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Extra Dimensions at LHC

Extra Dimensions at LHC. Sun Kun OH (Konkuk) 2007.08.24 CHEP, KNU. New physics at TeV scale. If there are new physics at the TeV scale, the LHC should see them. Some basic properties of new physics signals can be measured. One of the possible new physics is the extra dimensions. CMS PTDR.

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Extra Dimensions at LHC

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  1. ExtraDimensions at LHC Sun Kun OH (Konkuk) 2007.08.24 CHEP, KNU

  2. New physics at TeV scale • If there are new physics at the TeV scale, the LHC should see them. • Some basic properties of new physics signals can be measured. • One of the possible new physics is the extra dimensions. Extra Dimensions at LHC (오선근)

  3. CMS PTDR Extra Dimensions at LHC (오선근)

  4. Extra dimensions as Chap. 14 Extra Dimensions at LHC (오선근)

  5. Extra Dimensions at LHC (오선근)

  6. Contents • Why we need extra dimensions of space (ExDim) • Models on extra dimensions (Models) • LHC explores extra dimensions (LHC) Extra Dimensions at LHC (오선근)

  7. ExDim Models LHC Contents • Why we need extra dimensions of space (ExDim) Extra Dimensions at LHC (오선근)

  8. ExDim Models LHC Kaluza-Klein theory (1921) • Seeks to unify gravitation and electromagnetism. • Extends general relativity to a 5-dimensional space-time. • The resulting equations divided into further sets of equations: one is equivalent to Einstein field equations, another to Maxwell's equations for the electromagnetic field, and the last part to an extra scalar field now termed the "radion". Extra Dimensions at LHC (오선근)

  9. ExDim Models LHC String theory needs extra dimensions. Extra Dimensions at LHC (오선근)

  10. ExDim Models LHC Extra dimensions for strings • In string theories, the critical spacetime dimension is not 4 but 10. • The 6-dimensional spacetime is compactified. Slice of 6-dimensional Calabi-Yau manifold Extra Dimensions at LHC (오선근)

  11. ExDim Models LHC Tiny compactified extra dimensions Extra Dimensions at LHC (오선근)

  12. ExDim Models LHC Tiny compactified extra dimensions • Small R implies tight compactification. • Periodic conditions enables Fourier transformations. Extra Dimensions at LHC (오선근)

  13. ExDim Models LHC We may consider in this way . . . Up to higher dimensions • 0-dimensional object = point Extra Dimensions at LHC (오선근)

  14. ExDim Models LHC Up to higher dimensions • 1-dimensional object = line segment • Projection of a line segment onto 0-dimensional space = point Extra Dimensions at LHC (오선근)

  15. ExDim Models LHC Up to higher dimensions • 2-dimensional object = area Extra Dimensions at LHC (오선근)

  16. ExDim Models LHC Up to higher dimensions • Projection of an area onto 1-dimensional space = line segment Extra Dimensions at LHC (오선근)

  17. ExDim Models LHC Up to higher dimensions • 3-dimensional object = cube • Projection of a cube onto 2-dimensional space . . . Extra Dimensions at LHC (오선근)

  18. ExDim Models LHC Extra Dimensions at LHC (오선근)

  19. ExDim Models LHC Up to higher dimensions • 4-dimensional object = ??? ? Extra Dimensions at LHC (오선근)

  20. ExDim Models LHC Up to higher dimensions • Projection of 4-dimensional object ??? onto 3-dimensional space . . . = tesseract Extra Dimensions at LHC (오선근)

  21. ExDim Models LHC Tesseract in motion Extra Dimensions at LHC (오선근)

  22. ExDim Models LHC Tesseract model Extra Dimensions at LHC (오선근)

  23. ExDim Models LHC Up to higher dimensions • This is where our speculation ends . . . • We cannot imagine or realize what the 4-dimensional object would look like. • The objects in the space higher than 4-dimensional space are completely out of our perception or recognition. • However, the existence of the tesseract implies the existence of 4-dimensional space. Extra Dimensions at LHC (오선근)

  24. ExDim Models LHC Why we need extra dimensions • We may consider in yet another way . . . • A geometrical observation is that Boundaries have no boundary. Extra Dimensions at LHC (오선근)

  25. ExDim Models LHC Boundaries have no boundary • 0-dimensional object = point • A point has no boundary (trivial observation) Extra Dimensions at LHC (오선근)

  26. ExDim Models LHC Boundaries have no boundary • 1-dimensional object = line segment or curve • A curve has no boundary if it is closed. • It has two end points if it is open. Extra Dimensions at LHC (오선근)

  27. ExDim Models LHC Open curve • It has two end points, i.e., it has boundaries. • Its length is finite. • It does not divide the plane into two sections. • Thus, it is not a boundary of a section. Extra Dimensions at LHC (오선근)

