BLED WORKSHOPS
IN PHYSICS
VOL. 13, NO. 1
p. 23
Proceedings of the Mini-Workshop
Hadronic Resonances
Bled, Slovenia, July 1 - 8, 2012
Resonances in photo-induced reactions
M. Ostrick
Institut für Kernphysik, Johannes-Gutenberg-Universität Mainz, J.-J.-Becher-Weg 45,
55128 Mainz, Germany
Abstract. The extraction of baryon resonance parameters from experimental data and
their interpretationwithin QCD are central issues in hadron physics. To achieve these goals
it is an essential prerequisite to have a sufficient amount of precision data which allows an
unambiguous reconstruction of partial wave amplitudes for different reactions. Over the
last years an intense effort has started to study photon-induced meson production. Many
single and double spin-observables have beenmeasured for the first time. This experimen-
tal progress will be illustrated by means of single and double π0 photo-production. The
focus will be on the impact of the new data for the unambiguous reconstruction of partial
wave amplitudes.
1 Introduction
Meson scattering and meson production reactions below 3 GeV distinctively ex-
hibit resonances, clearly organized in terms of flavor content, spin and parity,
sitting on top of a non resonant ”background. In lack of stringent predictions
from strong QCD these resonances are usually interpreted in constituent quark
models as excitations of massive quasi-particles bound by a confining potential.
However, also the strong meson-baryon andmeson-meson interaction could give
rise to dynamically generated resonances. Chiral unitary methods and coupled
channel calculations provide a theoretical framework to study the importance
of resonances without including them explicitly in a model. Furthermore, lat-
tice QCD simulations started to become predictive for dynamical quantities like
strong decaywidths of resonances and scattering phase shifts [1]. In the past, only
calculations of approximate mass spectra in the heavy pion limit, where excited
baryons are stable particles, were possible.
Empirically, N∗ and ∆∗ baryon resonance parameters like mass, width or
pole position have been extracted for many years by partial-wave analyses of
elastic and charge-exchange pion-nucleon scattering experiments. The most re-
cent analysis of existing πN data has been performed by the George Washington
Group [2]. Today there is no running experiment dedicated to study πN scatter-
ing anymore. However, options for a new generation of experiments with pion
beams at Hades/GSI [3], ITEP [4] and J-PARC [5] are presently under discussion.
Instead of πN scattering, an immense effort started during the last decade
to study baryon resonances with electromagnetic probes at various laboratories,
24 M. Ostrick
mainly ELSA, Graal, JLAB, LEPS, LNS and MAMI. The motivation for this on-
going effort is 2-fold. The initial idea was to substantiate or to disprove the exis-
tence of questionable resonances or even to discover new states that couple only
weakly to πN. Especially, above 2 GeV an abundance of states is predicted by
quark models which are not identified in πN partial wave analyses. This fact
is often called the ”missing resonance” problem. As historically all information
about resonances came from pionic reaction, the hope was to discover new states
in e.g. KΛ, KΣ, ηN orωN final states. The PDG lists in their latest edition a couple
of new states which have been seen in some analyses of recent data [6]. However,
there are still many ambiguities and the discussion is ongoing.
The second objective are high precision measurements of the excitation of
established resonances with real and virtual photons in order to relax the model
constraints in the analyses and understand the influence of background on the
extraction and interpretation of resonance properties. Single and double spin ob-
servables turned out to be an indispensable prerequisite to address both issues.
Such measurements with sufficient acceptance and statistics became technically
feasibly only recently. A brief overview of the facilities is given in section 2.
A completely different approaches to baryon spectroscopy are presently be-
ing developed at the BES-III e+e− collider , where decays like J/ψ → N̄N∗ →
N̄Nπ have been observed, or at the COMPASS experiment at CERN,where diffrac-
tive processes like pp → ppππ clearly show resonant structures. One important
milestone in future experimental baryon spectroscopy will be the combination
of all empirical information from very different experiments in order to identify
universal, i.e. process independent, properties of genuine nucleon excitations and
to quantify the impact of coupled channel dynamics.
