Proton recoil polarimetry observables in meson

photoproduction

David Howdle, NPE Research Group - Second Year Report

September 1, 2009

1

Contents

1 Introduction 3

2 Background 32.1 Linearly Polarised Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Recoil Polarisation and Observables . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Beam Asymmetry - Σ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Beam-Recoil Observable - Ox . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 The Experimental Setup 83.1 The Mainz Microtron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 The Photon Tagger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 The Crystal Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3.1 The PID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.2 TAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 The Analysis 124.1 Σ Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.1.1 Event Selection - π0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.2 Σ Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Future Analysis 15

2

1 Introduction

The study of pseudo-scalar meson photoproduction from the nucleon can generally be describedby four helicity amplitudes, which then leads to sixteen observables in experiment [1, 2]. In orderto study these observables without physical model problems, it is necessary to measure at leasteight of these observables (Figure 1). The measurement of such observables helps to pin downmissing or poorly established resonances predicted by the Quark Model [3].

Polarisation ObservableSingle σ, Σ, T, P

Beam-Target E, F, G, HBeam-Recoil Ox, Oz, Cx, Cz

Target-Recoil Tx, Tz, Lx, Lz

Table 1: The four single-polarisation and twelve double-polarisation observables

The Experiment [4] made use of the MAMI-C Electron Accelerator [5], allowing energies upto 1.5GeV. The electron beam undergoes the bremsstrahlung process and is ′tagged′ using theTagged Photon Spectrometer [6]. The photon beam is incident on a Liquid Hydrogen target cellcontained at the centre of the carbon scatterer. Subsequent reactions are detected using theCrystal Ball [7] Spectrometer and the TAPS forward wall.

This report will discuss the background to the experiment as well as the setup used during thedata taking process in September 2008. Further discussion on analysis of the linearly polarisedobservables will be included.

2 Background

2.1 Linearly Polarised Photons

Using a continuous electron beam from the MAMI accelerator, and inducing the process ofCoherent Bremsstrahlung [8] it is possible to produce linear or transversely polarised photons.Scattering electrons off a rigid crystal structure induces this process.

When looking at an amorphous radiator, scattering occurs off individual nuclei or positivecores within the radiator, producing a bremsstrahlung photon. A crystal has a structure ofregular arrays of atoms, allowing recoiling momentum to be absorbed by the lattice rather thanthe individual nuclei. This allows the emmitance of energy related to specific momentum transfersfrom the initial electron on the crystal along the lattice vector −→g . This arrives from the LaueCondition [9],

−→q = −→g (1)

and−→q = p0 − p− k (2)

in which −→q is the momentum transferred to the crystal and −→g is the reciprocal lattice vectorresponding to coherent bremsstrahlung production. p0 is the electrons initial momentum, p isthe electrons final momentum and k is the energy of the bremsstrahlung photon produced.

3

Sensitive orientation of the crystalline radiator allows the selection of the desired reciprocallattice vector in reference to the initial electron beam. This allows the production of high degreepolarisation photons [9, 10].

The product of this interaction gives a linearly polarised region from the selected energyrange sitting on an incoherent background. The coherent enhancement increases with initialelectron energy, E0 [8] ((E0, p0) and (E, p) denote the initial and final energy-momentum pairsrespectively).

(a) Polarised Bremsstrahlung distribution (b) Unpolarised Bremsstrahlung distribution

Figure 1: Bremsstrahlung distributions displayed in tagged photon channels

(a) Enhancement of Coherent Spectra without Incoher-ent background

(b) Polarisation Calculated from Enhancement

Figure 2: Polarisation (In Photon Energy) calculated with the Analytical Bremsstrahlung Cal-culation [11]

Diamond was chosen over other rigid structures such as silicon, due to the high DebyeFactor [12] and therefore small amplitudes of thermal motion. Diamonds do however suffer fromimperfections in their structure.

Bremsstrahlung processes are symmetric in the azimuthal plane of the initial beam directionand are separated by longitudinal and transverse momentum components. With a high enoughenergy, the momentum transfer, −→q , is bound to a thin region of momentum space, coined the′′Uberall Pancake′′ [13]. The kinematic dimensions of this region are bound by the symmetry

4

around the initial momentum plane, and thus are restricted by the afore mentioned longitudinaland transverse momentum components of −→q , ql and qt (See Eqs. 3, 4).

