 (YITP, Kyoto University)!!!!!!in!collabora*on!with!

Frithjof Karsch (Universität Bielefeld, Brookhaven National Lab.)
Swagato Mukherjee (Brookhaven National Lab.)Peter Petreczky (Brookhaven National Lab.)
  20158314492

Introduc)onThermal0ﬂuctua)on0in0QCD0Modiﬁca)ons0of0hadrons00000000000000000000000Restora)ons0of0broken0symmetries
sequen*al!mel*ng!pa=ern!
!!!!of!quarkonium!and!!
!!!!!open@ﬂavor!mesons!
!!e.g.!J/ψ suppression!
!!!!!!!!!!!!!!!!!!!Matsui!and!Satz!(1986)

restored!pa=ern!!
!!!!of!chiral!and!UA(1)!symmetries!
!!the!nature!of!phase!transi*on!
!!!!!!!!!!!!!!!!!!!!!!!!!!Pisarski!and!Wilczek!(1984)!

Theore*cal!understanding!in!laMce!QCD!simula*ons!
from!spa*al!correla*on!func*ons
Previous:!strange4charm!!!!!!PRD91!(2015)!5,!054503!
This!work:!including!up/down0at0widely0T0rangeHadronic0excita)on0on0LaHce
Temporal!correla*on!func*on:!
!
†GT ( , T ) = d3 x JH(0, 0)JH ( , x)!

Ae m0!!!!!!!!!!!!!…diﬃcult!due!to!the!limita*on! < 1/T!!!!Spa*al!correla*on!func*on:!
1/Tz†S):!screening!mass!
G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!M(T(z, T ) =d dxdy JH(0, 0)JH ( , x)
Ae M (T )z
0!
No!limita*on!to!spa*al!direc*on:!more!sensi*ve!to!in4medium!modiﬁca*onHadronic0excita)on0on0LaHce
Temporal!correla*on!func*on:!
!
†GT ( , T ) = d3 x JH(0, 0)JH ( , x)!

Ae m0!!!!!!!!!!!!!…diﬃcult!due!to!the!limita*on! < 1/T!!!!Spa*al!correla*on!func*on:!
1/Tz†S):!screening!mass!
G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!M(T(z, T ) =d dxdy JH(0, 0)JH ( , x)
Ae M (T )z
0!
No!limita*on!to!spa*al!direc*on:!more!sensi*ve!to!in4medium!modiﬁca*onSpectral0func)onGT ( , T ) =d02dGS (z, T ) =cosh( (1/2T ))( ,T)sinh( /2T )e.g.)!reconstruc*on!of!σ:!MEM

dpz eipz z ( , pz , T )0No!T!dependence!in!Kernel:!direct!probe!of!thermal!modiﬁca*on!of!σ!!
GS (z, T )/GS (z, T = 0)

Hadronic0excita)on0on0LaHce
Parity0partner0of0meson0states
Vector!(vector!and!axial4vector)!!!!!!!!!!!!!!!Scalar!(pseudo4scalar!and!scalar)

¯ i
¯ i 5

Chiral

1+1MV (T )¯ 5
¯0+0MS (T )UA(1)

Degeneracy!of!parity!partners:!indicator!of!symmetry!restora*onsHadronic0excita)on0on0LaHce
Parity0partner0of0meson0states
Vector!(vector!and!axial4vector)!!!!!!!!!!!!!!!Scalar!(pseudo4scalar!and!scalar)

¯ i¯ i 5Chiral

1+1

MV (T )

¯ 5
¯

0+0

MS (T )

UA(1)

Degeneracy!of!parity!partners:!indicator!of!symmetry!restora*onsBehavior0in0limi)ng0cases:
At!low!T,!bound!state:!!!!!!!!!!!!!!!!!!!!!!!!!pole!mass!at!T=0
M (T ) m0( , 0, 0, pz , T )( 2 p2z m20 )!
At!T ~!Tc!,!in4medium!modiﬁca*on!and/or!dissolu*on!
!!!!!!!!!!!!!!!!!!!!degeneracy!of!parity!partner!states!
M
2 m2q + ( T )2
T
At!!!!!!!!!!!!!!!!,!free!quark4an*quark!pair:!!
!!!!!!!!!!!!!!!!!!!!!!!!!with!the!lowest!Matsubara!frequency!