2 Photon beam facilities
During the last ten years we noticed an enormous increase in high precision mea-
surements of many single and double spin observables in photo-induced meson
production. The experiments are still ongoing and many results are still prelim-
inary. The reason for this unprecedented development was the combination of
high-intensity polarized beams, polarized targets and hermetic detector systems
which was technically realized at the CLAS spectrometer in Hall B at Jefferson
Lab [7], the Crystal-Barrel experiment at the ELSA stretcher ring [8] and the Crys-
tal Ball experiment at the Mainz MicrotronMAMI [9]. CLAS is a large acceptance
spectrometer based on a toroidal magnetic field configuration. Tracking cham-
bers and time-of-flight detectors provide charge particle identification and mo-
mentum resolution. At CLAS, energy tagged, polarized photon beams with up to
6 GeV can be used. The Crystal Barrel calorimeter consisting of 1230 CsI(Tl) crys-
tals is the core of the experimental setup at ELSA and provides excellent accep-
tance and resolution for multi-photon final states. The Crystal Ball at MAMI (see
Fig. 2) consists of 672 NaI(Tl) crystals covering 93% of the full solid angle with
an energy resolution of 1.7% for electromagnetic showers at 1 GeV. For charged
particle tracking and identification two layers of coaxial multi-wire proportional
Resonances in photo-induced reactions 25
chambers and a barrel of 24 scintillation counters surrounding the target are in-
stalled. The forward angular range is covered by the TAPS calorimeter consisting
of BaF2 detectors and a Cerenkov detector.
The polarized target technique at all labs is based on Dynamic Nucleon Po-
larization (DNP) of solid-state target materials such as butanol, deuterated bu-
tanol, NH3 or 6LiD. The material is spin polarized by microwave pumping in
an external magnetic field of 2.5T at temperatures of about 100mK. During the
measurements, the spin orientation is frozen at temperatures of down to 20mK
by a moderate longitudinal or transverse magnetic holding field of about 0.5T.
The main technical challenge was the construction of a horizontal cryostat that
fits into the detector geometry and keeps a temperature of about 20mK without
adding too much material that would limit the particle detection. The underlying
concept of the targets presently used at ELSA, JLAB andMAMIwas developed in
Bonn [10] and was successfully used for the first time in 1998 for measurements
of the GDH sum rule in Mainz [11].
Fig. 1. Crystal-Ball detector at MAMI and the horizontal cryostat of the frozen spin target,
which keeps temperatures of about 20mK.
3 γN → πN
The photo-production of pseudoscalar mesons has four spin degrees of freedom
which define four complex scattering amplitudes for each isospin. These ampli-
tudes manifest themselves in 16 different single and double spin observables, in-
cluding experiments with polarized target, beam and nucleon recoil polarimetry.
It is well known for a long time that the full knowledge of 8 selected observables
at each energy and scattering angle completely determines all amplitudes in a
mathematical sense. Such a procedure is called a ”Complete Experiment” [12]. It
would then allow us to predict all remaining observables. However, in a real sit-
uation with statistical and systematic uncertainties this procedure is much more
difficult. Furthermore, the goal is not a ”Complete Experiment” and the recon-
struction of the 4 helicity amplitudes but an understanding of the underlying
dynamics. For this, the knowledge of all relevant partial wave or multipole am-
plitudes is much more important.
26 M. Ostrick
Up to a certain maximum orbital angular momentum lmax, all 4lmax com-
plex multipole amplitudes have to be determined from experiment (see Table 1).
It can be shown that even a ”Complete Experiment” is only of limited value to
reach this goal because of the freedom to choose an angular and energy depen-
dent overall phase [13]. Therefore, one has to determine the relevant multipoles
directly from experimental data. Each observable, Oi(W,θ), can be expanded in
term on Legendre polynomials:
Oi(W,θ) = sin
αi θ
kmax∑
k=0
aik(W)Pk(cos(θ)), αi = {0, 1, 2} . (1)
Here kmax is given by the truncation to a certain maximum angular momentum.
The coefficients aik(W) are bilinear combinations of the 4lmax complexmultipole
amplitudes which can be reconstructed from the coefficients. For a detailed dis-
cussion of the concepts of a “Complete Experiment” and such a truncated partial
wave analysis see [13].
Table 1. Multipole decomposition of the pion photo-production amplitude for lπ ≤
lmax = 2. For each isospin, 4lmax complex multipoles have to be determined from ex-
periment.
lπ 0 1 2
Jp 1
2
− 1
2
+ 3
2
+ 3
2
− 5
2
−
multiplole E0+ M1− M1+ E1+ M2− E2− M2+ E2+
A direct reconstruction of the relevant partial wave amplitudes was achieved
for the first time in the energy region of the ∆(1232) resonance using a truncation
to s- and p-waves (lmax < 2) and additional theoretical constraints [14].
At higher enegies this procedure requires precision measurements of sev-
eral spin observables with a sufficiently fine energy binning, e.g. 10 MeV, and a
full angular coverage. Below ECM ∼ 2 GeV, where a truncation to F- or G-wave
(lmax < 3 or 4) is possible, already the measurement of 4-6 spin and double-spin
observables could provide sufficient constraints for such a direct reconstruction.
