Study of the proton structure by measurements
of polarization transfers in Real Compton
scattering at the Th. Jefferson Natl. Lab
Cristiano Fanelli
January 7, 2013
Supervisors: Prof. G. Salmé, Dr. E. Cisbani
Introduction
The research activity proposed in present PhD thesis project is devoted to the
study of the structure of the proton. The first direct evidence that the proton
has an internal structure came from a measurement of its magnetic moment in
1933 by O. Stern. In the 1950s, a series of experiments led by R. Hofstadter at
SLAC (Stanford) using elastic electron scattering to explore nuclear structure,
measured for the first time the electric and magnetic form factors of the proton,
firmly establishing that the proton has an extended charge and magnetic distributions. In the late 1960s the first inclusive Deep Inelastic Scattering (DIS)
experiments were performed at SLAC with an electron beam. They showed
the scaling behavior of the structure functions for high momentum transfer Q2 ,
interpreted by Bjorken and Feynman as evidence of charged constituents inside
the proton. The DIS experiments allowed also the extraction of the unpolarized parton distribution functions (PDF)1 . Existence of the gluon (the gauge
bosons in Quantum Chromodynamics) in the nucleon has been observed at
DESY (Hamburg). Another remarkable discovery made at CERN by the EMC
Collaboration [1] showed that the total spin of the quarks contributes at most
by 25% to the spin of the nucleon (“spin crisis”); the nucleon spin SN can
be decomposed into three different components: SN = 21 ∆Σ + ∆G + Lz = 12 ,
where ∆Σ is the total spin of the quarks, ∆G the total spin of gluons, and Lz
the quarks and gluons orbital angular momentum. Recent measurements of ∆Σ
seem to indicate a contribution of order 30% (HERMES and COMPASS [2]).
While a vanishing value of ∆G has been measured, even if with low accuracy,
there is almost absolute ignorance on Lz .
In order to give more deep insights in the hadron structure, a new theoretical
framework, based on the so-called Generalized Parton Distributions (GPDs),
1 PDFs: the probability densities for finding a charge parton with given flavour, with a
certain fraction of the nucleon longitudinal momentum
1
has been introduced and developed in the last decade [3–6]. They are a generalization of the structure functions used to parametrize the hadronic tensor in
DIS, and allow a unified description of both elastic diffusion and DIS. Electric
and magnetic form factors can indeed be written as integrals over GPDs, while
PDFs can be recovered from GPDs in the ‘forward limit’2 . Therefore, a full
3-dimensional image of partons within hadrons can be obtained from GPDs,
which seem to be the most promising theoretical tool to determine the total angular momentum contribution of partons (quarks and gluons) to nucleon spin.
GPDs are observables difficult to be measured, and, at present, they are accessed through exclusive processes where all particles are detected in the final
state: therefore electromagnetic scattering is still a powerful technique suitable
for studying the nucleon structure.
Within such a scenario, Compton scattering with real photons (RCS) on the proton at high momentum transfers (Fig.1), is a very interesting method to study
the proton structure at short-distances, since the presence of two photons allows
one to access information not available from DIS and leastic electron scattering.
In particular, RCS, could shed light on the
GPDs. RCS is in an elegantly simple reaction,
involving only a real photon and ground-state
nucleon in both initial and final states, and,
as the elastic ep scattering, it characterizes the
electromagnetic response of the nucleon without complications from additional hadrons. In
the last twenty years, remarkable progress in the
experimental field has been achieved, with the
Figure 1: RCS (Real Compintroduction of polarized beams and targets in
ton scattering): a real photon
scattering experiments at increasingly higher luscatters on the proton.
minosity. Thomas Jefferson National Accelerator Facility (JLab) is one of the most advanced
laboratory for this kind of experiments, with an ongoing energy upgrade (to 12
GeV) of the electron (longitudinally polarized) beam, which will allow to carry
out experiments in larger phase-space with higher precision, and to measure
new observables. In this respect, a relevant program on precise and extended
investigation of the nucleon structure has been already approved. The upgraded
JLab will consist of four experimental Halls, with complementary facilities. RCS
experiments have been performed in Hall A and Hall C in the recent past [7, 8].
Those experiments are devoted to measure the components of the recoil proton
polarization in Real Compton Scattering (RCS) with longitudinally polarized
incident photons.
In this context, the aim of the present PhD project is twofold:
i) to carry out and to finalize the data analysis of the RCS experiment E07002 [8] dedicated to the study of the proton structure over a broader kinematic
range compared to E99-114 experiment [7];
ii) to contribute to new experimental proposals at the upgraded JLab for in2 By
setting to zero the ‘extra variables’ in the GPDs
2
vestigating the nucleon structure and to the development of charged particles
tracking detectors based on GEM (Gas Electron Multiplier, for position measurements) technologies.
Analysis of RCS experiment
Experimental Setup
The JLab RCS experiment E99-114 [7], demonstrated the feasibility of the experimental technique and produced remarkable results, that have driven to a
second experiment E07-002 in Hall C, whose setup is summarized in what follows
(cf. Fig.2):
- A photon beam, produced by bremsstrahlung of
a polarized electron beam crossing a 6% copper radiator, is scattered from a liquid hydrogen target,
transferring polarization to the recoiling protons.
