Lessons from Justus Liebig and Ulrich Mosel...Liebig’s law of the minimum principle developed in...

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Lessons from Justus Liebig and Ulrich Mosel

Stefan Leupold

former affiliation: Justus-Liebig-Universitat Giessen

Obergurgl, Austria, Feb. 2011

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

The academic who is who

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Justus von Liebig

1803-1873regarded as one of the greatestchemistry teachers of all time“father of the fertilizer industry”founder of company “LiebigExtract of Meat Company”(bouillon cube)

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Liebig’s law of the minimum

principle developed inagricultural science byCarl Sprengel (1828)popularized byJustus von Liebig

; growth is not controlled by thetotal of resources available,but by the scarcest resource(limiting factor)

Liebig’s barrel

often also physics is not one-dimensional(observed effect 6; unique reason)

; side feeding, coupled-channel effects can be important

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

The anti-Mosel approach

use simplest possible model which incorporates standardphysics

→ does not describe data→ conclude that you have found new, fancy physics

The Mosel approachtry as much as possible to describe data by standardeffectsin particular consider side feeding, coupled channels

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

The anti-Mosel approach

use simplest possible model which incorporates standardphysics

→ does not describe data→ conclude that you have found new, fancy physics

The Mosel approachtry as much as possible to describe data by standardeffectsin particular consider side feeding, coupled channels

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Table of Contents

1 Coupled-channel K matrix

2 The era of spectral functions

3 Coupled-channel BUU — mundane vs. fancy in-mediumeffects

4 Decoupling theorem

5 Summary

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Coupled-channel K matrix

typically hadronic reactions have sizable inelasticities→ coupled-channel treatment

take unitarity serious: S†S = 1 (S = 1 + 2iT )

→ ImT = T †T ⇔ ImT−1 = −1→ use exact relation

T =1

K−1 − i=

K1− iK

with two-particle irreducible kernel K(i.e. ImK = 0 in physical region)approximate K by tree-level s-, t- and u-channel processesincluded channels: πN, γN, ηN, ωN, KΛ,. . .Feuster, Penner, Shklyar,. . .

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Photoproduction of η on neutron

0

0.25

0.5

0.75

1

dσ/d

Ω, µ

b/st

r

0.5

1

0

0.25

0.5

0.75

dσ/d

Ω, µ

b/st

r

0.5

1

0

0.25

0.5

0.75

1.5 1.6 1.7 1.8W,GeV

dσ/d

Ω, µ

b/st

r

0.5

1

1.5 1.6 1.7 1.8 1.9W,GeV

Kuznetsov et al., Phys. Lett. B647, 23, 2007

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Photoproduction of η on neutron

peak at about 1.66 GeV for neutron, but not for protonPolyakov explanation: pentaquark state(non-exotic partner of θ+ with mass 1.675 GeV)experimental complication: deuteron data

; partial wave analysis complicated, momentum smearing

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Giessen K-matrix explanation

peak is just interplay of conventional S11(1650) and P11(1710)

1.6 1.8 2√

S (GeV)

0

10

σ (

µb)

γ n -> η n

Shklyar, Lenske, UMo, Phys. Lett. B650, 172, 2007

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

The era of spectral functions

spectral functions emerge from coupling a single state to acontinuum (e.g., decays, scattering)interesting aspect: if continuum states have/get alsospectral functions

→ changes induce changes→ self consistency important

; yes, we can!

→ Giessen group calculated spectral functions forhadron resonances in matter (Post, Muhlich); impact on QCD sum rulesnucleons in nucleus (Lehr)quarks in matter (Fromel)quarks in nucleon (Eichstadt ; previous talk)

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

The era of spectral functions

spectral functions emerge from coupling a single state to acontinuum (e.g., decays, scattering)interesting aspect: if continuum states have/get alsospectral functions

→ changes induce changes→ self consistency important ; yes, we can!

