In November 2010, the azimuthally symmetric WASA detector and the polarized
proton beam of COSY, have been used to collect a high statistics sample of
$\vec{p}p \rightarrow pp\eta$ reactions in order to determine the analyzing
power as a function of the invariant mass spectra of the two particle
subsystems. Here, we show studies of the influence of the beam and target
characteristics such as location and direction on the determination of the
polarization.Comment: Presented at Symposium on applied nuclear physics and innovative
  technologies, Krakow, 3-6.06.2013; Accepted to Acta Physica Polonica B
  Proceedings Supplement, Vol. 6 (2013); 12 page

Hodana, Malgorzata

Moskal, Pawel

Ozerianska, Iryna

Acta Physica Polonica B Proceedings Supplement

English

arXiv

In November 2010, the azimuthally symmetric WASA detector and the polarized proton beam of COSY have been used to collect a high statistics sample of $\vec{p}p \rightarrow pp\eta$ reactions in order to determine the analyzing power as a function of the invariant mass spectra of the two-particle subsystems. Here, we show studies of the influence of the beam and target characteristics such as location and direction on the determination of degree of the polarization

Hodana, Małgorzata

Moskal, Paweł

Schätti - Ozerianska, Iryna

Jagiellonian Univeristy Repository

Vol. 6 (2013) Acta Physica Polonica B Proceedings Supplement No 4STUDIES OF SYSTEMATIC UNCERTAINTIES OFPOLARIZATION ESTIMATION FOR EXPERIMENTSWITH THE WASA DETECTOR AT COSY∗M. Hodana, P. Moskal, I. OzerianskaThe Marian Smoluchowski Institute of Physics, Jagiellonian UniversityReymonta 4, Kraków, PolandandExperimental Hadron Structure (IKP-1), Forschungszentrum JülichWilhelm-Johnen-Straße 52428 Jülich, Germany(Received August 23, 2013)In November 2010, the azimuthally symmetric WASA detector and thepolarized proton beam of COSY have been used to collect a high statisticssample of ~pp → ppη reactions in order to determine the analyzing poweras a function of the invariant mass spectra of the two-particle subsystems.Here, we show studies of the influence of the beam and target character-istics such as location and direction on the determination of degree of thepolarization.DOI:10.5506/APhysPolBSupp.6.1041PACS numbers: 13.88.+e, 24.70.+s1. IntroductionIn the last decade, a vast set of unpolarized cross sections has been de-termined for the η production in the collision of nucleons [1–12]. However,the understanding of the production mechanism of this meson still requiresdetermination of spin observables. Up to now, there are only three measure-ments of the analyzing power for the ~pp → ppη reaction which have beenperformed with low statistics and the determined value of analyzing poweris essentially consistent with zero [13–15] within large error bars of about±0.15. The WASA detector installed at the Cooler Synchrotron COSY givesa possibility to measure the analyzing power with high statistics and highacceptance. Therefore, in November 2010, we have conducted an exclusivemeasurement of the ~pp → ppη reaction using the polarized proton beam of∗ Presented at the Symposium on Applied Nuclear Physics and Innovative Technolo-gies, Kraków, Poland, June 3–6, 2013.(1041)1042 M. Hodana, P. Moskal, I. Ozerianskathe COSY synchrotron and the WASA detector [16]. The measurement wasperformed for two beam momenta corresponding to 15 MeV and 72 MeVexcess energies. The choice of these values of excess energies was dictatedby the availability of the data for the spin averaged cross sections obtainedpreviously at COSY-11 [2], TOF [1] and WASA/CELSIUS [3] experiments.For the purpose of the monitoring of the degree of polarization, concur-rently to the ~pp→ ppη reaction, a proton–proton elastic scattering reactionshave been measured. In this contribution, we present an estimation of sys-tematic uncertainties of the determination of the degree of polarization ofthe COSY beam based on the elastically scattered protons measured bymeans of the WASA detector setup.2. PolarizationThe polarization is extracted