Baryons at finite temperature Gert Aarts Oxford, March 2017 p. 1 - PowerPoint PPT Presentation

Baryons at finite temperature Gert Aarts Oxford, March 2017 – p. 1

Introduction from hadronic to quark-gluon plasma thermodynamics: pressure, entropy, fluctuations symmetries: confinement, chiral symmetry spectroscopy quarkonia light mesons baryons real time transport far from equilibrium Oxford, March 2017 – p. 2

Introduction from hadronic to quark-gluon plasma thermodynamics: pressure, entropy, fluctuations symmetries: confinement, chiral symmetry spectroscopy quarkonia light mesons BARYONS real time transport far from equilibrium Oxford, March 2017 – p. 3

Mesons in a medium mesons in a medium very well studied hadronic phase: thermal broadening, mass shift QGP: deconfinement/dissolution/melting quarkonia survival as thermometer transport: conductivity/dileptons from vector current chiral symmetry restoration relatively easy on the lattice high-precision correlators what about baryons? Oxford, March 2017 – p. 4

Baryons in a medium lattice studies of baryons at finite temperature very limited screening masses De Tar and Kogut 1987 ... with a small chemical potential QCD-TARO: Pushkina, de Forcrand, Kim, Nakamura, Stamatescu et al 2005 temporal correlators Datta, Gupta, Mathur et al 2013 not much more ... holographic studies of baryons at finite temperature? Oxford, March 2017 – p. 5

Outline baryons across the deconfinement transition: some basic thermal field theory lattice QCD – FASTSUM collaboration baryon correlators in-medium effects below T c parity doubling above T c spectral functions Oxford, March 2017 – p. 6

Baryons α ′ G αα ′ ( x ) = � O α ( x ) O correlators (0) � in this work – N, ∆ , Ω baryons � � T O α N ( x ) = ǫ abc u α a ( x ) d b ( x ) Cγ 5 u c ( x ) � � � � �� T T O α 2 u α + d α ∆ ,i ( x ) = ǫ abc a ( x ) d b ( x ) Cγ i u c ( x ) a ( x ) u b ( x ) Cγ i u c ( x ) � � T O α Ω ,i ( x ) = ǫ abc s α a ( x ) s b ( x ) Cγ i s c ( x ) Oxford, March 2017 – p. 7

Baryons essential difference with mesons: role of parity P O ( τ, x ) P − 1 = γ 4 O ( τ, − x ) positive/negative parity operators P ± = 1 O ± ( x ) = P ± O ( x ) 2(1 ± γ 4 ) no parity doubling in Nature: nucleon ground state positive parity: m + = m N = 0 . 939 GeV m − = m N ∗ = 1 . 535 GeV negative parity: thread: what happens as temperature increases? Oxford, March 2017 – p. 8

Spectral properties in a medium euclidean correlators G ( x ) = � O ( x ) O † (0) � dispersion relation � ∞ dω ρ ( ω, p ) G ( iω n , p ) = 2 π ω − iω n −∞ imaginary part of retarded correlator ρ ( ω, p ) = 2Im G ( iω n → ω + iǫ, p ) back to euclidean time � ∞ dω G ( τ, p ) = 2 π K ( τ, ω ) ρ ( ω, p ) −∞ Oxford, March 2017 – p. 9

Spectral properties: mesons/bosons � ∞ dω G ( τ, p ) = 2 π K ( τ, ω ) ρ ( ω, p ) −∞ bosonic operators ( ˜ τ = τ − 1 / 2 T ) e − iω n τ cosh( ω ˜ τ ) � K boson ( τ, ω ) = T = ω − iω n sinh( ω/ 2 T ) n kernel symmetric around τ = 1 / 2 T , odd in ω spectral decomposition ρ B ( p ) = 1 |� n | O (0) | m �| 2 (2 π ) 4 δ (4) ( p + k n − k m ) � n /T − e − k 0 m /T � e − k 0 � Z n,m if O † = ± O ⇒ ωρ ( ω, p ) ≥ 0 positivity Oxford, March 2017 – p. 10