  28. ExDim Models LHC Closed curve (ellipse) Boundaries have no boundary. • It has no end, i.e., it has no boundary. • Its length is finite. • It divides the plane into two sections, inside and outside. • Thus, it is a boundary of a section. Extra Dimensions at LHC (오선근)

  29. ExDim Models LHC Boundaries have no boundary • 2-dimensional object = area or surface • A closed surface has no boundary. • An open surface has a closed curve as its boundary. Extra Dimensions at LHC (오선근)

  30. ExDim Models LHC Open surface • It has edges, i.e., it has boundaries. • Its area is finite. • It does not carve out the volume. • Thus, it is not a boundary of a volume. Extra Dimensions at LHC (오선근)

  31. ExDim Models LHC Closed surface (sphere) Boundaries have no boundary. • It has no end, i.e., it has no boundary. • Its area is finite. • It divides the volume into two parts, inside and outside. • Thus, it is a boundary of a volume. Extra Dimensions at LHC (오선근)

  32. ExDim Models LHC Boundaries have no boundary • 3-dimensional object = bulk or volume • A closed volume has no boundary. • An open volume has a closed surface as its boundary. Extra Dimensions at LHC (오선근)

  33. ExDim Models LHC Open volume (cylindrical volume) • It has sections and round surface, i.e., it has boundaries. • Its volume is finite. • It does not carve out the 4-dim space. • Thus, it is not a boundary of a 4-dim space. Extra Dimensions at LHC (오선근)

  34. ExDim Models LHC Closed volume (universe) • It has no end, i.e., it has no boundary. • Its size is finite. • Thus, it is a boundary of a 4-dim space. • Why? Because boundaries have no boundary. Extra Dimensions at LHC (오선근)

  35. ExDim Models LHC Extra dimensions • The assumption that our universe has no boundary implies the existence of a 4-dimensional space, of which our universe is the boundary. • The enveloped 4-dimensional space is a part of the whole 4-dimensional space. • Even if our universe has a boundary, the 4-dimensional space can be materialized. Extra Dimensions at LHC (오선근)

  36. ExDim Models LHC Assuming our universe as a plane . . . Direction of the extra dimension Our universe Extra Dimensions at LHC (오선근)

  37. ExDim Models LHC Assuming our universe as a line . . . Direction of the extra dimension Direction of the extra dimension Our universe Our universe Extra Dimensions at LHC (오선근)

  38. ExDim Models LHC Brane-bulk topology Extra Dimensions at LHC (오선근)

  39. ExDim Models LHC Brane-bulk topology Extra Dimensions at LHC (오선근)

  40. ExDim Models LHC Contents • Why we need extra dimensions of space (ExDim) • Models on extra dimensions (Models) • LHC explores extra dimensions (LHC) Extra Dimensions at LHC (오선근)

  41. ExDim Models LHC 21세기의 11개 물리 과제 (D Son)Discover 2002 1.  What is dark matter? 2. What is dark energy? 3.  How were the heavy elements from iron to uranium made? 4.  Do neutrinos have mass? 5.  Where do ultra-energy particles come from? 6.  Is a new theory of light and matterneeded to explain what happens at very high energies and temperatures? 7.  Are there new states of matter at ultrahigh temperatures and densities? (Quark-Gluon Plasma State) 8.  Are protons unstable? 9.  What is gravity? 10.  Are there additional dimensions? 11.  How did the Universe begin? Extra Dimensions at LHC (오선근)

  42. ExDim Models LHC Extra Dimensions at LHC (오선근)

  43. ExDim Models LHC Extra Dimensions at LHC (오선근)

  44. ExDim Models LHC Standard Model is • Constructed in 4-dimensional space-time • Based on SU(3)XSU(2)XU(1) Extra Dimensions at LHC (오선근)

  45. ExDim Models LHC Expanding it suggests . . . • Expanding 4-dimensional space-time into higher dimensional space-time, • Expanding gauge symmetry into larger group, • Embracing the supersymmetry, • Combining with gravity, etc. Extra Dimensions at LHC (오선근)

  46. ExDim Models LHC Extra Dimensions at LHC (오선근)

  47. ExDim Models LHC Lykken (Fermilab, 2004) Extra Dimensions at LHC (오선근)

  48. ExDim Models LHC Extra Dimensions at LHC (오선근)

  49. ExDim Models LHC Randall-Sundrum Model Extra Dimensions at LHC (오선근)

  50. ExDim Models LHC Randall-Sundrum Model (1999) • Only one more extra dimension. • The 5-th dimension is y. • It is compactified by periodicity, length 2L. • L is parametrized as L = rΦ • Further orbifolded by y  -y (0 ≤Φ ≤ π) • S1/Z2 Extra Dimensions at LHC (오선근)

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