using the following formulaP (θ) =1Ay(θ) cosφN(θ, φ)−N(θ, φ+ π)N(θ, φ) +N(θ, φ+ π), (1)were θ is the scattering angle of the forward going proton calculated in thecentre-of-mass frame, φ is its azimuthal angle, N denotes the number ofevents and Ay(θ) is the analyzing power of the ~pp→ pp reaction which wasextracted from the results of the EDDA Collaboration [17].The asymmetry, ε(θ, φ), is defined asε(θ, φ) =N(θ, φ)−N(θ, φ+ π)N(θ, φ) +N(θ, φ+ π)(2)and, according to Eq. (1), it can be written asε(θ, φ) = p0 cos(φ) , (3)where p0 = P (θ)Ay(θ). Polarization is, therefore, extracted by fitting offunction given by Eq. (3) to a ε(θ, φ) distributions as shown in Fig. 1.Asymmetry is calculated separately for each spin orientation of polarizedprotons, in four ranges of protons’ scattering angle starting from 30◦ up to46◦ in steps of 4◦. As a result, four polarizations are extracted for four rangesof the center-of-mass polar angle of the forward scattered proton, θCMs. Thefinal polarization for a given spin is then calculated as a weighted meanP =∑ni=1 P (θi)/σ2P (θi)∑ni=1 1/σ2P (θi), (4)where θi is the scattering angle of the forward going proton, calculated inthe centre-of-mass system.Studies of Systematic Uncertainties of Polarization Estimation . . . 1043Fig. 1. Experimental distributions of the asymmetry as a function of the proton’sazimuthal angle, made for the proton’s scattered into an angle given in histograms’title boxes. Black line represents the fit function given by Eq. (3). Left panel:protons with spin down. Right panel: protons with spin up.1044 M. Hodana, P. Moskal, I. Ozerianska2.1. Position of the vertexThe probable source of the systematic uncertainty in the determinationof the polarization might be false number of events in the individual θCMsranges, originating from the possible misalignment of the beam’s and/ortarget’s position.The reconstruction of tracks of particles registered in the Mini DriftChamber is free of any assumption of the position of the reaction vertex. Inthis respect, obtained angular information can be assumed to reflect actualsituation of particles going through the Mini Drift Chamber. Reconstructionof tracks of particles going in the forward direction, however, is based on theassumption that the interaction point is located at (xv, yv, zv) = (0, 0, 0).This may contribute to the systematic uncertainty of the polarization. Todetermine the size of this contribution, studies on the position of the inter-action point have been performed.Figure 2 (left) depicts trajectories of two protons p1 and p2 projectedonto the (x, y) plane.Fig. 2. Left: picture illustrating the concept of the extraction of the xv and yvcoordinates of the reaction vertex. Adopted from [18]. Right: simulated distri-butions of d(φd) made for vertex position (xv, yv, zv) = (0, 0, 0) (upper plot) and(xv, yv, zv) = (5, 0, 0) mm (lower plot). Points show positions of the mean of thed-distributions for given ranges of φd. Line shows a result of the fit of a functiongiven by Eq. (6).Studies of Systematic Uncertainties of Polarization Estimation . . . 1045The p2 proton corresponds to the proton registered in the Mini DriftChamber. Its reconstructed azimuthal angle, φ2, is therefore obtained inde-pendently of the position of the reaction vertex, always reflecting the ‘true’value of the emission angle. The p1 proton is going in the forward directionand it intersects the first plane of the Forward Trigger Hodoscope (FTH) ata radius ofR1 = ZFTH tan(θp1) , (5)where ZFTH is the distance from the vertex to the Forward Trigger Ho-doscope. The reconstruction of the path of the p1 proton is based on theassumption that the interaction point is located at (xv, yv, zv) = (0, 0, 0).Therefore, reconstructed azimuthal angle, φ1, differs from the real one, φ′1.This disagreement causes deviation from the coplanarity corresponding toφ′2 − φ1.To determine the shift of the reaction vertex, new variables d and φd areintroduced, where d is the distance between the point (0, 0, 0) and the inter-section point of dashed line and the solid line in Fig. 2. Dashed line includespoint (0, 0) and is perpendicular to the projection of proton’s trajectories.