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Nucleon Spin Structure at Low Q2 from EG4
Experiment.
Krishna Adhikari,
Physics Department, ODU
Dec. 04, 2007
Abstract
The main goal of the EG4 experiment is to measure the spin structure
function g1of the proton and the neutron, its first moment Γ1 and then the
GDH integral in the very low momentum transfer regime where it will
provide a test for the chiral-perturbation theory as the low-energy QCD
approximation which makes stringent predictions in this regime. Here, I will
give a brief overview of the experiment. I will also give the motivation,
procedure and the results of the EC-timing calibration work and rastercorrection work that I was involved in. A brief general overview of the
future work is also given.
Introduction and Motivation
The goal of the natural sciences as a whole is to understand the natural world – to
understand its structure and the underlying principles as much as possible and make the
things look simple, more appealing and easy to deal with. From years, decades and
centuries of experimental and theoretical scientific effort, we have come to know a lot
about our nature, and we have already been exploiting those scientific achievements
whenever and wherever we find them useful. From our own field of physics, for example,
we know a lot about the properties of the bulk matter, about the atomic structure and we
also know a little bit (if not a lot) about the even lower sub-stratum of the world, i.e. the
sub-microscopic world of nuclei, nucleons and many other sub-nuclear particles. In spite
of achieving such an unprecedented level of knowledge and understanding, there are still
a lot of problems and questions that remain unsolved and unanswered. One such thing
that has drawn a great attention from the nuclear and particle physics community is the
spin structure of the nucleons (i.e. of the protons and the neutrons).
Fig: Quarks as one of the the fundamental building blocks of matter. (17)
The interest in the nucleon structures began ever since the measurement/discovery
of the nucleon anomalous magnetic moments, which contradicted with the existing belief
that they were Dirac particles with spin-1/2 and no structure (i.e., point particles). Dirac’s
prediction for a point like particle of charge q, mass M and spin S is D = q S/M, but the
measurements showed that p = 2.79 N and n = - 1.91 N, where N = e /2Mp =
3.1525*10-14 MeV/T = 5.050 783 24(13) × 10-27 J.T.-1 is the Nuclear magneton. These
anomalous magnetic moments were the first concrete signatures of the nucleon
substructure. Many decades later, experiments at powerful accelerators provided
independent confirmations of the nucleon substructure. (4).
A truly vast amount of data on the inelastic structure of the nucleons has been
accumulated over the past 40 years from both fixed target and colliding beam
experiments with polarized as well as un-polarized incident photons, electrons, muons
and (anti-neutrinos) on a variety of targets (both polarized and un-polarized) from
hydrogen through iron. (2) [Photon and lepton scattering has been the predominant and
very powerful method to probe the composite systems like nucleons, nuclei or even atoms
for three primary reasons: (a) photons and leptons are point-like particles with no known
substructure or excited states; (b) the underlying electro-weak interaction is well
understood; (c) the interaction is sufficiently weak (so they can penetrate deeply into the
target without disturbing its substructure, thus enabling the extraction of the internal
structure of the target with a relatively easy interpretation following a perturbative
treatment.)] The initial measurements at SLAC confirmed the quark-parton picture of the
nucleon. Since then more precise measurements have been conducted at several
accelerators, improving our knowledge and understanding about the nucleon structure
(both spin-dependent and spin-averaged), and, at the same time, continuing to give us
new and sometimes very surprising results such as the original “EMC-Effect”, the
violation of Gottfried sum rule, even giving some hints that quarks might have
substructure. (2)
  : energy transfer
 Q2: - (4-momentum transfer) 2
 W2 = M2+2M-Q2: (Invariant mass)2
 Q = Q2/(2M): Bjorken scaling variable
(momentum fraction carried by struc
quark)
Spin Structure of Nucleons
With such a vast amount of experimental data available from DIS experiments, a
lot is known about the spin-averaged quark structure of the nucleon, but a lot less is
known about the spin-structure of the nucleon in terms of its constituents – quarks and
gluons. (2) In a simple non-relativistic model one would expect the quarks to carry the
