Phases of many flavors QCD some of our

Phases of many flavors QCD : (some of our) lattice results Maria Paola Lombardo INFN Albert Deuzeman, MPL , Kohtaroh Miura , Tiago Nunes da Silva, Elisabetta Pallante Work in progress + AD, Mp. L, TNd. S, EP : ar. Xiv: 1209. 5720 Submitted to PLB KM, Mp. L, EP: ar. Xiv: 1111. 1098, PLB 2012 AD, Mp. L, EP : ar. Xiv: 1201. 1863 , Lattice 2011

QCD with many flavors : Sketchy view of the phase diagram Quasi Conformal/ Walking dynamics Hadronic Ph Phase Conformal Window of QCD Nfc NAF Nf

(ideal) Outline • • • • • Nf=0 Nf=1 Nf=2 Nf=3 Nf=4 Nf=5 Nf=6 Nf=7 Nf=8 Nf=9 Nf=10 Nf=11 Nf=12 Nf=13 Nf=14 Nf=15 Nf=16 Summary

Outline • • • Nf=0 Nf=2 Nf=3 Nf=4 Introduction Nf=5 • Nf=6 Near Conformal: • Nf=8 Continuum and Lattice • Nf=9 • Nf=7 • • Nf=10 Nf=11 • Nf=12 • • Nf=13 Nf=14 Nf=15 Nf=16 Conformal Summary Nfc ≈ 12

Near Conformal: Continuum and Lattice Theme #1: precursors effects of conformality when approaching Nfc from the QCD side

Near Conformal: Continuum and Lattice Theme #1: precursors effects of conformality when approaching Nfc from the QCD side 1)Essential singularity Miransky-Yamawaki 1996: Preconformal dynamics likely different from QCD 2) Power law singularity Braun-Gies 2006 Preconformal dynamics likely different from QCD 3) Discontinuity – ‘Jump’ Sannino 2012 Preconformal dynamics likely similar to QCD

Conformal Theme #2 : Physics of the Conformal Window --’Large’ anomalous dimension? --Strongly Nf c 12 Interacting? ≈

We are looking for conformal theories different from free field and different from QED! Conformal Theme #2 : Physics of the Conformal Window --’Large’ anomalous dimension? --Strongly Nf c 12 Interacting? ≈

QCD-like : running coupling

Running vs Walking : Both compatible with IR slavery and UV freedom acr Running : L sets the scale Walking : Separation of Scales: Interesting for Phenomenology

The discovery of the conformal window of QCD Miransky-Yamawaki, 1997; Appelquist et al. 1997 • For Nf > 8 the perturbative b function of QCD develops a second 0 : the Banks. Zacs IRFP. • Then the coupling runs to IRFP • Chiral Symmetry Breaking requires • 1) IRFP < acr CONFORMAL WINDOW a>acr: acr a* 2) IRFP > acr IRFP disappears QCD-like, but: NEAR-CONFORMALITY, WALKING Relevant for Conformal NEAR-CONFORMALITY, Technicolor transition WALKING acr

i h S go Ei a i n nta 1 1 0 e 2 ic t t a t. L Running established up to 5 Flavors

Can we establish walking as well?

Can we establish walking as well? (if yes, it has to be for Nf > 5)

Near-Conformal behaviour On the QCD-side can be seen in: Different scales LUV and LIR Critical behaviour Nf Power law : Essential singularity: m m= OR Nfc

Thermal transition and near-conformal dynamics J. Braun , H. Gies 06 08 09

Towards Conformality: Continuum (from the lattice)

Ns x a Nt x a From the Lattice. . to the continuum Via old fashioned asymptotic scaling Must be approx. constant for several Nt (Old fashioned asymptotic scaling)

Nf = 6 Chiral crossover of order parameter Nt

Nf=6 : Chiral crossover of the chiral cumulant Rp

Summary of results for bc (updated at x. QCD 2012 - KM) Must be Nt independent

Nt-(quasi) independence of Tc/LLat for Nf = 6 KM, EP, MPL 2012

rom Slide f a K. Miur 2 01 x. QCD 2

Tc/L as a function of Nf Tc/L Conventional running Scale separation Nf

Fixing an UV scale KM@xqcd 2012

Tc/MUV KM@xqcd 2012

Trading LLAT for LIR stable KM, MPL, EP 2012

Alternative analysis Our results Shuryak and Sulejmanpasic , 2012 Line Of IRFP Shuryak and Liao, 2012 Strongest coupled QGP? Nf

