The search for meson-nucleus bound states

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1 The search for meson-nucleus boun states Volker Metag II. Physikalisches Institut Outline eeply boun pionic states search for η an η mesic states search for ω mesic states summary an outlook *fune by the DFG within SFB/TR16 MesonNet meeting Prague, Czech Republic June 17-19, 13 1

2 eeply boun pionic states recoil free π - prouction in (, 3 He) reaction on Sn isotopes Suzuki et al., PRL 9 (4) Sn: B1s = (3.8±.1) MeV; Γ1s= (.33±.5) MeV with Γ << bining energy B prerequisite for observing boun states

3 eeply boun pionic states recoil free π - prouction in (, 3 He) reaction on Sn isotopes Suzuki et al., PRL 9 (4) Sn: B1s = (3.8±.1) MeV; Γ1s= (.33±.5) MeV with Γ << bining energy B prerequisite for observing boun states pocket-like potential arising from superposition of repulsive nuclear potential an attractive Coulomb potential halo-like π - istribution aroun nucleus

4 eeply boun pionic states recoil free π - prouction in (, 3 He) reaction on Sn isotopes Suzuki et al., PRL 9 (4) Sn: B1s = (3.8±.1) MeV; Γ1s= (.33±.5) MeV with Γ << bining energy B prerequisite for observing boun states pocket-like potential arising from superposition of repulsive nuclear potential an attractive Coulomb potential halo-like π - istribution aroun nucleus o mesons-nucleus boun states exist purely boun by an attractive strong interaction??

5 preictions for η- an η -nucleus boun states preictions for bining energies an withs of η-boun states C. Garcia-Recio et al., PLB 55 () 47 most states have tails into the continuum, allowing η ecay of boun states recently: E. Frieman et al. arxiv:

6 preictions for η- an η -nucleus boun states preictions for bining energies an withs of η-boun states C. Garcia-Recio et al., PLB 55 () 47 preiction for bining energies an withs of η - 1 C boun states for ifferent η -nucleus potentials D. Jio et al., PRC 85 (1) 31 most states have tails into the continuum, allowing η ecay of boun states recently: E. Frieman et al. arxiv: Vopt(ρ) = Vreal(ρ) + i Wimag(ρ) many states with with Γ << bining energy preicte 3

7 preictions for η- an η -nucleus boun states preictions for bining energies an withs of η-boun states C. Garcia-Recio et al., PLB 55 () 47 preiction for bining energies an withs of η - 1 C boun states for ifferent η -nucleus potentials D. Jio et al., PRC 85 (1) 31 most states have tails into the continuum, allowing η ecay of boun states recently: E. Frieman et al. arxiv: Vopt(ρ) = Vreal(ρ) + i Wimag(ρ) many states with with Γ << bining energy preicte imaginary part W 1 MeV known from transparency ratio measurements M. Nanova, et al., PLB 71 (1) 6 3

8 inications for η mesic states coherent η photo prouction on 3 He (MAMI) M. Pfeiffer et al., PRL 9 (4) 51 F. Pheron et al., PLB 79 (1) 1 γ 3 He η 3 He PWIA very strong rise of coherent cross section irectly at threshol strong 3 He-η FSI; quasi boun state close to threshol?? same observation by COSY-ANKE in p η 3 He P. Goslawski et al., Prog. Part. Nucl Phys 67 (1) 37 4

9 inications for η mesic states coherent η photo prouction on 3 He (MAMI) M. Pfeiffer et al., PRL 9 (4) 51 F. Pheron et al., PLB 79 (1) 1 γ 3 He η 3 He COSY-GEM-collaboration A. Buzanovski et al. PRC 79 (9) 11 p+ 7 Al 3 He+ 5 Mg η 3 He+p+π - +X PWIA very strong rise of coherent cross section irectly at threshol strong 3 He-η FSI; quasi boun state close to threshol?? same observation by COSY-ANKE in p η 3 He P. Goslawski et al., Prog. Part. Nucl Phys 67 (1) 37 consistent with η mesic state with B=-(1.±.) MeV; Γ= (4.7±1.7)MeV 4