Spectral properties: baryons/fermions � ∞ dω G αα ′ ( τ, p ) = 2 π K ( τ, ω ) ρ αα ′ ( ω, p ) −∞ with α ′ G αα ′ ( x − x ′ ) = � O α ( x ) O ( x ′ ) � α ′ ρ αα ′ ( x − x ′ ) = �{ O α ( x ) , O ( x ′ ) }� fermionic Matsubara frequencies e − iω n τ e − ωτ 1 + e − ω/T = e − ωτ [1 − n F ( ω )] � K ( τ, ω ) = T = ω − iω n n kernel not symmetric, instead K (1 /T − τ, ω ) = K ( τ, − ω ) Oxford, March 2017 – p. 11

Kernels bosons cosh( ω ˜ τ ) sinh( ω/ 2 T ) = [1 + n B ( ω )] e − ωτ + n B ( ω ) e ωτ K boson ( τ, ω ) = fermions: even and odd terms K ( τ, ω ) = 1 2 [ K e ( τ, ω ) + K o ( τ, ω )] , cosh( ω ˜ τ ) cosh( ω/ 2 T ) = [1 − n F ( ω )] e − ωτ + n F ( ω ) e ωτ K e ( τ, ω ) = K o ( τ, ω ) = − sinh( ω ˜ τ ) cosh( ω/ 2 T ) = [1 − n F ( ω )] e − ωτ − n F ( ω ) e ωτ no singular behaviour 2 T/ω for fermions, no transport subtlety Oxford, March 2017 – p. 12

Spectral decomposition: Positivity � ρ ( x ) = γ µ ρ µ ( x ) + 1 1 ρ m ( x ) take trace with γ 4 , P ± = (1 1 ± γ 4 ) / 2 : m /T � 1 ρ 4 ( p ) = 1 4 |� n | O α (0) | m �| 2 (2 π ) 4 δ (4) ( p + k n − k m ) � n /T + e − k 0 e − k 0 � Z n,m,α m /T � 1 ρ ± ( p ) = ± 1 � 2 (2 π ) 4 δ (4) ( p + k n − k m ) n /T + e − k 0 � e − k 0 � � � n | O α � � ± (0) | m � Z 4 n,m,α ρ 4 ( p ) , ± ρ ± ( p ) ≥ 0 for all ω take trace with 1 1 ρ m ( p ) = [ ρ + ( p ) + ρ − ( p )] / 4 not sign definite Oxford, March 2017 – p. 13

Charge conjugation charge conjugation symmetry (at vanishing density): G ± ( τ, p ) = − G ∓ (1 /T − τ, p ) ρ ± ( − ω, p ) = − ρ ∓ ( ω, p ) relates pos/neg parity channels using G + ( τ, p ) and ρ + ( ω, p ) positive- (negative-) parity states propagate forward (backward) in euclidean time negative part of spectrum of ρ + ↔ positive part of ρ − example: single state G + ( τ ) = A + e − m + τ + A − e − m − (1 /T − τ ) ρ + ( ω ) / (2 π ) = A + δ ( ω − m + ) + A − δ ( ω + m − ) Oxford, March 2017 – p. 14

Chiral symmetry propagator � G ( x ) = γ µ G µ ( x ) + 1 1 G m ( x ) µ chiral symmetry { γ 5 , G } = 0 ⇒ G m = 0 hence G + ( τ, p ) = − G − ( τ, p ) = G + (1 /T − τ, p ) = 2 G 4 ( τ, p ) degeneracy of ± parity channels ρ + ( p ) = − ρ − ( p ) = ρ + ( − p ) = 2 ρ 4 ( p ) parity doubling in Nature at T = 0 : no chiral symmetry/parity doubling Oxford, March 2017 – p. 15

Baryons in a medium questions: in-medium effects below T c ? relevant for heavy-ion phenomenology? emergence of parity doubling? connection to deconfinement transition, chiral symmetry? chiral symmetry ⇔ parity doubling Oxford, March 2017 – p. 16

