STRONG INTERACTIONS WITH MANY FLAVORS

Transcription

1 GGI Firenze March Workshop on Holographic methods for strongly coupled systems STRONG INTERACTIONS WITH MANY FLAVORS Lattice results Maria Paola Lombardo INFN Based on M.P.L, K. Miura, T. Nunes da Silva, E.Pallante, Int.J.Mod.Phys. A29 (2014) arxiv: M.P.L, K. Miura, T. Nunes da Silva, E.Pallante, JHEP 1412 (2014) 183 arxiv:

2 Nf

3 1)Chirally Symmetric 2) M = m^δ(nf) 3) No thermal transition Banks, Zacs Appelquist et al Miransy-Yamawaki 3

4 Slide by R. Brower

5 CHIRAL SYMMETRY BREAKING NEEDS LARGE GAUGE COUPLING Chiral symmetry breaking is possible when the gauge coupling exceeds a critical value c 3 C 2 (R) = 2 N 3(N 2 1), where C 2 (R) is the quadratic Casimir of the the representation R. Thus we would expect that when N f is decreased below the value N c f at which = c, the theory undergoes a transition to a phase where chiral symmetry is spontaneously broken. The critical value N c f is given by N c f = N 100N! N 2 15 For large N, N c f approaches 4N, while for N =3, N c f is just below 12.

6 Hystorical overview N f N f N ** f S N ** f S N cr f S A N * f A N * f A A 2 2 g (0) g (0) cr g (0) PHASES OF QCD -- BANKS ZACS PHASES OF QCD - THE CONFORMAL WINDOW

7 Yet another axis.. T Nf 7

8 T S (QGP) A (QCD) Nf 8

9 Playground Playground for for this talk this talk

10 Outline Scaling and its probes Inside the conformal window The pre-conformal behavior Pre-conformality as a tool for QGP Scale separation Discussion and Outlook

11 From UV to IR ΛUV ΛIR Nfc 11

12 From UV to IR ΛUV ΛIR Scale separation Nfc 12

13 Physical scales & Lattice scales Lattice introduces two further technical scales a and L obscuring the UV and IR behaviour respectively Ratios of homogeneous quantities R = O1/O2 Miranski, Yamawaki Braun, Gies Kiritsis et al useful: Help controlling a and L systematic effects Display scale hierarchy with no need to fix the scale across different theories When O2 is an UV quantity non critical at Nfc -- taking the ratio is de facto a scale fixing procedure for O1 13

14 Arean, Iatrakis, Jarvinen, Kiritsis

15 Adimensional ratios below and above Nfc Ratios O(1) above Nfc Nfc IR fixed points O(Nf,m) = cₒ(nf) m^δ(nf) 15

16 Inside the conformal window

17 Hadron spectrum 17

18 Ratios in the conformal window at a glance: the Edinburgh plot 18

19 Lattice corrections to conformal scaling 1: Size 2: Coupling Del Debbio, Zwicky; Hasenfratz et al; MpL, da Silva, Miura, Pallante Our simulations are here 19

20 Anomalous dimension from the QED phase? 20

21 Summary of the results: accidental agreement?? 21

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23 Adimensional ratios below and above Nfc For Nf=12 we have observed conformal scaling, good agreement with four loops Nfc IR fixed points O(Nf,m) = cₒ(nf) m^δ(nf) 23

24 Conformal scaling observed for Nf=12 For Nf=12, T=0, we have observed conformal scaling, agreement among different groups once corrections to scaling are taken into account Nfc IR fixed points O(Nf,m) = cₒ(nf) m^δ(nf) Conformal phase at T=0 established 24

25 The preconformal behavior

26 Scaling for essential singularities Nogada, Hasegawa, Nemoto,PRL 2012 m <-> Chiral Condensate h <-> bare mass t <-> Nfc Nc m Chiral limit h=0 t Finite mass Within the scaling window data at finite mass contain information on the critical behaviour. They can can be approximativelydescribed as zero mass ones, but with a larger apparent critical point. 26

27 Choose an observable to monitor the approach to the conformal window, and work on the lattice first Our choices Critical temperature String Tension Wilson flow and w0

28 We studied the thermal transition for several Nf and several Nt Nf = 4 Nf = 8 Nf=6 All simulations : Gauge Action one loop Sym. Tadpole improved AsqTad 28

29 The critical number of flavor from lattice results

30 The critical number of flavor from bare results

31 Nt x a Ns x a From the Lattice....to the continuum Via old fashioned asymptotic scaling Must be approx. constant for several Nt 31

32 Nf = 6, asympt. scaling 32

33 Nf = 8, asympt scaling 33

34 Tc/Λ as a function of Nf Tc/Λ Λ = Λ(Nf) Conventional running Nf Scale separation? 34

35 Solution: Λ = Λ (Nf) ; use UV scale 35

36 Fixing an UV scale 36

37 Tc/M UV 37

38 Tc/M extrapolates to zero for Nf* ~

39 Tc/M extrapolates to zero for Nf* ~ 10.5 M fixed with the help of perturbation theory 39

40 String tension and w0 40

41 Lattice setup: β for Nf=8 Finite T results Nt=8 Choice for the T=0 simulation 41

42 Lattice setup: β for Nf=6 results Nt=8 Finite temperature, Nt=6 results βc = 5.025: Choice for the T=0 simulations And analogously for Nt=8 42

43 Nf=6: Creutz ratios Measurements code by M. Wagner and collaborators 43

44 Nf=8: Creutz ratios Measurements code by M. Wagner and collaborators 44

45 Heavy Quark Potential 45

46 Tc/ σ CAVEAT : no scaling check yet 46

47 Wilson flow Computationally easy Naturally smooth Well behaved at short distance 47

48 Scale from the flow, Nf=6 48

49 Scale from the flow, Nf=8 49

50 Results for Tc on the 1/w0 scale 50

51 Preconformality as a tool for the QGP

52 T /MUV Quark Gluon Plasma? Conformal Window Nf 52

53 Phases of Strong Interactions with many flavors Te m pe ra tu re Baryochemical Potential Nf

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57 Scale separation

58 Nf -> Nfc : Tc/M = 0 Tc w0 = 0 (?) Tc / σ ~

59 Different scales M ΛUV w0 ΛIR Tc, σ 59

60 Towards a quantitative comparison with holography Bigazzi and Cotrone, JHEP 2015 T increases with Nf on the scales used in these two studies 60

61 String tension, ratio Tc/sqrt(sigma) Adimensional ratios are free from the ambiguities of scale setting and might help comparing different approaches 61

62 For Nf=8 we have observed some evidence of scale separation, even with a nonzero mass Summary Nfc For Nf=12 we have measured conformal scaling, in good agreement with four loops and other lattice estimates. Perhaps surprisingly, the scaling appears to persist in the QEDlike region 62

63 Playground for this talk