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Current Landscape of Tensor Observables
Quasi-Elastic Tensor Asymmetry Azz

The goal of the C1-approved Jefferson Lab experiment C12-15-005 [1] is to measure tensor asymmetry Azz in the quasi-elastic and elastic regions using the same equipment as the b1 experiment. Tensor polarization enhances sensitivity to short-range QCD effects, which provide important insight to the deuteron wave-function [2]. Knowing the properties of the deuteron's nucleon-nucleon potential is essential for understanding short-range correlations as they are expected to be largely dependent on the tensor force [3]. In the quasi-elastic region, Azz provides a unique tool to experimentally constrain the ratio of the S- and D-state wave-functions at large momentum [4], which has been an ongoing theoretical issue for decades.

First calculated in 1980's [4], Azz was recently revisited using modern relativistic virtual-nucleon and light-cone methods, which are used in understanding short range correlations [5,6] and predict differences up to a factor of two in Azz that can be distinguished experimentally [1,7]. Additionally, the calculations were done using multiple wave-functions that diverge at large x, making Azz an ideal observable for providing insight into the decades-old question of whether the deuteron wave-function is hard or soft. This is only possible with a tensor-polarized target, as experiments using an unpolarized or vector polarized target are not capable of producing the statistics needed within a reasonable time-frame. The JLab PAC theory review has stated that this experiment "would further explore the nature of short-range pn correlations in nuclei, the discovery of which has been one of the most important results of the JLab 6 GeV nuclear program."

Prof. Elena Long is the lead Spokesperson for this C1-approved measurement that received a high A- physics rating from the Jefferson Lab Program Advisory Committee. It will be the first measurement of the quasi-elastic tensor asymmetry Azz and requires the same tensor polarized target and experimental equipment as the b1 [8] experiment described below and is an order-of-magnitude less sensitive to systematic uncertainties than b1 due to the much larger amplitude expected for the quasi-elastic Azz observable.

Projected statistical and systematic uncertainties for Azz are shown alongside modern relativistic calculations, and calculations with on- and off-shell effects. This plot is normalized to the light cone Azz calculation using the AV-18 potential [7] to emphasize how projected uncertainties compare between models.

World data on the unpolarized deuteron form factors A and [9].

Projected uncertainties for the elastic tensor analyzing power T20 are shown alongside the world data [9]. The point shown in blue, measured at Q  = 0.2 GeV   where T20 is well known theoretically and experimentally, will be used as a calibration for Pzz, and can potentially be used to further reduce the leading systematic uncertainty as indicated by the blue-dashed band.



Elastic Tensor Analyzing Power T20

The elastic cross section of the deuteron is described by the charge (GC), magnetic (GM), and quadrupole (GQ) form factors. In order to access all three form factors, measurements are needed for both polarized and unpolarized cross sections. In the unpolarized case, the cross section is determined by

where A and B are related to the charge, magnetic, and quadrupole form factors by

where                       . The A and B form factors have been measured to high precision by many experiments.

In order to separate out all three form factors, a measurement of the tensor analyzing powers is also needed. Although a number of tensor analyzing powers are available, T20 has proven to be the most informative and has been studied more in depth than the others. This analyzing power is defined by

and can be measured by knowing either the initial or final polarization state. With measurements of A, B, and T20, each of the three deuteron form factors can be extracted.

As shown, the world data for T20 is far less well-measured than A and B. There are systematic discrepancies present between the different datasets, with measurements from JLab coming out less negative than those from Bates and VEPP-3 at higher Q   > 0.5 GeV  , which affects model calculations particularly for determining GC [10]. Additionally, only a single experiment has been done for large Q   > 1 GeV   [11], and more data is needed in order to confirm our present understanding of T20.





An ideal measurement of T20 would be taken over a large range of Q  , which could use the lower Q   < 0.4 GeV   results to make sure that systematic uncertainties are well understood while simultaneously measuring the region of current discrepancies (Q   ~ 0.75 GeV  ) and extending to larger four-momentum transfer to confirm the single measurement taken at Q   > 1 GeV  . Such measurements will be done parasitically in C12-15-005 [1] by utilizing the same time-frame, kinematics, and equipment that will be used to determine Azz.








This experiment will measure the tensor analyzing power T20 over the largest Q   range ever done in a single experiment, providing valuable confirmation of the only measurement that currently exists at high Q  . In addition, it allows us to address one of the leading uncertainties that will effect all tensor polarized deuterium experiments: the absolute knowledge of the tensor polarization. We have found that by using the elastic reaction at low Q  , we can normalize our target's degree of polarization to the high-precision low Q   NIKHEF T20 measurement. The NIKHEF tensor polarization was created with an atomic beam source and they were able to measure the polarization of the gas with both a Breit-Rabi polarimeter as well as an ion-extraction polarimeter [12].





Deep-Inelastic Tensor Structure Function b1

The C1-approved experiment C12-13-011 [8] will measure the deuteron structure function b1 in Jefferson Lab's experimental Hall C. Tensor-polarized spin-1 systems have four structure functions that are inaccessible in other nuclear configurations. The leading twist tensor structure function, b1, provides a unique probe of partonic effects. If the deuteron was a simple combination of a proton and neutron, b1 would be zero. Additionally, b1 is defined as the momentum distribution of quarks dependent on the polarization of the deuteron. This makes the observable unique in that it directly probes nuclear effects at the quark level.

All conventional nuclear physics models, which include nuclear effects beyond a free proton and neutron, predict b1 to be very small (<10   ). However, a measurement from HERMES [13] showed a large negative value, although with large uncertainty, that can only be explained by exotic nuclear properties such as 6-quark, hidden color effects [14]. Additionally, b1 is sensitive to effects in the quark sea, and a recent model finds that a large polarization in sea anti-quarks fits the HERMES data better than without polarization [15]. This could provide an extremely valuable tool in solving the spin crisis, as only ~33% of the nucleons' spin is currently accounted for [16].


This C1-approved Jefferson Lab experiment with a high A- physics rating [8] will greatly reduce the uncertainty in b1 as well as map out an expected sign change. The approval is conditional upon the development of a high-luminosity target that achieves >30% tensor polarization. 


Projected statistical and systematic uncertainties for b1 are shown alongside world data, conventional nuclear physics models, and recent 6-quark hidden color models.

Future Landscape of Tensor Observables

[1] = Long:azz

[2] = Forest:1996kp

[3] = Arrington:2011xs

[4] = Frankfurt:1988nt

[5] = Arrington:1998ps

[6] = Fomin:2011ng

[7] = Sargsian:2014fla

[8] = Slifer:b1

[9] = Holt:2012gg

[10] = Gilman:2001yh

[11] = Abbott:2000fg

[12] = Bouwhuis:1998re

[13] = Airapetian:2005cb

[14] = Miller:2013hla

[15] = Kumano:2010vz

[16] = Myhrer:2009uq

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