Quasi Conformal QGP Strongly Coupled QGP Hadronic Phase

(Quasi)Conformality and High T QCD h/S < (3 – 5) / 4 p M. Panero 2010 S. Borsaniy et al. 2011

Conformality and near-Conformality at zero and finite T: coupling ‘walks’ in the plasma! NEAR-CONFORMAL QGP s. QGP GP – Q r e g n Stro “More” ly walking ow more sl Kaczmarez-Zantov 2005 J. Braun, H. Gies , 06 Conformal Window

Towards Conformality. Lattice

PHASES OF QCD ON THE LATTICE : Temperature = 0 Miransky, Yamawaki evidence of) ? And in progress

PHASES OF QCD ON THE LATTICE : Finite Nt evidence of) Finite T chiral transition finite Nf And in progress Nf=0 Yang. Mills finite T deconf ?

PHASES OF QCD ON THE LATTICE : Finite Nt Numerical results Phases of QCD below Nf_c

Critical number of flavor from thermal lines Nfc = 10(2) (preliminary) KM MPL 2012 (prel. )

Inside the Conformal window -and near the continuum-

Mass ratio : qualitative features discriminating broken and symmetric phases

The transition of 4 d. QED on a Lattice Kocic, Kogut, MPL, 1992 Symmetric Broken

Nf = 12

Nf=12: mass ratio Our results

The nucleon mass and the ‘Edinburgh Plot’ in the conformal window EP@Lat 2011 AD, MPL, EP 2012

Anomalous dimension EP@Lat 2011 AD, MPL, EP 2012 Caveat. . . Can we compute anomalous dimenions away from IRFP ? ? ?

Critical scaling of the chiral transition Critical scaling of IRFP Two Tasks: 1) Chiral Symmetry vs Chiral Symmetry Breaking 2) If we measure an anomalous dimension, is this associated to Chiral or Conformal Symmetries?

Inside the Conformal window -strong lattice coupling-

Precursors of Conformality at strong coupling: For Nf < 52 chiral symmetry is always broken at 1/g= 0 Hence, in the conformal window there is bulk transition at strong coupling Lin eo f ch ira l tr ymmetric an si tio na ymmetric t. T Continuum G= infty : De Forcrand, Kim, Unger 2012 =0 Nf = 16: Damgaard et al. 1996 Nf=12 AD, Mp. L, TNd. S, EP 20102012 ; A. Hasenfratz et al. 2012

Zooming in : Nf=12 Two transitions? AD, Mp. L, EP 2010; 2012 A. Hasenfratz et al 2011 NB: Towards the Continuum : same chiral ly symmetric phase with improve And un-improved actions Only one transition with a naive action ! AD, Mp. L, TNd. S, EP 2012

Zooming in : Nf=12 Effects of the improvement on the bulk transition Shift symmetry breaking, A. Hasenfratz et al 2012 Chiral symmetry realized in an unusual way AD, Mp. L, TNd. S, EP 2012 Towards the Continuum : same chiral ly symmetric phase Improved actions Positivity Violation Different realizations of charge neutrality

Summary

Near-conformal dynamics : v. Scale separation likely for Nf > 6 v. Two consistent estimates of Nf critical: From continuum scaling Nf critical = 11 (3) From lattice pseudocritical lines: Nf critical = 10(2) (preliminary ) .

Near-conformal dynamics : v. Scale separation likely for Nf > 6 v. Two consistent estimates of Nf critical: From continuum scaling Nf critical = 11 (3) From lattice pseudocritical lines: Nf critical = 10(2) (preliminary ) Conformal dynamics: ØMeasured anomalous dimension for Nf=12 – caveat on gauge coupling dependence ØInteresting features of the strong coupling regime with an unusual realization of chiral symmetry for improved actions .

Near-conformal dynamics : v. Scale separation likely for Nf > 6 v. Two consistent estimates of Nf critical: From continuum scaling Nf critical = 11 (3) From lattice pseudocritical lines: Nf critical = 10(2) (preliminary ) Conformal dynamics: ØMeasured anomalous dimension for Nf=12 – caveat on gauge coupling dependence ØInteresting features of the strong coupling regime with an unusual realization of chiral symmetry for improved actions Outlook : o. Scale setting from physics observables for Nf = 4, 6, 8 o. Direct observation of IRFP for Nf=16. o. Issues on anomalous dimensions away from IRFP to be clarified . . . more generally, interplay with thermal QCD and the physics of the strongly interactive Quark Gluon Plasma