The X(3872) boson: Molecule or charmonium Page: 4 of 23
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:
D
>7t
D D*
FIG. 1. The r-exchange in the scattering DD* - D*D. The intermediate state at the hori-
zontal dotted line occurs on mass shell for 7r0 exchange.
of this paper we shall write DD* + DD* simply as DD* unless it may cause a confusion.
The potential is extracted from the Born amplitude near the threshold:
2
where q is the pion momentum, and E and E' are the polarizations of D*O and D*O, respec-
tively. It is important to notice here a peculiarity of kinematics in the pion propagator.
Since the decay D*" - D1r0 actually occurs with a tiny Q-value, the denominator of the
propagator is practically zero as compared with m,. in the nonrelativistic limit;
2 2 2
m-q2_2 m- mD* -mD+8mD* 8mD)+'
\ )4mDmD* m )' (3)
where A = mD* - mD - m,- is very small (~ 7 MeV). Let us denote the static limit of the
denominator by
p2 = 2m,0(~ 0.IM2). (4)
With the two powers of q from the derivative DD*r coupling in the numerator, the Born
amplitude TB survives only at q2 2m, A and varies slowly there. The Fourier transform
of TB gives the one-pion exchange potential. Since D*O - DOO can occur on mass shell,
the principal part of the pion denominator is relevant to the potential:
4mDmD*V(r) = ReTB (q)eiq r 3 q
g2eiqr d3q
J (E * ' q)(E - q) 2 - q2 (27)3
2 _ 2 (22)
~v - 1g2 (E'* -E)6(r) + g2(E'* -)(E - ) 2 cos pr
3 4rr r
+ (*)(s r sin r .
2 r ( ( )E ) 3+ r 54
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.
Suzuki, Mahiko. The X(3872) boson: Molecule or charmonium, article, August 1, 2005; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc875479/m1/4/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.