δ ≤ ql . 2δ (3)

0 ≤ qt . 2x (4)

Where δ is the minimum recoil momentum deposited in the longitudinal direction, and x isthe quantum energy, defined by the ratio between the energy of the bremsstrahlung photon andthe incident electron energy. This well defined ′pancake′ and the alignment of the crystal [14]allows for the production of a high degree of linear polarisation.

Collimation of the polarised beam is also key to gaining the highest degree of linear polarisationpossible. As described by Timm [8] and Lohmann [9], the coherent photons will be very stronglyforward focused, whereas the incoherent background is dependant much on the energy of photonitself, thus the introduction of a tight collimator [15] can increase the degree of linear polarisation.

2.2 Recoil Polarisation and Observables

With Photoproduction of pseudoscalar mesons, observables involving polarisation transfer aresensitive probes. In particular, measurement of a combination of observables allows for model in-dependent analysis. These observables arise from transversity amplitudes related to the scatteringamplitude of the reaction process. For Beam-Recoil measurement, the relationship between theseobservables and experiment can be derived from four helicity amplitudes to give the followingequation [1]

ρfdσ(θ, φ)

dΩ=

12

dσ0(θ)dΩ

[1− P lγΣcos2φ− ω + τ − η] (5)

Where:

ω = σx′ (P l

γOxsin2φ + P cγCx); τ = σy

′ (P − P lγTcos2φ); η = σz

′ (P lγOzsin2φ + P c

γCz) (6)

Each of the observables are as shown in Table 1. P lγ and P c

γ are the degree of linear andcircular polarisation respectively and σi

′ are the hadron quatisation axes of Eqn 8, as well asρf being the respective density matrix ρf = 1

2(1 + σPf ) [1] where Pf is the Recoil hadron

polarisation.dσ0

dΩrepresents the unpolarised cross section.

Normal or unprimed coordinate systems used to describe a reaction process in the centre-of-mass are relative to the incoming photon beam momentum.

z =k

|k|; y =

k × q

|k × q|; x = y × z (7)

Where as the coordinate system to describe the reaction products are relative to the mesonmomentum in the centre of mass.

z′=

q

|q|; y

′= y; x

′= y

′ × z′

(8)

In both cases k is the photon beam momentum and q is the meson momentum.

Using the primed coordinate system, and the manipulation of Eqn 5 with Pauli Matrices [1,16], it is possible to extract the components of polarisation.

5

Px = −P l

γOxsin2φ + P cγCx

1− P lγΣcos2φ

(9)

Py =P − P l

γTcos2φ

1− P lγΣcos2φ

(10)

Pz = −P l

γOzsin2φ + P cγCz

1− P lγΣcos2φ

(11)

For a linearly polarised beam (P cγ = 0) all C terms are removed leaving the polarisation

components dependant on Σ

2.2.1 Beam Asymmetry - Σ

Σ, or the beam asymmetry is given by the relationship between the polarised and unpolarisedphoton cross-section:

dσ(θ, φ)dΩ

=dσ0(θ)

dΩ[1 + PγΣcos2φ− φ0] (12)

Where σ is the polarised photon cross-section with respect to θ and φ (polar and azimuthalangles respectively, with respect to the initial photon beam direction), σ0 is the unpolarisedcross-section with respect to θ, Pγ is the degree of linear polarisation and φ0 is effective zeroin the φ scale (This offset is normally constant). In order to measure the asymmetry withoutmeasuring both cross-sections, it is possible to reconstruct the unpolarised input by using differentpolarisation vectors (See Section 2.1). Two polarisation planes with a angular difference of 90

provides phase difference of 180 in the cos2φ distribution, thus a cross-section can be expressedfor both planes (It is assumed that the degree of polarisation for both planes is approximatelythe same):

σ1 = σ0[1 + PγΣcos(2φ− φ0)] (13)

σ2 = σ0[1− PγΣcos(2φ− φ0)] (14)

Where σ1 and σ2 are the cross-sections at the two different plane settings. Equivalence ofthese equations allows the rearrangement for Σ:

PγΣcos(2φ− φ0) =σ1 − σ2

σ1 + σ2(15)

Another consideration with regards to the Σ Observable is the case when Pγ1 and Pγ2 arenot equivalent and the scaling method for each reaction plane, as well as the exclusion of anyamorphous contribution.

