Lattice QCD vs. Hadron Resonance Gas: Do we need more or ...Lattice QCD Bazavov al. (2014) cont....

Lattice QCD vs. Hadron Resonance Gas:Do we need more or better resonances?

Pasi HuovinenUniwersytet Wroc lawski

YSTAR2016

Nov 17, 2016, Thomas Jefferson National Accelerator Facility

in collaboration with

Pok Man Lo

and M. Marczenko, K. Redlich, C. Sasaki

The speaker has received funding from the European Union’s Horizon 2020 research and innovation programme

under the Marie Sk lodowska-Curie grant agreement No 665778 via the National Science Center, Poland, under

grant Polonez DEC-2015/19/P/ST2/03333

Lattice QCDB

aza

vovetal.

,P

RL

11

3,

07

20

01

(20

14

)

cont. est.

PDG-HRG

QM-HRG

0.15

0.20

0.25

0.30- χ11

BS/χ2

S

Nτ=6: open symbols

Nτ=8: filled symbols

B1S/M1

S

B2S/M2

S

B2S/M1

S

0.15

0.25

0.35

0.45

140 150 160 170 180 190

T [MeV]

P. Huovinen @ YSTAR2016, Nov 17, 2016 1/16

Hadron resonance gas

Dashen-Ma-Bernstein:

If interactions mediated by narrow resonances, properties of interactinghadron gas are those of noninteracting hadron-resonance gas

⇒ Hadron resonance gas model

treat resonances as free particles:

P (T, µ) =∑i

±gi(2π)3

T

∫d3p ln

(1± e−

E−µiT

)• but what is m of resonances?

• usually pole mass is used


Dashen-Ma-Bernstein:

If interactions mediated by narrow resonances, properties of interactinghadron gas are those of noninteracting hadron-resonance gas

⇒ Hadron resonance gas model

Dashen-Ma-Berstein: S-matrix formulation of statistical mechanics:

⇒ Second virial coefficient can be evaluated in terms of scattering phaseshift (as far as interaction is manifested in elastic scattering)

⇒ relativistic Beth-Uhlenbeck form


Beth-Uhlenbeck• effects of interactions expressed in terms of scattering phase shifts

nIJ =

∫d3p

∫dm

dρIJdm

f(p,m) withdρIJdm

=1

π

dδIJdm

• ππ scattering, P-wave, i.e. ρ resonance

0

20

40

60

80

100

120

140

160

180

0.4 0.6 0.8 1 1.2

δ (d

egre

e)

M (GeV)

Estabrooks & MartinFroggatt & Petersen

0

1

2

3

4

5

0.4 0.6 0.8 1 1.2

1/π

dδ/d

m (

GeV

-1)

M (GeV)


ρ-density

0

0.005

0.01

0.015

0.02

0.025

0.03

120 130 140 150 160 170 180

n (f

m-3

)

T (MeV)

no widthBeth-Uhlenbeck


χQ2 and χQ4 in HRG vs. lattice

continuum extrapolated

0.1

0.2

0.3

0.4

0.5

0.6

0.7

120 130 140 150 160 170 180 190 200 210

χQ

2

T (MeV)

R. Bellwied et al., PRD92, 114505 (2015)

χQ2 =∂2P

∂µ2Q


0.2

0.4

0.6

0.8

1

1.2

1.4

120 130 140 150 160 170 180 190 200 210

χQ

4

T (MeV)

Nt=6Nt=8

P. Petreczky, PoS ConfinementX, 028 (2012)

χQ4 =∂4P

∂µ4Q




0.1

0.2

0.3

0.4

0.5

0.6

0.7

120 130 140 150 160 170 180 190 200 210

χQ

2

T (MeV)


χQ2 =∂2P

∂µ2Q


0.2

0.4

0.6

0.8

1

1.2

1.4

120 130 140 150 160 170 180 190 200 210

χQ

4

T (MeV)


χQ4 =∂4P

∂µ4Q


χQ2 and χQ4 in π-ρ gas

0.1

0.15

0.2

0.25

0.3

0.35

0.4

120 130 140 150 160 170 180 190 200 210

χQ

2

T (MeV)

pole massS-matrix

χQ2 =∂2P

∂µ2Q

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

120 130 140 150 160 170 180 190 200 210

χQ

4

T (MeV)

pole massS-matrix

χQ4 =∂4P

∂µ4Q


S-wave ππ scattering

-50

0

50

100

150

200

250

300

0.4 0.6 0.8 1 1.2

δ (d

egre

e)

M (GeV)


Grayer et al.