entire spin of the nucleon, but one of the early rather realistic theories that explained the
partonic substructure of the nucleon, the Naïve Parton Model (NPM), predicted that 60%
of the nucleon spin is carried by the quarks. (7)
After the polarized beam and target technologies were greatly advanced during
the last two decades, many subsequent experiments have contributed to the extraction of
the spin structure functions g1 and g2, which are related to the spin carried by the quarks
in the nucleon. One of the first experiments carried out at SLAC, in a limited kinematic
region, seemed to confirm the predictions of the NPM. However, subsequent more
precise measurement at a larger kinematic region performed by the EMC experiment at
CERN reported that, contrary to the NPM predictions, only 1217% (i.e., practically
none) of the spin is carried by the quarks. This discovery of the so-called “spin crisis” has
sparked a large interest in measuring the spin content of the nucleon, giving birth to
several experiments (underway and proposed) around the globe. The subsequent
theoretical developments of QCD have clarified our picture of the nucleon spin structure
in great detail. The so-called Bjorken sum rule, which relates results of the inclusive,
polarized deep inelastic lepton-nucleon scattering to the fundamental axial coupling
constant (gA), is a precise test of QCD. The interpretation of existing DIS results has
verified the Bjorken sum rule at the level of 10% accuracy and has shown that only about
3010% of the nucleon spin is carried by the quarks; the rest of the spin must reside
either in gluons or orbital angular momentum of its constituents. Experiments to measure
the gluon contribution are underway at DESY, BNL and CERN. (7)
Probing the nucleon structure at the other end of the energy scale provides
information about the long distance structure, which is associated with static properties of
the nucleon. At the real photon point (four-momentum transfer squared, Q2 = 0), the
Gerasimov-Drell-Hearn (GDH) sum rule, which is based on very general principles,
relates the total cross-section of polarized photons on polarized nucleons with the
anomalous magnetic moment of the nucleon. Although formulated in the 1960’s, the sum
rule remained unappreciated until Anselmino et al. pointed out the importance of it in an
attempt to solve the “spin crisis”. They showed that the GDH sum rule is intimately
connected to the DIS region and, in fact, is the analytic extension of the Bjorken sum rule
towards the real photon point. It implies a negative slope (w. r. t. Q2) of 1, the first
moment of the spin structure function g1, at the photo-absorption point. Later, Burkert et
al. pointed out that the rapid transition of 1 between the real photon point and the DIS
region is saturated by contributions from nucleon resonances. Since then Ji et al. have
extended the GDH sum rule beyond the real photon point. (7)
This progress in theoretical work has triggered a large interest in measuring the
spin structure functions and their moments in this relatively unexplored transition regime,
between the real photon point and the DIS region. There is a large experimental program
underway at Jlab, in Newport News, VA to make precise measurements in this region.
Experiment E03 – 006 (also called EG4-experiment) “The measurement of the GDH
integral on the proton and deuteron at low Q2 (0.01 – 0.5 GeV2)” was performed in Hall B
(from February to May 2006) with the goal of measuring the spin structure function g1, its
first moment 1, and the GDH sum over the largely unexplored kinematic range Q2 =
(0.01 – 0.5 GeV2) by measuring the helicity (projection of spin in the momentum
direction; see fig. below) dependent absolute inclusive cross-section difference. The
topics that can be studied from the data set of this experiment include an experimental
verification of chiral perturbation theory (PT) and future lattice QCD calculations for
1.
[Fig: Positive (right-handed) and negative (left-handed) helicities for a particle]
The Gerasimov-Drell-Hearn (GDH) sum rule:
Sum rules are relations linking an integral over structure functions to quantities
characterizing the target. (19) Polarized sum rules involving the spin structure of the
nucleon like those due to Bjorken, Burkhardt-Cottingham, the one due to Ellis and Jaffe
and the one due to Gerasimov, Drell and Hearn offer the opportunity to study the structure
of strong interactions. At long distance scales i.e., in the confinement regime, the
Gerasimov-Drell-Hearn (GDH) Sum Rule (derived in 1966) connects static properties of
the nucleon like the anomalous magnetic moment and the nucleon mass M, with the
spin dependent absorption of real photons with total cross sections 3/2 and 1/2:
2 2
 d
 3 2     12    2 



