Sessions - DPG-Tagungen

Nuclear Physics Tuesday
And unlike to H(x, ξ, t) where at least the forward limit H(x, 0, 0) =
q(x) is known from inclusive measurements, the shape of E(x, ξ, t) could
not be determined up to now. Especially the second moment of this
function is of great interest since it is connected via Ji’s sum rule to the
angular momentum of quarks.
We discuss X. Ji’s sum rule and the form factor J(t) of the energymomentum
tensor that gives us information about the spacial distribution
of the quark angular momentum inside the nucleon. Both objects
are investigated in the framework of the Chiral Quark Soliton Model.
This model has successfully been used to describe many nucleonic properties,
like parton distributions and form factors.
HK 13.3 Tue 13:30 Foyer
Chiral Dynamics and Nuclear Matter — •Stefan Fritsch 1 , Norbert
Kaiser 1 , and Wolfram Weise 2,1 — 1 Physik Department der
Technischen Universität München, Garching, Germany — 2 ECT*, Villazzano
(Trento), Italy
We calculate the equation of state of isospin-symmetric nuclear matter
in the three-loop approximation of chiral perturbation theory. The
contributions to the energy per particle Ē(kf) from one- and two-pion exchange
diagrams are ordered in powers of the Fermi-momentum kf (modulo
functions of kf/mπ). Already at order O(k 4 f) two-pion exchange produces
realistic nuclear binding. Without inclusion of any further short-
range terms the empirical saturation point, nuclear compressibility and
) with a momen-
asymmetry energy are well reproduced at order O(k5 f
tum cut-off of Λ ≃ 0.65GeV. We also evaluate the momentum and density
dependent single particle potential of nucleons in isospin-symmetric
nuclear matter. Furthermore, we extend our scheme to finite temperatures
and observe the liquid–gas phase transition of nuclear matter at
Tc ≃ 25.5 MeV and ρc ≃ 0.5ρ0. In addition to that, we investigate the
influence of additional explicit short range NN-interaction terms on the
momentum dependence of the single particle potential and on the critical
temperature of the phase transition. The effects of higher order diagrams
with virtual ∆ excitations are also considered.
Work supported in part by BMBF, GSI and DFG.
HK 13.4 Tue 13:30 Foyer
Nuclear energy density functional from chiral pion-nucleon dynamics:
Isovector spin-orbit terms — •Norbert Kaiser — Physik
Department T39, Technische Universität München, D-85747 Garching,
Germany
We extend a recent calculation of the nuclear energy density functional
in the systematic framework of chiral perturbation theory by computing
the isovector spin-orbit terms: (�∇ρp − �∇ρn) · (�Jp − �Jn) Gso(kf) + (�Jp −
�Jn) 2 GJ(kf). The calculation includes the one-pion exchange Fock diagram
and the iterated one-pion exchange Hartree and Fock diagrams.
From these few leading order contributions in the small momentum expansion
one obtains already a good equation of state of isospin-symmetric
nuclear matter. We find that the parameterfree results for the (densitydependent)
strength functions Gso(kf) and GJ(kf) agree fairly well with
that of phenomenological Skyrme forces for densities ρ > ρ0/10. At very
low densities a strong variation of the strength functions Gso(kf) and
GJ(kf) with density sets in. This has to do with chiral singularities m −1
π
and the presence of two competing small mass scales kf and mπ. The
novel density dependencies of Gso(kf) and GJ(kf) as predicted by our
parameterfree (leading order) calculation should be examined in nuclear
structure calculations.
N. Kaiser, S. Fritsch, W. Weise, Nucl. Phys. A724 (2003) 47.
N. Kaiser, Phys. Rev. C68, 014323 (2003).
Work supported in part by BMBF, GSI and DFG.