φd is the azimuthal angle between dashed line and the x-axis.With the use of the introduced d and φd variables, the xv and yv coordi-nates of the reaction vertex became two parameters in the following formulad(φd) = xv cos(φd) + yv t sin(φd) . (6)Thus, xv and yv can be extracted by fit of the above function to the d(φd) dis-tribution as shown in the right-hand side of Fig. 2 for two cases of vertex loca-tion, at (xv, yv, zv) = (0, 0, 0) (upper plot) and at (xv, yv, zv) = (5, 0, 0) mm(lower plot).Figure 3 (left) depicts the angular dependencies between the two protonsp1 and p2, used to determine the zv coordinate of the reaction vertex. In thepicture, the reaction vertex is placed on the z-axis at the position of zv > 0.The trajectory of proton p2, reconstructed in the planes of the Mini DriftChamber, is traced back to the actual reaction vertex, whereas the track ofthe forward going proton, p1, is assumed to origin from the (0, 0, 0) point.Therefore, scattering angle, θ1, of the forward going proton deviates fromthe real value, θ′1. The relation between the true and reconstructed valuesof the scattering angle of the forward going proton can be written as1tan(θ′1)=1tan(θ1)(1− zvZFTH). (7)1046 M. Hodana, P. Moskal, I. OzerianskaFig. 3. Left: picture illustrating the concept of the extraction of the zv coordinateof the reaction vertex. Adopted from [18]. Right: simulated distributions of θ′2(θ1)made for vertex position (xv, yv, zv) = (0, 0, 0) (upper plot) and (xv, yv, zv) =(5, 0, 0) mm (lower plot). Points show positions of the mean of the θCD distributionfor given ranges of θFD. Line denotes result of the fit of a function given by Eq. (9)to these points.Additionally, in an elastic collision the kinematic relation between scatteringanglestan(θ1) tan(θ2) =2mp2mp + T(8)must be satisfied, where mp stands for the proton mass and T is the kineticenergy of the proton beam.Solving equations (7) and (8) for tan(θ′2) results intan(θ′2) =1− zvZFTHtan(θ1)(1 + T2mp) . (9)Thus, zv coordinate can be extracted by fitting the θ′2(θ1) distribution. Thisis shown in the right-hand side of Fig. 3 for two cases of vertex location, at(xv, yv, zv) = (0, 0, 0) (upper plot) and at (xv, yv, zv) = (5, 0, 0) mm (lowerplot).A set of simulations have been made for different locations of the vertexwhere only one of the vertex coordinates was changed at once, leaving theothers at zero. The accuracy of the method used to extract the vertexposition [18] is shown in Fig. 4.Studies of Systematic Uncertainties of Polarization Estimation . . . 1047Fig. 4. Plots showing results of Monte Carlo tests made on the x-, y-, z-coordinatesof the reaction vertex (first, second and third row, subsequently). See the text fordetails.In the first row, pictures corresponding to the change in the x-coordinate(xset) of the vertex are shown. In the second row, the y-coordinate (yset)was changed and in the third row, the z-coordinate (zset). All pictures aredistributions of the extracted (fit) value of the given coordinate as a functionof the true value (set) of the coordinate being changed. Therefore, points inpictures placed diagonally should be arranged along fit(set) = set line whileother distributions should show fit(set) = 0 behavior.Fits of the polynomial of the first order to the points in pictures placeddiagonally (solid/red lines) show that in all cases, the extracted values devi-ate slightly from the set ones (up to 14% in the case of the yfit(yset)). Thisneeds to be taken into account while extracting the vertex position in exper-imental data. We can also notice that if the change in a given coordinate isnot bigger than about 0.5 cm, the extraction of other coordinates is accurate.To determine how the wrong assumption about the vertex position affectsthe polarization, the polarization was calculated individually for each datasample, simulated with a change in the position of a certain coordinate.Then, each of the simulated