Thrust

The Thrust (Engl. Thrust ) is a size in the particle physics . It is a parameter used to describe particle jets that arise during particle collisions in particle accelerators . The thrust can assume values ​​between and . ${\displaystyle 1/2}$ ${\displaystyle 1}$

The thrust of an event is defined as: ${\displaystyle T}$

${\displaystyle T=\max _{\vec {n}}{\frac {\sum _{j}|{\vec {p}}_{j}\cdot {\vec {n}}|}{\sum _{j}|{\vec {p}}_{j}|}}}$

Here, the pulses of the particles and a normalized vector to one . The one that maximizes the thrust is called the thrust axis . ${\displaystyle {\vec {p}}_{j}}$ ${\displaystyle {\vec {n}}}$ ${\displaystyle |{\vec {n}}|=1}$ ${\displaystyle {\vec {n}}}$ ${\displaystyle {\vec {n}}_{T}}$

A thrust of implies a spherical distribution of the particle momentum, while a thrust of two pen-like particle jets indicates. ${\displaystyle T\approx 1/2}$ ${\displaystyle T\approx 1}$

Connection with other quantities

The Thrust Major is defined as ${\displaystyle T_{\text{Ma}}}$

${\displaystyle T_{\text{Ma}}=\max _{{\vec {n}}_{\text{Ma}}\cdot {\vec {n}}_{T}=0}{\frac {\sum _{j}|{\vec {p}}_{j}\cdot {\vec {n}}_{\text{Ma}}|}{\sum _{j}|{\vec {p}}_{j}|}}}$

The axis of the thrust major is perpendicular to the thrust axis.

The Thrust Minor is defined as ${\displaystyle T_{\text{Mi}}}$

${\displaystyle T_{\text{Mi}}={\frac {\sum _{j}|{\vec {p}}_{j}\cdot ({\vec {n}}_{T}\times {\vec {n}}_{\text{Ma}})|}{\sum _{j}|{\vec {p}}_{j}|}}}$

The axes of Thrust Minor, Thrust Major and Thrust are thus perpendicular to each other. It always applies . ${\displaystyle T\geq T_{\text{Ma}}\geq T_{\text{Mi}}}$

The oblateness (engl. Flattening ) is the difference between Thrust Major and Minor Thrust: ${\displaystyle O}$

${\displaystyle O=T_{\text{Ma}}-T_{\text{Mi}}}$

literature

• Yorikiyo Nagashima: Elementary Particle Physics: Foundations of the Standard Model . Wiley-VCH, Weinheim 2013, ISBN 978-3-527-40966-2 .
• Matthew D. Schwartz: Quantum Field Theory and the Standard Model . Cambridge University Press, New York 2014, ISBN 978-1-107-03473-0 .