****c****(T)****  **

**Taylor ****coefficients of   ****cosh(x)**

**require****s****:   **

##  Isovector and electric charge  fluctuations                             

** ****related with space-like screening limit of the**
** **
**retarded photon self-energy****  **

**=0 for **

**In LGT:   **** ****        ****obtained from                           ,however**
**                  ****requires independent Monte-Carlo  calculations **

**;**

## Charge Fluctuations Near Deconfinement

**S.N Jeon &  V. Koch**
**E. Shuryak & M. Stephanov**
**U. Heinz & B. Muller **
**...****.**

**Mass and quantum number**
**gap between confined**
**and deconfined phase**

##           Isovector susceptibility  in LGT   and                            resonances  gas                            

**on the lattice****: **

**expanding cosh(x) one expects:**
**                                                           **

**LGT result support****s**** decomposition of ****meson**
**baryon  contribution**** **** in confined phase**

##                quark condensate at finite density 

**Baryon contribution:**

**Net baryon pressure**

**In 2-flavour LGT  calculations:**

##   From LGT to HRG Phenomenology: quantitative analysis  of T-dependence of thermodynamics 

**In ****HRG  ****the ****  pressure **
**can be ****appr. ****obtained from the Taylor  coefficients ****of**
** **
**                              **
** **

**LGT results from**
**Integral method**

**                                ****provides good T-dependence of ****LGT pressure**

**use ****c’s**** from LGT check ****P****?**

##          Hadron  Mass Spectrum versus  quark mass

-   chiral limit

- quenched  limit

**       ****extrapolate:**
**from LGT or model**

##  Hadron  Mass Spectrum – LGT and Bag model results

** ****Hadron  Mass Spectrum – LGT and Bag model results**

**LGT results for pion mass**
**dependence of **
**and their parity partners**

**2**

**QCDSF Coll., M. Göckeler, et al..**

**F. Karsch, A. Tawfik, K.R.**

##       Bag Model and Hadron Masses 

-  --------------------
-  --------------------
- ---------------------
-  -------            ---
- ----------------------
- ----------B-----------                          :surface boundary
-                                                                      conditions
- Hadron Masses from:
- for              and                  :

- q

-  q

- g

- g

- q

##       Hadron resonance gas model  and    LGT                                                                                              Thermodynamics       

**phenomenological  partition function of hadron resonance gas with**
**LGT mass spectrum provides good description of lattice ****results below deconf.**

##       Hadron resonance gas model  and    LGT                                                                                               thermodynamics       

##       Hadron resonance gas model  and    LGT                                                                                               thermodynamics       

- Critical structure due to    QCD End-Point

- ?

- How large the singular contribution could be in the actual LGT calculations ?

- ?

## Charge Fluctuations near QCD critical end-point                                                                                                   

-     The appearance of the critical and-point  results in a long-range correlations induced by the sigma field

-               Consequently: observables that are coupled to the sigma field
-                                       should exhibit a critical behavior
-                                                  and                    expected to be divergent at
-                                        the critical end-point, thus:

- Consider only isodublet sector through         contribution, then
-                                                                              describes statistical
-                                                                              fluctuaitons in a thermal
-                                                                              system

-     What could be the contribution of             if indeed the critical end-point appears at                                          ?

## Singular contribution to the quark number susceptibility                                                                                                    

- Consider effective Langrangian

- Calculate Free energy  + take                    get:

- +

- Hatta & Stephanov, Ejiri, Karsch & K.R

**From the NJL model  (G. E. Brown et al.)**

**Take parameters from actual  LGT calculations at and get:  **

**  ****The quark mass on the lattice is still too large  to**
** ****  ****possibly see the contribution of the singular part in**
** **** **** ****the net quark number susceptibility**
**   ****Rather no connection between ****NA49 HORN and LGT data****  **

##      Isovector and baryon number susceptibilities                                                                    

**Model****l****ing isovector fluctuations:**
**At               only ~10%                is due to pion contribution**
**Including interactions e.g.**
** ****actually  reduces fluctuations**
**Model****l****ing fluctuations within  models that**
** ****account ****for**** interactions between only a very**
** ****few low lying particles is not sufficient.  **

**strong Debye mass**

##                    Higher moments are important to search for                                deconfinement transition 

**  **

##   Mixed susceptibilities

**Mixed susceptibilities: important observables to search for deconfinement**

- _[V. Koch](http://131.169.91.193/spires/find/wwwhepau/wwwscan?rawcmd=fin+Koch,+V.)_, _[A. ](http://131.169.91.193/spires/find/wwwhepau/wwwscan?rawcmd=fin+Majumder,+A.)__[Majumder](http://131.169.91.193/spires/find/wwwhepau/wwwscan?rawcmd=fin+Majumder,+A.)_, _[J. ](http://131.169.91.193/spires/find/wwwhepau/wwwscan?rawcmd=fin+Randrup,+J.)__[Randrup](http://131.169.91.193/spires/find/wwwhepau/wwwscan?rawcmd=fin+Randrup,+J.)_

