Hélicité (physique des particules)

Pour les articles homonymes, voir Hélicité.

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Schéma de l'hélice. (R) droitier, (L) gaucher

En physique des particules, l'hélicité $h$ est la projection du spin ${\vec {S}}$ sur la direction de la quantité de mouvement ${\vec {p}}$ (cette projection correspond donc à la composante suivant la direction de propagation) :

h={\vec {S}}\cdot {\hat {p}},\qquad {\hat {p}}={\frac {\vec {p}}{\left|{\vec {p}}\right|}}

étant la direction de

{\vec {p}}

Si $h>0$ , on dira d'une particule que son hélicité est droite (positive) selon que son spin est orienté dans le même sens que son mouvement.
Si $h<0$ , on dira d'une particule que son hélicité est gauche (négative) selon que son spin est orienté dans le sens opposé à son mouvement.

Ainsi par exemple, il semble bien que tous les neutrinos aient une hélicité gauche, et que les antineutrinos aient une hélicité droite.

Cas général

De façon plus générale, l'hélicité d'une particule correspond à la projection de son moment cinétique total ${\vec {J}}$ , c'est-à-dire la somme de son moment cinétique orbital ${\vec {L}}$ et de son moment cinétique intrinsèque (ou spin) ${\vec {S}}$ , sur la direction de sa quantité de mouvement :

h={\vec {J}}\cdot {\hat {p}}={\vec {L}}\cdot {\hat {p}}+{\vec {S}}\cdot {\hat {p}}

Cependant, puisque le moment cinétique orbital ${\vec {L}}$ est relié au vecteur position ${\vec {r}}$ de la particule et à sa quantité de mouvement ${\vec {p}}$ par la relation suivante :

{\vec {L}}={\vec {r}}\wedge {\vec {p}}

les vecteurs ${\vec {L}}$ et ${\vec {p}}$ sont perpendiculaires entre eux, de sorte que ${\vec {L}}\cdot {\hat {p}}=0$

Propriétés

L'hélicité est constitutive de la nature de la particule (comme la masse). Il s'agit d'un nombre quantique conservé.

Si une particule n'a pas de masse alors son hélicité est un invariant de Lorentz.

Puisque les valeurs propres du spin selon un axe sont discrètes, les valeurs propres de l'hélicité sont aussi discrètes. Pour une particule de spin S, les valeurs propres de l'hélicité sont S, S − 1 ..., −S ^{[citation nécessaire]}. L'hélicité du spin d'une particule va donc de −S à +S.

Notes et références

(en) Cet article est partiellement ou en totalité issu de l’article de Wikipédia en anglais intitulé « Helicity (particle physics) » (voir la liste des auteurs).

[Taillet, Villain et Febvre 2018] Richard Taillet, Loïc Villain et Pascal Febvre, Dictionnaire de physique, Louvain-la-Neuve, De Boeck Supérieur, hors coll., janvier 2018, 4^e éd. (1^re éd. mai 2008), X-956 p., 24 cm (EAN 9782807307445, OCLC 1022951339, SUDOC 224228161, présentation en ligne, lire en ligne), s.v.hélicité, p. 360-361.

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