M2
 th 
(1)
Hence the full spin-dependent excitation spectrum of the nucleon is related to its
static properties. The sum rule has not been investigated experimentally until recently.
For the first time, this fundamental sum rule is verified by the GDH-Collaboration with
circularly polarized real photons and longitudinally polarized nucleons at the two
accelerators ELSA and MAMI.
The "sum" on the left hand side of the GDH Sum Rule can be generalized to the
case of virtual photons (i.e. Q 2> 0):
I  Q 2  


 d
 12 x, Q 2    3 2 x, Q 2 



Q 2 2M 
8 2

Q2
2
2 
2

0 dx g1 x, Q    g 2  x, Q 

K
0 x
x
(2)
Here x = Q2/2Mν0 and K is the flux factor of virtual photons ν √ 1+γ2 , and γ2 = Q
2 2
/ ν . This reduces to the GDH sum rule for Q2=0. In the DIS limit the integral becomes:
8 2
2


IQ  


Q2
x0
16 2


g
x
dx

1
 1
2
Q
0
(3)
Where Γ1 is the first moment of g1. Studying the GDH sum rule at various Q2 allows us to
establish a Q2 dependency and to investigate the question of the transition from the high
Q2 to the low Q2 regimes of QCD. The change of signs that occurs in the region 0 < Q2 <
1 GeV2 is particularly interesting. This is the subject of several experiments such as
EG1a, EG1b and EG4 at JLab for the resonance region and of the HERMES experiment at
DESY for higher Q2. (10)
In this paper, I will briefly describe the EG4 experiment, which I am related to. Then, I
will focus more on the work that I did so far as a member of this experimental group.
After that I will give an overview of the future work.
Method:
The goal of the EG4 experiment is to extract g1, Γ1 and finally to determine the
extended GDH sum by directly measuring the helicity dependent absolute inclusive cross
section differences for scattering of longitudinally polarized electrons from the
longitudinally polarized NH3 and ND3 targets in Hall B, Jlab at Q2 = 0.01 – 0.5 GeV2
and in a large x (or W) range. This kinematics extends the existing measurements to the
region of applicability of Chiral theories and low energy expansion, providing the tool to
experimentally test these predictions as well as other phenomenological models. In
addition the minimum Q2 is low enough to allow the evaluation of the GDH sum rule by
extrapolating to the photon point. (18)
The method to be employed in this experiment is to measure the helicity
dependent cross-section difference at very low Q2.
d  d  4 2 E '
E  E ' cos  g1 x, Q 2  2Mxg2 x, Q 2
(4)


dE ' d dE ' d Q 2 ME





Where   and   are the inclusive cross sections for anti-parallel and parallel
beam-target spins. From the difference one can extract the structure function g1 (because
the second term with g2 is negligible at very low Q2 values), which in turn, can be used to
evaluate its first moment , and the GDH sum over the kinematic range.
xth
2