This has been shown in [15] using generated pseudo-datawith realistic uncertain-
ties that will be achieved with the Crystal-Ball experiment at MAMI within the
next years. Preliminary results formany new target and beam-target asymmetries
from ELSA, JLAB and MAMI have been presented e.g. at the last NSTAR con-
ference [16]. However, the direct reconstruction of multiploles has not yet been
achived above the ∆(1232) resonance region and one has to rely on fits using
models for the energy-dependent amplitudes. Figure 3 summarizes the current
status of suchmodel dependent analyses in the case of the important lowest order
multipole amplitudes, Jp = 1/2+(M1−) and Jp = 1/2−(E0+). Even at relatively
low energies in the second resonance region there are significant deviations be-
tween different models. A summary of our current knowledge of multipole am-
plitudes for different flavor states can be found in [21].
Resonances in photo-induced reactions 27
1200 1400 1600 1800 2000
−6
−4
−2
0
2
1200 1400 1600 1800 20000
2
4
6
8
10
12
1200 1400 1600 1800 2000
−4
−3
−2
−1
0
1200 1400 1600 1800 2000
0
1
2
3
4
5
6
W/MEVW/MEV
Re(E0+)
Re(M1−)
Im(M1−)
Im(E0+)
Fig. 2. Lowest order multipole amplitudes of the γp → π0p reaction in units of 10−3/Mπ.
The curves are derived from fits of different models to existing data. The black solid and
dashed lines represent the SAID 2011 and the SAID Chew-Mandelstam fits [17, 18], the
MAID analysis gives the red dotted line [19]. Finally, the blue dashed-dotted curve is de-
rived from the Bonn-Gatchina analysis [20].
In the case of the γp → π0p reaction close to threshold a direct reconstruc-
tion of the amplitudes is more simple as the dynamics is dominated only by one
s-wave, E0+ and 3 p-waves,M1−,M1+ and E1+. Furthermore, these multipoles
are real between the π0p and π+n production thresholds. Above the π+n thresh-
old the E0+ amplitude becomes complex and shows a strong energy dependence
due to the unitary cusp [22]. The imaginary parts of the p-waves remain negligi-
ble below ∼ 180MeV. With this truncation, the real parts of the multipoles can be
reconstructed from measurements of two observables only, namely the differen-
tial cross section and the photon beam asymmetry
Σ =
σ⊥ − σ||
σ⊥ + σ||
. (2)
Here σ⊥ and σ|| denote the differential cross sections with the photon polariza-
tion vector perpendicular and parallel to the pπ0 reaction plane. Both observables
have recently been measured from threshold up to the ∆ resonance region with
unprecedented accuracy at the Crystal-Ball experiment at MAMI [23]. Fig. 3 show
as an example the results of these measurements at the CM angle of 90o as func-
tion of the incoming photon energy. The new data are compared to existing data
and ChPT calculations with updated low-energy parameters [25] as well as the
2001 version of the DMT dynamical model [26]. The reconstruction of the multi-
poles is almost final and will be published soon [24].
With all relevant multipoles fixed by experiment the additional measure-
ment of target (T) and beam-target (F) spin asymmetries will provide sensitivity
to the charge exchange π+n→ π0p scattering length from the unitary cuspwhich
enters directly in the imaginary part of the E0+ amplitude. Therefore, threshold
28 M. Ostrick
Fig. 3. Preliminary results fromCrystal Ball at MAMI (solid circles) of the differential cross
section and photon asymmetry for the γp → πop reaction at pion CM angle of 90o com-
pared to the older data from MAMI ( [22], open squares) as well as some theory calcula-
tions. The solid lines are preliminary ChPT fits to the new data [25] and the dashed lines
are a dynamical model [26].
π0photo-production will enable us to study strong and electromagnetic isospin
breaking in πN scattering by comparing the charge exchange scattering lengths
for π+n → π0p and π−p → π0n [23]. The ladder has recently been measured in
pionic hydrogen [27].
4 γN → ππN
When looking at the production of meson pairs like ππ of πη it is obvious that the
dynamics can be much more complex and an analysis will be even more model
dependent than in the case of single meson photo-production. Nevertheless, ππN
and πηN finals states have attracted a lot of interest during the last years. These
processes allow us to study resonances which have no significant branching ratio
for a direct decay into the nucleon ground state. This is possible via sequential de-
cays which involve intermediate excited states like R→ R ′π→ Nππ. Here R and
R ′ denote nucleon resonances. Such decay chains are a phenomenon that can be
observed in other quantum systems like atoms or nuclei as well. The theoretical
interpretation is usually based on isobar models or effective field theories [28–32].