**See e.g.:**

##        Phase  boundary of fixed energy density versus                             chemical freezeout

**SPS 40 AGeV**

** ****Spliting of chemical**** ****freezeout**** ****and phase  boundary surface most  likely appearswhen the **** densities  of**** ****mesons  and baryons are comparable **
** ****For E<****30**** AGeV** ** strong collective effects in****  ****hadronic medium are to be expected **

**LGT**

**J. Cleymans et al..**

** **

**Mesons**** **

**Baryons**

**           **

**          **** **

**                 **

##                  Kinetics of abelian charges                          C.M. Ko, V. Koch, Z. Lin,  M. Stephanov, Xin-Nian Wang, K.R

- Consider:
- Rate equation
- :

- Size of fluctuations

- Equilibrium limit

- T,V

##  conservation on the average                 exact conservation

-  conservation on the average                 exact conservation

- Consider thermal system with  S=0

-  suppression factor       1

- S=0

- S=-1

- S=1

- suppression increases with S  and with decreassing collision energy

- A

- A

- A

- A

- S

- S

##             Correlated strangeness production  

**            ****Correlated**** strangeness ****production**** **** **

- KaoS (GSI-SIS)

**H. Oeschler, et al.**

## Strangeness enhancement: energy and      strangeness content dependence

-  Tounsi & K.R

**Strangeness enhancement: energy and****      strangeness content dependence**

- decrease of enhancements from SPS to RHIC predicted ( A. Tounsi)
- Predicted order of magnitude of enhancements at RHIC close at 40AGeV too large
- Centrality dependence not correct when assuming                         ,however
-                                                                            (i)    V do not need to scale linearly!!
-                                                                            (ii)    eq.  S-S is not Pb-Pb with 60
- Ideal test of  C=>GC: changing             by atomic number in central A—A collisions
-                                     and not impact parameter in Pb—Pb !!

##            Statistical Model  and Energy          dependence of strangeness enhancement                                                                                                                          

**        ****               ****Strangeness  enhancement**
**                               ****larger for lower energy****                ****                  ****                                                ****                                                         **

**A. Mishke, ****A. Tounsi ****& K.R**

##   Strange particle yields energy and centrality                                 dependence    

- Au+Au

- STAR preliminary

- STAR p+p           =200 GeV

** **** ****Strange particle yields energy and centrality    ****                             dependence****    **

## Thermal Model in pp and pA collisions

**    ****good description of stable particle yields**
**with  the value of temperature similar as expected**
**   ****in A-A collision:    however,**
**   ****Observed deviations**** of short lived resonances**
**    ****by a  few sigma: **

**J. Cleymans, S. Wheaton & K.R**

**U. Heinz & F. Becattini**

**The             ratios measured by NA49 in p-Pb and Pb-Pb  consistent with  thermal model **

##         Chemical equilibration: strangeness? 

- H. Oeschler, et al..,

**Andronic, Braun-Munzinger &K.R.                           **

**RHIC**

**SPS**

## Scaling relations of              production    

**However, since                                               thus                                            and       **

##       Conclusions 

-    However, improvement of flavor symmetry in the staggered fermion formulation
-    may have an impact on the phase transition;          dependence

-  There is a substantial progress at finite  baryon density  in LGT
-    but we are far from final results: one needs to be closer to the continuum
-    and chiral limit. No results for EQS at small quark mass

-   Lattice data provide evidence for Hagedorn type transition in full QCD
-  (a density driven deconfinement transition). Good description of LGT thermodynamics
-   and particle produciton yields by phenomenological statistical operator
-   of hadron resonance gas

-   The splitting of chemical freezeout and critical line  appears when
-    meson/baryon ratio is of the order of unity (E<40AGeV)

**      ****Conclusions**** **

##                   and                  ratios  along the freezout curve                                             NA49  data

- J.Cleymans,** **H. Oeschler & K.R.

- Include .

- F. Becattini, M. Gazdzicki, A. Keranen,
- J. Manninen & R. Stock

- very sensitive to contributions from weak decays (  A. Andronic J. Stachel).

##          Particle Ratios along freezout curve 

**Nu Xu & K.R**

- H. Oeschler, J. Cleymans & K.R

**SPS**

##       N()/K- independent of  centrality

- STAR

-       N()/K- independent of  centrality

- Should be centrality  dependent
- as

- P. Steinberg et al..