(5)
 g1 x, Q dx


0
The cross-section difference on the left of equation (4) is obtained using the
following relation,
I
2
 Q 2   16 
GDH 

Q2
d  d  N   N   1


dE ' d dE ' d
N i t  f Pb Pt
(6)
Where N   and N   are the number of events detected for the parallel and antiparallel beam-target spin configurations respectively. Likewise, N i , t,  , f and Pb Pt
are the number of incident electrons (to be obtained from the charge measured in Faraday
cup), the so-called target areal-density (the product of the target number density () and
the target length along the beam direction), the detector acceptance for the given
kinematic bin, corresponding detector efficiency and the product of beam & target
polarizations respectively.
The Experiment
As said before, the goal of the EG4 experiment is to measure the GerasimovDrell-Hearn integral and investigate the nucleon spin-structure at very low Q2 range
where chiral perturbation theory as the low-energy QCD approximation makes stringent
predictions. This experiment took place at the experimental Hall B of the Thomas
Jefferson National Accelerator Facility (TJNAF), where the Continuous Electron Beam
Accelerator Facility (CEBAF) delivers beam to three experimental halls. The CEBAF
Large Acceptance Spectrometer (CLAS detector) in hall B was used to make the
scattering measurements. The set-up can be roughly divided into three parts: beam,
target and the CLAS detector. A schematic of the experimental set-up (with a vertical
cross-sectional view along the beam line) is shown below.
1) The beam: The CEBAF can generate polarized as well as un-polarized
electron beams. By exposing a semiconductor material surface such as that of GaAs with
a circularly polarized laser photon beam, the polarized electrons are produced and then
sent to CEBAF for acceleration. (7) These longitudinally polarized (Pb = 85 – 87 %) high
intensity ‘continuous’ beams - with energies 3.0, 2.3, 2.0, (1.5 – for commissioning), 1.3
and 1.0 GeV (in our case) are then sent to the Hall-B for the experiment. The beam
polarization is measured by the usual Hall B Moller polarimeter, but the product of beam
and target polarization is being extracted from the quasi-elastic data.
2) Polarized Target:
In this experiment, the standard cryogenic NH3 and ND3 targets were polarized
using the technique of Dynamic Nuclear Polarization (DNP) and used as the proton and
deuteron targets respectively. The targets were maintained in a liquid helium bath at 1K
and a 5T longitudinal magnetic field. (This field also serves another important purpose:
focusing the low momentum Moeller electrons in the forward direction, which are then
collected by the “Moeller Shield”). The targets were positioned 1m upstream of the usual
CLAS center to enhance/extend the low Q2 coverage to Q2 = 0.015 GeV2. NMR signals
were used to monitor the target polarization during the experimental run. One can also
evaluate the target polarization from the off-line analysis of quasi-elastic events, which
are recorded simultaneously with the inelastic events thanks to the large CLAS
acceptance.
A 12C and an empty cell targets were used to have data for background
measurements.
3) The CLAS detector:
CLAS (the CEBAF Large Acceptance Spectrometer), housed in JHall B (Jlab), is a
nearly 4
-particle final-state reactions
34
induced by photons and electrons at luminosities up to 10 cm-2sec-1. (11) The CLAS
detector [3] is divided into 6 identical sectors (each functioning as independent magnetic
spectrometers) with a super-conducting coil (called Torus) located in between each two
of them. Each sector has three layers of drift chambers (DC) and one layer of time-offlight (TOF) or scintillator counters (SC), which cover the full detector acceptance. Each
sector also has a Cherenkov counter (CC) and an electromagnetic calorimeter (EC)
installed in the forward region from 8o to 45o.
Fig: A schematic view of CLAS sectors and a cross-section (along the beamline) showing two sectors
The torus magnet setup consists of 6 super-conducting coils to produce a magnetic
field up to 2.7 Tesla in the  direction, surrounding the beam line. The magnetic field
causes the charged particles to bend when they are flying through. If the electron bends
towards the beam line, we call it in-bending, otherwise out-bending. This allows one to
judge the charge type and measure the momenta of charged particles according to their
bending trajectories.
In order to perform an absolute cross section measurement, the CLAS set-up with
a few modifications was used. In contrast to the usual configuration, an out-bending (for
electrons) Torus magnetic field was applied in this experiment to be able to make
measurements down to as low as 6 degrees.
A new (Moeller) Shield made of Tungsten (higher density than Lead) was put in
place to suppress low-momentum background electrons (also called Moeller electrons
because they originate due to the Moeller scattering from the atomic electrons),
optimized for small angle () operation at high luminosity.
CLAS Drift Chambers:Charged particles in CLAS are tracked by a set of drift
chambers (DC). A drift chamber has thin wires fixed in a volume filled with a special gas
in a way that the wires form cells. Inside these cells a traversing charged particle ionizes
the gas. Due to the positive electrical potentials applied to the wires, the electrons drift to
the sense wires. The connected electronics measures the charge of the signals and the
corresponding times the signals appear. The difference between this signal arrival time
and the time when the particle traversed the cell (measured by other detectors) is used to
reconstruct the particle impact points in the chamber virtual planes. (22) Using such
impact points, one can re-construct the track of the traversing particle.
Charged Track Events in CLAS showing signals in all 6
superlayers (2 per region) of 2 DC sectors. (21)
The CLAS drift chambers are arranged in three regions: Region 1 is located