Σp(~γ, p)π0 ≈ 0.8 (16)

Eqn ?? shows the prediction for Σ within the region of the polarised photon peak, and resultson this are shown in Section 4.1.

6

2.2.2 Beam-Recoil Observable - Ox

Polarisation of of a recoiling nucleon is measured by a secondary scatter interaction on a nucleartarget. In particular, selection of a charged particle will be sensitive to small angle Coulombscattering from the nuclear target. Separation of these charge scatter events from the stronginteracting events of interest can be seen through larger scattering angles (∼ 12 − 15%) withreference to the coupled meson vector of the reaction. Of interest in the reaction is the spin-orbitcoupling from the initial state, and the narrower spread of Coulomb scattering does not dependon this state with the proton. It therefor important to look at events with a larger scattering angle.

If there is no spin precession, then on the x and y components are accessible (No measurementof Oz). This is done in the secondary scatter or polarimeter reference plane at the graphiteanalyser, in reference to the recoiling proton momentum.

x′′

= y′′ × z

′′; y

′′=

k × q

|k × q|; z

′′=

p

|p|(17)

Using the double prime frame an azimuthal distribution can be given [16, 1] with respect tothe scattering angles of the proton.

n(θsc, φsc) = n0(θsc)[1 + A(θsc)[P′′y cosφsc − P

′′x sinφsc]] (18)

Where n0(θsc) is the number of protons incident on the graphite analyser for scatteringangle θsc, A(θsc) is the analysing power of the graphite analyser and P

′′x and P

′′y are the vector

components of polarisation (Section 2.2) in the double prime reference frame.

(a) Ox in Energy (b) Ox in Theta

Figure 3: MAID Calculations of the Ox Observable

Taking the standard asymmetry and the effective analysing power due to the polarimeteracceptance [16] and substituting in for the vector components of polarisation we can reduce to aform involving two double polarisation observables Ox

′′ and T [4] with respect to the azimuthaldistribution of the meson and the recoil proton.

N⊥(φq, φp)−N‖(φq, φp)N⊥(φq, φp) + N‖(φq, φp)

= AeffP lγ(Ox

′′sin2φqsin2φp + Tcos2φqcos2φp) (19)

7

Where Aeff is the effective analysing power of the polarimeter due to its acceptance, p andq have the meanings determined in the reference frames (See Section 2.2). ‖ and ⊥ refer to theplane of coherent beam.

3 The Experimental Setup

3.1 The Mainz Microtron

The Mainzer Microtron (MAMI) is based in the Johannes Gutenburg Universtat. Comprised ofthree RTM (Racetrack Microtron), a Harmonic Double-Sided Microton (HDSM) and a Linearinjector or linac, MAMI can provided continuous, intense and stable electron beam. The machineitself was first in operation in 1979 with the first stage of MAMI-A. MAMI-A is a linear injector,passing beam into a single RTM. This allowed stable beam up to 14MeV. The upgrade ofMAMI-A introduced a second RTM to the system, where the first microtron (MAMI-AI) wouldpass the 14MeV beam into the second microtron (MAMI-AII), increasing the beam energy upto a maximum of 183MeV Additionally, in 1990 the addition of a third microtron (MAMI-B)increased the maximum energy up to 855MeV. Finally, the HDSM was added, and the facilitycan now run up to energies 1.5-1.6GeV.

Figure 4: Racetrack Microtron Schematic

The linac is a short accelerator placed between two bending magnets (See Figure 4). Elec-trons are passed through the linac where it they are accelerated through a series of RF (RadioFrequency) cavities. The path is deflected through both bending magnets by 180 returning thebeam of electrons back through the cavities. The field in the magnets is kept at a constant,and as the beam makes several passes through the RF cavities, it gains higher energies. Higherenergies propagate through the gradually larger tracks on the microtron. This gives a steady risein energy and allows for a continuous beam of electrons as apposed to a pulsed system, due tothere being no need for a large acceleration gradient.