Lattice simulations! Setup!in!HISQ!
! Modiﬁca*ons!of!Mesons!
! Restora*ons!of!broken!symmetries

Highly0Improved0Staggered0Quark
Reduc*on!of!taste!viola*on!
Control!of!cutoﬀ!eﬀects!!!
!!!!!!!!!!!!Bazavov!et!al.!`11,!!Hot4QCD!`11,!`14!
LaMce!parameters!
! 2+1!ﬂavor!QCD!!
!!!!!!(charm!quenched)!
! ms:$physical,$ml$/ms$=!1/20!
!!!!!(mπ~160!MeV,!mK~504!MeV)!
! Nτ=!8!!(T$=!110—207!MeV)!
!!!!!!!!!!!!!10!(T!=!139—166!MeV)!
!!!!!!!!!!!!!12!(T!=!149—400!MeV)!
!!!!!!!!!!!!!keeping!Ns/Nτ=4!
! 32444483x64!at!T$=!0!
! scale:!fk!input!
! calcula*ng!quark4line!connected!
!!!!!!part!of!meson!correlators!

Mesons0contents
J P ud¯ us̄ uc̄
ss̄sc̄ cc̄0K D( ss̄ )Ds5c1 0+ – K0 D0–Ds0 c0
1
K D
Ds J/i+– K1 D1 f1 (1420) Ds1 c1
i 5 1

Highly0Improved0Staggered0Quarks
Reduc*on!of!taste!viola*on!
Control!of!cutoﬀ!eﬀects!!!
!!!!!!!!!!!!Bazavov!et!al.!`11,!!Hot4QCD!`11,!`14!
LaMce!parameters!
! 2+1!ﬂavor!QCD!!
!!!!!!(charm!quenched)!
! ms:$physical,$ml$/ms$=!1/20!

Meson0spectra0at0T0=000!(input:!!!!)

!!!!!(mπ~160!MeV,!mK~504!MeV)!
! Nτ=!8!!(T$=!110—207!MeV)!
!!!!!!!!!!!!!10!(T!=!139—166!MeV)!
!!!!!!!!!!!!!12!(T!=!149—400!MeV)!
!!!!!!!!!!!!!keeping!Ns/Nτ=4!
! Corresponding!to!T$=!0!!
! scale:!fk!input!
! calcula*ng!quark4line!connected!
!!!!!!part!of!meson!correlators!

Mesons0contents
J P ud¯ us̄ uc̄
ss̄
sc̄ cc̄0
K D( ss̄ )Ds
5
c1 0+ – K0 D0–Ds0 c0
1K D
Ds J/i+– K1 D1 f1 (1420) Ds1 c1
i 5 1Ra)o0of0spa)al0correla)on0func)ons
Probe0of0thermal0modiﬁca)ons0of0spectral0func)onGS (z, T )/GS (z, T = 0)

=1
1 the!same!σ!at!T = 0,!or!!!!!!!!!modiﬁed!
Tc = (154 ± 9) MeV

Pseudo4scalarJP = 0DKπS(z, T )/GS (z, 0) 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!short!distance!!!!!!!!!!physics:!not!sensi*ve!to!TS(z, T )/GS (z, 0) = 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!large!distance!!!!!!!!!!!thermal!modiﬁca*on!of!
σ$Ra)o0of0spa)al0correla)on0func)ons
Probe0of0thermal0modiﬁca)ons0of0spectral0func)onGS (z, T )/GS (z, T = 0)

=1
1 the!same!σ!at!T = 0,!or!!!!!!!!!modiﬁed!
Tc = (154 ± 9) MeV

Pseudo4scalarJP = 0DKπ
S(z, T )/GS (z, 0) 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!short!distance!!!!!!!!!!physics:!not!sensi*ve!to!TS(z, T )/GS (z, 0) = 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!large!distance!!!!!!!!!!!thermal!modiﬁca*on!of!
σ$Ra)o0of0spa)al0correla)on0func)ons
Probe0of0thermal0modiﬁca)ons0of0spectral0func)onGS (z, T )/GS (z, T = 0)

=1
1 the!same!σ!at!T = 0,!or!!!!!!!!!modiﬁed!
Tc = (154 ± 9) MeV

Pseudo4scalarJP = 0DKπS(z, T )/GS (z, 0) 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!short!distance!!!!!!!!!!physics:!not!sensi*ve!to!TS(z, T )/GS (z, 0) = 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!large!distance!!!!!!!!!!!thermal!modiﬁca*on!of!
σ$! modiﬁca*on!at!T < Tc$Ra)o0of0spa)al0correla)on0func)ons
Probe0of0thermal0modiﬁca)ons0of0spectral0func)onGS (z, T )/GS (z, T = 0)

=1
1 the!same!σ!at!T = 0,!or!!!!!!!!!modiﬁed!
Tc = (154 ± 9) MeV

Pseudo4scalarJP = 0DKπS(z, T )/GS (z, 0) 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!short!distance!!!!!!!!!!physics:!not!sensi*ve!to!TS(z, T )/GS (z, 0) = 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!large!distance!!!!!!!!!!!thermal!modiﬁca*on!of!
σ$! modiﬁca*on!at!T < Tc,!explicit!ﬂavor!dependence!at!T > Tc

Ra)o0of0spa)al0correla)on0func)ons
Probe0of0thermal0modiﬁca)ons0of0spectral0func)onGS (z, T )/GS (z, T = 0)

