Describing and understanding atomic nuclei is a puzzle that has intrigued scientists for decades. Approximately ten years ago, a description of nucleon structure, referred to as Generalized Parton Distribution (GPD), was introduced. GPDs are a way of describing scattering and production processes in a single framework. Deeply Virtual Compton Scattering (DVCS) is a process that scatters a photon from a proton and detects a scattered electron, a proton, and one photon in the fi nal state. From DVCS, GPDs can be extracted in order to lead us to a more complete picture of nucleon structure. The focus of this study is to understand the beam spin asymmetry (BSA) of the neutral π° meson, a main source of background during the DVCS process. To calculate the BSA, the number of π° events with positive helicity (spin) and negative helicity were counted by integrating histograms with Gaussians fi ts. It is shown that there is a signifi cant non-zero BSA in production of exclusive π°, namely 0.0655±0.0022. In the analysis of previous experiments, the BSA of π° was assumed to be zero and therefore ignored. Now, future analyses of DVCS data may incorporate this evidence of BSA. A deeper understanding of background processes (π°) in the DVCS will allow precision measurements of GPDs, providing new insight concerning the structure of nucleons

Avagyan, H.

Howley, I.

UNT (University of North Texas) Digital Library

32 U.S. Department of Energy Journal of Undergraduate Research http://www.scied.science.doe.govSTUDY OF BEAM SPIN ASYMMETRY IN EXCLUSIVE Π° PRODUCTIONIAN HOWLEY AND HARUT AVAGYANABSTRACTDescribing and understanding atomic nuclei is a puzzle that has intrigued scientists for decades.  Approximately ten years ago, a description of nucleon structure, referred to as Generalized Parton Distribution (GPD), was introduced. GPDs are a way of describing scattering and production processes in a single framework.  Deeply Virtual Compton Scattering (DVCS) is a process that scatters a photon from a proton and detects a scattered electron, a proton, and one photon in the fi nal state.  From DVCS, GPDs can be extracted in order to lead us to a more complete picture of nucleon structure.  The focus of this study is to understand the beam spin asymmetry (BSA) of the neutral π° meson, a main source of background during the DVCS process.  To calculate the BSA, the number of π° events with positive helicity (spin) and negative helicity were counted by integrating histograms with Gaussians fi ts.  It is shown that there is a signifi cant non-zero BSA in production of exclusive π°, namely 0.0655±0.0022.  In the analysis of previous experiments, the BSA of π° was assumed to be zero and therefore ignored. Now, future analyses of DVCS data may incorporate this evidence of BSA.  A deeper understanding of background processes (π°) in the DVCS will allow precision measurements of GPDs, providing new insight concerning the structure of nucleons.INTRODUCTIONSince the discovery of quarks in the 1960s, research in nuclear physics has been focused on understanding the role quarks play in nucleon structure.  Early theories simplifi ed the momentum distribution of quarks to a one-dimensional model.  By limiting quark distributions to the longitudinal momentum (in the infi nite momentum frame), theorists made relatively accurate predictions about the complex structure of the proton.  Each quark carries a fraction of the total momentum of the proton, represented by x (Figure 1a).  Many studies were conducted concerning form factors, which are descriptions of the charge distribution inside a proton (Figure 1b).  Combining these methods allow for a three dimensional model of nucleon structure (Figure 1c) [1].  Deeply virtual Compton scattering (DVCS) is the cleanest process available to study general parton distributions (GPDs). Th e DVCS processes follow the pattern ep→e’p’γ.  However, other processes such as the Bethe-Heitler process yield the same result, except that the photon is emitted by the incoming or outgoing electron, rather than as a result of proton excitation (Figure 2).  Th e decay of π° (ep→e’p’γγ) is another process which creates extraneous events that must be separated from desirable events when observing the DVCS process.  An understanding of background processes in the exclusive photon production allows measurement of DVCS asymmetry with a high degree of accuracy.  Th erefore, an asymmetry in the background must be taken into account in order to ensure the quality of the results.  The AsymmetryTh e number of photons in the exclusive photon sample from π° and their asymmetry are the two most important factors in DVCS asymmetry measurement.  Also, wide acceptance detectors, such as the Continuous Electron Beam Accelerator Facility (CEBAF) Large Acceptance Spectrometer (CLAS) at Jeff erson Laboratory (JLab), require a wide range of kinematics to study the asymmetry, ALU, where the beam is polarized (subscript L) and the target is unpolarized (subscript U).  