How many scales in many-flavor QCD ?
March 6 2014
Maria Paola Lombardo
INFN1

Maria Paola Lombardo
Kohtaroh Miura
Elisabetta Pallante
Tiago Nunes da Silva

INFN, Italy
KMI, Nagoya University, Japan
University of Groningen, Netherlands
University of Groningen, Netherlands

We study Nc=3,Fundamental fermions :Nf = 0 -Nf = 4 -Nf = 6 -Nf = 8 -Nf = 12 -Nf = 16 -At zero and non-zero temperature.

MpL,KM,TndS,EP : work in progress
Talk by KM at Lat2013
Talk by TndS at Lat20132
KM,MpL Nuclear Physics B 871 (2013)

From UV to IR
LUV

LIR
Nfc

3

From UV to IR
LUV
Scale separation

LIRNfc4

Physical scales & Lattice scales Lattice introduces two further technical scales a and Lobscuring the UV and IR behaviour respectively

 Ratios of homogeneous quantities
R = O1/O2
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 forO15Plan• Critical temperature : Nf = (0,4,6,8)• String tension: Nf = 6,8• Wilson flow: Nf = 6,8• Spectrum and anomalous dimension: Nf=126

THE (PSEUDO)CRITICAL TEMPERATURE
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Lattice setup
All simulations :--Gauge Action: one loop Symanzyk improved--Fermion Action: Tadpole improved AsqTadm = 0.02 : only one mass
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Scaling for essential singularities
Nogada, Hasegawa, Nemoto,PRL 2012

m <-> Chiral Condensateh <-> bare masst <-> Nc - Nfc

Finite mass

Chiral limit

Within the scaling window
data at finite mass contain
information on the criticalbehaviour . They cancan beapproximativelydescribedas zero mass ones, butwith a larger apparent
critical point.
9

We studied the thermal transition for several Nf and several
Nt

All simulations :Gauge Action one loop Sym.
Tadpole improved AsqTad10

Ns x aNt x aFrom the Lattice..
..to the continuum
Via old fashioned asymptotic
scaling

Must be approx. constant for several Nt

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The quest for continuum limit
Explore different
prescriptions for Tc/LC. Allton, 200712

Nf = 6, asympt. scaling13

Nf = 8, asympt scaling

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Tc/L as a function of Nf

Tc/L
L = L(Nf)

NfScale separation ?

Conventional running15

Puzzle??

16

Solution: L = L (Nf) ; use UV scale

17

Fixing an UV scale18

Tc/MUV

19

Tc/M extrapolates to zero for Nf* ~ 10.5

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

21

Talk by K. Miura@Lattice2013

THE STRING TENSION

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Lattice setup: b for Nf=8

Finite Tresults Nt=8

Choice for the T=0
simulation
23Lattice setup: b for Nf=6results Nt=8Finitetemperature,
Nt=6 results

bc = 5.025:
Choice for the T=0simulations24

Nf=8: Creutz ratios25

Nf = 8 : String tension26

Nf=6: Creutz ratios27

Nf=6 String tension28

Tc/√ s29

Lim Nf -> Nfc Tc/√ s = Const.

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RESULTS FOR W031

Wilson flow

Computationally easyNaturally smoothWell behaved at short distance32

W0 vs r0

R. Sommer@Lat201333

With and without improvement

Nf=8Nf=634

Results for w0 – improved and unimprovedb = bc(Nt=8)

Control on thecontinuum limit:
Improved andunimprovedb = bc(Nt=6)

Two different b in the
more challenging
Nf=8 model35

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

Tc / √ s ~ 0.337

T.Nunes da Silva, Talk@Lattice 2013 (update of previous results)

NF=12 SPECTRUM

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Nf = 12 – Pion39

Nf=12- Rho40

Nf=12 Mass anomalous dimension
g = 0.33 (2)(rho) ; 0.35(3) (pion)
at b=3.9
E.Itou Lat2013

B.Schrock201341

mp/mr42

... A simple test of hyperscaling

Violation ofhyperscaling

43Summary
Indication of preconformality for Nf=8:--Scale separation-- Tc measured on a UV scale approaches 0Tc and the string tension have a similarsensitivity to the IRFP . Their ratio is weakly
dependent on Nf
Anomalous dimension g = 0.35(5) for Nf=12(Indication of violation of hyperscaling)44• Backup slides

45

46

Thermal coupling and IRFP
We consider the critical coupling at the temperaturescale 1/Nt

And we match it with the phenomenological zerotemperature critical coupling47IRFP from couplings

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