closest to the target, within the (nearly) field free region inside the Torus bore, and is
used to determine the initial direction of charged particle tracks. Region 2 is located
between the six super-conducting Torus coils, in the region of strong toroidal magnetic
field (up to 2.7 Tesla (23)), and is used to obtain a second measurement of the particle
track at a point where the curvature is maximal, to achieve good energy resolution.
Region 3 is located outside the coils, again in a region with low magnetic field, and
measures the final direction of charged particles headed towards the outer TOF, CC and
the EC counters. All three regions consist of six separate sectors, one for each of the six
sectors of the CLAS. So, there are 18 different drift chambers in CLAS (21).
The DC information is important for energy, momentum and angle determination
as well as for particle identification. In this experiment, the drift chamber system was
used in the standard CLAS configuration.
CLAS Cherenkov counters: The Cherenkov Counter (CC) serves the dual
function of triggering on electrons and separating electrons from pions (or identifying
charged particles). These detectors use the light emitted by Cherenkov radiation
(emission of light when the charged particle travels faster than light in the medium) to
measure the particle velocity (and therefore ). The knowledge of  combined with the
particle momentum (from the tracking detectors) determines the particle mass, thus
giving us the clue for the particle ID. Choosing different gases to fill in, the index (n) of
refraction is carefully optimized for the particle masses and momentum range of the
experiment in question. Threshold counters record all light produced, thus providing a
signal whenever  is above the threshold t = 1/n. CLAS uses one Cherenkov threshold
detector in each of the six sectors in the forward region from 8o to 45o.
A new gas threshold Cerenkov counter designed and built by INFN – Genova,
Italy, was installed in the 6th sector. This detector is specifically designed for the outbending field configuration, which is necessary to reach the desired low momentum
transfer (measurements down to 6 degrees). This new detector has a very high and
uniform electron detection efficiency (~99.9%) to allow the measurement of the absolute
Old CLAS-Cherenkov detector optics
New Cherenkov detector.
cross-section with minimal corrections and a high pion rejection ratio (of the order of 103
). Because, we’ll have an overwhelmingly large amount of scattering at smaller angles,
for reasons of limited data storage capability, only those events corresponding to the
scattering in the 6th sector will be taken into account. (6)
CLAS Time of Flight (TOF) or Scintillator Counters (SC): The TOF system
(here used in the standard CLAS configuration) provides a high-resolution (~ 140 ps)
timing measurement that can be used for the velocity and mass calculation purpose. A
scintillation counter measures ionizing radiation using a scintillator, consisting of a
transparent crystal, usually phosphor, plastic (CLAS uses 5 cm thick BC408) (23) that
fluoresces when struck by the ionizing radiation. A sensitive photo-multiplier tube (PMT)
attached to an electronics measures the light from the crystal. Scintillation counters
typically have a poor spatial resolution but a very good time resolution. They are also
continuously sensitive, and are therefore often used as triggers for other types of
detectors.
In EG4, the CLAS was triggered by requiring a coincidence between the forward
electromagnetic calorimeter (EC) and the new INFN Cerenkov counter (CC) which
was installed only in the sixth sector. (9)
Forward electromagnetic calorimeters (EC): Each CLAS sector has an
electromagnetic sampling calorimeter (EC) in the forward region (8<<45). These
electromagnetic shower calorimeters are optimized for measuring the energies and
positions of electrons and gammas. (11) EC helps to discriminate electrons from hadrons
and photons from neutrons. When a high-energy particle passes through, a fraction of its
energy is deposited in the form of an electromagnetic shower (because of Bremsstrahlung
and electron pair production). This shower produces a signal (in the scintillators – the
active material) proportional to the energy deposit, which is recorded by the EC read-out.
The calorimeter is made of alternating layers of scintillator (SC) strips (36 strips per
layer) and lead (Pb) sheets with a total thickness of 16 radiation lengths. In order to
match the hexagonal geometry of the CLAS, the Pb-SC sandwich is made to have the
shape of an equilateral triangle. There are 39 layers in the sandwich, each consisting of a
10 mm thick SC followed by a 2.2 mm thick lead sheet.
Exploded view of one of the six
electromagnetic calorimeter modules.
CLAS
Schematic vertical cut of EC light readout system.
PMT – Photomultiplier, LG – Light Guide, FOBIN
– Fiber Optic Bundle Inner, FOBOU – Fiber Optic
Bundle Outer, SC –Scintillators, Pb – 2.2 mm Lead
Sheets, IP – Inner Plate (for support)
The calorimeter has a “projective” geometry, in which the area of each successive
layer increases. This minimizes shower leakage at the edges of the active volume and
minimizes the dispersion in arrival times of signals originating in different scintillator
layers. The active volume of the sandwich thus forms a truncated triangular pyramid with
a projected vertex at the CLAS target point 5 meters away and an area at the base of 8 m2.
The projective geometry to maximizes position resolution for neutral particles.
For the purposes of readout, each SC layer is made of 36 strips parallel to one side
of the triangle, with the orientation of the strips rotated by 120 in each successive layer.
Thus there are three orientations or view (labeled U, V, and W), each containing 13
layers, which provide stereo information on the location of energy deposition. Each view
is further subdivided into an inner (5 layers) and outer (8 layers) stack, to provide
longitudinal sampling of the shower for improved hadron identification (or electron-pion
