1

Determination of the ω- and η’ -nucleus optical potential

II. Physikalisches InstitutVolker Metag

*funded by the DFG within SFB/TR16

Outline:◆ theoretical predictions for in-medium modifications of hadron properties ◆ exp. approaches and results on the real part of the ω, η’- nucleus potential◆ exp. approaches and results on the imaginary part of the ω, η’- nucleus potential◆ search for meson-nucleus bound states◆ summary & outlook

Mesons in NucleiInternational workshop

31.7.-2.8.2016, Kyoto, Japan

2

T. Hatsuda and S. Lee,PRC 46 (1992) R34

G.E. Brown and M. Rho,PRL 66 (1991) 2720

V. Bernard and U.-G. Meißner,NPA 489 (1988) 647

m?

m⇡ < q̄q >?

< q̄q >0⇡ 0.8(� ⇡ �0)

m�V

mV= (1� �

⇥

⇥0);� ⇡ 0.18widespread theoretical and experimental

activities to search for in-medium modifications of hadrons

hadron masses

J. Wambach • mesons = excitations of the QCD vacuum

• QCD vacuum: complicated structure characterized by condensates

• in the nuclear medium: condensates are changed

➯ change of the hadronic excitation energy spectrum

how do hadron properties (mass, width) change in a dense nuclear medium ??

3

V. Bernard, R.L. Jaffe, U.-G. Meissner, NPB 308 (1988) 753

S. Klimt, M. Lutz, U. Vogel, W Weise, NPA 516 (1990) 429

W. Weise, NBI Copenhagen, 1993mass as a result of symmetry breaking

symmetry breaking

symmetry breaking pattern for pseudoscalar mesons

H. Nagahiro et al.,PRC 87 (2013) 045201 D. Jido et al.,arXiv:1208.0982

partial restoration of chiral symmetry predicted to occur in a nucleus ⟹ impact on meson masses ??

partial symmetry restoration

4

V. Bernard und U.G. Meissner, Phys. Rev. D 38 (1988) 1551

V. Bernard and U.-G. Meissner,Phys. Rev.D 38 (1988) 1551

almost no dependence of η’ mass on density

S. Bass and A. Thomas, PLB 634 (2006) 368

Δmη’ (ρ0)≈−40 MeV for θηη’ = −200

Δmη’ (ρ0)≈−150 MeV Δmη (ρ0) ≈ +20 MeV

H. Nagahiro et. al, Phys. Rev. C 74 (2006) 045203

SU(2)

SU(3)

S. Sakai and D. JidoPRC 88 (2013) 064906

Δmη’ (ρ0)≈−80 MeV

NJL-model NJL-model linear σ model

QMC-model

hadronic models: predictions for η’ in-medium mass

5

hadronic models: predictions for ω-spectral functionsF. Klingl et al.,

NPA 610 (1997) 297; NPA 650 (1999) 299

◆ lowering of in-medium mass◆ broadening of resonance with increasing nuclear density Re(U) ≠0; Im(U) ≠0

M. Lutz et al., NPA 706 (2002) 437

splitting into ω-like and N*N-1 modedue to coupling to nucleon resonances

P. Mühlich et al., NPA 780 (2006) 187

spectral function for ω meson at rest:almost no mass shift; strong in-medium broadeningRe(U) ≈0; Im(U) large

experimental task: search for { }mass shift ?broadening?structures?

of hadronic spectral functions

6

meson-nucleus optical potential

U(r) = V (r) + iW (r)

mass and lifetime (width) may be changed in the medium

V (r) = �m(�0) · �(r)�0

real part

in-medium mass modification

⬄W (r) = ��0/2 · �(r)

�0

= � 12 · ~c · ⇥(r) · ⇤inel · �

imaginary part

in-medium width, absorption inelastic cross section

lifetime shortened

⬄

H. Nagahiro an S. Hirenzaki, PRL 94 (2005) 232503

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experimental approaches to determine the meson-nucleus optical potential