At MAMI, the electron beam is injected at ∼4MeV to the first microtron. Here they undergo18 circulations of the microtron, bringing them up to ∼11MeV. Proceeding to RTM 2, the beamprocesses through the linac 51 times before being extracted at ∼180MeV. At this point the beamenters the MAMI-B RTM. This third microtron can accelerate the beam up to 855MeV in stepsof 15MeV depending on the chosen number of re-circulations.

8

The beam can then be passed into the HDSM (MAMI-C) [5, 17] for energies ranging from855MeV up to 1508MeV (Currently the actual energy capability is 1557MeV).

Figure 5: The Harmonic Double-Sided Microtron, MAMI-C

The proposal of the HDSM was to allow a new stage to be added to the MAMI setup withminimal interuption to the beamtime and institute. Using the institutes expertise, the plan wasoriginally to build another RTM, however the space feasibility of the bending magnets wouldnot allow for this. Using four bending magnets rather than two, and two RF-linacs allows thedesired energies to be reached by bending each pass by 180 into one linac and then again intothe second. This was possible in the existing space using 90 bending magnets similar to thosein the current standard RTMs.

3.2 The Photon Tagger

The Photon Tagging Spectrometer [6, 18] (Tagger) is a key detector in real photon experimentsand is the Nuclear Physics groups major contribution of hardware to the A2 Collaborationexperimental hall. The Tagger provides all the information on the incoming photon beamsfour-vector on an event-by-event basis, as well critical timing information for the triggeringsystem.

The Tagger sits ∼3m upstream of the main detector layout and ∼15cm downstream of theradiator selection and crystal orientation system (Goniometer). The major components of theTagger are a large dipole magnet set a to specific field for the initial electron beam energy (variableup to ∼2T), an array of plastic scintillators (The Focal Plane) to tagg the electrons, and housedphoton beam collimator.

When an incoming electron undergoes the bremsstrahlung process on the selected radiator inthe Goniometer, a mixed electron-photon beam enters the magnetic spectrometer. The fixed fieldin the spectrometer will bend the electron into the focal plane, dependent on the energy loss inthe radiator. If there is no significant energy loss in the radiator scatter, the field will bend theelectron beam into a Pb beam dump. The electron will cause scintillation in the given channelit strikes, and measurement of the recoiling electrons energy can provide us with the necessaryinformation on the outgoing photon:

Eγ = E0 − Ee− (20)

Where Eγ is the energy of the outgoing photon, E0 is the energy of the electron beam, andEe− is the recoiling electrons energy as measured by the tagger.

9

The Focal plane arrangement is made up of 353 overlapping plastic scintillators, approxi-mately 80mm in length and 2mm thick. The width of the channels is variable around ∼13mmwhich accounts for the varying geometry of the focal plane. A hit in the focal plane triggers iftwo overlapping scintillators are fired, giving the tagger overall 352 channels. Each channel hasan energy resolution of ∼4MeV.

(a) Tagger Schematic (b) GEANT4 Tagger Magnet

Figure 6: Tagged Photon Spectrometer

The outgoing photon beam passes through a collimator, whose width is selected based on theexperimental parameters (Section 2.1), and insures the beam divergence will not be greater thanthe diameter of the target cell. In principle the photons reaching the experimental area will be thesame as the number of electrons tagged, however the introduction of the collimator significantlyreduces this number. Using a low intensity beam in conjunction with a Pb-Glass CherenkovDetector, the rate of accepted photons can be calculated. Comparison of this rate with the FocalPlane Hits (Figure 1) produces a tagging efficiency of the experiment. Regular measurements ofthis are essential for the calculation of cross-sections, and frequent measurements are useful forthe approximation of a running polarisation (Figure 2).

3.3 The Crystal Ball

The Crystal Ball [7] is the main detector system within the experimental hall. Covering anacceptance range of nearly 4π, the CB is a segmented electromagnetic calorimeter. It consists of672 NaI crystals, geometrically arrayed from an approximation of an icosahedron. The crystalsare split into two hemispheres with a entrance and exit tunnel at opposing sides of the targetcell on the beamline. The shell for both hemispheres are separated by two 1.6mm stainless steelplates on which the crystals sit, and the shells themselves have an inner wall of 1.5mm thickstainless steel.