10 population of ω-mesic states in photo inuce reactions γa ω (Z-1) (A-1) + p in recoil free prouction E. Marco an W. Weise, PLB 5 (1) 59 H. Nagahiro et al., Nucl. Phys. A 761 (5) 9 attractive potential: mesic state; ω mass rop repulsive potential boun states quasi-free prouction boun states quasi-free prouction Ex - E = - Bω + Snj - Snj(gs) two ways of measuring excitation energy of mesic nucleus: 1.) missing mass spectrometry: measure spectrum of forwar going proton.) measure kinetic energy of ecay proucts of mesic state 5

11 population of ω-mesic states in photo inuce reactions γa ω (Z-1) (A-1) + p in recoil free prouction E. Marco an W. Weise, PLB 5 (1) 59 H. Nagahiro et al., Nucl. Phys. A 761 (5) 9 attractive potential: mesic state; ω mass rop repulsive potential boun states quasi-free prouction boun states quasi-free prouction Ex - E = - Bω + Snj - Snj(gs) two ways of measuring excitation energy of mesic nucleus: 1.) missing mass spectrometry: measure spectrum of forwar going proton.) measure kinetic energy of ecay proucts of mesic state search for boun states hampere by large in-meium ω with: Γ(ρ=ρ) 14 MeV from transparency ratio measurement: M.Kotulla et al. PRL 1 (8) 193 5

12 search for ω mesic states at CBELSA/TAPS p γ ω forwar going proton takes up momentum of incoming photon beam, leaving ω meson almost at rest capture by nucleus in case of an attractive interaction γ 1 C ω 11 B+p Eγ=15-31 MeV 6

13 search for ω mesic states at CBELSA/TAPS p γ ω forwar going proton takes up momentum of incoming photon beam, leaving ω meson almost at rest capture by nucleus in case of an attractive interaction in TAPS [MeV] p-ientification by ΔE vs. TOF Carbon 1 γ 1 C ω 11 B+p Eγ=15-31 MeV E eposite Time of Flight [ns] -1 1 coincient etection of proton in TAPS an ω π γ 3γ in CBELSA 6

14 [1/1 MeV] 4 35 N E -78 [MeV] ω π γ γ 1 C ω + X + p in TAPS (θp = 1-11 ) PhD-thesis S.Frierich (Univ. Giessen) Eγ=15-31 MeV -78 [MeV] E ] [MeV/c ] M curves for constant momenta of π γ pairs of,3,6 an 9 MeV/c backgroun etermine from π π,π η 4γ events, omitting one photon [1/1 MeV/c N [MeV/c ] M 7

15 kinetic energy an invariant mass istribution of π γ pairs projections onto Eπγ-78 MeV an Mπγ axes kinetic energy istribution invariant mass istribution [1/1 MeV] N 15 Carbon ] [1/1 MeV/c 5 4 Carbon =3. MeV/c N E - 78 [MeV] [MeV/c ] M 8

16 acceptance for π γ pairs from simulaton π γ pair in coincience with proton in TAPS (1 <θp<11 ) -78 [MeV] E pixel-wise acceptance correction [MeV/c ] M contourlines: increments by 1%.5 9

17 cross sections for kinetic energy an invariant mass of π γ pairs [nb/mev/sr] kinetic energy /sr] /m [nb/mev/c σ= 8.9±1.4 MeV/c invariant mass [MeV] E boun state region: Eπγ - 78 MeV < MeV no structures; yiel?? [MeV/c ] M tailing towars small masses 1

18 comparison to reference measurement on the free proton [nb/mev/sr] Carbon peak: (54±9) MeV S. Frierich, CBELSA/TAPS collaboration photo prouction of ω mesons on LH, C in coincience with forwar going proton Eγ =15-31 MeV [nb/mev/sr] [MeV] 1 peak: (57±3) MeV E LH kinetic energy istributions of π γ pairs peak at almost the same energy for free proton an carbon: Epeak 55 MeV at first sight: ω-nucleus potential neither strongly attractive nor strongly repulsive [MeV] E 11