HK 13.5 Tue 13:30 Foyer
Spectral functions of isoscalar scalar and isovector electromagnetic
form factors of the nucleon at two-loop order — •Norbert
Kaiser — Physik Department T39, Technische Universität München,
D-85747 Garching, Germany
We calculate the imaginary parts of the isoscalar scalar and isovector
electromagnetic form factors of the nucleon up to two-loop order in chiral
perturbation theory. Particular attention is paid on the correct behavior
of ImσN(t) and ImG V E,M (t) at the two-pion threshold t0 = 4m 2 π in
connection with the non-relativistic 1/M-expansion. We recover the wellknown
strong enhancement near threshold originating from the nearby
anomalous singularity at tc = 4m 2 π − m 4 π/M 2 = 3.98m 2 π. In the case
of the scalar spectral function ImσN(t) one finds a significant improvement
in comparison to the lowest order one-loop result. Higher order
ππ-rescattering effects are however still necessary to close a remaining
20%-gap to the empirical scalar spectral function. The isovector electric
and magnetic spectral functions ImG V E,M(t) get additionally enhanced
near threshold by the two-pion-loop contributions. After supplementing
their two-loop results by a phenomenological ρ-meson exchange term
one can reproduce the empirical isovector electric and magnetic spectral
functions fairly well.
N. Kaiser, Phys. Rev. C68, 025202 (2003).
Work supported in part by BMBF, GSI and DFG.
HK 13.6 Tue 13:30 Foyer
The anomalous decays η/η ′ → π + π − γ — •Robin Nißler and
Bu¯gra Borasoy — Institute for Theoretical Physics (T39), TU
München, Germany
The axial anomaly of QCD dominates various low-energy processes involving
light mesons. Interesting examples for such anomalous processes
are the decays of η and η ′ into π + π − γ, since they reveal information
on both the chiral and the axial U(1) anomaly and, furthermore, yield
constraints for η-η ′ mixing.
The shape of the photon spectra in these decays cannot be understood
without considering resonances. We show the results of a calculation
within a chiral effective field theory including dynamically generated resonances
[1]. Financial support of the Deutsche Forschungsgemeinschaft
is gratefully acknowledged.
[1] B. Borasoy and R. Nißler, in preparation
HK 13.7 Tue 13:30 Foyer
η − η ′ mixing in Lage NC ChPT — •E. Lipartia and B. Borasoy
— Institute for Theoretical Physics (T39), TU München, Germany
We critically investigate the η −η ′ mixing up to one-loop order in large
NC Chiral Perturbation Theory . It is demostrated that it provides a consistency
check for large NC Chiral Perturbation Theory. Work supported
by Deutsche Forschungsgemeinschaft.
[1] B. Borasoy, E. Lipartia,
In preparation.
HK 13.8 Tue 13:30 Foyer
Isospin breaking and nucleon structure — •Tobias Gail and
Thomas R. Hemmert — Physik Department Technische Universität
München
We study the three vector and three axial vector weak form factors of
the nucleon including isospin breaking effects in the pion and nucleon sector,
using both the heavy baryon and the relativistic approach of SU(2)
chiral perturbation theory to O(p 3 ). Two of these form factors have not
been considered previously in these frameworks, since they parametrize
second class currents, currents of unnatural G-parity. We discuss the implications
of isospin breaking on low energy neutrino nucleon scattering
and ordinary muon capture. Consequences of isospin violation for the
unitarity of the CKM matrix are also discussed.
This work has been supported in part by BMBF, DFG and GSI.
HK 13.9 Tue 13:30 Foyer
Spectrum and decays of the kaonic hydrogen — •Udit Raha 1 ,
Ulf-G. Meissner 1,2 , and Akaki Rusetsky 1 — 1 HISKP (Th), Universität
Bonn, Bonn, Germany — 2 IKP (Th), FZ Jülich, Jülich, Germany
Recent accurate measurements of the strong energy shift and the lifetime
of the ground state of kaonic hydrogen by DEAR collaboration at
LNF-INFN[1] allow one to extract the precise values of the KN scattering
lengths from the data. To this end, one needs to relate the latter
quantities to the observables of the kaonic hydrogen at the accuracy that
matches the experimental precision. In our recent investigations[2], the
problem is considered within the non-relativistic effective Lagrangian approach,
which has been previously used to describe the bound π + π − and
π − p systems. We obtain a general expression of the strong shift of the
level energy and the decay width in terms of the KN scattering lengths,
at O(α, md − mu) as compared to the leading-order result. It is shown
that, due to the presence of the unitarity cusp in the K − p elastic scattering
amplitude above threshold, the isospin-breaking corrections turn
out to be very large. This, however, does not affect the accuracy of the
extraction of the scattering lengths from the experiment.
[1] Michael Cargnelli et al. (DEAR Collaboration), in proceedings of the
4th International Workshop on CHIRAL DYNAMICS 2003 (Theory and