Each crystal element is a truncated triangular based pyramid 40.6cm in height. The largetriangular face has side length of 12.7cm, the small being 5.1cm in length. In the approximationof the icosahedron, the small faces of the crystal elements all face inward to the centre pointof the ball. The external facets face individual Photomultiplier Tubes (PMT) attached to the

10

outside of the shells, separated by optical windows.

Figure 7: Schematic of the Crystal Ball and Child Detectors

Because of the high granularity of the CB the angular resolution is ∼ 3 in θ and 2

sinθ in φ.The Ball itself is optimised for neutral particle detection, specifically photons. However, with theaddition of the PID and TAPS Veto (Section 3.3.1, 3.3.2) the measurement of charged particlesis also possible.

3.3.1 The PID

The Particle Identification Detector (PID) provides charged particle ID in support with the CB.The PID is a cylindrical array of 24 plastic scintillators and PMTs situated around the targetcell (Figure 7). The barrel as a whole covers the same θ-φ range as the ball, having two holes inthe same angular range as the balls entrance and exit holes.

Figure 8: E-∆E Plot, the curved ridge structure shows the proton region

When the PID and the CB are used in conjunction, charged particles can be identified bylooking first at the φ angular ranges of the two detectors. As a first stage, in order for a particle

11

to be registered as charged in the system, there must be a correlation between the φ angle of thecrystal element fired in conjunction with the PID scintillator element. The second stage is usedin order to sort successive charged particles. This is done by looking at the energy deposition ofboth detectors (referred to as E-∆E). The plot shows a clear separation for proton events andcharged pion events, as well as other charged events (Figure 8).

3.3.2 TAPS

The TAPS Detector [19] (Classically Two/Three Armed Photon Spectrometer) is used as aforward wall electromagnetic calorimeter as a cover for the CB exit hole, bringing overallcoverage to ∼ 97% of 4π. TAPS is constructed as a wall of 522 hexagonal BaF2 crystal. Eachcrystal is 250mm in length and is attached to PMT.

Figure 9: Schematic of a single TAPS Crystal and Plastic Scintillator

As TAPS is not covered by the PID detector, each crystal is capped with an individual plasticscintillator (Figure 9). These scintillators are connected to a light guide and then to their ownPMT system. These small scintillators provide charged particle identification in a similar way tothe PID. However, unlike the PID-CB ID, the scintillators are are individual to each crystal, soangular information is not necessary. Instead of looking for angular correlation it is acceptableto simply look for a correlation between the TAPS crystal and its scintillator neighbour.

4 The Analysis

4.1 Σ Analysis

Analysis of the beam asymmetry, Σ−→γ ,pπ0 (Section 2.2.1) was achieved for linearly polarised photonenergies 500 - 650MeV, for θ in the centre of mass 40 - 160. Careful event selection was required(Section 4.1.1) for the −→γ p → pπ0 reaction. Initial calculations using the MAID [20] (Figure 10)database to show the predicted behaviour of the asymmetry for both Eγ and θCM

And MAID was used to compare results of the asymmetries taken for 35MeV sections of thecoherent peak as well as 10 sections across θ.

4.1.1 Event Selection - π0

Neutral Pions have a large branching ratio (∼ 99%) decay to two photons, as well as decayingvery rapidly within the system (∼ 0.6 × 10−16s). These events are defined by the scintillationwithin the Crystal Ball, as well as no charge deposit in the PID within the reaction timingframe. Using the AcquRoot Analysis Framework [21, 22] to decode the data from its raw format,

12

(a) Beam Asymmetry in Energy (b) Beam Asymmetry in Theta

Figure 10: MAID Calculations

event selection is processed within the code with the use of four-vectors as well as raw detectorinformation. In order to select a pπ0 event, events were restricted to meeting the conditions oftwo photon four-vectors being detected as well as non-zero within the PID in order to select aproton.

There was no request for a single proton within the Crystal Ball or TAPS detectors, as thecarbon scatterer breaks the correlation of φ between the PID and Crystal Ball for scatteredprotons. Protons that do not scatter or scatter under coulomb forces will also lose energy to thescatterer and will fall outside of any standard ID performed via these methods.

Additional to these conditions was an restriction on the total energy deposited within thetwo calorimeters for a single event to be greater than 500MeV.

