Varying Nf in QCD: scale separation, topology (and hot axions) - - PowerPoint PPT Presentation

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Varying Nf in QCD: scale separation, topology (and hot axions) - - PowerPoint PPT Presentation

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Varying Nf in QCD: scale separation, topology (and hot axions) Maria Paola Lombardo INFN I. Zero temperature: String tension, Critical temperature, Wilson flow MpL, K. Miura, T. J. Nunes da Silva and E. Pallante, Int. J. Mod. Phys. A 29 , no.

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Varying Nf in QCD: scale separation, topology (and hot axions)

Maria Paola Lombardo INFN

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  • I. Zero temperature:

String tension, Critical temperature, Wilson flow

  • II. High temperature:

Topological susceptibility

MpL, K. Miura, T. J. Nunes da Silva and E. Pallante,

  • Int. J. Mod. Phys. A 29, no. 25, 1445007 (2014),

+ work in progress

  • A. Trunin, F. Burger, E. M. Ilgenfritz, MpL and M. M¨

uller-Preussker,

  • J. Phys. Conf. Ser. 668, no. 1, 012123 (2016),
  • J. Phys. Conf. Ser. 668, no. 1, 012092 (2016),

+ work in progress

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  • I. Zero temperature:

String tension, Critical temperature, Wilson flow

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Y es

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Next

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From UV to IR

11

ΛIR ΛUV

Nfc

x = Nf/Nc In the conformal phase IR scales vanish but UV ones survive

Standard picture of scale separation

The coupling walks for

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From UV to IR

12

ΛIR ΛUV

Nfc

Scale separation

Standard picture of scale separation

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Arean, Iatrakis, Jarvinen, Kiritsis 2013

(Essential) singularity in the chiral limit and mass ratios: example from holographic V-QCD Not Unique

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Power-law corrections to essential singularity

Gies et al. 2013 Alho, Evans, Tuominen 2013

Miranski scaling

Power-law X Quasi-Goldstone nature of the scalar

not unique:

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Mass deformed theory: EoS approach for IR quantities

y = f(x) y = m/ < ¯ ψψ >δ δ = 6−η

2−η

Second order transition: x = (Nf

c − Nf)/ < ¯

ψψ >

1 β

< ¯ ψψ >= (Nf

c − Nf)β

Essential singularity: x = e √

(Nf c−Nf )/ < ¯

ψψ > < ¯ ψψ >= e √

(Nf c−Nf )

Continuity of f(x) plus asymptotic forms for m → 0 and Nf → Nf

c imply

< ¯ ψψ >∝ e √

(Nf c−Nf ) for m smallish and (Nf c − Nf) largish

< ¯ ψψ >∝ m1/δ for m largish and (Nf

c − Nf) smallish

Nogawa, Hasegawa, Nemoto, 2012

Anomalous dimension appears naturally below Nfc

Scaling limited by Goldstone singularities in the chiral limit (Wallace Zia)

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Alho, Evans, Tuominen 2013

Mass deformed theory Analogous to KMI, LSD These features are seen in model calculations:

With mass

With mass

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Mutatis mutandis, Eos approach reproduces KMI scenario: Mass deformed theory II: KMI discussion

Scaling with anomalous dimension

KMI 2013

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IR IR IR….. Conformal scaling IR Griffith’s analyticity Analogies in the broken phase Essential sing. Differences in the symmetric phase 2nd order transition (X power-law) Approaching conformality from below and above EoS

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Observables: Critical temperature W0, W1, … induced by Wilson flow String tension Technical lattice scale defined at one lattice spacing

Strategy: consider dimensionless ratios R = O1/O2 When O2 is UV this is the facto a conventional scale setting Observation: R relatively stable wrt mass variations

Preliminary Preliminary

ΛLAT

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Results

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From an IR to a UV scale: T c decreases

KM, MpL, EP 2012

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Asymptotic scaling

  • f Tc

gives Tc/Λ More difficult to reach for Nf=8

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Towards a quantitive comparison with holography