U(r) = V (r) + iW (r)

V (r) = �m(�0) · �(r)�0

real part

W (r) = ��0/2 · �(r)�0

= � 12 · ~c · ⇥(r) · ⇤inel · �

imaginary part

◆ transparency ratio measurement

TA =��A!⌘0X

A · ��N!⌘0X

D. Cabrera et al., NPA 733 (2004)130

◆ line shape analysis◆ excitation function◆ momentum distribution◆ meson-nucleus bound states

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CBELSA/TAPS experiment

MiniTAPS

Crystal Barrel

photon beam

Eγ=0.7-3.1 GeVForward Plug

solid target: 12C and 93Nb

Eγ=0.7 - 3.1 GeV

1320 CsI

216 BaF2

4π photon detector: ideally suited for identification of multi-photon final states

η’→π0π0η→6γ BR 8.5%ω→π0γ→ 3γ BR 8.2%

]2 [MeV/cη0π0πM900 1000 1100

2 /

8 M

eV/c

η0 π0 πN

0

500

1000

1500

2000Nb

20.3 MeV/c±= 11.9σ

20.4 MeV/c±m=957.1

≈ 1.2%σm

m

η’→π0π0η→6γ

ω→π0γ→ 3γ

]2 [MeV/cγ0πM600 650 700 750 800 850 900 950

)]2 [1

/(4 M

eV/c

γ0 πN

410

97563 counts

C20.1 MeV/c±=26.4σ

≈ 3%σm

m

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The real part of the meson-nucleus optical potential

J. Weil, U. Mosel and V. Metag, PLB 723 (2013 ) 120

the real part of the ω-nucleus potential

ω→π0γsensitive to nuclear density at production point and not at decay point

γ+93Nb→π0γ+X

Eγ=0.9-1.3 GeV

π0γ momentum distribution

◆ momentum distribution of the meson:in case of dropping mass - when leaving the nucleus hadron has to become on-shell;mass generated at the expense of kineticenergy

➯ downward shift of momentum distribution

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➯ cross section enhancementπ0γ excitation function

◆ measurement of the excitation function of the mesonin case of dropping mass - higher meson yield for given √s because of increased phase space due to lowering of the production threshold

Eγthr

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Eγthr

excitation function for ω photoproduction off Ccomparison with GiBUU calculation

CB/TAPS @ MAMI V. Metag et al., PPNP, 67 (2012) 530

data not consistent with strong mass shift scenario (Δm/m≈-16%)

vacuumcollisional broadening(CB)CB+mass shift (-16%)mass shift (-16%)

M. Thiel et al., EPJA 49 (2013) 132

momentum distribution

V(ρ=ρ0) = −(42±17(stat)±20(syst)) MeV

[GeV]γE0.9 1 1.1 1.2 1.3 1.4

b]µ/A

[σ

-210

-110

Carbon

★CB/TAPS@MAMI ● CBELSA/TAPS

GiBUUcollisional broad.and mass shift V = 0 MeV V = -20 MeV V = -40 MeV V = -55 MeV V = -94 MeV V = -125 MeV

Carbon

excitation function

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data: M. Nanova et al., PLB 727 (2013) 417

data disfavour strong mass shifts

Eγ[MeV]

ση

’ [µ

b]

V(ρ=ρ0) = 0 MeV

V(ρ=ρ0) = -75 MeVV(ρ=ρ0) = -100 MeVV(ρ=ρ0) = -150 MeV

V(ρ=ρ0) = -50 MeVV(ρ=ρ0) = -25 MeV

Eγ[MeV]

ση

’ [µ

b] σtotC data

σdiff

Eγthr

10-1

1

10

1000 1500 2000 2500

Vη’(ρ=ρ0) = −(40±6) MeV

ση’N=11 mb

CBELSA/TAPS @ ELSA

pη’ [GeV/c ]

dση

’/dp η

’ [µ

b/G

eV/c

]