In order to select polarised events, the four-vector if the incoming photon had to be restrictedto the region of the coherent peak (500 - 650MeV). Once these conditions were met, the nextstep was to reduce the background within each event and ensure the selection of pπ0. Addingthe two four-vectors of the photons which made it through the initial filter conditions and thecorresponding mass allows the selection the π0

Figure 11(a) shows the calculated π0 invariant mass minus the Particle Data Group (PDG)mass. There is a strong peak around zero indicating the π0 events. Making a gaussian fit to thepeak allowed for a selection parameter to be derived from the standard deviation (σ) of the fit.The restriction to follow the fit was a 3σ cut around the centre of the of the peak to ensure theselection of as many π0 events.

Similarly, Figure 11(b) shows the missing mass of the π0 minus the PDG proton mass. Themissing vector is calculated by summing the incoming photon and target four-vectors and sub-tracting the π0 four-vector in order to leave the remainder of the reaction as a single four-vector.The mass of this vector showed a strong peak around zero, indicating proton events. Taking asimilar fit to the invariant mass, a 3σ cut is applied in order to select the full pπ0 channel.

4.1.2 Σ Results

Once the event selection is complete, extracting information on Eγ , θ and φ is all that is requiredin order to extract the asymmetry. As mentioned above, the asymmetries are extracted over

13

(a) Pion Invariant Mass (b) Pion Missing Mass

Figure 11: Plots for selecting events with fits

varying Eγ and θ. For each energy and θ position a cos2φ is fitted to the corresponding cos2φdistribution extracted from both the parallel and perpendicular beam settings.

Figure 12: Fit to the distribution for a single position

Extraciting the amplitude of these results for each section, as well as the associated errorgives the asymmetry value multiplied by the polarisation. Using the AnB [11] (Section 2.1) tocalculate a relative polarisation for each section of the coherent peak, the polarisation was thendivided out of the PΣ value and its error, in order to give a straight result for Σ

This preliminary analysis shows a good agreement between the theory and the experiment.While the drop off at backward angles in the first energy bin is not well understood, it is suspectedthat a lack of world data in this particular energy range has lead to a slight miscalculation inthe theory. However, it will be important to examine various possible contributing effects suchas unwanted background contamination at backward angles.

While the agreement with the results seems good, the polarisation is inaccurate, as it is anaverage over each Eγ range. A solution for this will be discussed in Section 5.

14

Figure 13: Asymmetry values for varying energy and theta. Black Line: MAID, Blue Points:Analysis

5 Future Analysis

While the preliminary beam asymmetries look promising, there are some aspects that will needto be refined before they are complete. The polarisation calculated was relative to a singlerun during the beamtime, and thus should not be used as an absolute value over the wholeexperiment, as the polarised peak can experience a certain level drift, which over time will smearan absolute value of polarisation. While a high level of vigilance was encouraged during therunning of the experiment, it is still important to determine a timeline of the relative shift inpolarisation from the run the AnB calculation was implemented on.

In order to achieve this, it will be necessary to create an enhanced asymmetry for all θ andall Eγ under the coherent peak for each run. Comparing this timeline to the calculation will helpdetermine areas of polarisation drift, and thus be useful in the creation of a table of polarisation.

Moving on to the event selection for the Ox observable will be the next priority after the po-larisation monitor. As discussed in Section 2.2.2, event selection will need to be carefully achievedin order to select the strong scattering over the coulomb scattered events. The relative polari-sation monitor determined for the beam asymmetry will also be of great use for the Ox observable.

Finally, once a complete analysis of the −→γ p → pπ0 channel has been achieved, a preliminaryanalysis of the −→γ p → p2π channel will be carried out if time permits.

15

References

[1] RA Adelseck and B. Saghai. Kaon photoproduction: Data consistency, coupling constants,and polarization observables. Physical Review C, 42(1):108–127, 1990.

[2] IS Barker, A. Donnachie, and JK Storrow. Complete experiments in pseudoscalar photopro-duction. Nuclear Physics B, 95(2), 1975.

[3] K.S. Krane and D. Halliday. Introductory nuclear physics. Physics Today, 42(1), 1989.