Cross section dependency on the azimuthal angle φ, defi ned as the angle between the scattering and production planes (Figure 3), gives rise to observable asymmetries. In order to understand the asymmetries’ dependence on this angle φ, the general form of a cross section is used:  (1)Ian J. Howley is currently studying at Th e College of William and Mary, in Williamsburg, Virginia, and spent the spring of 2007 at St Andrews University in Scotland. He is studying physics and music, and will graduate in the spring of 2008. Ian will pursue a Ph.D. in either particle physics or astrophysics. He enjoys hiking, soccer, and golf.Harut Avagyan is a staff  scientist at the Th omas Jeff erson National Accelerator Facility (JLab). He received his Ph.D. from Yerevan Physics Institute (Yerevan, Armenia) in 1986, for the research of radiation energy loss by relativistic electrons and positrons in crystals. As a member of INFN-Frascati group (1993–2000) in HERMES collaboration (Hamburg, Germany), he introduced the subject of single-spin asymmetries to Hermes analysis and was responsible for coordinating the analysis of single-spin asymmetries (SSAs) in azimuthal distributions of pions produced in the semi-inclusive deep inelastic scattering (DIS). Th is study led to the fi rst observation of SSAs in hadron electroproduction in DIS. At JLab (since 2001) his research activities have focused on studies of SSAs in semi-inclusive and exclusive electroproduction of pions and photons with polarized beam or target. Since 2004, he has been co-convener of the JLab semi-inclusive working group involved in preparation of proposals for future measurements at upgraded to 12 GeV JLab.U.S. Department of Energy Journal of Undergraduate Research   33http://www.scied.science.doe.govHere, σ is the probability of a π° being produced, λ is the helicity and φ is the azimuthal angle.  σ0 and σ1 defi ne the spin independent and spin dependent portions of the cross section, respectively, and are the primary parameters to be determined. Helicity is the projection of the spin of a particle with respect to the direction it’s traveling.  Electrons, including those at CEBAF, can have helicity ‘+’ corresponding to positive beam polarization or helicity ‘-’ corresponding to negative polarization.  Th e beam polarization changes every 33ms and allows for more degrees of freedom while measuring the kinematic distribution inside the proton.  Equation 1 then becomes:  and                       (2) (3)for positive and negative beam polarizations respectively. Th e asymmetry is defi ned as:  (4)which, when equations 2 and 3 are substituted in, yields:  (5)From equation 5 it is clear that the ratio 01σσ is the amplitude of sinφ and the most important quantity of this experiment.  Since the detector detects particles within a certain acceptance (and effi  ciency), the number of events, N+/-, can be written as the product of the detectors acceptance, a, and the cross section:   (6)Th e acceptance of the detector accounts for its ability to detect particles.  Factors that limit the acceptance of the detector include areas where there is no detector (to allow room for superconducting magnets), very small angles, or even dead spots in the equipment itself.  Th e factor a should be the same for both positive and negative Figure 1a.  Longitudinal Momentum Distribution; at large x, the probability is small since it is unlikely that one quark will carry all the momentum for the proton.Figure 1b.  Form factors showing the charge distribution inside the proton.Figure 3.  The Scattering and Production Planes. Figure 2.  This fi gure shows how the three detected particle are the same (scattered electron, photon, and proton), but are not the result of the same process.34 U.S. Department of Energy Journal of Undergraduate Research http://www.scied.science.doe.govhelicities so when equation 6 is substituted into equation 4 the form used for the calculation of asymmetry is found:  (7)Previous experiments have attempted to measure the ratio  01σσbut have failed to produce a result with a reasonable degree of accuracy. In order for the accuracy of an experiment to increase to the point where the asymmetry is observed, a large number of π° events must be detected.  More recent DVCS experiments [2] [3] have relied on estimates of π° background.  Th anks to a new CLAS experiment, the π° background can fi nally be measured. The ExperimentTh e 5.776GeV CEBAF electron beam was aimed at a 2.5cm long liquid hydrogen target placed 66cm upstream from the CLAS center.  Th e experiment, e1-DVCS gathered data during the period from March to May 2005.  It operated with 80% beam polarization. Developed and installed in CLAS for the purpose of studying DVCS, the Inner Calorimeter’s (IC) main goal is to detect particles produced at very small angles, 4°-15°.  Th e 1.3cm x 1.3cm x 16cm IC consists of 424 crystals with Avalanche Photo Diodes (APDs) attached to the back of each crystal to record the light readout.  Th e IC is placed inside CLAS very near the target which is surrounded by the superconducting magnet to protect from Møller background (Figure 4).  When the π° decays into two photons, they are detected by the IC and organized into events which are then able to be analyzed. METHODSPaw++, a data analysis software, was used to organize data and to create and fi t all plots.  Th e fi rst major step to determine the π° asymmetry is to calculate the number of detected events with positive helicity and the number of events with negative helicity.  To ensure the data quality, cuts were made to the approximately 250,000 events in the data set.  In addition to fi ducial cuts, three particle identifi cation cuts were made to (1) the invariant mass, Mγγ, (2) the missing mass of e’p’X, MX, and (3) the scattering angle, θ’.    (8a)  (8b)  (8c)In equations 8b and 8c the subscript π represents the known or expected value.  Also another cut was made on the measured energy inside the calorimeter, mEπ .  (8d)  (8e)In order to calculate the number of events; the variables t, the momentum transfer to the proton, and φ were fi xed and divided into bins four bins in t (.05<t<.85GeV) were created, each containing twelve bins in φ (0<φ<2π).  