Effects of resonance widths on EoS and particle distributions
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1 Effects of resonance widths on EoS and particle distributions Pasi Huovinen Uniwersytet Wroc lawski Phase diagram of strongly interacting matter: From Lattice QCD to Heavy-Ion Collision Experiments November 28, 217, ECT*, Trento in collaboration with Pok Man Lo and M. Marczenko, K. Redlich, C. Sasaki The speaker has received funding from the European Union s Horizon 22 research and innovation programme under the Marie Sk lodowska-curie grant agreement No via the National Science Center, Poland, under grant Polonez DEC-215/19/P/ST2/3333
2 Pion p T spectrum at LHC (Pb+Pb at s NN = 2.76 TeV) 1 4 PCE15 dn/dydp 2 T [GeV 2 ] % viscous hydro initial state: pqcd+saturation τ.2fm/c PCE15: fit to π, K, p yields no fit to spectrum ALICE p T [GeV] c H. Niemi P. ECT*, November 28, 217 1/32
3 Pion p T spectrum at LHC (Pb+Pb at s NN = 2.76 TeV) dn/dydp 2 T [GeV 2 ] % PCE15 PCE175 viscous hydro initial state: pqcd+saturation τ.2fm/c PCE15: fit to π, K, p yields no fit to spectrum ALICE p T [GeV] PCE175: no fit to yields fits the spectrum c H. Niemi P. ECT*, November 28, 217 1/32
4 need more resonances yield proportional to Boltzmann factor N exp ( m T ) resonance mass? P. ECT*, November 28, 217 2/32
5 need more resonances yield proportional to Boltzmann factor N exp ( m T ) resonance mass? P. ECT*, November 28, 217 2/32
6 need more resonances yield proportional to Boltzmann factor N exp ( m T ) resonance mass? usually no width, i.e. resonances have their pole mass P. ECT*, November 28, 217 2/32
7 effect of Breit-Wigner width on number density: n = n = d 3 p f(p) d 3 p dm 2 dρ f(p, m) dm2 where with normalisation dρ dm 2 = 1 N m R Γ (m 2 m 2 R )2 + m 2 R Γ2, N = dm 2 m R Γ m (m 2 m 2 R )2 + m 2 R Γ2 For ρ m R = MeV and Γ = MeV P. ECT*, November 28, 217 3/32
8 effect of Breit-Wigner width on number density: n = n = d 3 p f(p) d 3 p dm 2 dρ f(p, m) dm2 where with normalisation dρ dm 2 = 1 N m R Γ (m 2 m 2 R )2 + m 2 R Γ2, N = dm 2 m R Γ m (m 2 m 2 R )2 + m 2 R Γ2 For ρ m R = MeV and Γ = MeV P. ECT*, November 28, 217 3/32
9 effect of Breit-Wigner width on number density: n = n = d 3 p f(p) d 3 p dm 2 dρ f(p, m) dm2 where with normalisation dρ dm 2 = 1 N m R Γ (m 2 m 2 R )2 + m 2 R Γ2, N = dm 2 m R Γ m (m 2 m 2 R )2 + m 2 R Γ2 For ρ m R = MeV and Γ = MeV P. ECT*, November 28, 217 3/32
10 effect of Breit-Wigner width on number density: n = n = d 3 p f(p) d 3 p dm 2 dρ f(p, m) dm2 where with normalisation dρ dm 2 = 1 N m R Γ (m 2 m 2 R )2 + m 2 R Γ2, N = dm 2 m R Γ m (m 2 m 2 R )2 + m 2 R Γ2 For ρ m R = MeV and Γ = MeV P. ECT*, November 28, 217 3/32
11 ρ-density no width Breit-Wigner.12 n (fm -3 ) T (MeV) P. ECT*, November 28, 217 4/32
12 Breit-Wigner dn/dm m (GeV) P. ECT*, November 28, 217 5/32
13 Breit-Wigner dn/dm m (GeV) P. ECT*, November 28, 217 5/32
14 Mass dependent width dρ dm 2 = 1 N m R Γ(m) (m 2 m 2 R )2 + m 2 R Γ(m)2, with width where r = 6.3 GeV 1 Γ(m) = 1 2 p 3 CMS r2 1 + p 2 CMS r2 P. ECT*, November 28, 217 6/32
15 Breit-Wigner dn/dm m (GeV) Γ = const. Γ = Γ(m) P. ECT*, November 28, 217 7/32
16 ρ-density no width Γ = const. Γ = Γ(m) n (fm -3 ) T (MeV) P. ECT*, November 28, 217 8/32
17 relativistic Breit-Wigner dρ dm 2 = 1 N m R Γ(m) (m 2 m 2 R )2 + m 2 R Γ(m)2 or: dρ dm 2 = 1 N m Γ(m) (m 2 m 2 R )2 + m 2 Γ(m) 2 P. ECT*, November 28, 217 9/32
18 relativistic Breit-Wigner dρ dm 2 = 1 N m R Γ(m) (m 2 m 2 R )2 + m 2 R Γ(m)2 or: dρ dm 2 = 1 N m Γ(m) (m 2 m 2 R )2 + m 2 Γ(m) 2 But if Γ(m) m at large m, N = dm 2 m Γ(m) m (m 2 m 2 R )2 + m 2 Γ(m) 2 = P. ECT*, November 28, 217 9/32
19 Particle Data Group about ρ:...the line shape does not correspond to a relativistic Breit-Wigner function...but requires some additional shape parameter P. ECT*, November 28, 217 1/32
