6,410 research outputs found
Optimization of ultrafine entanglement witnesses
The ultrafine entanglement witness, introduced in [F. Shahandeh, M.
Ringbauer, J.C. Loredo, and T.C. Ralph, Phys. Rev. Lett. \textbf{118}, 110502
(2017)], can seamlessly and easily improve any standard entanglement witness.
In this paper, by combining the constraint and the test operators, we rotate
the hyperplane determined by the test operator and improve further the original
ultrafine entanglement witness. In particular, we present a series of new
ultrafine entanglement witnesses, which not only can detect entangled states
that the original ultrafine entanglement witnesses cannot detect, but also have
the merits that the original ultrafine entanglement witnesses have.Comment: 8 page
Joint resummation for pion wave function and pion transition form factor
We construct an evolution equation for the pion wave function in the
factorization theorem, whose solution sums the mixed logarithm
to all orders, with () being a parton momentum fraction (transverse
momentum). This joint resummation induces strong suppression of the pion wave
function in the small and large regions, being the impact parameter
conjugate to , and improves the applicability of perturbative QCD to hard
exclusive processes. The above effect is similar to those from the conventional
threshold resummation for the double logarithm and the conventional
resummation for . Combining the evolution equation for the
hard kernel, we are able to organize all large logarithms in the scattering, and to establish a scheme-independent
factorization formula. It will be shown that the significance of
next-to-leading-order contributions and saturation behaviors of this process at
high energy differ from those under the conventional resummations. It implies
that QCD logarithmic corrections to a process must be handled appropriately,
before its data are used to extract a hadron wave function. Our predictions for
the involved pion transition form factor, derived under the joint resummation
and the input of a non-asymptotic pion wave function with the second Gegenbauer
moment , match reasonably well the CLEO, BaBar, and Belle data.Comment: 31 pages, 7 figure
- …