Joint thrust and TMD resummation in electron-positron and electron-proton collisions

We present the framework for obtaining precise predictions for the transverse momentum of hadrons with respect to the thrust axis in e+e− collisions. This will enable a precise extraction of transverse momentum dependent (TMD) fragmentation functions from a recent measurement by the Belle Collaboration. Our analysis takes into account, for the first time, the nontrivial interplay between the hadron transverse momentum and the cut on the thrust event shape. To this end, we identify three different kinematic regions, derive the corresponding factorization theorems within Soft Collinear Effective Theory, and present all ingredients needed for the joint resummation of the transverse momentum and thrust spectrum at NNLL accuracy. One kinematic region can give rise to non-global logarithms (NGLs), and we describe how to include the leading NGLs. We also discuss alternative measurements in e+e− collisions that can be used to access the TMD fragmentation function. Finally, by using crossing symmetry, we obtain a new way to constrain TMD parton distributions, by measuring the displacement of the thrust axis in ep collisions.

QCD resummation on single hadron transverse momentum distribution with the thrust axis

We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution (jT) for the single hadron production with the thrust axis in an electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit jT « Q, and joint transverse momentum and threshold limit jT « Q(1 − zh) « Q, where Q and zh are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms ln(Q/jT) and ln(1 − zh) to all orders. In the end, we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration.

Finite Element Analysis of Side-Load Springs for McPherson Front Suspensions

In the present work, the operating conditions of “side-load” springs, which are typically employed in McPherson suspensions, were analysed by finite element analysis. The finite element model, including the spring and the upper and lower spring seats, is firstly described in the paper; the spring geometry was accurately obtained by a reverse engineering procedure based on two video cameras and a video projector. Surface to surface contact elements were defined between spring and seats; the initial assembling phase of the spring between the seats was also included in the finite element analysis. The experimental rig, employed for spring characterisation, and the performed numerical analyses are then presented; results are discussed in comparison with experimental data, in terms of spring characteristic, side-load force and thrust axis spatial position, as a function of spring compression. A fully satisfactory agreement was generally observed between numerical results and experiments. The effect of lower spring seat orientation on results was also investigated by numerical analysis. A higher inclination of the lower seat appeared to increase the side-load force; at the same time, for a given configuration, the thrust axis orientation, remained almost constant during suspension compression.