20 Garbage in, garbage out P. ECT*, November 28, /32
21 Dashen-Ma-Bernstein: Phys. Rev. 187, 345 (1969) If interactions mediated by narrow resonances, properties of interacting hadron gas are those of noninteracting hadron-resonance gas Dashen-Ma-Bernstein: S-matrix formulation of statistical mechanics: Second virial coefficient can be evaluated in terms of scattering phase shift (as far as interaction is manifested in elastic scattering) relativistic Beth-Uhlenbeck form P. ECT*, November 28, /32
22 Dashen-Ma-Bernstein: Phys. Rev. 187, 345 (1969) If interactions mediated by narrow resonances, properties of interacting hadron gas are those of noninteracting hadron-resonance gas Dashen-Ma-Bernstein: S-matrix formulation of statistical mechanics: Second virial coefficient can be evaluated in terms of scattering phase shift (as far as interaction is manifested in elastic scattering) relativistic Beth-Uhlenbeck form P. ECT*, November 28, /32
23 S-matrix effects of interactions expressed in terms of scattering phase shifts n = d 3 p dm dρ dm f(p, m) with dρ dm = 1 dδ π dm ππ scattering, P-wave, i.e. ρ resonance δ (degree) Estabrooks & Martin Froggatt & Petersen 1/π dδ/dm (GeV -1 ) M (GeV) M (GeV) P. ECT*, November 28, /32
24 S-matrix effects of interactions expressed in terms of scattering phase shifts n = d 3 p dm dρ dm f(p, m) with dρ dm = 1 dδ π dm ππ scattering, P-wave, i.e. ρ resonance δ (degree) Estabrooks & Martin Froggatt & Petersen 1/π dδ/dm (GeV -1 ) M (GeV) M (GeV) P. ECT*, November 28, /32
25 S-matrix effects of interactions expressed in terms of scattering phase shifts n = d 3 p dm dρ dm f(p, m) with dρ dm = 1 dδ π dm ππ scattering, P-wave, i.e. ρ resonance δ (degree) Estabrooks & Martin Froggatt & Petersen 1/π dδ/dm (GeV -1 ) M (GeV) M (GeV) P. ECT*, November 28, /32
26 S-matrix effects of interactions expressed in terms of scattering phase shifts n = d 3 p dm dρ dm f(p, m) with dρ dm = 1 dδ π dm ππ scattering, P-wave, i.e. ρ resonance δ (degree) Estabrooks & Martin Froggatt & Petersen 1/π dδ/dm (GeV -1 ) M (GeV) M (GeV) P. ECT*, November 28, /32
27 S-matrix effects of interactions expressed in terms of scattering phase shifts n = d 3 p dm dρ dm f(p, m) with dρ dm = 1 dδ π dm ππ scattering, P-wave, i.e. ρ resonance δ (degree) Estabrooks & Martin Froggatt & Petersen 1/π dδ/dm (GeV -1 ) M (GeV) M (GeV) P. ECT*, November 28, /32
28 S-matrix effects of interactions expressed in terms of scattering phase shifts n = d 3 p dm dρ dm f(p, m) with dρ dm = 1 dδ π dm ππ scattering, P-wave, i.e. ρ resonance δ (degree) Estabrooks & Martin Froggatt & Petersen 1/2π B(m) (GeV -1 ) /π dδ/dm Breit-Wigner zero width M (GeV) M (GeV) P. ECT*, November 28, /32
29 ρ-density S-matrix Breit-Wigner zero width n (fm -3 ) M (GeV) P. ECT*, November 28, /32
30 Pions from ρ decays dn/(p T dp T ) (GeV -2 ) zero width S-matrix p T (GeV) static source, T = 155 MeV P. ECT*, November 28, /32
31 Thermal pions + pions from ρ decays dn/(p T dp T ) (GeV -2 ) π + thermal π + decays p T (GeV) static source, T = 155 MeV P. ECT*, November 28, /32
32 Thermal pions + pions from ρ decays 1.4 dn/(p T dp T ) (GeV -2 ) π + thermal π + decays π + thermal+decays p T (GeV) static source, T = 155 MeV P. ECT*, November 28, /32
33 Pions from blast wave 1/2π dn/(dy p T dp T ) (GeV -2 ) Pb+Pb s = 2.76 TeV ALICE -5%, π + zero width S-matrix p T (GeV) τ = 14.1 fm R = 1 fm v max =.8 all resonances up to 2 GeV Beth-Uhlenbeck for rhos zero width for everything else P. ECT*, November 28, /32
34 Pions from blast wave 1/2π dn/(dy p T dp T ) (GeV -2 ) 1 1 Pb+Pb s = 2.76 TeV ALICE -5%, π + zero width S-matrix p T (GeV) τ = 14.1 fm R = 1 fm v max =.8 all resonances up to 2 GeV Beth-Uhlenbeck for rhos zero width for everything else P. ECT*, November 28, /32