C data Eγ=1500-2200 MeV

V(ρ=ρ0) = 0 MeV

V(ρ=ρ0) = -75 MeV

V(ρ=ρ0) = -25 MeV

V(ρ=ρ0) = -100 MeVV(ρ=ρ0) = -150 MeV

V(ρ=ρ0) = -50 MeV

10-1

1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Vη’(<pη’>≈1.1 GeV/c;ρ=ρ0) = −(32±11) MeV

ση’N=11 mb

excitation function and momentum distribution for η' photoproduction off C

calc.: E. Paryev, J. Phys. G 40 (2013) 025201γ C →η’X

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excitation function and momentum distribution for η' photoproduction off Nb

CBELSA/TAPS @ ELSA

Vη'(<pη'>≈1.14 GeV/c;ρ=ρ0) = −(41±10) MeV

M. Nanova et al., arXiv:1607.07228; accepted for publication in PRC

data disfavour strong mass shifts

γ Nb →η’X

[GeV]γE1 1.5 2 2.5

b]µ [ 'η

σ

1

10

Nbtotσ

diffσ

= 13 mbinel'η

σ

) = 0 MeV0ρ=ρV(

) = - 25 MeV0ρ=ρV(

) = - 50 MeV0ρ=ρV(

) = - 75 MeV0ρ=ρV(

) = -100 MeV0ρ=ρV(

) = -150 MeV0ρ=ρV(' thrη

γE

[GeV/c]'η

p0.5 1 1.5 2 2.5

b/G

eV/c

]µ

/ [ 'η/d

pσd

1

10

Nb =1.3 - 2.6 GeVγE

= 13 mbinel'η

σ

) = 0 MeV0ρ=ρV(

) = - 25 MeV0ρ=ρV(

) = - 50 MeV0ρ=ρV(

) = - 75 MeV0ρ=ρV(

) = -100 MeV0ρ=ρV(

) = -150 MeV0ρ=ρV(

Vη'(ρ=ρ0) = −(40±12) MeV

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compilation of results for the real part of the ω- and η’-nucleus optical potential

Vη’A(ρ=ρ0) =

−(40±8(stat)±15(syst)) MeV

VωA(ρ=ρ0) =

−(29±19(stat)±20(syst)) MeV

[MeV]'AηV80− 60− 40− 20− 0 20

excitation function

kinpeak E

average

C

[MeV]'AηV80− 60− 40− 20− 0

excitation function

mom. distribution

weighted average

CNb

ω η’

first (indirect) observation of in-medium mass shift of η’ at ρ=ρ0 and T=0in good agreement with QMC model predictions (S. Bass et al. , PLB 634 (2006) 368)

M. Nanova et al., arXiv:1607.07228; accepted for publication in PRC

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The imaginary part of the meson-nucleus optical potential: momentum dependence

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momentum differential cross section for ω, η’produced off C, Nb

ω η’γ C,Nb → ωX

Eγ = 1.2- 2.9 GeV

TNb/C (pm) = 12 ⦁σγNb→mX (pm)93 ⦁σγC→mX (pm)

mmomentum differential cross sections ⇒

P R E L I M I N A R Y

[MeV/c]ω

p0 500 1000 1500 2000 2500

b/(G

eV/c

)]µ

/A [

ω/d

pσd

0

0.5

1

1.5

2

2.5

3

3.5

4

NbC

[MeV/c]'η

p0 500 1000 1500 2000 2500

b/(G

eV/c

)]µ

/A [

'η

/dp

σd

0

0.05

0.1

0.15

0.2

0.25

NbC

γ C,Nb →η’X

P R E L I M I N A R Y

P R E L I M I N A R Y

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ω η’

momentum dependence of transparency ratio for ω, η’

absorption of η’ mesons much weaker than for ω mesons !!