For each of these 48 bins, the graph of Mγγ was plotted.  A minimum of 125 events were required for each bin to assure the quality of the fi t.  Just as the π° is a background to DVCS, there is background during π° production.  While this eff ect is much less than that of π° on DVCS, it must be accounted Figure 1c.  Three dimensional model of quark distribution. Figure 4.  Schematic of CLAS detector with superconducting magnets (blue) and internal calorimeter (purple).U.S. Department of Energy Journal of Undergraduate Research   35http://www.scied.science.doe.govfor.  A combination of Gaussian and linear functions was used for the graphs because a Gaussian curve fi ts the decay of π° properly and the linear terms accounts for the background (Figure 5).  Th e parameters listed in Figure 5 are used to calculate the events.  (9)is the integral of the Gaussian curve, and:   (10)are the linear terms used for the background events.  After performing the integral, in order to get the appropriate number of events, it was necessary to divide by the width of each bin, defi ned as:  (11)where xmax and xmin defi ne the boundaries of the graph, 0.03 and 0.005 respectively, and n represents the number of histogram bins under the curve, in this case 50.  Also listed in Figure 5 is the number of events.  Th is number of events cannot be used to calculate the BSA because they include the background.  Rather, this number is used to check the accuracy of the integration.  Th e background (equation 10) and signal (equation 9) events calculated from the integral are added together and compared to the total number of known events.  In all 96 bins the diff erence between the known events and the calculated events was within 10%.  Th is magnitude of error is acceptable because the calculation of the background, which is quite small and diffi  cult to measure accurately, accounts for most of this discrepancy.  However, an accurate measurement of the BSA can still be made.  Th e fi nal equations to calculate the events were: Figure 5.  Two examples of the 96 graphs of Mγγ, positive helicity on the left, negative helicity on the right.  (12)where erf(x) is the error function defi ned as:  (13)and:  (14)Once all of the events were known from the fi t function (equation 12), the events in the four bins for each helicity were added together and the asymmetry was calculated from equation 7.  Naturally, because of equation 5, a sine function was used to fi t the asymmetry graph. Also, a standard calculation to fi nd the error:   (15)was used.  Th e asymmetry is also plotted against the individual bins of t but must fi rst be divided by the average polarization, 0.79 to account for the beam polarization not being 100%.  RESULTSTh e key to unlocking the BSA was to measure the amplitude of the sinφ term in equation 5.  Figure 6 shows the amplitude of the asymmetry, which is 0.0655±0.0022, plotted against degrees.  Th is is the fi rst time this amplitude has been measured to be signifi cantly non-zero. Also, for the fi rst time, the t dependence of the BSA for π° was measured (Figure 7). No signifi cant variation with t was observed within the error bars.  Th e error no longer eclipses the size of the measured asymmetry as it has in previous experiments; instead the BSA of exclusive π° production is observed to within 3%. CONCLUSIONSFor the fi rst time, a non-zero BSA for exclusive π° production has been measured.  With more than 250,000 events in the data set, this experiment well exceeded the results and accuracy of any previous experiment.  Th e χ2 values are reasonable, and the error in the asymmetry fi t is small, 3%.  Th e success of this experiment was due almost entirely to the detection of more π° events than ever before.Th is result will be used for precision GPD measurements from the CLAS DVCS data.  DVCS asymmetries will no longer include an estimated π° subtraction.  With this result accurately measured, DVCS processes will be better understood, and in turn they will ultimately shed light on the structure of the proton.  36 U.S. Department of Energy Journal of Undergraduate Research http://www.scied.science.doe.govFigure 7.  The asymmetry plotted against the momentum transfer of the proton shows no signifi cant variation with t.Figure 6.  The azimuthal dependence of the asymmetry.  P1 is the amplitude, P3 the error.ACKNOWLEDGMENTSI would like to thank fi rst and foremost my mentor Dr. Harut Avakian.  Without his endless patience and unbridled enthusiasm, I most certainly would not have had this kind of success.  Second, I would like to thank the Th omas Jeff erson National Accelerator Facility, in conjunction with the US Department of Energy, Offi  ce of Science for providing all the necessary resources to complete this project.  A note of thanks also goes out to Dr. Keith Griffi  eon, Jan Tyler, and Dave Abbott for their support and companionship.REFERENCES[1] X.-D Ji, Phys. Rev. D55, 7114 (1997), hep-ph/9609381.; A. V. Radyushkin, Physics. Letters. B380, 417 (1996), hep-ph/9604317.[2] M. Airapetian et. al, Phys. Rev. Lett. 87 (2001).[3] S. Stepanyan et al, CLAS Collaboration Phys. Rev. Lett. 87 (2001).

Study of Beam Spin Asymmetry in Exclusive π° Production

https://digital.library.unt.edu/ark:/67531/metadc832173/m2/1/high_res_d/1051821.pdf

Study of Beam Spin Asymmetry in Exclusive π° Production

Abstract

Similar works

Full text

Available Versions

UNT (University of North Texas) Digital Library