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The Hierarchy Problem and New Dimensions at a Millimeter

The Hierarchy Problem and New Dimensions at a Millimeter. Ye Li Graduate Student UW - Madison. Hierarchy Problem. Two “Fundamental” Energy Scale Electroweak Scale: m EW ~ 10 3 GeV Planck Scale: M Pl = G N -1/2 ~ 10 18 GeV New Framework with Extra dimensions

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The Hierarchy Problem and New Dimensions at a Millimeter

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  1. The Hierarchy Problem and New Dimensions at a Millimeter Ye Li Graduate Student UW - Madison

  2. Hierarchy Problem • Two “Fundamental” Energy Scale • Electroweak Scale:mEW ~ 103 GeV • Planck Scale:MPl = GN-1/2~ 1018 GeV • New Framework with Extra dimensions • One Fundamental Scale: Weak Scale • United Gravitational & Gauge Interaction • Independent of SUSY or Technicolor

  3. nextra spatial dimensions of radius ~ R • Gravitational Potential : • Effective 4-D MPl: MPl2~MPl(4+n)2+n Rn • One Scale Assumption: MPl(4+n) ~mEW

  4. Experimental Consequences • Gravity comparable in strength to gauge interaction at weak scale • Gravitational force law: deviation from 1/r2 on distance R • SM particle with energy > weak scale escape to extra dimensions • Specific Cases • n = 1, R ~ 1013 cm • n = 2, R ~ 100 μm - 1 mm Excluded !!! Particularly Exciting !!!

  5. Phenomenological & Astrophysical Constraints Energy available to the graviton • Total Emission Rate of Graviton Rate of emitting a single graviton 1/MPl2 All Kaluza-Klein (KK) excitations of graviton recurring once every 1/R, per extra dimension n • Branching Ratio of Emitting a graviton:

  6. High Energy Experiments: • Missing Energy carried by massless particles • Absence of relevant decay modes puts strong constraints to the scalemEWand/orn • Astrophysics: • Relate to Goldstone boson’s emission rateF: • Accelerate star’s cooling dynamics Supernova SN1987A: F ~ 108 GeV < 1010 GeVInteresting ! Sun: ΔE ~ KeV → F ~ 1012 GeV > 107 GeV (largest F probed by far)

  7. Construction of a Realistic Model x5, x6 probed by gravitational force • Six Dimensions: g = (-1,1,1,1,1,1) • The extra two dimensions →two-sphere • 6-D Scalar Field: Φ • Non-zero VEV: Λ • Two zeros: vortex & anti-vortex (north & south pole) • Nielsen-Olesen Solution:

  8. What if it’s a torus instead of a two-sphere? • Equivalent to a two-torus with zero inner radius • Two 4-D vortices become a single one

  9. 1. Localization of Fermions and Higgs scalar • A pair of 6-D left-handed Weyl spinors • Couple to the vortex field: • 6-D Dirac Eq. in the vortex bkg Written in 4-D Weyl spinors Solutions with localized massless fermions:

  10. Provided the spinors satisfies • have definite 4-D chirality • Similar discussion for The vortex supports a single 4-D massless chiral mode which can be

  11. How to generate mass ? Higgs mechanism still works ! • Higgs field potential: m2,h’,c > 0 In the vortex core: r=0 In the bulk: r >Λ-1 Vortex as an attractive potential If h’φbulk-m2 > 0, positive mass

  12. 2. Localization of Gauge Fields Flux Conservation • Field confinement Coulomb’s Law: 1/r Two infinite planes repelling the field lines Coulomb’s Law: 1/r2 Same sort of model in our case

  13. 4-D Lagrangian: • Higgs mechanism applied on the string • Inside the vortex: • 2 out of 3 gluons: large masses ~ M • the 3rd gluon: a massless photon • Outside the vortex: the photon → non-Abelian gauge theory Confines and develops a mass gapΛ ~ mEW

  14. 3. A Realistic Theory • Standard Model embedded in Pati-Salam group: • In addition: a U(1)V factor and a singlet scalar field Φ • Gauge group spontaneously broken to • Crucial Assumption: Gauge group strongly coupled, developing a mass gap ~ Λ(cutoff)

  15. Thank you ! • Reference: N. Arkani-Hamed et al., Phys. Letter B 429 (1998) 263-272

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