Fast-rolling relaxion KMI, Nagoya University Yutaro Shoji In collaboration with M. Ibe and M. Suzuki in ICRR, IPMU PPP 2019, YITP, 29 Jul - 2 Aug 2019 1904.02545/hep-ph
Introduction
Little Hierarchy Photo by Azuma Makoto New physics (100GeV)^2 (10TeV)^2 ? SM
Dynamical solution (100)^2 (110)^2 (90)^2 Many vacua vacua with different Higgs mass Photo by Naser Mizban The EW scale is chosen by dynamics of a field
Relaxion mechanism <latexit sha1_base64="32SCcZ9I1EPtBDVI3e5o9Vt5/0A=">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</latexit> <latexit sha1_base64="32SCcZ9I1EPtBDVI3e5o9Vt5/0A=">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</latexit> <latexit sha1_base64="32SCcZ9I1EPtBDVI3e5o9Vt5/0A=">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</latexit> <latexit sha1_base64="32SCcZ9I1EPtBDVI3e5o9Vt5/0A=">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</latexit> <latexit sha1_base64="7C81iEPHYucQCa/AZl8nUiA/xw8=">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</latexit> due to inflation [P. W. Graham, D. E. Kaplan, S. Rajendran; ’15] Slow-roll <latexit sha1_base64="LbkRZBsaJagOeVK/pmZr0Smb0u8=">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</latexit> <latexit sha1_base64="LbkRZBsaJagOeVK/pmZr0Smb0u8=">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</latexit> <latexit sha1_base64="LbkRZBsaJagOeVK/pmZr0Smb0u8=">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</latexit> <latexit sha1_base64="LbkRZBsaJagOeVK/pmZr0Smb0u8=">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</latexit> <latexit sha1_base64="giKEdmkKl5RscScQ5u6gx27sv/s=">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</latexit> <latexit sha1_base64="giKEdmkKl5RscScQ5u6gx27sv/s=">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</latexit> <latexit sha1_base64="giKEdmkKl5RscScQ5u6gx27sv/s=">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</latexit> <latexit sha1_base64="giKEdmkKl5RscScQ5u6gx27sv/s=">ACdXichVHLSsNAFD2Nr1pfUTeCMWquLHeFkERhKIbN4KvasFHSeK0DqZJSNJCLf6AP+BCNwoq4me48Qdc+AniUsGNC2/TgKiod5iZM2fuXNmRndM6flEjxGlqbmltS3aHuvo7OruUXv7Njy7Boia9im7eZ0zROmtETWl74pco4rtJuik39YKG+v1kRridta92vOmKnpBUtWZCG5jOV9Wl3fTEtnA8adpWPDdHeTVBSQoi/hOkQpBAGMu2eo1t7MGgTJKELDgMzahweO2hRQIDnM7qDHnMpLBvsARYqwtc5bgDI3ZAx6LvNoKWYvX9ZpeoDb4FJO7y8o4RumBbuiF7umWnuj91q1oEbdS5VnvaEVTr7neGDt7V9ViWcf+5+qPz37KGAm8CrZuxMw9VsYDX3l8ORlbXZ1tDZGF/TM/s/pke74Blbl1bhcEauniPEHpL4/90+wkU6mGK9MJTLz4VdEMYhjPN7TyODRSwjy+dWcIZLXEXelCFlRBlrpCqRUNOPL6FMfgBxrY+M</latexit> Back reaction Higgs mass Slope Relaxion Higgs We assume V ( Φ , X ) = ( M 2 − ✏ X ) | Φ | 2 − r ✏ M 2 X + Λ 4 ( | Φ | 2 ) cos X f + � 4 | Φ | 4 , V M 2 − ✏ X = 0 M = O (10TeV) X
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