Typically, the reaction amplitude is constructed as a sum of background and res-
onance contributions. The background part contains nucleon Born terms as well
as meson exchange in the t channel. The resonance part is a coherent sum of
s-channel resonances decaying into ππN via intermediate formation of meson-
nucleon and meson-meson states (“isobars”). Despite significant differences be-
tween the models, all of them provide an acceptable description of the existing
data. This observation clearly demonstrates, that further experimental and theory
studies are necessary.
With the Crystal-Ball at MAMI we have recently studied the γN → π0π0N
reactions by measurements of cross sections [33] and beam helicity asymmetries
[34, 35].
Resonances in photo-induced reactions 29
Eγ   [GeV]
σ 
[µ
b]
GRAAL-2003
MAMI-DAPHNE-2005
MAMI-TAPS-2008
CB-ELSA-2008
MAMI-Crystal Ball/TAPS-2010
This work
0
2
4
6
8
10
0.4 0.6 0.8 1 1.2 1.4
Fig. 4. Total cross section for the γp →
π0π0p reaction as function of the in-
coming photon energy. The open cir-
cles show the precision that has been
obtained at MAMI. Further information
and references can be found in [33].
2
γ
q
1
Θ
q
Y
Z
X
pΦ
k
Fig. 5. The coordinate system is fixed by
the momenta of the incident-photon, k,
out-going proton, p and the two pions,
q1, and q2, in the center of mass system.
Fig. 4 shows the existing data for the total cross section. It is widely ac-
cepted that the D13(1520) resonance decaying to π∆ channel is responsible for
the first peak at Eγ ≈ 730 MeV. However, the underlying dynamics down to
threshold as well as the behavior at higher energies have not been well under-
stood so far. E.g., the minimum at W = 1.6 GeV and the second maximum at
W = 1.7 GeV are described in Ref. [32] by the destructive interference between
D13 andD33 partial wave amplitudes. In other models this behavior is explained
by different resonance contributions, e.g. in the F15 partial wave. The high ac-
curacy of the MAMI new data allowed us to make first steps towards a model
independent partial wave analysis for the first time. In case of meson pair pro-
duction the helicity amplitudes depend on the incoming photon energy, Eγ, the
meson energies,ω1 andω2 (Dalitz-Plot) and two angles, Θ andΦ, which are ex-
plained in Fig. 5. The angular distributions normalized to the total cross section,
W(Eγ,ω1,ω2, Θ,Φ) =
1
σ
· dσ
dΩ
can now be expanded in terms of spherical har-
monics YLM(Θ,Φ). In a first step, we average the distributions over the meson
energies,ω1,ω2:
W(Eγ, Θ,Φ) ≡
1
σ
∫
dω1dω2
dσ
dΩ
=
∑
L≥0
L∑
M=−L
√
2J+ 1
4π
WLM(Eγ) · YLM(Θ,Φ)
(3)
This expansion determines the general structure of an angular distribution anal-
ogous to the expansion of the cross section for single-meson photo-production
in terms of the Legendre polynomials (see Eq. 1). The moments WLM(Eγ) are
bilinear combinations of the partial wave amplitudes. The exact relations have
been worked out explicitly by Fix and Arenhoevel in ref. [36]. With the high pre-
cision data from MAMI it was possible to determine the moments WLM(Eγ) for
the first time. The results are shown in Fig. 6. In case of the production of two
30 M. Ostrick
−0.1
0
0.1
−0.02
0
0.02
0.5 1
Eγ [GeV]
W11 W20 W22
W31 W33 W40
0.5 0.5 11
Fig. 6. First moments WLM (normalized such that W00 = 1) as a function of the incident-
photon energy. Our experimental results are shown by filled circles. The solid lines show
the results of an isobar model fit [37].
identical particles, e.g. γp → π0π0p, it can be shown, that the imaginary parts
vanish exactly (Im( WLM) = 0). Already at low energies, the quantities W20
and W22, which are given by an incoherent sum J
P = 3/2− and 3/2+ partial
wave amplitudes, achieve relatively large values. This observation indicates an
additional strong 3/2− contribution, interfering with the D13(1520) resonance.
