New Frontiers of Lattice Field Theories

Transcription

1 QCD with many flavors at zero and non-zero temperature Maria Paola Lombardo Albert Deuzeman, MPL, Kohtaroh Miura, Tiago Nunes da Silva, Elisabetta Pallante New Frontiers of Lattice Field Theories GGI Firenze 17 September 2012

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

3 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 (ideal) Outline

4 Outline Nf=0 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 Introduction Near Conformal: Continuum and Lattice Conformal Nfc 12 Summary

5 Near Conformal: Continuum and Lattice This talk s main theme: precursors effects of conformality when approaching Nfc from the QCD side

6 QCD-like : running coupling

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

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

9 Running established up to 5 Flavors

10 Can we establish walking as well?

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

12 Near-Conformal behaviour On the QCD-side can be seen in: Different scales LUV and LIR Critical behaviour Nf Nfc m

13 Thermal transition and near-conformal dynamics J. Braun, H. Gies

14 Towards Conformality: Continuum (from the lattice)

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

16 Nf = 6 Chiral crossover of order parameter Nt

17 Nf=6, Polyakov loop

18 Nf=6 : Chiral crossover of the chiral cumulant Rp

19 Summary of results for bc (updated at xqcd2012) Must be Nt independent

20 Nt-(quasi) independence of Tc/LLat for Nf = 6

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

23 Fixing an UV scale

24 Tc/MUV

25 Trading LLAT for LIR stable

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

28 Quasi Conformal QGP Strongly Coupled QGP Hadronic Phase

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

30 Conformality and near-conformality at zero and finite T: coupling walks in the plasma! Kaczmarez-Zantov 2005 J. Braun, H. Gies, 06 Conformal Window

31 Towards Conformality- Lattice

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

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

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

35 Critical number of flavor from thermal lines Nfc = 10(2) (preliminary)

36 Inside the Conformal window

37 The nucleon mass and the Edinburgh Plot in the conformal window

38 Mass ratio : qualitative features discriminating broken and symmetric phases

39 The transition of 4dQED on a Lattice Kocic, Kogut, MPL, 1992 Symmetric Broken

40 Nf = 12

41 Nf=12: mass ratio Our results

42 Chiral Partners, and anomalous dimension Caveat... Can we compute anomalous dimenions away from IRFP???

43 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?

44 Summary

45 Near-conformal dynamics (continuum): Tc/L suggests scale separation for Nf > 6 Pre-conformal (critical) behaviour observed for Nf > 6, with Nf critical = 11 (3) Shuryak s (equivalent) view : coupling at (Tc, Nfc) = coupling at IRFP Near-conformal dynamics (lattice) : Thermal pseudocritical lines meet at (g*, Nf critical), with Nf critical = 10(2) (preliminary) All estimates confirm that twelve flavors is close to the conformal transitions Nf=12 difficult to study directly (as we know!) Interesting interplay with finite temperature QCD with implications for the physics of the strongly interactive quark gluon plasma