Speaker
Noriyoshi Ishii
(University of Tokyo)
Description
We propose a new method to calculate scattering amplitudes above
inelastic thresholds as an extention to the Luescher's finite volume
method for elastic scattering phase shifts.
In the inifinite volume, the asymptotic form of hadronic
Bethe-Salpeter (BS) wave functions at spatial infinity can be derived
in exactly the same manner as given in Ref.[1,2,3]. It contains the
information of the T-matrix of QCD in quite analogous way as the
scattering theory of quantum mechanics. We introduce an
energy-independent generally non-local coupled-channel interaction
kernel so that it can simultaneously generate BS wave functions in
wide range of energy region with an effective Schroedinger equation
(coupled channel version). Note that this interaction kernel can
generate T-matrix of QCD by construction.
In a finite volume, scattering spectrum is discretized. Each state
obtained in a finite volume system corresponds to a particular linear
combination of multiple incomming states in the infinite volume. To
calculate T-matrix above inelastic thresholds, we need states with
different linear combinations at the same energy. However,
corresponding states are located at different energies due to the
discretized spectrum, which is the reason why the standard Luescher's
method is usually restricted to the elastic region.
Our plan is to avoid this difficulty by using the interaction kernel
introduced above. We first construct the interaction kernel in a
finite volume, and then use it to generate BS wave function in the
infinite volume. Note that the energy independent interaction kernel
is constructed by using BS wave functions from multiple energies, by
which the states with different linear combinations of incomming
states can be taken into account. For an interaction with finite
range, the interaction kernel constructed in a finite volume is
insensitive to the spatial size. (as long as the spatial size is
sufficiently large) This implies that, once such interaction kernel is
constructed, it can be used to generate BS wave functions at arbitrary
spatial volume, which enables us to access the S-matrix of QCD in the
inifinite volume.
We will also discuss possible applications.
Reference:
[1] C.-J.D.Lin, G.Martinelli, C.T.Sachrajda, M.Testa,
Nucl.Phys.B619(2001)467.
[2] S.Aoki et al., CP-PACS Coll., Phys.Rev.D71(2005)094504.
[3] S.Aoki, T.Hatsuda, N.Ishii., Prog.Theor.Phys.123(2010)89.
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Primary author
Noriyoshi Ishii
(University of Tokyo)
