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. 25, 1445007 (2014), + work in progress II. High temperature: Topological susceptibility 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
I. Zero temperature: String tension, Critical temperature, Wilson flow
Y es
Next
Standard From UV to IR picture of scale separation Λ UV In the conformal phase IR scales vanish but UV ones Λ IR survive Nfc The coupling walks for 11 x = N f /N c
Standard From UV to IR picture of scale separation Λ UV Scale separation Λ IR Nfc 12
(Essential) singularity in the chiral limit and mass ratios: example from holographic V-QCD Not Unique Arean, Iatrakis, Jarvinen, Kiritsis 2013
not unique: Power-law corrections to essential singularity Gies et al. 2013 Alho, Evans, Tuominen 2013 Power-law X Miranski scaling Quasi-Goldstone nature of the scalar
Mass deformed theory: EoS approach for IR quantities y = f ( x ) y = m/ < ¯ δ = 6 − η ψψ > δ 2 − η Second order transition: 1 c − N f ) / < ¯ < ¯ c − N f ) β x = ( N f ψψ > ψψ > = ( N f β Nogawa, Hasegawa, Nemoto, 2012 Essential singularity: √ √ ( N f c − N f ) / < ¯ < ¯ ( N f c − N f ) x = e ψψ > ψψ > = e c imply Continuity of f ( x ) plus asymptotic forms for m → 0 and N f → N f √ ( N f c − N f ) for m smallish and ( N f < ¯ c − N f ) largish ψψ > ∝ e ψψ > ∝ m 1 / δ for m largish and ( N f < ¯ c − N f ) smallish A nomalous dimension appears naturally below Nfc Scaling limited by Goldstone singularities in the chiral limit (Wallace Zia)
These features are seen in model calculations: Alho, Evans, Tuominen 2013 Mass deformed theory With mass With mass Analogous to KMI, LSD
Mass deformed theory II: KMI discussion Mutatis mutandis, Eos approach reproduces KMI scenario: Scaling with anomalous dimension KMI 2013
Approaching conformality from below and above IR IR IR….. Essential sing. Conformal scaling (X power-law) Analogies Differences in the broken phase in the symmetric phase EoS IR 2nd order transition Griffith’s analyticity
Observables: Critical temperature Preliminary W0, W1, … induced by Wilson flow Preliminary String tension Technical lattice scale defined at one lattice spacing Λ LAT 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
Results
From an IR to a UV scale: T c decreases KM, MpL, EP 2012
Asymptotic scaling of Tc gives T c / Λ More difficult to reach for Nf=8
Towards a quantitive comparison with holography
Nf = 6, Wilson Flow Nf = 8, Wilson Flow
Scale from Wilson flow Nf=6 0.6 Beta = 5.025, Wilson Beta = 5.025, Symanzik Beta = 5.2, Wilson Beta = 5.2, Symanzik 0.5 0.4 t d/dt t 2 E 0.3 0.2 Preliminary 0.1 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 w0Tc
T c on the 1/w0 scale Preliminary
Moving the scale with Wilson flow Qualitatively as expected, limited by lattice artifacts 0.45 Nf = 6 0.21 Nf = 8 0.4 T c W r ( N f =6) − T c W r ( N f =8) 0.2 0.35 T c W r ( N f =6) (Tcw0(Nf=6) - Tcw0(Nf=8))/Tcw0(Nf=6) 0.19 0.3 0.18 0.25 t d/dt t 2 E 0.2 0.17 0.15 0.16 0.1 0.15 0.05 0.14 0 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Reference value w0Tc UV
T c and the string tension Mild decrease, possibly constant as N f → N c f Preliminary Again similar to the prediction of the WSS model: T c √ σ ∝ (1 − ✏ N f /N c ) communicated by F. Bigazzi
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 0 important at finite T ..
S c a l e d s i f e f p e a r e r a n t t i o f n r o : m Q C D Ok
II. High temperature: Topological susceptibility
T Tc sQGP Nf
Axion freezout : 3H(T) = m a (T) Berkowitz Buchoff Rinaldi 2015 Yang Mills Freezout Axion density at freezout controls axion density today
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
TMFT, prel. Sanity check + confirms dynamical charm does not affect the critical region
Shape of distributions of topological charge: different flow time = (0.1,0.15,0.2,0.3,0.4,0.45,0.66) Beta = 2.1 Beta = 2.1 0.07 0.7 ’gWF-b2.10nt20.tout2’ using 1:3 ’gWF-b2.10nt20.tout3’ using 1:3 ’gWF-b2.10nt20.tout4’ using 1:3 0.06 ’gWF-b2.10nt20.tout5’ using 1:3 0.6 ’gWF-b2.10nt20.tout1’ using 1:3 Cold Hot ’gWF-b2.10nt20.tout6’ using 1:3 0.05 0.5 0.04 0.4 0.03 0.3 0.02 0.2 0.01 0.1 0 0 -20 -15 -10 -5 0 5 10 15 20 -4 -3 -2 -1 0 1 2 3 4 Q Q
TMFT Decrease with T much slower than DIGA Bonati, D’Elia, Mariti, Martinelli,Mesiti,Negro,Sanfilippo, Villadoro arXiv:1512.0674
Continuum limit , 0.6 for different scales 220 200 < T < 210 400 < T < 430 150 < T < 153 160 < T < 165 200 240 < T < 250 340 < T < 350 180 160 Chi**0.25 140 120 100 80 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 a 2
A preliminary continuum extrapolation shows an even milder decrease wrt to Nf = 2+1 strong sensitivity to Nf χ ( T ) 1 / 4 ..to be continued T
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.
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