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

Maria Paola Lombardo INFN

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. Muller-Preussker,

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

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

+ work in progress

I. Zero temperature:

String tension, Critical temperature, Wilson flow

Yes

Next

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

From UV to IR

12

ΛIR

ΛUV

NfcScale

separatio

n

Standard picture of scale

separation

14

Arean, Iatrakis, Jarvinen, Kiritsis 2013

(Essential) singularity in the

chiral limit and mass ratios: example from holographic

V-QCD

Not Unique

Power-law corrections to essential singularity

Gies et al. 2013 Alho, Evans, Tuominen 2013

Miranski scalingPower-law X

Quasi-Goldstone nature of the scalar

not unique:

Mass deformed theory: EoS approach for IR quantities

y = f(x)

y = m/ <

¯

>

�� =

6�⌘2�⌘

Second order transition:

x = (Nfc �Nf )/ <

¯

>

1�

<

¯

>= (Nfc �Nf )

�

Essential singularity:

x = e

p(Nf

c�Nf )/ <

¯

> <

¯

>= e

p(Nf

c�Nf )

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

<

¯

>/ e

p(Nf

c�Nf )for m smallish and (Nf

c �Nf ) largish

<

¯

>/ m

1/�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)

Alho, Evans, Tuominen 2013

Mass deformed theory

Analogous to KMI, LSD

These features are seen in model calculations:

With mass

With mass

Mutatis mutandis, Eos approach reproduces KMI scenario:

Mass deformed theory II: KMI discussion

Scaling with anomalous dimension

KMI 2013

IR IR IR…..

Conformal scaling

IR

Griffith’s analyticity

Analogiesin the broken phase

Essential sing.

Differencesin the symmetric phase

2nd order transition

(X power-law)

Approaching conformality from below and above

EoS

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

PreliminaryPreliminary

⇤LAT

Results

From an IR to a UV scale: Tc decreases

KM, MpL, EP 2012

Asymptotic scaling of Tc givesTc/⇤

More difficult

to reach for Nf=8

Towards a quantitive comparison with holography

Nf = 6, Wilson Flow

Nf = 8, Wilson Flow

Nf=6

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

t d/d

t t2 E

w0Tc

Beta = 5.025, WilsonBeta = 5.025, Symanzik

Beta = 5.2, WilsonBeta = 5.2, Symanzik

Preliminary

Scale from Wilson flow

Preliminary

Tc on the 1/w0 scale

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

(Tcw

0(N

f=6)

- Tc

w0(

Nf=

8))/T

cw0(

Nf=

6)

Reference value

Moving the scale with Wilson flow

TcWr(Nf=6)�TcWr(Nf=8)TcWr(Nf=6)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

t d

/dt

t2 E

w0Tc

Nf = 6Nf = 8

UV

Qualitatively as expected, limited by lattice artifacts

Tc and the string tension

Preliminary

Tcp�/ (1� ✏Nf/Nc)

Again similar to the prediction of the WSS model:

communicated by F. Bigazzi

Mild decrease, possibly constant as Nf ! N c

f

Scale separation in the

preconformal region of QCD

Preliminary

Results by LSD

Scale separation

0++

Scale separation

Puzzle? Role of UA(1)

symmetry ? It’s important at finite T..

0++

Ok

Scale

separ

ation:

differe

nt fro

m QCD

II. High temperature: Topological susceptibility

Nf

T

Tc sQGP

: 3H(T) = ma(T) Axion freezout

Berkowitz Buchoff Rinaldi 2015

Axion density at freezout controls axion density today

Freezout

Yang Mills

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

Ammitted but

Postulate axions, coupled to Q:

How many flavors?

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

Sanity check + confirms dynamical charm

does not affect the critical region

TMFT, prel.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-20 -15 -10 -5 0 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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-4 -3 -2 -1 0 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)

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

TMFT

Decrease with T much slower than DIGA

80

100

120

140

160

180

200

220

0 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 < 430150 < T < 153160 < T < 165240 < T < 250340 < T < 350

, 0.6Continuum limit for different scales

�(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

Summary

We have studied the evolution of different dimensionless observables 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 of fermions.