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Nf = 6, Wilson Flow Nf = 8, Wilson Flow

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Nf=6

0.1 0.2 0.3 0.4 0.5 0.6 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 t d/dt t2 E w0Tc Beta = 5.025, Wilson Beta = 5.025, Symanzik Beta = 5.2, Wilson Beta = 5.2, Symanzik

Preliminary Scale from Wilson flow

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Preliminary

T c on the 1/w0 scale

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0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 (Tcw0(Nf=6) - Tcw0(Nf=8))/Tcw0(Nf=6) Reference value

Moving the scale with Wilson flow

TcWr(Nf=6)−TcWr(Nf=8) TcWr(Nf=6)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 t d/dt t2 E w0Tc Nf = 6 Nf = 8

UV

Qualitatively as expected, limited by lattice artifacts

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T c and the string tension

Preliminary

Tc √σ ∝ (1 − ✏Nf/Nc)

Again similar to the prediction

  • f the WSS model:

communicated by F. Bigazzi

Mild decrease, possibly constant as Nf → N c

f

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Scale separation in the preconformal region of QCD

Preliminary

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Results by LSD

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Scale separation

++

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Scale separation

Puzzle? Role of UA(1) symmetry ? It’s important at finite T .. ++

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Ok

S c a l e s e p a r a t i

  • n

: d i f f e r e n t f r

  • m

Q C D

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  • II. High temperature:

Topological susceptibility

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Nf T Tc sQGP

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: 3H(T) = ma(T) Axion freezout Berkowitz Buchoff Rinaldi 2015 Axion density at freezout controls axion density today Freezout Yang Mills

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Axions ‘must’ be there: solution to the strong CP problem

Ammitted but

Postulate axions, coupled to Q:

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How many flavors?

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In the region of interest T > 500 MeV 1) We need 2+1+1 2) 2+1+1 = 4 (approximatively)

We can place the region of interest in the Nf, T diagram

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Sanity check + confirms dynamical charm does not affect the critical region TMFT, prel.

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0.01 0.02 0.03 0.04 0.05 0.06 0.07

  • 20
  • 15
  • 10
  • 5

5 10 15 20 Beta = 2.1 ’gWF-b2.10nt20.tout2’ using 1:3 ’gWF-b2.10nt20.tout3’ using 1:3 ’gWF-b2.10nt20.tout4’ using 1:3 ’gWF-b2.10nt20.tout5’ using 1:3 ’gWF-b2.10nt20.tout1’ using 1:3 ’gWF-b2.10nt20.tout6’ using 1:3 0.1 0.2 0.3 0.4 0.5 0.6 0.7

  • 4
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  • 2
  • 1

1 2 3 4 Beta = 2.1

Cold Hot Shape of distributions of topological charge: different flow time Q Q = (0.1,0.15,0.2,0.3,0.4,0.45,0.66)

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Bonati, D’Elia, Mariti, Martinelli,Mesiti,Negro,Sanfilippo, Villadoro arXiv:1512.0674

TMFT Decrease with T much slower than DIGA

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80 100 120 140 160 180 200 220 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 Chi**0.25 a2 200 < T < 210 400 < T < 430 150 < T < 153 160 < T < 165 240 < T < 250 340 < T < 350

, 0.6

Continuum limit for different scales

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χ(T)1/4 T A preliminary continuum extrapolation shows an even milder decrease wrt to Nf = 2+1 ..to be continued strong sensitivity to Nf

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Summary

We have studied the evolution of different dimensionless

  • bservables with Nf, for a fixed quark mass.

An external mass enables communication between different phases, which are no longer qualitatively different. The dynamics retain features of the precritical behavior, in accordance with an EoS analysis:we have observed scale separation which indirectly supports walking of the coupling. The theory with eight flavors is qualitatively different from QCD.

Topological susceptibility at high T, which is relevant for axion physics, seems to be particularly sensitive to the number

  • f fermions.