data samples was analyzed with the defaultassumption that the particle going forward origins from the (xv, yv, zv) =(0, 0, 0) point1.1 Tracking algorithm of the MiniDrift Chamber do not assume a certain vertex position.1048 M. Hodana, P. Moskal, I. OzerianskaThe result is presented in the left panel of Fig. 5 which shows polarizationfor different vertex locations.Fig. 5. Left: polarization versus vertex shift along the x-, y- and z-axis (see thelegend) determined assuming acceptance for the vertex position at (0, 0, 0). Datawere simulated at positions as indicated in the figure. Right: polarization as a func-tion of the scattering angle of the forward going proton (center-of-mass scattering),determined from the simulated data with different values of the x-coordinate of theinteraction point (see the legend).While the change of the yv or zv coordinate does not have influenceon the result, a certain sensitivity of polarization is seen in the case ofchanging the xv coordinate of the interaction point. Namely, the calculatedvalue of polarization changes linearly with the shift of the vertex along thex-axis. The influence of moving the interaction point along the x-axis onthe polarization depends on the scattering angle of the forward going pro-ton, θCMs. The right panel of Fig. 5 shows distribution of the polarizationas a function of the scattering angle of the forward going proton calcu-lated in the centre-of-mass system, θCMs, made for different vertex positions(x-coordinate of the vertex was varied). It is seen that for θCMs > 38◦ thepolarization strongly deviates from the expected value when changing thexv coordinate by more than 5 mm. Therefore, since the polarization forhigher angles is biased by the systematics, we should restrict the allowedθCMs angle to less than 38◦. On the other hand, the observed dependency,if seen in experimental data, would be a clear sign of the wrong assumptionof the x-position of the interaction point. It is important to notice that,based on the results shown in Fig. 6 (left) in order to achieve uncertaintiesof the polarisation determination of about 0.03, the vertex position must becontrolled with the accuracy better than 1 mm.Studies of Systematic Uncertainties of Polarization Estimation . . . 1049Fig. 6. Left panel: polarization versus shift of the vertex location along the x-axis,taken in determining the acceptance correction, xacceptancevertex . The polarization wascalculated for four locations of the interaction point (see the legend). Right side:coplanarity dependence on the protons’ azimuthal angle.In the left panel of Fig. 6, a result of further studies is shown how,wrongly assumed, location of the interaction point influences the polariza-tion. Data, simulated with four different vertex positions (as indicated in thelegend), have been acceptance corrected assuming different values of the xvcoordinate, xacceptancevertex . In this case, a result is similar as shown in Fig. 5. Itshows that in order to control polarisation determination with the precisionof about 0.03, we need to control the determination of the x-coordinate ofthe vertex with the precision of about 1 mm. Comparison of circles (black)and triangles (red) indicates that this conclusion is independent of the ‘true’position of the vertex, at least within the range of 5 mm. It might be no-ticed as well that data, generated with yv or zv set to 5 mm and correctedto different xacceptancevertex , do not influence the polarization significantly.1050 M. Hodana, P. Moskal, I. OzerianskaAnother way to control the location of the vertex position in the exper-iment is to monitor the coplanarity, C, defined asC =(~p1 × ~p2) · ~pbeam|~p1 × ~p2| · |~pbeam|, (10)where ~p1 and ~p2 correspond to two scattered protons and ~pbeam is the vectorof the beam. Coplanarity dependence on the protons’ azimuthal angle showssinusoidal behavior for misallocated vertex. This is shown in the right-handside of Fig. 6. The left plot corresponds to simulated data with the vertexlocated at (xv, yv, zv) = (0, 0, 0) cm, the