=1
1 the!same!σ!at!T = 0,!or!!!!!!!!!modiﬁed!
Tc = (154 ± 9) MeVPseudo4scalarJP = 0DKπ
S(z, T )/GS (z, 0) 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!short!distance!!!!!!!!!!physics:!not!sensi*ve!to!TS(z, T )/GS (z, 0) = 1! G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!at!large!distance!!!!!!!!!!!thermal!modiﬁca*on!of!
σ$! modiﬁca*on!at!T < Tc,!explicit!ﬂavor!dependence!at!T > Tc

Mass0diﬀerenceM (T ) = M (T )Pseudo4scalarJP = 0m0 ~0change0of0“binding0energy”

π$KD¯ us̄, uc̄
!u!!!!!!!!!!!!!!!!!!!!!!!!!!:!explicit!thermal!modiﬁca*on!below!T
d,c ,!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!similar!modiﬁca*on!pa=ern!at!T < Tc ,!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!explicit!ﬂavor!dependence!at!T > Tc!
!

Mass0diﬀerenceM (T ) = M (T )Pseudo4scalarJP = 0m0 ~0change0of0“binding0energy”

π$
KD
ηss$
DS$
ηc$

¯ us̄, uc̄
!u!!!!!!!!!!!!!!!!!!!!!!!!!!:!explicit!thermal!modiﬁca*on!below!T
d,c ,!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!similar!modiﬁca*on!pa=ern!at!T < Tc ,!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!explicit!ﬂavor!dependence!at!T > Tc!
! ss̄,!!!!!!!!!!!!!!:!slight!modiﬁca*on!below!Tsc̄c!
! cc̄!!!!!:!stable!beyond!Tc!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!PRD91!(2015)!5,!054503!

Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!

Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!

Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!

Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!

Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!
! Scalar!partner!degenerates!at!T ~ 1.4Tc--1.6Tc!

Restora)on0of0broken0symmetries
Degeneracy!of!vector!partners!!!!!!!!!restora*on!of!chiral!symmetry!
Degeneracy!of!scalar!partners!!!!!!!!!!(eﬀec*ve)!restora*on!of!UA(1)!symmetry!

GS (z, T )! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!
! Scalar!partner!degenerates!at!T ~ 1.4Tc--1.6Tc!

Restora)on0of0broken0symmetries
Large0distance0behavior0of0spa)al0correlatorGS (z, T ) z

Ae M (T )zLight4unﬂavored

ud¯

Open:!Nτ = 8
Black:!Nτ = 10!
Filled:!Nτ = 12

ml /ms = 1/20

! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!
! Scalar!partner!degenerates!at!T ~ 1.4Tc--1.6Tc!!!!!!!chiral:!restored,!UA(1):!broken!at!Tc ,!!no!dependence!on!laMce!spacingRestora)on0of0broken0symmetries
Large0distance0behavior0of0spa)al0correlatorGS (z, T ) z

Ae M (T )zLight4unﬂavored

ud¯Open:!Nτ = 8
Black:!Nτ = 10!
Filled:!Nτ = 12y 1/27
raniPrelim /ms =Nml,2
1=ml /ms = 1/20

! Vector!partner!degenerates!at!T ~ 1.0Tc--1.1Tc!
! Scalar!partner!degenerates!at!T ~ 1.4Tc--1.6Tc!!!!!!!chiral:!restored,!UA(1):!broken!at!Tc ,!!no!dependence!on!laMce!spacingSummaryIn@medium0mesons0from0spa)al0correla)on0func)onSensi*ve!to!thermal!eﬀect!at!ﬁnite!T on!laMce• Direct!probe!of!modiﬁca*on!of!meson!spectral!func*on!
• Indicator!of!restora*ons!of!broken!symmetries!
(2+1)4ﬂavor!QCD!laMce!simula*ons!with!HISQ!of!
zGS (z, T )GS (z, T )/GS (z, T = 0)!!!ra*o:!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!,!!screening!mass:!

Ae M (T )z¯ us̄, uc̄
!u!!!!!!!!!!!!!!!!!!!!!!!!!!:!explicit!thermal!modiﬁca*on!below!T
d,c ,!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!similar!modiﬁca*on!pa=ern!below Tc ,!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!explicit!ﬂavor!dependence!above Tc!
! ss̄,!!!!!!!!!!!!!!:!slight!modiﬁca*on!below!Tsc̄c!
! cc̄!!!!!:!stable!beyond!Tc!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!PRD91!(2015)!5,!054503!
! Degeneracies!of!parity!partners!!!!!!!!!!!!!chiral:!restored,!UA(1):!broken!at!Tc !
!!!!!!!!!!!!!!!!!!!!!!!!!!!in!con*nuum!and!physical!quark!mass!(preliminary)