28 May 2019 Topology of strong interactions, between the QCD and the EW transition. Maria Paola Lombardo INFN Firenze Florian Burger, Ernst-Michael Ilgenfritz, MpL and Anton Trunin Phys. Rev. D 98, 094501 Andrey Kotov, MpL, Anton Trunin arXiv:1903.05633, Phys. Lett. B, in press
Preamble
The two faces of QCD topology Strong interactions dynamics Window to Dark Matter
History of the Universe Time We will concentrate on the topology of QCD transition gauge fields in this range of temperatures, and on their observable properties EW transition Temperature Cambridge, DAMTP
Topology: geometric properties which do not change under continuous deformations.. how do we ‘measure’ them?
Topological charge Q : adding up a local - P Q ( x ) = P ( x ) Q = butterfly-like - operator Topological fluctuations measured by the susceptibility < Q 2 > − < Q > 2
History of the Universe Time # DoF QCD transition large change of #DoF = Symmetry change EW transition Cambridge, DAMTP Temperature
QCD Lagrangian symmetries: Always exact Breaking/restoration Always broken if topological charge at Tc fluctuates! DOES IT? studied a lot BUT: on the lattice the ‘amount' of breaking, may depend on temperature! HOW ARE THESE RELATED?? IMPLICATIONS?
A mystery of QCD…
χ PT predicts Pseudoscalar light spectrum: eight pseudoGoldstones SU (3) L XSU (3) R → SU (3) V U (1) A should be broken as well producing a 9th Goldstone BUT: Exception! η 0 is too heavy
η 0 too heavy A mystery of QCD: can be solved by topological charge fluctuations! < Q 2 > 6 = 0 Crucial ingredient: < Q (0) Q ( t ) > and (more later. …)
It is possible to couple QCD to topological charge Q — topological charge CP-violating term but: phenomenology tells us that θ must be unnaturally small This is the strong CP problem of QCD!
A second mystery of QCD… the strong CP problem ..can be solved by introducing the AXION a new particle which is a viable dark matter candidate < Q 2 ( T ) > Crucial ingredient: (more later..)
The experimental side
Time HI experiments: T < 500 MeV Lattice: T < 600-700 MeV - sufficient for Tc , hadron spectrum in the plasma QCD transition and QGP dynamics EW transition Lattice + extrap. T about 1000 MeV — and more needed to study axions Topology plays a major role in all this
Plan Axions Topology in QCD Results: Topological Susceptibility Bounds on the QCD axion’s mass η 0 The and its fate in the plasma
Axions ‘must’ be there (?) θ term, strong CP problem and topology electric dipole moment of the neutron = ( < Q 2 > − < Q > 2 ) /V
Axion potential Axion mass weakly coupled
After freezout constant Wantz, Shellard 2010
Cold Dark Matter candidates might have been created after the inflation Several CDM candidates are highly speculative - but one, the axion , is Theoretically well motivated in QCD Amenable to quantitative estimates once QCD topological properties are known: Post-inflationary axions Appear Freeze
QCD topology and phenomenology Almost all hadrons can be Hadron cosmology: described taking into account chiral symmetry breaking Origin of mass and confining potential Quarks Hadrons Nuclei time Nucleosynthesys QCD transition Chiral symm. breaking Confinement: Chiral perturbation theory + Potential models = Hadron spectrum
Almost all hadrons can be Hadron cosmology: described taking into account chiral symmetry breaking Origin of mass and confining potential With an important exception Quarks Hadrons Nuclei time Nucleosynthesys QCD transition Chiral symm. breaking Confinement: Chiral perturbation theory + Potential models = Hadron spectrum
χ PT predicts Pseudoscalar light spectrum: eight pseudoGoldstones SU (3) L XSU (3) R → SU (3) V U (1) A should be broken as well producing a 9th Goldstone BUT: Exception! η 0 is too heavy
η 0 U A (1) Topology, and the problem: The symmetry : ¯ qq would be broken by the (spontaneously generated) the candidate Goldstone is the η 0 (900 MeV) too heavy!! BUT: the divergence of the current contains a mass independent term 6 = 0 IF symmetry is explicitly broken The U A (1)
It can be proven that = Q Gluonic definition and Fermionic definition Q = n + − n − F ˜ F η 0 The mass may now be computed from the decay of the correlation Successful which at leading order gives the Witten-Veneziano formula at T=0
It can be proven that = Q Gluonic definition and Fermionic definition Q = n + − n − η 0 The mass may now be computed from the decay of the correlation which at leading order gives the Witten-Veneziano formula
It can be proven that = Q Gluonic definition and Fermionic definition Q = n + − n − η 0 The mass may now be computed from the decay of the correlation Q(y) Q(x) Successful which at leading order gives the Witten-Veneziano formula at T=0
solution ETMC 2017
Results Twisted mass Wilson Fermions, Nf=2+1+1
Wilson fermions with a twisted mass term Frezzotti Rossi 2003 A twisted mass term in flavor space: iµ τ 3 γ 5 for two degenerate light flavors iµ σ τ 1 γ 5 + τ 3 µ δ for two heavy flavors is added to the standard mass term in the Wilson Lagrangian Consequences: -simplified renormalization properties -automatic O(a) improvement -control on unphysical zero modes Successful phenomenology at T=0 ETMC collaboration 2003—
Why Nf = 2 +1 +1 ?
