Il Nuovo Cimento A (1965-1970)

, Volume 70, Issue 4, pp 525–541 | Cite as

Scaling laws in high-energy neutrino reactions

  • P. V. Landshoff


Bjorken has proposed that the structure functionsF1,F2,F3 of deep inelastic neutrino scattering are functions of ω=−2Mν/q2 only. These scaling laws are studied in Veneziano-like models and are found to emerge naturally for the scattering of neutrinos on a neutron or of antineutrinos on a proton, together with the Callan-Gross sum rule for\(\int\limits_1^\infty d \omega F_2 /\omega ^2 \), the Gross-Llewellyn Smith sum rule for\(\int\limits_1^\infty d \omega F_3 /\omega ^2 \) and the relationF1=1/2ωF2. (It is assumed that certain equal-time commutators of currents contain no operator Schwinger terms). The models suggest the possibility that the structure functions for the scattering of neutrinos on a proton, or of antineutrinos on a neutron, are small in the deep inelastic limit.


Axial Current Current Conservation Condition Deep Inelastic Neutrino Scattering Deep Inelastic Electron Scattering Deep Inelastic Region 
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Законы подобия в нейтринных реакциях при высоких энергиях


Бьёркен предположил, что структурные функцииF1,F2,F3 для сильно неупругого нейтринного рассеяния являются функциями только ω=−2Mν/q2. Исследуются эти законы подобия в моделях, подобных модели Венециано, и получается, что они возникают естественно для рассеяния нейтрино на протоне или антинейтрино на протоне, вместе с правилом сумм Челлена-Гросса для\(\int\limits_1^\infty d \omega F_2 /\omega ^2 \), с правилом сумм Гросса-Левеллина-Смита для\(\int\limits_1^\infty d \omega F_3 /\omega ^2 \) и соотношениемF1=1/2ωF2. (Предполагается, что некоторые равно-временные коммутаторы токов не содержат операторных швингеровских членов.) Эти модели дают возможность предположить, что структурные функции для рассеяния нейтрино на протоне или антинейтрино на нейтроне являются малыми в сильно неупругом пределе.


Bjorken ha avanzato l’ipotesi che le funzioni di strutturaF1,F2,F3 dello scattering profondamente anelastico del neutrino siano funzioni di ω=−2Mν/q2 soltanto. Queste leggi sono studiate in modelli simili a quello di Veneziano ed emergono in modo naturale per lo scattering dei neutrini su un neutrone o degli antineutrini su un protone, assieme alla regola di somma di Callan-Gross per\(\int\limits_1^\infty d \omega F_2 /\omega ^2 \), alla regola di somma di Gross-Llewelyn-Smith per\(\int\limits_1^\infty d \omega F_2 /\omega ^2 \) e alla relazioneF1=1/2ωF2. (Si suppone che alcuni commutatori di «ugual tempo» di correnti non contengano termini di Schwinger.) I modelli suggeriscono la possibilità che le funzioni di struttura per lo scattering di neutroni su un protone o di antineutrini su un neutrone siano piccole nel limite di profonda anelasticità.


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Copyright information

© Società Italiana di Fisica 1970

Authors and Affiliations

  • P. V. Landshoff
    • 1
  1. 1.CERNGeneva

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