19 comparison to reference measurement on the free proton kin [nb/mev/sr] Carbon peak: (54±9) MeV C S. Frierich, CBELSA/TAPS collaboration photo prouction of ω mesons on LH, C in coincience with forwar going proton Eγ =15-31 MeV [nb/mev/sr] E -78 [MeV] 1 peak: (57±3) MeV LH LH kinetic energy istributions of π γ pairs peak at almost the same energy for free proton an carbon: Epeak 55 MeV at first sight: ω-nucleus potential neither strongly attractive nor strongly repulsive [MeV] E 11

20 [nb/mev/sr] theoretical preictions for γ 1 C ω 11 B + p formation cross section after averaging over Eγ=15-31 MeV; 1 Θp H. Nagahiro an S. Hirenzaki, priv. com [MeV] E (V, W ) no structures ue to large ω in-meium with peak in kinetic energy istribution correlate with epth of real potential - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV 1

21 [nb/mev/sr] theoretical preictions for γ 1 C ω 11 B + p formation cross section after averaging over Eγ=15-31 MeV; 1 Θp [MeV] E (V, W ) no structures ue to large ω in-meium with peak in kinetic energy istribution correlate with epth of real potential - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV H. Nagahiro an S. Hirenzaki, priv. com. absorption correction factor Γω πγ/γtot γ nucleon hole target emitte proton π γ ecay [MeV] E effective π γ ecay + escape probability from GiBUU expecte π γ cross section: σπγ= σformation Γω πγ/γtot [nb/mev/sr] (V, W ) - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV [MeV] E 1

22 [nb/mev/sr] theoretical preictions for γ 1 C ω 11 B + p formation cross section after averaging over Eγ=15-31 MeV; 1 Θp [MeV] E (V, W ) no structures ue to large ω in-meium with peak in kinetic energy istribution correlate with epth of real potential - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV H. Nagahiro an S. Hirenzaki, priv. com. absorption correction factor Γω πγ/γtot γ nucleon hole target emitte proton π γ ecay [MeV] E effective π γ ecay + escape probability from GiBUU peak in kinetic energy istribution for ifferent potential epth expecte π γ cross section: σπγ= σformation Γω πγ/γtot [nb/mev/sr] peak position [MeV] (V, W ) - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV [MeV] E potential epth [MeV] 1

23 comparison with experiment [nb/mev/sr] (V, W ) - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV peak position [MeV] kinetic energy peak (5±7) MeV PRELIMINARY [MeV] E potential epth [MeV] V(ρ=ρ) = -(6±4) MeV 13

24 [nb/mev/sr] formation cross sections: GiBUU Nagahiro et al. comparison with GiBUU [nb/mev/sr] comparison: exp. GiBUU (V, W ) - (,7) MeV - (15,7) MeV (V, W ).6 1 Nagahiro - (1,7) MeV Nagahiro - (,7) MeV GiBUU - (,7) MeV.4. GiBUU - (15,7) MeV [MeV] E goo agreement between quantum mechanical an transport calculation peak position [MeV] GiBUU PRELIMINARY Nagahiro Γω πγ/γtot [MeV] E within moel epenencies: V -(7±5) MeV potential epth [MeV] 14

25 Summary meson-nucleus boun states establishe by eeply boun pionic states (superposition of Coulomb an strong interaction) are there boun states only ue to strong interaction?? inications for η boun states preictions for η boun states search for ω boun states: no structures observe etermination of the ω-nucleus potential: Vreal = -7±5 MeV Wimag -7 MeV (from transparency ratio measurements) Γω(ρ=ρ) 14 MeV > Vreal > bining energy ω not a goo case to search for boun states 15

26 extraction of in-meium with an inelastic cross section for ω transparency ratio normalize to carbon: TA C = 11.4 σ γa ωx A eff σ γc ωx comparison to calculations: Mühlich an Mosel; Ramos an Oset M. Kotulla et al., PRL 1 (8) 193 C ω-meson Γω(<pω> =1.1 GeV/c; ρ=ρ) MeV low ensity approximation: Γ(ρ )=c β ρ σ inel 6 mb σ inel ωn 16