→ Giessen group calculated spectral functions forhadron resonances in matter (Post, Muhlich); impact on QCD sum rulesnucleons in nucleus (Lehr)quarks in matter (Fromel)quarks in nucleon (Eichstadt ; previous talk)

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Spectral information from many-body theory

Example 1: rho meson in cold nuclear matter

0.2 0.4 0.6 0.8 1.0 1.20.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Im R

s [GeV]

in-medium vacuum

resonance model with parametersfrom πN → (2π)N,Post/Leupold/UMo,

Nucl.Phys.A741 (2004) 81

0.4 0.6 0.8 1.0 1.20

2

4

6

8

10

0.4 0.6 0.8 1.0 1.20

5

10

15

20

25

2 0

0

= 0

- Im

D (

) [G

eV -2

]

[Gev]

2 0

0

= 0

- Im

D (

) [G

eV -2

]

[Gev]

dynamical generation of resonances,Lutz/Wolf/Friman,

Nucl.Phys.A706 (2002) 431

results differ due to different input from/interpretation ofelementary reactions (here: strength of coupling ρ-N-N∗(1520))

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Spectral information from many-body theory

Example 2: omega meson in cold nuclear matter

0.4 0.6 0.8 1.0 1.20

2

4

6

8

10

0.4 0.6 0.8 1.0 1.20

5

10

15

20

25

2 0

0

= 0

- Im

D (

) [G

eV -2

]

[Gev]

2 0

0

= 0

- Im

D (

) [G

eV -2

]

[Gev]

dynamical generation of resonances,Lutz/Wolf/Friman,

Nucl.Phys.A706 (2002) 431

0.5 0.6 0.7 0.8 0.9 1.010-1

100

101

102

=0

=20

-1/

Im

D (

q 0,q=

0) [

1/G

eV2 ]

q2 [GeV]

=0

coupled-channel K-matrixfor πN, ωN, KΛ, . . .Muhlich/Shklyar/Leupold/UMo/Post,

Nucl.Phys.A780 (2006) 187

similar results (but different from results of other groups . . . )

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Spectral information from many-body theory

Example 3: N∗(1520) baryon in cold nuclear matter

-0.2 0.0 0.2 0.4-0.2 0.0 0.2 0.40

1

2

3

4

5

6

k2-mR [GeV]

k = 0.8 GeV

D13

[GeV

-2]

k2-mR [GeV]

g s=0.1

g s=0.0 vacuum

k = 0 GeV

Post/Leupold/UMo,

Nucl.Phys.A741 (2004) 81

from all examples:typically sizable in-medium changes of hadron properties:

collisional broadeningnot much of a mass shiftnew structures (resonance-hole excitations)

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Impact on QCD sum rule analysis

QCD sum rules for rho meson in nuclear medium do not predictmass shift but correlation between mass and width

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

width in GeV

mass in GeV

Leupold, Peters, UMo, Nucl. Phys. A628 (1998) 311

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Spectral function for nucleons in nucleus

0.00 0.05 0.10 0.15 0.20 0.251E-5

1E-4

1E-3

0.01

0.1

1

p = 0.787 fm-1

P( ω

,p)

[M

eV -1

]

0.0 0.1 0.2 0.31E-5

1E-4

1E-3

p = 1.797 fm-1

0.0 0.1 0.2 0.3 0.41E-6

1E-5

1E-4

1E-3

p = 2.26 fm-1

P( ω

,p)

[MeV

-1]

- ω [GeV]

0.0 0.1 0.2 0.3 0.4 0.51E-7

1E-6

1E-5

p = 3.591 fm-1

- ω [GeV]

important finding: details of interaction irrelevantLehr, Effenberger, Lenske, Leupold, UMo, Phys. Lett. B483, 324, 2000

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Spectral function for quarks in cold matter

-0.2 0.0 0.20.01

0.1

1

10

100

1000

-0.2 0.0 0.20.01

0.1

1

10

100

1000

-0.4 -0.2 0.0 0.2 0.40.01

0.1

1

10

100

1000

-0.4 -0.2 0.0 0.2 0.40.01

0.1

1

10

100

1000

p = 0.05 GeV

r 0(w

,p) [

GeV

-1]

w [GeV]

p = 0.1 GeV

r 0(w

,p) [

GeV

-1]w [GeV]

p = 0.2 GeV

r 0(w

,p) [

GeV

-1]

w [GeV]

p = 0.3 GeV

r 0(w

,p) [

GeV

-1]

w [GeV]

interactionsfrom NJL model

Fromel, Leupold, UMo, Phys. Rev. C67, 015206, 2003

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Coupled-channel BUU

The anti-Mosel approachuse simplest possible model which incorporates standardphysics

→ does not describe data→ conclude that you have found new, fancy physics

The Mosel approachtry as much as possible to describe data by standardeffectsin particular for reactions on nuclei consider side feeding,coupled channels, final-state interactions

; transport theory, GiBUU

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Coupled-channel BUU

The anti-Mosel approachuse simplest possible model which incorporates standardphysics