Trace anomaly: effects of a dynamical charm Tmft Wuppertal-Budapest Staggered
For each lattice Fixed Nf = 2 +1+1 Setup spacing we explore varying Table 1. Number and parameters of used configurations a range of scale temperatures T = 0 (ETMC) N 3 a [fm] [6] T [MeV] # confs. β N τ nomenclature σ 150MeV — 500 5 422(17) 585 MeV by varying Nt 6 351(14) 1370 7 301(12) 341 8 263(11) 970 24 3 9 234(10) 577 We repeat this for A60.24 1.90 0.0936(38) 10 211(9) 525 three different lattice 11 192(8) 227 12 176(7) 1052 spacings following 13 162(7) 294 32 3 ETMC T=0 14 151(6) 1988 5 479(22) 595 simulations. 6 400(18) 345 7 342(15) 327 8 300(13) 233 Advantages: we Four pion 9 266(12) 453 rely on the setup of 10 240(11) 295 32 3 B55.32 1.95 0.0823(37) masses 11 218(10) 667 ETMC T=0 12 200(9) 1102 13 184(8) 308 simulations. Scale is 14 171(8) 1304 set once for all. 15 160(7) 456 16 150(7) 823 6 509(20) 403 Disadvantages: 7 436(18) 412 8 382(15) 416 mismatch of 32 3 10 305(12) 420 temperatures - need D45.32 2.10 0.0646(26) 12 255(10) 380 14 218(9) 793 interpolation before 16 191(8) 626 40 3 18 170(7) 599 taking the 48 3 20 153(6) 582 continuum limit
Outcome: twisted mass ok; and the results Overview of Chiral observables confirm that a dynamical charm does not contribute Nf 2 + 1 +1 around Tc spacing effects below statistical errors
Topology
Kogut, Lagae, Sinclair 1999 Topological and chiral susceptibility HotQCD, 2012 χ top = < Q 2 top > /V = m 2 From: l χ 5 ,disc χ top = < Q 2 top > /V = m 2 l χ disc
Chiral susceptibility ψψ /T 2 ψψ /T 2 ψψ /T 2 χ ¯ χ ¯ χ ¯ 10 2 10 2 10 2 A260 A370 A470 10 1 B260 B370 B470 10 1 10 1 D210 D370 � 10 0 � 10 0 � 10 0 10 − 1 10 − 1 10 − 1 10 − 2 10 − 2 10 − 2 10 − 3 10 − 3 10 − 3 10 − 4 10 − 4 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 T [MeV] T [MeV] T [MeV] Within errors, no discernable spacing dependence
Rescaled according to Results for physical pion mass 100 D370 â phys ê m p L @ MeV D AB260 Û ı 50 Ì D210 370 continuum 135 MeV 20 @ Borsanyi et al. D 1 ê 4 ¥ H m p 10 c top 5 100 200 300 400 500 600 T @ MeV D
χ 0 . 25 ( T ) = aT − d ( T ) Power-law decay? d ( T ) ⌘ const ' (7 + N f For instanton gas 3 ) d ( T ) = − T d dT ln χ 0 . 25 ( T ) Possibly consistent with instant -dyon? 20 Shuryak 2017 DIGA H N f = 2 L DIGA H N f = 3 L 15 d eff H T L 10 5 250 300 350 400 450 T @ MeV D Faster decrease before DIGA sets in
Effective exponent d(T): χ 1 / 4 top = aT − d ( T ) 6 Fermionic, all masses Gluonic (nearly linear) Borsanyi et al. 5 Bonati et al. Petreczky et al. DIGA, Nf = 2 4 DIGA, Nf = 3 d(T) 3 2 1 <- Revised? 0 250 300 350 400 450 T [MeV]
QCD axion
From exponent d to axion mass in three steps 1. 150 100 2. 70 50 1 ê 4 @ MeV D 3. 30 Χ top 20 Ì 470 MeV 15 370 MeV · 260 MeV 10 Û 210 MeV ı 200 300 500 T @ MeV D
0.0 0.2 0.4 370 MeV W a ê W DM DM Á 260 MeV â ê 210 MeV 0.6 ‡ d = 8 H DIGA L Ï d = 4 Ì 0.8 Ú A ¥ 10 4 Ù A ê 10 4 1.0 1 5 10 50 100 500 Axion mass @ m eV D Axion mass @ eV D
0.0 0.2 0.4 370 MeV W a ê W DM DM Á 260 MeV â ê 210 MeV 0.6 ‡ d = 8 H DIGA L Ï d = 4 Ì 0.8 Ú A ¥ 10 4 Ù A ê 10 4 1.0 1 5 10 50 100 500 Axion mass @ m eV D Axion mass @ eV D Example: if axions constitute 80% DM, our results give a lower bound for the axion mass of ' 30 µ eV
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