Lessons from Justus Liebig and Ulrich Mosel...Liebig’s law of the minimum principle developed in agricultural science by Carl Sprengel (1828) popularized by Justus von Liebig growth

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


The academic who is who


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)


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


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


The anti-Mosel approach

use simplest possible model which incorporates standardphysics


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


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

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,. . .


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


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


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


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)


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)


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))



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 . . . )



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)


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


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


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 BUU

The anti-Mosel approachuse simplest possible model which incorporates standardphysics


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 BUU

The anti-Mosel approachuse simplest possible model which incorporates standardphysics


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


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


The GiBUU transport model

input: elementary reaction rates→ theoretical and experimental understanding of

elementary reactions mandatoryuniversal framework for various observables


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


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)

+ . . . .


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


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


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


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


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


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.


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

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





Decoupling theorem





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


Summary


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:




Summary


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”





Summary





stress your own work —

sorry, I failed again


Summary






Lessons from Justus Liebig and Ulrich Mosel...Liebig’s law of the minimum principle developed in agricultural science by Carl Sprengel (1828) popularized by Justus von Liebig growth

Documents