discrimination; the electron-pion rejection factor is ~0.01.). Each module thus requires 36
(strips)* 3(views)*2(stacks) = 216 PMTs. Altogether there are 1296 PMTs and 8424
scintillator strips in the six EC modules used in CLAS. The intrinsic energy resolution for
showering particles is 10%/ E , with approximately a 3 cm position resolution at 1 GeV.
These detectors have up to 60% efficiency for detecting high momentum neutrons. (23)
With its good energy and position resolution, the main functions of EC are:
(a)
Detection and primary triggering of electrons at energies above 0.5
GeV. The total energy deposited in the EC is available at the trigger
level to reject minimum ionizing particles or to select a particular
range of scattered electron energy.
(b)
Detection of photons at energies above 0.2 GeV. Allowing 0 and 
reconstruction from the measurement of their 2 decays.
(c)
Detection of neutrons, with discrimination between photons and
neutrons using TOF measurements. (11)
In our experiment, DC, SC and EC counters were used in the standard CLAS
configuration. The modifications were only in CC, Torus polarity, the Moeller shield, and
the position of the target relative to the CLAS center.
My Work and Results:
(A) EC-timing Calibration:
Introduction and Purpose: As with any measurement, it is expected that, for
various reasons, the measured signals from various detector components suffer unwanted
changes and biases that need some adjustments. Also, during the experiment, digital
signals from Amplitude (ADC) and Time (TDC) sensitive electronics are written to tape.
Such signals from all devices have to be converted into meaningful physical quantities
like time, position etc., before the first pass of the data analysis can begin. Getting rid of
such unwanted changes, and converting the recorded signals into corresponding
meaningful physical quantities before the data is actually analyzed is called Calibration.
Depending on what signals and quantities we are interested in, there are several types of
calibrations that is to be done on the EG4 data. One of them is the EC timing calibration.
Systematic changes over the time in the time response of the EC and SC
detectors can appear due to hardware changes. For example, the replacement of the
cables connecting the PMTs (Photo-multiplier tubes) to the front-end electronics, the
replacement of PMTs themselves etc. may result in such changes. This kind of things can
happen whenever some hardware work is done (usually in between different
experiments). In addition, the calibrations of different detector systems are somewhat
interconnected. For example, in our case, the EC time is calibrated with respect to the
time of flight, as we look at (EC_t -SC_t). Similarly the time of flight are calibrated with
respect to the RF signals coming from the accelerator. Changes in other systems (the RF,
for example, which can change every time the machine is retuned) can affect the
calibrations of the TOF and EC. (3,14)
There are several possible uses for good EC timing calibration in CLAS.
Discriminating neutrons from photons is crucial in many channels studied in Hall B.
Since the EC counter is particularly sensitive to neutral particles like photons and
neutrons (DCs don’t detect them), good calibration of its timing is a requirement for any
analysis that looks at events containing such particles. In particular, one can use the time
of flight from the target to the EC to discriminate between the neutral particles such as
photons and neutrons, and to calculate the neutron kinetic energy. Neutrons are
discriminated from photons based on ; the current code considers that neutrals with
<0.9 are neutrons and photons otherwise. In order to achieve good separation, good EC
timing is essential. (26) In addition, timing information is also needed to convert the
signal from the drift chambers into precise position information and to determine from
which beam "bucket" a scattered electron originated. The EC can fulfill this function in
cases where any channels in the time-of-flight counters are inoperative in the forward
region of the spectrometer, the EC timing resolution for the charged particles is sufficient
to provide a start time for the drift chambers and to identify the RF pulse corresponding
to the beam electron initiating the event. (3,11)
Procedure: The timing calibration of the EC was performed by comparing the EC
and SC time for each SC paddle using charged particles which passed through both the
time-of-flight scintillators (TOF or SC) and the forward calorimeter (EC). Electrons and
charged pions were used simultaneously to span the full range of angles and deposited
energy. Only events with a single charged track in a given sector were used. Using a large
sample of data (1-2 M charged particle events), a chi-squared minimization was
performed to compare the timing from the TOF detectors to that of the EC using a fiveparameter model for the EC time. The five parameters of the model included an additive
constant, a TDC slope parameter, one walk correction parameter, and two parameters to
take into account time slewing due to geometric effects. The signal propagation velocity
was assumed to be constant. Although each calculation of the chi-squared involved a
separate pass through all data, the entire calibration procedure required only about 30 min
for a given data set. (11)
Assuming a first set of calibration constant is already in place, an iteration to
improve them took 3 steps:
1) Analyze/process/cook the raw data.
2) Then the command '/home/adhikari/bin/LinuxRHEL3/ec_time' is
used to execute the updated calibration code.
3) Check if the calibration run was successful by looking at the various
types of resultant monitoring histograms. If the results are satisfactory,
execute /home/adhikari/bin/LinuxRHEL3/fout_map
(creates
several text files that can be used to insert the constants in the
calibration database) to retrieve the generated calibration constants and