## Thermal calculations  Do not reproduce ratios of short-lived resonances (P. Fachini for STAR Coll.)

**J. Rafelski**

**NA49**
**PbPb**

**SPS model**

**pp Na49**

**pp 27GeV**

**pp**
**27GeV**

##                Collision broadening – vector mesons 

-         pion cloud modification
-        direct interactions with  hadrons

**N**

**N**

**   ****M. Post, S. Leupold, U. Mosel;**
**   ****M. F.M. Lutz, G. Wolf, **
**   ****B. Friman;**
**   ****M. Urban, M. Buballa, J.  **
**   ****Wambach**
**   ****R. Rapp, et al..; W. Weise, et al..;**
**   ****T. Hatsuda, S.H. Lee;**
**   ****Ch. Gale, et al..;****  G. Chanfray et al..; ****G.E. Brown, et al..;**** ...**

**B. Friman **
**& H. Pierner**

##        Vector meson spectral function           effective Lagrangian approach                          

- and

**low M => significant contribution from couplings  of: **

**R. Rapp et al..**

**        ** **to** the

-  **to the**

-  **states**

**M. Post, S. Leupold, U. Mosel**

##     Chiral Symmetry Restoration                          needs in-medium spectral function  

**Weinberg sum rules: ****(Kapusta &Schuryak****)**

**in vacuum: spontaneous chir. sym. breaking**

**in medium (phase tran. ):  chir. sym. restor****ed**

**critical region very  narrow**

**Boyd et al**

##        In medium effects and dilepton yield

**       ****In medium effects and dilepton yield**

**M. Post, S. Leupold, U. Mosel**

**vacuum **

**enhancement increases with decreasing**

** ****/ Baryon**** ****ratio**

**1-loop **

##       Isospin multiplets contribution to QCD                      thermodynamics

**Diferent Isospin states contribution to the thermodynamic pressure****:**

**Connected with LGT coefficient in the Taylor expansion of susceptibilities:**

**Largest deviations**
**in mesonic **
**channel **

##       Quark mass dependence of the QCD thermodynamics                       below deconfinement

**Linear dependence of  ****          ****on the **
**qua****r****k mass**** in LGT**

## Strangeness enhancement: energy and      strangeness content dependence

-  Tounsi & K.R

**Strangeness enhancement: energy and****      strangeness content dependence**

## {

- Yields/Participant  in   A-A/p-p collisions

- In UrQMD by M. Bleicher et al..

- In SM by A.Tounsi et al..

- enhancement decreases
- as energy increases

- the opposite behaviour

- Obtained with predicted thermal parameters:

- Compare with recent values from the fit
- to NA49 data (F. Becattini et al..):

##   Antikaon nuclear Bound state in heavy ion collisions 

-      strongly attractive        -- potential results in formation of deeply bound
-              -- nuclear states

**            **** ****                                **A. Andronic, P. Braun-Munzinger & K.R**         **

**Y. Akaishi & T. Yamazaki****        **

**                    ****nuclear state **
**seen in KEK experiment **
** ****reaction**** **

- M. Iwasaki et al

## Hagedorn  resonance gas and particle         multiplicity ratios at RHIC  

**DATA**

**                                  **

**Hagedorn  resonance gas and particle ****        multiplicity ratios at RHIC  **

** ****Particle multiplicity ratios**

**P. Braun Munzinger, D. Magestro, J. Stachel & K.R**

**Only 2-parameters  needed to fix all   particle yield****s**** ratios**
** ****obtained at  SIS through AGS, SPS up to RHIC energy**

##     space-time evolution -- thermalization

**    ****space-time evolution**** ****-- thermalization**

- Initial conditions, momentum distribution
-           L. McLerran & R. Venugopalan  model
- Thermalization:
- pQCD+kinetics                                                       R. Baier, A.H. Mueller, D.Schiff,  D.T.Son
- At LHC and RHIC:       thermalization occurs
-                                   relatively fast  due to
-                                   emission of  gluons
-  also from  Parton Cascade Model
-    K. Geiger,  J. Kapusta, B. Müller,   D.K.Srivastava
- Large elliptic flow at RHIC                       fast  <  1fm
- thermalization of partonic medium

## Chemical freeze-out: particle abundances are frozen in                                           
Thermal   freeze-out: particle spectra are frozen in

   Test of equilibration requires to specify:
   level of observation: multiplicities, spectra,  correlations        

- Thermal   freeze-out: particle spectra are frozen in
-    Test of equilibration requires to specify:
-    level of observation: multiplicities, spectra,  correlations

**            ****Heavy Ion ****collisions**** **

- Statistical operator ??

**           **

**include conservation laws: strangeness, isospin, baryon number**