[4] D.P. Watts, G. Rosner, D.I. Glazier, and P. Pedroni. Recoil nucleon polarimetry observablesin meson photoproduction at MAMI. Experimental Proposal.

[5] K.H. Kaiser, K. Aulenbacher, O. Chubarov, M. Dehn, H. Euteneuer, F. Hagenbuck, R. Herr,A. Jankowiak, P. Jennewein, H.J. Kreidel, et al. The 1.5 GeV harmonic double-sided mi-crotron at Mainz University. Nuclear Inst. and Methods in Physics Research, A, 593(3):159–170, 2008.

[6] J.C. McGeorge, J.D. Kellie, J.R.M. Annand, J. Ahrens, I. Anthony, A. Clarkson, D.J. Hamil-ton, P.S. Lumsden, E.F. McNicoll, R.O. Owens, et al. Upgrade of the Glasgow photon taggingspectrometer for Mainz MAMI-C. The European Physical Journal A-Hadrons and Nuclei,37(1):129–137, 2008.

[7] B.M.K Nefkens. Crystal Ball Internal Report. Technical report, UCLA, 1995.

[8] U. Timm. Coherent bremsstrahlung of electrons in crystals. Fortschritte der Physik, 17(12),1969.

[9] D. Lohmann, J. Peise, J. Ahrens, I. Anthony, HJ Arends, R. Beck, R. Crawford, A. Hunger,KH Kaiser, JD Kellie, et al. Linearly polarized photons at MAMI (Mainz). Nuclear Instru-ments and Methods in Physics Research-Section A Only, 343(2):494–507, 1994.

[10] H. Bilokon, G. Bologna, F. Celani, B.D.E. Piazzoli, R. Falcioni, G. Mannocchi, and P. Picchi.Coherent bremsstrahlung in crystals as a tool for producing high energy photon beams to beused in photoproduction experiments at CERN SPS. Nuclear Inst. and Meth, 204:299–310,1983.

[11] FA Natter, P. Grabmayr, T. Hehl, RO Owens, and S. Wunderlich. Monte Carlo simulationand analytical calculation of coherent bremsstrahlung and its polarisation. Nuclear Inst. andMethods in Physics Research, B, 211(4):465–486, 2003.

[12] JD Kellie, PJM Clive, GL Yang, R. Beck, BC Evans, C. Gordon, C. Hall, JW Harris,RT Jones, D. Laundy, et al. The selection and performance of diamond radiators used incoherent bremsstrahlung experiments. Nuclear Inst. and Methods in Physics Research, A,545(1-2):164–180, 2005.

[13] H. Uberall. High-energy interference effect of bremsstrahlung and pair production in crystals.Physical Review, 103(4):1055–1067, 1956.

[14] K. Livingston. The stonehenge technique: a new method of crystal alignment for coherentbremsstrahlung experiments. In Proceedings of SPIE, volume 5974, page 59740G, 2005.

[15] F. Rambo, J. Ahrens, H.J. Arends, R. Beck, G. Galler, JD Kellie, H.P. Krahn, A. Kraus,U. Ludwig, J. Peise, et al. Enhancement of the linear polarization of coherent bremsstrahlungby collimation of the photon beam. Physical Review C, 58(1):489–501, 1998.

16

[16] D.I. Glazier. Recoil Polarisations and Photoproduction Observables. Technical Note.

[17] A. Jankowiak. The Mainz Microtron - Past and Future. 2006.

[18] SJ Hall, GJ Miller, R. Beck, and P. Jennewein. A focal plane system for the 855 MeV taggedphoton spectrometer at MAMI-B. Nuclear Instruments and Methods in Physics Research-Section A Only, 368(3):698–708, 1996.

[19] R. Novotny. The BaF 2 photon spectrometer TAPS. IEEE transactions on nuclear science,38(2 Part 1):379–385, 1991.

[20] S.S. HEP. MAID Analysis Techniques. Arxiv preprint nucl-th/0603012, 2006.

[21] JRM Annand. Data Analysis within an AcquRoot Framework. University of Glasgow, 2005.

[22] R. Brun, F. Rademakers, et al. ROOT-an object oriented data analysis framework. NuclearInstruments and Methods in Physics Research-Section A Only, 389(1):81–86, 1997.

17