update the code accordingly.
4) Repeat the procedure until the Gaussian fit of the EC time mean and
the resolution is brought to the satisfactory level (mean within 50 ps
and the width below 300 ps).
Results: One of the histograms resulting from the EC-timing calibration run, showing
the distribution of ECt – SCt for all charged particles in the sector-6, from a typical run
51057 can be seen below (left one).
In the right side figure above, we can see one of many 2-dimensional histograms, which
shows  of all the neutral particles in the first sector (for the run 50808). The vertical axis
represents the distance (in cm) of the calorimeter hit from the target vertex. The two
bands represent the hits in the inner and outer part of the calorimeter.
The plot above shows the stability of the calibration achieved (from the latest pass-zero
iteration) where the mean and sigma of ECt–SCt (in nanoseconds) for electrons is plotted
as a function of the run number.
The average timing resolutions/accuracies obtained after the calibration so far is of the
order of 300 ps for electrons and 400-500 ps for the hadrons.
The beta spectrum for neutral particles
reconstructed from the EC. The peak at
beta=1 is or he photons while the shoulder
on the left of the peak is for the
neutrons.
The invariant mass of two photons as
reconstructed from the EC (The clear
peak at the 0 mass, indicates that there
was an undetected 0 in the reaction.)
B) Raster-correction:
(i)Why beam rastering: The electron beam generated at CEBAF is a high current beam,
with a very small transverse size (200 m FWHM). This beam is rastered using the socalled fast raster system, 25 meters upstream of the target, designed to increase the
effective beam size in order to prevent damage to the target or the beam dump and also to
prevent local boiling in the cryogenic targets. The fast raster system consists of two sets
of steering magnets. The first set rasters the beam vertically, and the second rasters the
beam horizontally. The current driving the magnets are varied sinusoidally, at frequencies
and phases such that the beam spirals continuously to cover a circular area of the target.
(ii)Why Raster-correction: In EG4, the beam was rastered using two magnets up-beam
of the target. ADC’s recorded the current going to these magnets, and the values are
stored in the BOS files for each trigger. To make the similar ADC values for an earlier
similar experiment (EG1b) useful, a procedure was developed and employed by P.
Bosted et al. (12) to translate ADC counts into the corresponding x and y values relative
to the CLAS beam line. This could then be used to make corrections to the tracking
(which assumes x and y are zero), which allows better z vertex reconstruction. This
allows better rejection of events from up-beam and down-beam windows (especially for
particles at small angles), and could also be used to reduce accidental coincidences in
multi-particle final states (or to look for offset decays such as from the ). Knowing x
and y allows a correction to the  angle of the particles to be made, improving missing
mass resolution for multi-particle final states. Finally, plotting the number of events as a
function of raster information is useful in looking for mis-steered beam that hit the edges
of the target cups.
(iii) Goal: My task for EG4 was to repeat the raster system calibration following the
same procedure as for EG1. This required me to find the conversion factors and offsets
for both the x and the y direction.
(iv) Method: Assuming the raster magnets have a linear relation to position, we fit the x
and y raster ADC values using the form:
where Xo, Yo, cx and cy are the fit parameters to be fitted, X and Y are the ADC values
and x, y are the raster positions in cm. For the fitting we select electrons from the
exclusive events and the we minimize the 2 as defined below.
Where z0 is also a fit parameter that defines the target center and z c is the corrected vetex
position given by
zc = znom + x’/tan()
where znom is the vertex z found by the tracking code assuming x = y = 0,  is the particle
angle relative to the beam line, and
x’ = [x cos(s) + y sin(s)] / cos( - s)
is a measure of the distance in cm along the track length that was not taken into account
in the tracking. Here, s is the sector angle given in degrees by s = (S-1)*60, where S is
the sector number from 1 to 6 and  is the azimuthal angle of the particle in the same
coordinate system, defined as  = atan2(px, py), where px and py are the RECSIS
momentum components in the x and y directions.
(iv) Results: A code has been written using the standard data analysis and visualization
code ROOT (developed by CERN), which evaluates the five raster-coefficients (i.e. the
fit parameters) mentioned above using the Minuit package available in ROOT. The
following table shows the values of the raster coefficients (the fit–parameters) for a few
runs evaluated from the Minuit fitting using the exclusive data.
For the 3 GeV runs:
run
50808
50815
50833
50855
50894
50924
50937
50938
50951
Xo
4279.4
4500.6
4304.3
4367.7
4269.3
4389.4
4134.3
4041.0
4309.9
Cx
0.00017
0.00013
0.00017
0.00017
0.00017
0.00015
0.00016
0.00015
0.00016
Yo
3026.0
3140.2
2997.6
2859.2
2802.7
2786.3
3186.5
3032.8
2775.1
Cy
-0.00018
-0.00018
-0.00018
-0.00017
-0.00017
-0.00017
-0.00019
-0.00018
-0.00018
-Zo
100.77
100.89
100.83
100.78
100.77
100.76
100.79
100.80
100.78
3951.0 -0.00032
4111.8 -0.00032
100.82
101.12
For the 1.3 GeV runs:
51191
51209
4216.4 0.00039
4229.7 0.00030
51230
51252
4246.4 0.00034
4217.8 0.00034
4144.2 -0.00037
4105.8 -0.00032
101.00
100.99
Using the coefficient calculated as above, I plotted the raster-x and raster-y values (in
cm) to get the target images for several runs. One such plot for a typical run 50808 is
shown below.
Exclusive: 50808
The angle correction part is yet to be done.
Future Work:
Momentum Correction:
Why Momentum Correction?
Since this experiment is focused on the low momentum transfer behavior of the