35 caveats so far only rho mesons P. ECT*, November 28, 217 2/32
36 caveats so far only rho mesons Beth-Uhlenbeck applicable to elastic scatterings only! P. ECT*, November 28, 217 2/32
37 caveats so far only rho mesons Beth-Uhlenbeck applicable to elastic scatterings only! how about σ a.k.a. f (5)? P. ECT*, November 28, 217 2/32
38 S-wave ππ scattering Estabrooks & Martin Froggatt & Petersen Grayer et al. δ (degree) M (GeV) P. ECT*, November 28, /32
39 S-wave ππ scattering δ (degree) Estabrooks & Martin Froggatt & Petersen Grayer et al /π dδ/dm (GeV -1 ) I= M (GeV) M (GeV) P. ECT*, November 28, /32
40 S-wave ππ scattering δ (degree) Estabrooks & Martin Froggatt & Petersen Grayer et al. I= I= /π dδ/dm (GeV -1 ) I= I= M (GeV) M (GeV) P. ECT*, November 28, /32
41 S-wave ππ scattering δ (degree) Estabrooks & Martin Froggatt & Petersen Grayer et al. I= I= /π dδ/dm (GeV -1 ) I= I=2 I=+5*I= M (GeV) M (GeV) P. ECT*, November 28, /32
42 P. ECT*, November 28, /32
43 as advocated by Broniowski, Giacosa & Begun, PRC92, 3495 (215) Prakash & Venugopalan, NPA546, 718 (1992) P. ECT*, November 28, /32
44 1/π dδ/dm (GeV -1 ) S-wave ππ scattering I= I=2 I=+5*I= M (GeV) f (98) nicely described P. ECT*, November 28, /32
45 P 33 πn scattering, a.k.a. δ (degree) Arndt et al. GW W18 1/2π B(m) (GeV -1 ) /π dδ/dm UrQMD Breit-Wigner zero width M (GeV) M (GeV) P. ECT*, November 28, /32
46 P 33 πn scattering, a.k.a. n (fm -3 ) S-matrix UrQMD zero width 1/2π B(m) (GeV -1 ) /π dδ/dm UrQMD Breit-Wigner zero width M (GeV) M (GeV) P. ECT*, November 28, /32
47 Pions from blast wave, T = 15 MeV 1/2π dn/(dy p T dp T ) (GeV -2 ) τ = 14.1 fm R = 1 fm v max =.8 Pb+Pb s = 2.76 TeV ALICE -5%, π + zero width S-matrix, ρ only S-matrix p T (GeV) all resonances up to 2 GeV Beth-Uhlenbeck for ρ,, f (98), K (892), K (143) zero width for everything else P. ECT*, November 28, /32
48 Pions from blast wave, T = 12, T chem = 15 MeV 1/2π dn/(dy p T dp T ) (GeV -2 ) Pb+Pb s = 2.76 TeV ALICE -5%, π + zero width S-matrix, ρ only S-matrix p T (GeV) τ = 31. fm R = 1 fm v max =.87 all resonances up to 2 GeV Beth-Uhlenbeck for ρ,, f (98), K (892), K (143) zero width for everything else P. ECT*, November 28, /32
49 v 2 of pions from blast wave, T = 12, T chem = 15 MeV zero width S-matrix.1 v v 2 π p T (GeV) τ = 31. fm R = 1 fm v max =.87 all resonances up to 2 GeV Beth-Uhlenbeck for ρ,, f (98), K (892), K (143) zero width for everything else P. ECT*, November 28, /32
50 and EoS? P. ECT*, November 28, 217 3/32
51 π,k,n,ρ,f (98),K,K (143), (ε-3p)/t zero-width T (MeV) P. ECT*, November 28, /32
52 π,k,n,ρ,f (98),K,K (143), (ε-3p)/t zero width S-matrix T (MeV) P. ECT*, November 28, /32
53 the whole zoo zero-width S-matrix (ε-3p)/t T (MeV) P. ECT*, November 28, /32
54 Summary Resonance widths change the low-p T distribution of pions P. ECT*, November 28, /32
55 Summary Resonance widths change the low-p T distribution of pions Fortunately v 2 (p T ) is not affected P. ECT*, November 28, /32
56 Summary Resonance widths change the low-p T distribution of pions Fortunately v 2 (p T ) is not affected Effect on EoS uncertain P. ECT*, November 28, /32
57 Summary Resonance widths change the low-p T distribution of pions Fortunately v 2 (p T ) is not affected Effect on EoS uncertain Better treatment of resonances needed P. ECT*, November 28, /32
58 Summary Resonance widths change the low-p T distribution of pions Fortunately v 2 (p T ) is not affected Effect on EoS uncertain Better treatment of resonances needed - we are working on it... This talk consisted of 1% recycled electrons P. ECT*, November 28, /32
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