27 C extraction of in-meium with an inelastic cross section for ω transparency ratio normalize to carbon: TA C = 11.4 σ γa ωx A eff σ γc ωx comparison to calculations: Mühlich an Mosel; Ramos an Oset M. Kotulla et al., PRL 1 (8) 193 C ω -meson ω-meson Γω(<pω> =1.1 GeV/c; ρ=ρ) MeV low ensity approximation: Γ(ρ )=c β ρ σ inel 6 mb σ inel ωn no strong variation of transparency ratio with meson momentum; no evience for two-step processes 16

28 [nb/mev/sr] Carbon [MeV] E 17

29 formation cross sections [nb/mev/sr] formation cross sections: GiBUU Nagahiro et al., W ) [MeV] E there is no absorption in this GiBUU calculation (t=; before propagation); the Nagahiro curves are calculate with imaginary part (V Nagahiro - (1,7) MeV Nagahiro - (,7) MeV GiBUU - (,7) MeV GiBUU - (15,7) MeV formation cross section (Nagahiro) for same real but ifferent imaginary part [nb/mev/sr] , W ) (V - (156,9) MeV - (156,7) MeV - (1,5) MeV - (1,7) MeV - ( 5,5) MeV - ( 5,7) MeV [MeV] is the integral over the full energy range for the same real part but ifferent imaginary part the same or not? i.e., oes the imaginary part only smear out or also reuce the ω yiel?? E

30 GiBUU calculations in comparison to ata [nb/mev/sr] ω prouction before meson propagation [MeV] E [nb/mev/sr] π γ cross section after meson propagation (V, W ) - (,7) MeV - (15,7) MeV [MeV] E the branching ratio factor Γω πγ/γtot ω (1-Pabs π ) is obtaine by iviing the kinetic energy spectra after propagation by those before propagation

31 branching ratios Γω πγ/γtot ω (1-Pabs π ) etermine from GiBUU by comparing π γ kinetic energy spectra before an after in-meium propagation of ω an π mesons Γtot ω = Γfree+Γel.+Γinel. Pabs π = probability for π absorption after in-meium ω π γ ecay K=; Γ(ρ=ρ)=14 MeV.6 absorption correction factor [MeV] E K=1; Γ(ρ=ρ)=75 MeV.7 absorption correction factor [MeV] E absorption correction factor Γtot ω = Γfree no ω collisions [MeV] E Γω πγ/γtot ω (1-Pabs π ) = Γω πγ/γfree (1-Pabs π ) = 8.3% (1-Pabs π ) eviation from 8.3% ue to π absorption

32 σπγ=σformation Γω πγ/γtot (1-Pabs π ) [nb/mev/sr] branching ratio calculate for K=; Γ(ρ=ρ)=14 MeV (V, W ) - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV [nb/mev/sr] branching ratio calculate for no ω collisions (V, W ) - (156,7) MeV - (1,7) MeV - ( 5,7) MeV - (,7) MeV - (-,7) MeV - (-5,7) MeV [MeV] E [MeV] E

33 Hieko: 4 scenarios for ω absorption an ecay

34 In the (γ,p) reaction, the incient photon interacts with a proton insie the nucleus, proucing the η meson almost at rest so that it can be capture by the nucleus. The proton takes up the momentum of the incoming photon an is ejecte at forwar angles. Nagahiro et al. (NPA 761 (5) 9; arxiv111.56) factorizes this prouction process into the elementary prouction process an the nuclear response S(E). with The summation is taken over all final states. The transition amplitue Tf enotes the transition of the incient photon to the proton hole an the outgoing ejectile, involving the proton hole wave function ψjp an the istorte waves χi an χf of the projectile an ejectile, respectively. Ylφ is the meson angular wave function an ξ is the spin wave function of the ejectile The in-meium Greens function is obtaine by solving the Klein-Goron equation with the meson-nucleus optical potential. The nuclear response S(E) is then obtaine by numerical integration. The calculation of the formation spectra is one separately for each subcomponent of the η - mesic nuclei labele by (nlj) -1 lη. The total formation spectrum is obtaine by summing up the ifferent subcomponents taking into account the ifference in the separation energies for the ifferent proton hole states. The energy of the emitte proton etermines the energy of the η - nucleus system uniquely.