Impact of nuclear spallation process to the Big-Bang nucleosynthesis induced by long lived charged particle Kenichi Sugai (Saitama University) Collaborators Masafumi Koike, Joe Sato,Toshifumi Jittoh (Saitama University) Kazunori Kohri (Tohoku University) Koichi Yazaki (YITP, RIKEN) Masato Yamanaka (ICRR University of Tokyo) Saturday, February, 20,2010;KEK

Contents Introduction Nuclear spallation process of 4 He Summary

Introduction

The Premordial Lithium Problem

New Destruction process of the Lithium 7 Be ( 7 Li) 7 Li ( 7 He) Bound State Model MSSM LSP: Neutralino,NLSP: Stau Long-lived stau due to quasi- degenerate stau-neutralino Internal Conversion Jittoh et al., PRD (2007, 2008)

New Destruction process of the Lithium Over production of 6 Li Model MSSM LSP: Neutralino,NLSP: Stau Long-lived stau due to quasi- degenerate stau-neutralino Internal Conversion Jittoh et al., PRD (2007, 2008) Excessive 6 Li: Catalyzed Fusion Presence of staus enhances the cross section by 10 8 (Pospelov, PRL (2007))

Competing against the Catalyzed Fusion Overproduction of 6 Li due to catalyzed fusion Overproduction of 6 Li Competing process: Nuclear spallation etc. Over production of 6 Li

Competing against the Catalyzed Fusion Competing process: Nuclear spallation etc. Overproduction of 6 Li due to catalyzed fusion Recovery ?

Nuclear Spallation Proceeds Rapidly Catalyzed fusion K.Hamaguchi et al.,PLB650, 268 (2007) at T = 50 keV n( 4 He-stau) > n( 6 Li) at T~(50-100) keV

Nuclear Spallation Proceeds Rapidly Internal conversion, as a reference to the spallation T.Jittoh et al.,Phys.Rev.D78, (2007) Time Scale of Internal Conversion 7 Be ( 7 Li) 7 Li ( 7 He) Bound State << Spallation would outnumber Catalyzed Fusion Stau can’t survive until the BBN era

Motivation Nuclear spallation will dominate catalyzed fusion!! We investigate the spallation processes Applying the result for the BBN with long- lived stau, we show the allowed region for MSSM

Nuclear spallation process of 4 He

Spallation of the 4 He

How to calculate spallation process Forming wave function of nuclear ・ spin and isospin component → antisymmetric for exchange of inner particles ・ space component → symmetric for exchange of inner particles Calculating the amplitude Integrating the square amplitude over all final state’s momentum As a whole, completely antisymmetric for exchange of inner particles

Wave Function of the 4 He Spin and Isospin Component Space Component

Calculation of the Amplitude and the Cross Section Inner Products

Calculation of the Amplitude and the Cross Section Calculation of the Amplitude Calculation of the Cross Section

Time Scale of 4 He Spallation due to Bound Stau ~30MeV Nuclear Spallation dominates Catalyzed Fusion Order of Time Scale of Catalyzed Fusion m stau = 350 GeV Lifetime[s] Deltam[MeV]

Recovery of the Allowed Region Overproduction of 6 Li

Recovery of the Allowed Region Allowed region recovers!! (expectaition) Overproduction of 6 Li

Summary

Spallation process of 4 He suppresses over production of 6 Li caused by the catalyzed fusion. Prediction to the MSSM parameters Calculation applies to X - particles. Calculation of spallation process of 4 He into a deuterium and two neutrons Calculation of spallation process of 7 Li and 7 Be Future works

Thank you for your attention!

Calculation of the Amplitude and the Cross Section Non-relativistic Approximation The Square Amplitude

Calculation of the Amplitude and the Cross Section Calculation of the Cross Section Calculation of the Rate and the Lifetime RateLifetime

Time Scale of 4 He Spallation due to Bound Stau ~30MeV Nuclear Spallation dominates Catalyzed Fusion Order of Time Scale of Catalyzed Fusion m stau = 350 GeV

Calculation of the Amplitude and the Cross Section The Amplitude Calculation