Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof

In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with the XXZ spin-$\frac12$ chain on the segment with two generic integrable boundaries acting on the Bethe vector. The essential step is to prove that the expression of the action of a modified creation operator on the Bethe vector has an off-shell structure which results in an inhomogeneous term in the eigenvalues and Bethe equations of the corresponding transfer matrix.Comment: V2 published version, 16 page

The average longitudinal air shower profile: exploring the shape information

The shape of the extensive air shower (EAS) longitudinal profile contains information about the nature of the primary cosmic ray. However, with the current detection capabilities, the assessment of this quantity in an event-by-event basis is still very challenging. In this work we show that the average longitudinal profile can be used to characterise the average behaviour of high energy cosmic rays. Using the concept of universal shower profile it is possible to describe the shape of the average profile in terms of two variables, which can be already measured by the current experiments. These variables present sensitivity to both average primary mass composition and to hadronic interaction properties in shower development. We demonstrate that the shape of the average muon production depth profile can be explored in the same way as the electromagnetic profile having a higher power of discrimination for the state of the art hadronic interaction models. The combination of the shape variables of both profiles provides a new powerful test to the existing hadronic interaction models, and may also provide important hints about multi-particle production at the highest energies.Peer Reviewe

The muonic longitudinal shower profiles at production

In this paper the longitudinal profile of muon production along the shower axis is studied. The characteristics of this distribution is investigated for different primary masses, zenith angles, primary energies, and different high energy hadronic models. It is found that the shape of this distribution displays universal features similarly to what is known for the electromagnetic profile. The relation between the muon production distribution and the longitudinal electromagnetic evolution is also discussed