→ does not describe data→ conclude that you have found new, fancy physics

The Mosel approachtry as much as possible to describe data by standardeffectsin particular for reactions on nuclei consider side feeding,coupled channels, final-state interactions

; transport theory, GiBUU

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Transport theory

describe, e.g., γ + A→ h + X by transport theory

succession of single scattering events, e.g.γ + N1 → h + X , h + N2 → h + N2, . . . ; rescatteringγ + N1 → h′ + X , h′ + N2 → h + X , . . . ; cross feeding

definitely appropriate for (very) low densitiescan account for finite size of medium (nucleus)and finite duration of reactioncoupled-channel treatment (cross feeding)beyond Glauber (non straight-line, cross feeding),but no quantum interference between different scatterings

one particular model:The Giessen Boltzmann-Uehling-Uhlenbeck transport model

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

The GiBUU transport model

input: elementary reaction rates→ theoretical and experimental understanding of

elementary reactions mandatoryuniversal framework for various observables

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Example: sigma meson

suppose sigma and pion (chiral partners)become degenerate at chiral restoration

→ sigma mass drops and width shrinks (limited phase space)(with increasing density ρ and dropping order parameter Φ(ρ))

Hatsuda/Kunihiro/Shimizu, Phys.Rev.Lett.82 (1999) 2840

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Sigma meson in nuclear matter

dropping mass model predicts that spectral strength ofsigma meson moves downwards(Hatsuda/Kunihiro/Shimizu, Phys.Rev.Lett.82 (1999) 2840)

alternative scenario with same qualitative result:sigma meson dynamically generated in pion-pion scatteringdressing of pions by resonance-hole loops,... shifts strengthdownwards

(Chiang/Oset/Vicente-Vacas, Nucl.Phys.A644 (1998) 77)

Fig. 2

+ + +

+

a) b) c)

d) e)

+ . . . .

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Double pion production and sigma meson

Hatsuda/Kunihiro/Shimizu,

Phys.Rev.Lett.82 (1999) 2840

260 280 300 320 340 360 380 400 420 440

M I(π0π0) [MeV]

0

0.5

1

1.5

2

2.5

dσ/d

MI /A

[nb

/MeV

] 12C

EγLab.

:[400,460] MeV

208Pb

Roca/Oset/Vicente-Vacas,

Phys.Lett. B541 (2002) 77

expect to see downward shift in π0π0, but not in π±π0

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Double pion production and sigma meson II

expect to see downward shift in π0π0, but not in π±π0

0

5

0

2.5

0

2

250 300 350 400 450

σ d /

dM (

nb/M

eV)

1 A

ππM [MeV]

H

c)

b)

a)

Pbnat

C12

1

← π0π0

π±π0 →

0

20

0

5

0

2.5

250 300 350 400 450A1

σ d /

dM (

nb/M

eV)

Pb

ππM [MeV]

C

H

c)

b)

a)

12

nat

1

TAPS@MAMI, Phys.Rev.Lett.89 (2002) 222302

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Double pion production and sigma meson III

alternative (transport) scenario: scattering of pions in themedium shifts strength downwards

→ should be similar for π0π0 and π±π0

0

1

2

3

dσ/d

M[n

b/M

eV/A

]

πoπo

Eγ = 400 - 500 MeV

0

2

4

6 πoπo

Eγ = 500 - 550 MeV

0

5

10

15

250 300 350 400 450Mππ[MeV]

πoπ+/-

0

10

20

30

300 400 500

πoπ+/-

experiment:

γ+40Ca, TAPS@MAMI,

Eur.Phys.J.A32 (2007) 219

theory:

Buss et al. (GiBUU),

Eur.Phys.J.A29 (2006) 189

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Double pion production and sigma meson III

alternative (transport) scenario: scattering of pions in themedium shifts strength downwards

→ should be similar for π0π0 and π±π0

0

1

2

3

dσ/d

M[n

b/M

eV/A

]

πoπo

Eγ = 400 - 500 MeV

0

2

4

6 πoπo

Eγ = 500 - 550 MeV

0

5

10

15

250 300 350 400 450Mππ[MeV]

πoπ+/-

0

10

20

30

300 400 500

πoπ+/-

experiment:

γ+40Ca, TAPS@MAMI,

Eur.Phys.J.A32 (2007) 219

theory:

Buss et al. (GiBUU),

Eur.Phys.J.A29 (2006) 189

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

BUU summary

one should be cautious with claims that fancy in-mediumeffects are seen (dropping masses, many-body effects, . . . )

→ first check if there is mundane explanation by standardtransport theory (successive scatterings)

→ need sophisticated transport approach, in particularprecise elementary input (e.g. also reactions on neutrons)one code which describes many reactions (γA, πA, pA, AA)

input for transport and for many-body field theory:elementary reaction rates

→ theoretical and experimental understanding of elementaryreactions mandatory

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Decoupling theorem

first met Ulrich in 1992 at GSI theory workshop(“Rauischholzhausen workshop”) in Rauischholzhausen

same time: European soccer championship 1992(“We are red, we are white, we are Danish dynamite”)

decoupling theorem: In every conceivable Universe Ulrichand soccer are uncorrelated.

prediction: Whatever Ulrich will do during his retirement, itwill not be soccer.

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Decoupling theorem

first met Ulrich in 1992 at GSI theory workshop(“Rauischholzhausen workshop”) in Rauischholzhausensame time: European soccer championship 1992

(“We are red, we are white, we are Danish dynamite”)

decoupling theorem: In every conceivable Universe Ulrichand soccer are uncorrelated.

prediction: Whatever Ulrich will do during his retirement, itwill not be soccer.

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Decoupling theorem

first met Ulrich in 1992 at GSI theory workshop(“Rauischholzhausen workshop”) in Rauischholzhausensame time: European soccer championship 1992(“We are red, we are white, we are Danish dynamite”)

decoupling theorem: In every conceivable Universe Ulrichand soccer are uncorrelated.

prediction: Whatever Ulrich will do during his retirement, itwill not be soccer.

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Decoupling theorem

first met Ulrich in 1992 at GSI theory workshop(“Rauischholzhausen workshop”) in Rauischholzhausensame time: European soccer championship 1992(“We are red, we are white, we are Danish dynamite”)

decoupling theorem: In every conceivable Universe Ulrichand soccer are uncorrelated.

prediction: Whatever Ulrich will do during his retirement, itwill not be soccer.

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Decoupling theorem

first met Ulrich in 1992 at GSI theory workshop(“Rauischholzhausen workshop”) in Rauischholzhausensame time: European soccer championship 1992(“We are red, we are white, we are Danish dynamite”)

decoupling theorem: In every conceivable Universe Ulrichand soccer are uncorrelated.

prediction: Whatever Ulrich will do during his retirement, itwill not be soccer.

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Summary

Lessons from Ulrich:

coupled-channel effects are importantthink twice,

i.e. do not get swept away with the wave ofenthusiasm about fancy new physicswork hard to find mundane explanationsdo not become a “Fachidiot”

change research topic after some timesee and use cross relations:

; one transport code for many reactions; elementary hadron and in-medium physics

stress your own work — sorry, I failed again

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Summary

Lessons from Ulrich:

coupled-channel effects are importantthink twice, i.e. do not get swept away with the wave ofenthusiasm about fancy new physicswork hard to find mundane explanations

do not become a “Fachidiot”change research topic after some timesee and use cross relations:

; one transport code for many reactions; elementary hadron and in-medium physics

stress your own work — sorry, I failed again

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Summary

Lessons from Ulrich:

coupled-channel effects are importantthink twice, i.e. do not get swept away with the wave ofenthusiasm about fancy new physicswork hard to find mundane explanationsdo not become a “Fachidiot”

change research topic after some timesee and use cross relations:

; one transport code for many reactions; elementary hadron and in-medium physics

stress your own work — sorry, I failed again

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Summary

Lessons from Ulrich:

coupled-channel effects are importantthink twice, i.e. do not get swept away with the wave ofenthusiasm about fancy new physicswork hard to find mundane explanationsdo not become a “Fachidiot”

change research topic after some timesee and use cross relations:

; one transport code for many reactions; elementary hadron and in-medium physics

stress your own work —

sorry, I failed again

Coupled-channel K matrix Spectral functions Coupled-channel BUU Decoupling theorem Summary

Summary

Lessons from Ulrich:

coupled-channel effects are importantthink twice, i.e. do not get swept away with the wave ofenthusiasm about fancy new physicswork hard to find mundane explanationsdo not become a “Fachidiot”

change research topic after some timesee and use cross relations:

; one transport code for many reactions; elementary hadron and in-medium physics

stress your own work — sorry, I failed again