C(φ) distribution is flat. Moving thevertex position to point (xv, yv, zv) = (0.5, 0, 0) cm results in a sinusoidalshape. This is shown in the middle plot in the right-hand side of Fig. 6.Experimental data are presented in the lower, right corner of Fig. 6.2.2. Tilt of the beamThe maximum allowed range of tilts of the beam at the WASA-at-COSYis between −0.05 mrad and 0.05 mrad (symmetrically around the z-axis)[19]. To determine how the tilt of the beam affects the polarization, thebeam was leaned in the yz-plane or xz-plane at different αx and αy anglesrespectively. In Fig. 7, the polarization as a function of the α angle for bothtypes of studied beam tilts is shown. There are no effects observed in thestudied range of the α angle (α ∈ [−0.5, 0.5] mrad) except that polarizationslightly differs from zero (up to 0.01).Fig. 7. Distribution of the polarization as a function of the degree of the beam tiltin the yz-plane (filled triangles) and xz-plane (open circles). (Simulations.) Thestudied range is by factor of ten larger than the range of the possible tilt allowedby the COSY optics [19].Studies of Systematic Uncertainties of Polarization Estimation . . . 10513. SummaryMethods to monitor the location of the vertex have been demonstratedand it was shown how the misallocation of the vertex impacts the obtaineddegree of polarization. The study concluded that to have systematic uncer-tainty of the polarization smaller than 0.03, we need to control the positionof the interaction point with the precision higher than 1 mm. In this article,we presented three methods for the determination of the vertex position:(i) based on the d(φ) distribution, (ii) coplanarity distribution, (iii) polar-ization as a function of θCMs. Due to the large statistics of collected dataand the usage of the listed methods, the vertex position will be determinedwith the precision much better than 1 mm. Due to the large sensitivity ofthe result to the scattering angle, it is better to calculate polarization takinginto account the scattering angle not bigger than θCMs = 38◦.It was also presented that the beam, tilted within the maximum allowedrange, should have no significant influence on the obtained degree of polar-ization.We acknowledge support by the Polish National Science Center throughgrant No. 2011/03/B/ST2/01847, by the FFE grants of the Research Cen-ter Jülich, by the EU Integrated Infrastructure Initiative Hadron PhysicsProject under contract number RII3-CT-2004-506078 and by the EuropeanCommission under the 7th Framework Programme through the ResearchInfrastructures action of the Capacities Programme, Call: FP7- INFRA-STRUCTURES-2008-1, Grant Agreement N. 227431.REFERENCES[1] M. Abdel-Bary et al., Eur. Phys. J. A16, 127 (2003).[2] P. Moskal et al., Phys. Rev. C69, 025203 (2004).[3] H. Petren et al., Phys. Rev. C82, 055206 (2010).[4] P. Moskal et al., Eur. Phys. J. A43, 131 (2010).[5] H. Calen et al., Phys. Lett. B366, 39 (1996).[6] H. Calen et al., Phys. Rev. Lett. 79, 2642 (1997).[7] F. Hibou et al., Phys. Lett. B438, 41 (1998).[8] J. Smyrski et al., Phys. Lett. B474, 182 (2000).[9] A.M. Bergdolt et al., Phys. Rev. D48, 2969 (1993).[10] P. Moskal et al., Phys. Rev. C79, 015208 (2009).[11] P. Moskal, arXiv:hep-ph/0408162.[12] S. Abd El-Samad et al., Phys. Lett. B522, 16 (2001).1052 M. Hodana, P. Moskal, I. Ozerianska[13] R. Czyżykiewicz et al., Phys. Rev. Lett. 98, 122003 (2007).[14] P. Winter et al., Eur. Phys. J. A18, 355 (2003).[15] F. Balestra et al., Phys. Rev. C69, 064003 (2004).[16] P. Moskal, M. Hodana, J. Phys. Conf. Ser. 295, 012080 (2011).[17] M. Altmeier et al., Phys. Rev. Lett. 85, 1819 (2000).[18] L. Demirors, Ph.D. Thesis, Hamburg University, 2005.[19] D. Prashun, private communication, 2013.

Studies of systematic uncertainties of polarization estimation for experiments with the WASA detector at COSY

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Studies of systematic uncertainties of polarization estimation for experiments with WASA detector at COSY

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