0

2

4

6

8

10

12

0.4 0.6 0.8 1 1.2

1/π

dδ/d

m (

GeV

-1)

M (GeV)

I=0



-50

0

50

100

150

200

250

300

0.4 0.6 0.8 1 1.2

δ (d

egre

e)

M (GeV)


Grayer et al.I=0I=2

0

2

4

6

8

10

12

0.4 0.6 0.8 1 1.2

1/π

dδ/d

m (

GeV

-1)

M (GeV)

I=0I=2



-50

0

50

100

150

200

250

300

0.4 0.6 0.8 1 1.2

δ (d

egre

e)

M (GeV)


Grayer et al.I=0I=2

0

2

4

6

8

10

12

0.4 0.6 0.8 1 1.2

1/π

dδ/d

m (

GeV

-1)

M (GeV)

I=0I=2

I=0+5*I=2

• f0(500) and repulsive I = 2 S-wave cancel

• for nπ, P , etc.


nIJ =

∫d3p

∫dm

dρIJdm

f(p,m) withdρIJdm

=1

π

dδIJdm

where I isospin and J spin

I = 2 =⇒ π+π+ and π−π− pairs

Q = ±2 =⇒ effect on χQn =∂nP

∂µnQlarge!


χQ2 and χQ4 in π + S-wave

0.1

0.15

0.2

0.25

0.3

0.35

0.4

120 130 140 150 160 170 180 190 200 210

χQ

2

T (MeV)

pole massS-matrix

χQ2 =∂2P

∂µ2Q

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

120 130 140 150 160 170 180 190 200 210

χQ

4

T (MeV)

pole massS-matrix

χQ4 =∂4P

∂µ4Q


χQ2 and χQ4 in π + S-wave + P-wave

0.1

0.15

0.2

0.25

0.3

0.35

0.4

120 130 140 150 160 170 180 190 200 210

χQ

2

T (MeV)

pole massS-matrix

χQ2 =∂2P

∂µ2Q

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

120 130 140 150 160 170 180 190 200 210

χQ

4

T (MeV)

pole massS-matrix

χQ4 =∂4P

∂µ4Q


χQ2 and χQ4 , interacting πKN gas

0.1

0.2

0.3

0.4

0.5

0.6

0.7

120 130 140 150 160 170 180 190 200 210

χQ

2

T (MeV)

pole massS-matrix

χQ2 =∂2P

∂µ2Q

0.2

0.4

0.6

0.8

1

1.2

1.4

120 130 140 150 160 170 180 190 200 210

χQ

4

T (MeV)

pole massS-matrix

χQ4 =∂4P

∂µ4Q

• S-matrix treatment of ρ, K∗(892), K∗0(1430), ∆(1232) + repulsive ππ




0.1

0.2

0.3

0.4

0.5

0.6

0.7

120 130 140 150 160 170 180 190 200 210

χQ

2

T (MeV)

pole massS-matrix


χQ2 =∂2P

∂µ2Q


0.2

0.4

0.6

0.8

1

1.2

1.4

120 130 140 150 160 170 180 190 200 210

χQ

4

T (MeV)

pole massS-matrix


χQ4 =∂4P

∂µ4Q


Summary

• So do we need better or more resonances?

• Better treatment of resonances needed!


Summary


• We need better treatment of resonances!


Summary


• We need better treatment of resonances!

– finite widths– repulsive interactions


Lattice QCD vs. Hadron Resonance Gas: Do we need more or ...Lattice QCD Bazavov al. (2014) cont....

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Transcript of Lattice QCD vs. Hadron Resonance Gas: Do we need more or ...Lattice QCD Bazavov al. (2014) cont....