These protons are detected in a high resolution
magnetic spectrometer, used to reconstruct their
kinematics, including their scattering angles, momenta, and position of the interaction vertex. A
focal plane polarimeter measures the polarization
of the recoiling protons by the azimuthal asymmetry in the angular distribution of protons scattered
in carbon based analyzers. The scattered photon
is detected in a large acceptance electromagnetic Figure 2: Experimental
calorimeter (hodoscope) [9]. Scattered electrons setup of HallC-RCS
can also reach the calorimeter and constitute one
of the main sources of background to discriminate.
The main goal of the RCS experiment is the measurement of the following
observables, sensitive to RCS form factors, and in turn, to GPDs:
(1) the cross section for RCS on the proton, for a given electron beam energy
and fixed scattering angles;
(2) the longitudinal and transverse polarization transfer asymmetries [10], KLL
and KLT .
The polarization transfer observables are defined by:
h
i
dσ(↓↑)
1 dσ(↑↑)
KLL dσ
=
−
dt
2h
dt
dt
i
dσ(↓→)
dσ
1 dσ(↑→)
KLT dt = 2
−
dt
dt
where the first arrow refers to the incident photon helicity and the second to the
recoil proton helicity (↑) or transverse polarization (→). Within the “handbag”
formalism [11, 12] (cf. Fig.3), it turns out that these polarization observables
are related to the RCS form factors (RV , RA , RT )3 . Moreover, it has been
3 V:
vector, A: axial-vector, T: tensor form factors
3
demonstrated that KLL is related to the ratio RA /RV (and therefore to the
PDF ratio ∆q a (x)/q a (x)), while KLT /KLL is related to RT /RV . It is worth of
mentioning that form factor RT is linked to J a , the total angular momentum of
a quark with flavor a, which cannot be directly measured in DIS experiments.
Analysis
For RCS, under the condition that all the Mandelstam variables s, −t and −u
are large enough in comparison with the proton mass (or, equivalently, when the
transverse momentum transfer p⊥ is large), the hard scale is achieved. Then,
the transition amplitude is expected to factorize into the convolution between
a perturbative hard scattering amplitude (which involves the coupling of the
external photons to the active quarks) and an overlap of initial and final soft
(non perturbative) wave functions (describing the coupling of the active quarks
to the proton). This can be written as:
Tif (s, t) = Ψf ⊗ K(s, t) ⊗ Ψi
where K(s, t) is the perturbative hard scattering amplitude, and the Ψ’s are the
soft wave functions. Different factorization schemes have been applied to RCS in
recent years: the “handbag mechanism” [11, 12] involves only one active quark
(cf. Fig.3), while the perturbative QCD (pQCD) mechanism [13–15] involves
all three constituents. At sufficiently high energy, the pQCD mechanism is
expected to dominate, but it is unclear how the transition to the purely pQCD
mechanism emerges.
By means of the measurements listed in (1) and
(2), one can test the existing theoretical descriptions and identify the dominant mechanism for
this process, as well as determine RCS form factors. In the JLab RCS experiment E99-114 [7]
at s=7 GeV 2 and θpcm = 120◦ , the longitudinal
polarization transfer KLL resulted in agreement
with the handbag description, but completely
inconsistent with the pQCD mechanism. Nevertheless, statistics are not yet sufficient to constrain the GPDs extracted from the handbag
model of RCS. Therefore there is large interest
in getting some additional information on the
Figure 3: The handbag (up)
behavior of the transfer polarization observables
and the 2-gluon exchange
in an exclusive reaction. In fact the KLL was
pQCD (down) diagrams for
measured at a single kinematic point [7], and
RCS.
thus the factorization regime might not have
been reached in this case. The additional data
of the Hall C experiment, will improve and extend over a broader kinematic
range the existing KLL measurement. This is the main task of the analysis,
carried out in this project. A byproduct of the analysis will be the measurement of the ratio of the transverse and longitudinal polarization components
4
of the elastic electron scattered proton, which is directly proportional to the
M
ratio of form factors GE
p /Gp [16] . The technicalities developed in this analysis
(polarized beam and polarization transfer), will open the possibility to participate in proposals of new experiments at 12 GeV, where measurements at higher
photon energy will be performed, allowing in this way to meet the factorization
condition.
Experimental preparation for 12 GeV
The 12 GeV experiments will benefit of the high intensity polarized electron
beam and thicker targets providing high luminosity up to few 1038 cm−2 s−1 .
New technologies must be developed to tackle the challenging backgrounds,
mostly of high energy photons, accounting for about 200 MHz/cm2 (in one of
the most demanding experiment), and about 150 kHz/cm2 for charged particles. Such a flux cannot be sustained by traditional tracking detectors, such as
drift chambers; in fact, the expected hits rate in a gaseous detector is about 550
kHz/cm2 (assuming few % photon efficiency and 100% for charged particles).
For this reason, GEM based trackers are under development for the new spectrometers that will operate in the high luminosity experiments at JLab. The
GEMs offer spatial resolution below 100 µm on large areas, with much more
affordable costs compared to other competing detectors, such as for instance
silicon microstrips.
Therefore, in parallel with the RCS analysis, from the third year it is expected
to be involved in characterization of GEMs for 12 GeV experiments and in the
development of a related tracking algorithm. GEMs will be installed in a new
spectrometer to track the particles, in order to measure angles and momenta,
and in the polarimeter, to replace wire chambers in the determination of the
azimuthal angular asymmetries. Clearly, in such a high luminosity (high background) environment, it is also crucial to have a ‘smart’ and efficient particle
tracking algorithm. During the PhD project diverse solutions can be explored,
such as Bayesian techniques, neural networks or Kalman filter.
References
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generalized parton distributions. Physics Reports, 418, 2005.
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