nucleons, the momentum measurement with great precision and least amount of error is
very crucial. But, it is a well known fact that the particle momenta as measured by CLAS
and reconstructed with RECSIS show systematic deviations, as evidenced by shifted and
broadened invariant mass (W) distributions for inclusive data and missing mass peaks for
more exclusive data. In inclusive data, for example, the centroid for the W distribution of
the elastic peak is moved from its theoretical value, W = M (the target rest mass) and
significantly broader than expected from the intrinsic momentum resolution of CLAS. A
clear dependence of the shift on both  and  can be observed. (15) If the momentum
(and other kinematical quantities such as the angles  and ) remains uncorrected, our
capability to separate signals from background will be affected which will have
undesirable effects on the determination of physics quantities. (16)
Sources of errors:
These systematic momentum deviations could in principle arise from several
sources (15):
1)
Misalignment of the drift chambers relative to their nominal positions,
inaccurate or out-of-date survey results.
2)
Neglect to properly incorporate effects like wire sag, wire take-off
position on the “trumpet lips”, thermal and stress distortions of the
drift chambers, and other factors affecting wire position.
3)
Insufficient or incorrect information in the reconstruction code on the
exact location of the wire feed-through holes in the drift chamber
endplates as actually drilled, especially for the very complicated
compound angles involved in the stereo superlayers.
4)
Incomplete knowledge of the torus (or mini-torus) magnetic field
distribution.
A general procedure:
In the past, there have been several schemes tried and employed to at least
approximately correct for these errors. They make different assumptions depending on
the predominant sources of errors that need to be addressed and the level of sophistication
embraced. The common approach is to make some basic assumptions about the form of
the necessary corrections (which will be either multiplied or added to the measured
momenta), with a modest amount of free parameters, and then attempt a fit over a given
(usually very large) data set to fix these parameters. Most methods that we are aware of
concentrate (or at least start) on elastically scattered electrons and then make assumptions
about at least two parameters (e.g., the beam energy and the scattering angle are “known
absolutely”) to determine very detailed corrections for electron momenta and/or angles.
(15) A more general and comprehensive correction method has been developed at ODU
by S. Kuhn and will be employed for EG4. I will adopt the existing code to the specific
conditions of EG4 and determine all fit parameters necessary via a Chi-square
minimization routine. (3)
Conclusion:
The main goal of the EG4 experiment is to measure the spin structure function g1, its first
moment Γ1 and the GDH integral in the very low momentum transfer regime. This study
will give us a glimpse of the nucleon spin structure in this relatively unexplored
kinematic regime. As one of many members of the experimental group, I was involved in
the EC-timing calibration and Raster correction. EC-timing calibration is now almost
done whereas the work on raster correction is underway. After the raster correction part is
done, the work on momentum correction will begin immediately. There are following
further more tasks to be done, part of which will be done by myself and the rest will be
done by others from the EG4 collaboration:
 background subtraction,
 final definition of all cuts,
 beam and target polarization determination,
 acceptance and efficiency of electron detection in CLAS (via simulation and
comparison with known cross sections),
 radiative corrections,
 development of models,
 extraction of g1, integration,
 neutron information extraction. (3)
References:
(1) Wikipedia: Standard Model. (http://en.wikipedia.org/wiki/Standard_Model)
(2) S. E. Kuhn, Nucleon Structure Functions: Experiments and Models, HUGS ’97.
(3) S. E. Kuhn and G. E. Dodge, Private communications.
(4) K. J. Slifer, Ph. D. thesis, Temple University.
(5) R. Milner;HERMES physics, a historical perspective (A ppt presentation for HERA
symposium June 30, 2007)
(6) M. Ripani, Private communication.
(7) K.G. Vipuli G. Dharmawardane, Ph.D. thesis, Old Dominion University
(8) K.J. Slifer and A. Deur Private communications.
(9) M.Battaglieri, et al. 2003 Jefferson Lab proposal E03-006
(10) http://galileo.phys.virginia.edu/classes/sajclub/gdh.html
(11) M. Amarian et al., The CLAS forward electromagnetic calorimeter, Nucl. Instr. And
Meth. 460 (2000) 239 – 265.
(12) P. Bosted et al., Raster Corrections for EG1b, CLAS-NOTE-2003-008.
(13) http://www.krl.caltech.edu/~johna/thesis/node19.html
(14) R. De Vita, Private communications.
(15) A. Klimenko and S. Kuhn, Momentum corrections for E6, CLAS-NOTE-2003-005.
(16) K. Park et al., Kinematics Corrections for CLAS, CLAS-NOTE-2003-012.
(17) http://people.virginia.edu/~xz5y/Research.html
(18) M. Anghinolfi et al., The GDH Sum Rule with Nearly-Real Photons and the Proton
g1 Structure Function at Low Momentum Transfer. Jlab PR 03-006.
(19) A. Deur, Experimental Studies of Spin Stucture in Light Nuclei, EINN07.
(20) J. Zhang, Measurement of Exclusive - Electro-production from the Neutron in the
Resonance Region, Oral qualifying exam report, 2006.
(21) http://www-meg.phys.cmu.edu/~bellis/dc/dcintro.html
(22) http://ikpe1101.ikp.kfa-juelich.de/cosy11/exp/drift_chambers/DriftChambers_E.html
(23) W. Brooks, CLAS – A Large Acceptance Spectrometer for Intermediate Energy
Electromagnetic Nuclear Physics.
(24) B.A. Mecking, et al, The CEBAF large acceptance spectrometer (CLAS), Nucl.
Instr. And Meth. A 503 (2003) 513 – 553.
(25) http://www.shef.ac.uk/physics/teaching/phy311/scintillator.html
(26) Matthieu Guillo et al., EC Time Calibration Procedure For Photon Runs in CLAS,
CLAS-NOTE 2001-014, August 20, 2001.