This could support the dynamics found in Ref. [32] where a strong contribution
from theD33(1700) resonance was found. Of course, the analysis of the moments
WLM(Eγ) is only a very first step towards a full partial wave analysis of meson
pair production processes. Nevertheless, it shows that data with very high preci-
sion, which will be available also for other observables in the future, will allow us
to reduce the model dependence in the analysis procedures even for more com-
plex final states significantly.
5 Conclusion
During the last decade an immense effort started to study baryon resonances in
photo-induced meson production at various laboratories, mainly ELSA, Graal,
JLAB, LEPS, LNS and MAMI. New high precision data for many spin observ-
ables are expected in the near future. A prerequisite for an unambiguous, model-
independent extraction of resonance parameters is the reconstruction of partial
wave or multipole amplitudes from experimental data. Resonances as well as ef-
fects from coupled channel dynamics manifest themselves in the analytic proper-
ties of these amplitudes. The upcoming data will allow us to minimze the model
dependence in the determination of partial wave amplitudes in a systematic way.
Resonances in photo-induced reactions 31
This goal has already been achieved in π0 photo-production close to threshold.
The methods will be extended to higher photon energies and other final states
(ηN, KΛ, ππN, etc.).
References
1. S. Prelovsek, C. B. Lang, and D. Mohler, Bled Workshops in Physics 12, 73 (2011).
2. R. Arndt et al., Physical Review C 74, 045205 (2006).
3. Symposium on baryon resonance production and electromagnetic decays,
www.hades2012.pl
4. I. I. Alekseev, arXiv:1204.6433v1 (2012).
5. H. Fujioka, Hadron nd Nuclear Physics 9 , 150 (2010).
6. J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012)
7. B. Mecking et al., Nucl. Instr. and Meth. A 503, 513 (2003).
8. D. Elsner, Int. J. of Mod. Phys. E 19, 869 (2010).
9. A. Thomas, Eur. Phys. J. Special Topics 198, 171 (2011).
10. C. Bradtke et al., Nucl. Inst. and Meth. A 436, 430 (1999).
11. J. Ahrens et al., Phys. Rev. Lett. 97, 1 (2006).
12. I. Barker, A. Donnachie, and J. Storrow, Nucl. Phys. B 95, 347 (1975).
13. L. Tiator, AIP Conf. Proc. 162, 162 (2012) and contribution to this workshop.
14. R. Beck et al., Phys. Rev. C 61, 1 (2000).
15. R. L. Workman et al., Eur. Phys. J. A 47, 143 (2011).
16. V.Burkert, M.Jones, M.Pennington, D.Richards (ed.) AIP Conf. Proc. 1432, 1 (2012).
17. R. L. Workman, W. J. Briscoe, M. W. Paris, and I. I. Strakovsky, Phys. Rev. C 85, 025201
(2012).
18. R. Workman et al., Phys. Rev. C 86, 1 (2012).
19. D. Drechsel, S. S. Kamalov, and L. Tiator, Eur. Phys. J. A 34, 69 (2007).
20. A. V. Anisovich et al., Eur. Phys. J. A 48, 15 (2012).
21. A. V. Anisovich et al., Eur. Phys. J. A 48, 88 (2012).
22. A. Schmidt et al., Phys. Rev. Lett. 87, 1 (2001).
23. D. Hornidge and a. M. Bernstein, Eur. Phys. J. Special Topics 198, 133 (2011).
24. D. Hornidge et al., submitted to Phys. Rev. Lett. (2012).
25. C. Fernández-Ramı́rez et al., Phys. Lett. B 679, 41 (2009).
26. S. Kamalov et al., Phys. Rev. C 64, 1 (2001).
27. D. Gotta et al., AIP Conference Proceedings 1037, 162 (2008).
28. J. Gómez Tejedor and E. Oset, Nucl. Phys. A 600, 413 (1996).
29. M. Ripani et al., Nucl. Phys. A 672, 220 (2000).
30. A. Fix and H. Arenhövel, Eur. Phys. J. A 135, 115 (2005).
31. H. Kamano, B. Juliá-Dı́az, T. S. H. Lee, a. Matsuyama, and T. Sato, Phys. Rev. C 80
(2009).
32. U. Thoma et al., Phys. Lett. B 659, 87 (2008).
33. V. Kashevarov et al., Phys. Rev. C 85, 1 (2012).
34. F. Zehr et al., Eur. Phys. J. A 48, 1 (2012).
35. M. Oberle et al., submitted to Eur. Phys. J. A (2012).
36. A. Fix and H. Arenhövel, Phys. Rev. C 85, 035502 (2012)
37. V. L. Kashevarov et al., Phys. Rev. C 85, 1 (2012).