TNb/C (pm) = 12 ⦁σγNb→mX(pm)93 ⦁σγC→mX (pm)

m

bbbbbbbbbbbb blablabla

[MeV/c]ω

p0 500 1000 1500 2000 2500

ω Nb/

CT

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PRL 100 (2008) 192302this experiment

M. Kotulla et al., PRL 100 (2008) 192302

[MeV/c]'η

p0 500 1000 1500 2000 2500

'η N

b/C

T

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PLB 710 (2012) 600this experiment

M. Nanova et al., PLB 710 (2012) 600

TNb/C ≈ 0.7-0.8 η’TNb/C ≈ 0.4-0.6 ω

P R E L I M I N A R Y

P R E L I M I N A R Y

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[MeV/c]'η

p0 500 1000 1500 2000 2500

[MeV

]'η 0

Γ0

10

20

30

40

50

60

70

80

90PLB 710 (2012) 600this experiment

[MeV/c]ω

p0 500 1000 1500 2000 2500

[MeV

]ω 0

Γ

0

50

100

150

200

250

300

350PRL 114 (2015) 199903this experiment

momentum dependence of the ω, η’ in-medium width

Glauber model: high energy Eikonal approximation

TNb/C (pm) ⇒ Γ0 (ρ=ρ0) (pm) m m

ω η’

ω in-medium width ≈ 50-150 MeV η’ in-medium width ≈ 10-30 MeV

S. Friedrich et al., submitted to EPJA

M. Nanova et al., PLB 710 (2012) 600M. Kotulla et al., PRL 114 (2015) 199903

P R E L I M I N A R Y

P R E L I M I N A R Y

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[MeV/c]ω

p0 500 1000 1500 2000 2500

[MeV

]ω 0

Γ

0

50

100

150

200

250

300

350PRL 114 (2015) 199903this experiment

[MeV/c]'η

p0 500 1000 1500 2000 2500

[MeV

]'η 0

Γ

0

10

20

30

40

50

60

70

80

90PLB 710 (2012) 600this experiment

ω in-medium width in comparison to theoretical predictions

two groups of calculations:

ω→ρπ : A. Ramos et al., EPJA 49(2013) 148D. Cabrera and R. Rapp, PLB 729 (2014) 67

NN*ω coupl.: F. Klingl et al., NPA 650 (1999) 299B. Friman et al., arXiv: 9811040M. Lutz et al., NPA 706 (2002) 437P. Mühlich et al., NPA 780 (2006) 187

GiBUU

S. Friedrich et al., submitted to EPJA ω η’M. Nanova et al., PLB 710 (2012) 600M. Kotulla et al., PRL 114 (2015) 199903

P R E L I M I N A R Y

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imaginary part of the potential for ω, η’

Glauber model: high energy Eikonal approximation

TNb/C (pm) ⇒ Γ0 (ρ=ρ0) (pm) = - 2 Im U0 (pm)m m m

ω η’M. Nanova et al., PLB 710 (2012) 600

Im U0(ρ=ρ0,pω=0) = −(30±10) MeV ω

◆ extension to higher energies allows for dispersion relation analysis, providing link between real and imaginary part of potential

M. Kotulla et al., PRL 114 (2015) 199903

Im U0(ρ=ρ0,pη’=0) = −(10±3) MeV η’

blablabla

S. Friedrich et al., submitted to EPJA

[MeV]thrs-ωs0 500 1000 1500 2000

) [M

eV]

ω 0-(I

m U

0

20

40

60

80

100

120

140

160

180PRL 114 (2015) 199903

this experiment

◆ extrapolation to production threshold: [MeV]thrs-'ηs

0 500 1000 1500) [

MeV

]'η 0

-(Im

U0

5

10

15

20

25

30

35

40

45PLB 710 (2012) 600

this experiment

P R E L I M I N A R Y

P R E L I M I N A R Y

21

compilation of results for real and imaginary part of the ω, η’ -nucleus optical potential

UωA(ρ=ρ0)= −((29±19(stat)±20(syst) + i(48±10±9)) MeV

Uη’A(ρ=ρ0)= −((40±8(stat)±15(syst) + i(13±3±3)) MeV

ω not a good candidate

to search for meson-nucleus bound states!