FASTSUM anisotropic N f = 2 + 1 Wilson-clover ensembles FASTSUM collaboration Ale Amato (Swansea->Helsinki->) GA (Swansea) Wynne Evans (Swansea->Bern->) Chris Allton (Swansea) Pietro Giudice (Swansea->Münster->) Simon Hands (Swansea) Tim Harris (TCD->Mainz->Milan) Seyong Kim (Sejong University) Benjamin Jaeger (Swansea->ETH) Maria-Paola Lombardo (Frascati) Aoife Kelly (Maynooth) Sinead Ryan (Trinity College Dublin) Bugra Oktay (Utah->) Don Sinclair (Argonne) Kristi Praki (Swansea) Jonivar Skullerud (Maynooth) Davide de Boni (Swansea) Oxford, March 2017 – p. 17

This work GA, Chris Allton, Simon Hands, Jonivar Skullerud Davide de Boni, Benjamin Jäger, Kristi Praki PRD 92 (2015) 014503, arXiv:1502.03603 [hep-lat] in preparation Oxford, March 2017 – p. 18

FASTSUM ensembles N f = 2 + 1 dynamical quark flavours, Wilson-clover many temperatures, below and above T c anisotropic lattice, a s /a τ = 3 . 5 , many time slices strange quark: physical value two light flavours: somewhat heavy m π = 384(4) MeV N s 24 24 24 24 24 24 24 24 N τ 128 40 36 32 28 24 20 16 T/T c 0.24 0.76 0.84 0.95 1.09 1.27 1.52 1.90 N cfg 140 500 500 1000 1000 1000 1000 1000 N src 16 4 4 2 2 2 2 2 tuning and N τ = 128 data from HadSpec collaboration Oxford, March 2017 – p. 19

Baryons in a medium technical remarks studied various interpolation operators Gaussian smearing for multiple sources and sinks same smearing parameters at all temperatures Oxford, March 2017 – p. 20

Lattice correlators nucleon positive parity ne gative T/ T c parity 1.90 0 10 1.52 N 1.27 1.09 G( ) 0.95 10 1 0.84 0.76 0.24 10 2 τ/a τ pos/neg parity channels nondegenerate more T dependence in negative-parity channel Oxford, March 2017 – p. 21

Lattice correlators ∆ positive parity ne gative T/ T c parity 1.90 0 10 1.52 ∆ 1.27 1.09 G( τ ) 0.95 − 1 10 0.84 0.76 0.24 − 2 10 τ/a τ pos/neg parity channels nondegenerate more T dependence in negative-parity channel Oxford, March 2017 – p. 22

Lattice correlators Ω positive parity ne gative T/ T c parity 1.90 0 10 1.52 Ω 1.27 1.09 G( τ ) 0.95 − 1 10 0.84 0.76 0.24 − 2 10 0 10 20 0 10 20 τ / a τ pos/neg parity channels nondegenerate more T dependence in negative-parity channel Oxford, March 2017 – p. 23

Baryons in the hadronic phase determine masses of pos/neg-parity groundstates T/T c 0.24 0.76 0.84 0.95 PDG ( T = 0 ) m N 1158(13) 1192(39) 1169(53) 1104(40) 939 + m N 1779(52) 1628(104) 1425(94) 1348(83) 1535(10) − m ∆ 1456(53) 1521(43) 1449(42) 1377(37) 1232(2) + m ∆ 2138(114) 1898(106) 1734(97) 1526(74) 1710(40) − m Ω 1661(21) 1723(32) 1685(37) 1606(43) 1672.4(0.3) + m Ω 2193(30) 2092(91) 1863(76) 1576(66) 2250–2380–2470 − δ N 0.212(15) 0.155(35) 0.099(40) 0.100(35) 0.241(1) δ ∆ 0.190(31) 0.110(31) 0.089(31) 0.051(28) 0.162(14) δ Ω 0.138(9) 0.097(23) 0.050(23) -0.009(25) 0.147–0.175–0.192 δ = m − − m + masses in MeV m − + m + Oxford, March 2017 – p. 24