Isoscalar Meson Exchange Currents and the Deuteron Form Factors Page: 4 of 7
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
Hummel and Tjon [14], the large Q2 dependence of these form factors may be sen-
sitive to these exchange currents, and it is this sensitivity which will be examined
in this letter.
The differential cross section for the scattering of unpolarized electrons from
deuterium can be written
d = -Mott (fE) A(Q2) + B(Q2) tan2 (1)
where 0Mott is the Mott cross section, E and E' are the incident and final electron
energies, 0 is the electron scattering angle, and A(Q2) and B(Q2) are structure
functions related to the squares of the deuteron form factors. At high momentum
transfers previous calculations of the RIA have underestimated A(Q2) by an or-
der of magnitude at Q2 = 4 GeV2/c2 and also have failed to predict the correct
location for the dip in B(Q2), as shown in Fig. 2. Because the MEC contribu-
tions provide a mechanism for sharing the incoming photon momentum equally
between the two nucleons, they are expected to dominate at large momentum
transfers [11-13], and recently Rummel and Tjon [14] used isoscalar meson ex-
change currents derived from the pry and way vertices to resolve the discrepancy
at high Q2. However, the size of these contributions depends critically on the
Q2 dependence of the form factors associated with the pry and way vertices; if
no form factors are used (for example) the result from the pry exchange current
alone would overestimate A(Q2) by two order of magnitudes (Fig. 2a). In order
to predict the high Q2 dependence of the deuteron structure functions we must
have a reliable estimate of the Q2 dependence of the form factors at the pry and
way vertices, and such an estimate should take into account the composite nature
of the r, a, p, and w mesons. In this letter we calculate these form factors from
quark loop diagrams which include the qq composite structure of the r, a, p, and
w mesons, and discuss the implications of our results for the MEC contributions
to the deuteron form factors.
In their calculation, Hummel and Tjon used a simple monopole form factor
. =m,/(mw + Q2) where mo, is the mass of the w meson. Such a
form factor is justified by the vector meson dominance (VMD) hypothesis. The
applicability of VMD is a controversial topic in particle physics and using it to
estimate the pry form factor is particularly questionable if the photon momentum
is large and space-like. Though it may work well at low Q2, it is expected to
deviate at high Q2. Using asymptotic power counting based on perturbative
QCD, Chernyak and Zhitnitsky [15] have shown that the f,,7(Q2) -4, where
the extra power in the fall off (the typical asymptotic meson form factor is -~ Q-2)
is due to the helicity flip of a quark. Apparently, at some momentum scale, the
form factor must start to deviate from the monopole function. Our estimates,based on a quark loop calculation which takes the structure of the mesons in
account, give a similar result.
To calculate the form factor at the pry vertex we use a relativistic quark model
of the pion and the rho which was previously used to calculate a variety of pion
observables [16]. In this model the Betie-Salpeter vertex function for the pibI
is taken to be I'(k,p)= N "y5yx D (k2), where k and p are the relative and
total four momenta of qq pair which couple to the pion, Ds(k2) = k2 - A2 with
A an adjustable parameter, Xc = I/v i the color wave function, and 1f = r+
the flavor wave function of the ir+. The function US '(k2) is a parameterization
of the momentum distribution of the qq pair in the pion. The normalization
constant, N., is fixed by the requirement that the charge form factor of pion,
F~(Q2), be normalized to Fx(0) = 1. In Ref. [16] the form factor and low-energy
observables of the pion were very well reproduced by choosing the quark mass
mq = 248 MeV and A = 450 MeV. This model also successfully described the
Q2 dependence of both the pion form factor and the form factor in 7* + r1 - 7
process [17], which has been recently measured at space-like virtual photon (7*)
momenta in the range Q2 = 1 - 3 GeV2/c2 [18]. For the p meson vertex we
choose the form 1p(k, p) = NG"(p)xY xeDy'(k2), where G"(p) = [7"- /pv/p2],
and the normalization constant, , , is calculated from the residue of the qj
scattering amplitude in the vector channel [16]. A dipole momentum distribution
Dv(k2) (k2_ Ai)(k2 -A) - k4 was chosen in order to insure that the integrals
involving the rho converge. Using the same quark mass, the choice At -. 6{){1
MeV and A2 ~i 1000 MeV fits the empirical values of the yp coupling and the
rho width. In this calculation, in order to avoid threshold singularities, we found
it convenient to use a larger quark mass of ma ~ 390 MeV > mn,/2. Using this
larger quark mass changes the fitted observables by only about 25%, which is
sufficiently close for our estimates.
Now we use this model to calculate the pry vertex, which is defined by [12],(p(P2)J Ir(pi)) = g(Q2),r/ploqr , E
(2)
where the antisymmetric tensor er"gp assures electromagnetic gauge invariance, q
2n _.2) in the fnur rnnmnentium ofthe virtual nhntnn a _nd _ is the nnlariva irn
vector of the p meson. The dependence on the momentum of photon is expressed
by Q(QZ) = -i-g-,y fpxy(Q), where the form factor f,T(Q2) is normalized tL
unity at Q2 = 0 and Ppr, is the coupling constant. We calculated the product of
this form factor and the coupling constant from the quark loop diagram shown
im Figlc, which gives6
7
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Gross, Franz & Gross, Franz. Isoscalar Meson Exchange Currents and the Deuteron Form Factors, article, April 1, 1993; [Newport News, Virginia]. (https://digital.library.unt.edu/ark:/67531/metadc928481/m1/4/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.