⎮Im U ⎮≳⎮Re U⎮; ➯ η’ promising candidate to search for mesic states

⎮Re U⎮ >>⎮Im U⎮; ➯

ω η’

potential depth [MeV]0 10 20 30 40 50 60 70 80

imag

inar

y pa

rt [M

eV]

0

10

20

30

40

50

60

70

80

ω

'η

⎮Im U ⎮>⎮Re U⎮

⎮Re U⎮ >⎮Im U⎮

22

outlook: search for η’-mesic states in photo-nuclear reactions

12C(γ,p) η’X @ 1.5-2.8 GeV

Δp/p ≈ 1-2 %

B1: BGO-OD@ELSA

BGO-OD ideally suited for exclusive measurement

approved proposal: ELSA/3-2012-BGO

η’ γp

formation and decay of η’-mesic state

N

η

LEPS2@SPring-8 12C(γ,p) η’X @ 1.5-2.4 GeV

23

FRS@GSI 12C( , )

K. Itahashi et al., Prog. Theo. Phys. 128(2012) 601

missing mass spectrometry: Δm =2.5 MeV/c2

12C targetS2

S4

2.5 GeV protons 2.7-2.9 GeV/c deuterons(protons)

MWDC

aerogelCerenkov

aerogelCerenkov

p/d separation byaerogel CerenkovTOF S2-S4 (diff.≈20 ns)

plastic scintillators

search for η’-mesic states in hadronic reactions

FRS@GSI:12C(p,d)η’⦻11C

K. Itahashi et al., PETP 128 (2012) 601H. Nagahiro et al., PRC 87 (2013) 045201

particle identification by time-of-flight

no structures in bound state region

observed;deep potentials with

V0 > 100 MeV excluded

FRS@GSI operated as spectrometer

24

Summary & Outlookhow do the hadron properties (mass, width) change

in a dense nuclear medium ??

◆ all mesons are broadened; their lifetime is shortened through inelastic collisionsΓω(ρ=ρ0; p=0) ≈ 90 MeV; Γη’(ρ=ρ0; p=0) ≈ 25 MeV;

◆ large mass modifications Δm > 100 MeV (as predicted by some calculations) have not been observed

◆ for the η’ meson an in-medium mass drop of Δm (ρ=ρ0) ≈ −40 MeV has been determined

◆ the η’ meson is a good candidate for forming meson-nucleus bound states since Im U << Re U

◆ search for η’ mesic states ongoing

◆ in-medium effects described within meson-nucleus optical

meson properties do change in a strongly interacting medium !!

25

BACKUP

26

ω line shape from ω→π0γ in photo-nuclear reactionM. Thiel et al., EPJA 49 (2013) 132

γ Nb→ω+X →π0γ+X at Eγ = 0.9-1.3 GeVCB/TAPS@MAMI

different in-medium modificationscenarios almost indistinguishable

fraction of ω decays in Nb: ≈36%

cτ = 22 fm/cfor <pω>≈600 MeV/c: βγcτ = 17 fm ⦁

only mass shifts ≫ σm/m=3% observable⦁ω signal smeared out due to in-medium broadening (Γ≈140 MeV)

⦁

due to π0 absorption (π0-FSI) ω→π0γ decays in the center of the nucleus are suppressed

⦁

ω meson

η’ mesoncτ = 1000 fm/cfor <pη’>≈1000 MeV/c: βγcτ = 1000 fm fraction of η’ decays in Nb: ≈ 0.5%

⦁

line shape analysis very difficult or even impossible

]2 [MeV/cγ0πm600 650 700 750 800 850 900

]2co

unts

/ [9

MeV

/c + Xω → Nb γ

4

3

2

1

0

3x 10 Eγ=900-1300 MeV

scenarios:no mod.coll. broad.shift + broad.shift only

30 000

GiBUUω→π0γ σm≈3%