Large Extra Dimensions Jared Schmitthenner The Hierarchy Problem

Large Extra Dimensions Jared Schmitthenner

The Hierarchy Problem Two fundamental energy scales - electroweak symmetry breaking (MEW¼ 1 Te. V) and quantum gravity 1/2 (MPL=1/GN ¼ 1016 Te. V) There is a “desert” between these scales where gravity is unmodified Gravity has not been tested at scales close to 1/MPL

Extra Dimensions We can suppose that there are n compact extra dimensions of radius R and that MEW is the only fundamental scale At distances less than R, gravity will propagate in all 4+n dimensions. Standard model fields can be confined to our 4 -dimensional brane.

Size of Extra Dimensions We can find R using the gravitational potential in each regime: R>>r R<<r Letting M=MEW and setting the potentials equal at r¼R gives

Dynamic compactification SM particles can be localized to the 4 D brane by coupling field in the higherdimensional manifold. Ã(r) falls off rapidly with r, so the (4+n)dimensional fermions are effectively localized in 4 dimensions

Compactification Scalar and gauge bosons can be confined to the submanifold in the same way Other mechanisms (like string theory) can also confine standard model fields to our 4 D brane.

Graviton Production Gravitons could be produced in high energy collisions, resulting in apparent missing energy Extra-dimensional excitations of the graviton occur with multiplicity (ER)n, at a rate 1/MPL 2

Escaping particles SM fields are only localized to within 1/MEW, so at high energies (E>MEW) they can acquire momentum in the extra dimensions These particles would seem to disappear, causing a sharp cuttoff For certain higher-dimensional manifolds such particles could periodically return

Modified Gravity As gravity propagates through the extra dimensions the force will fall off more rapidly at small scales, / r-(n+2) Experiments to measure gravity at very small distances can limit the size and number of extra dimensions

Other Branes The 4+n-dimensional bulk could be inhabited by other branes These branes would be able to interact with our own gravitationally The shape of the manifold and our submanifold could also allow interactions with distant regions of our own brane

Conclusions Extra dimensions much larger than the Plank length can solve the hierarchy problem. Theories with large extra dimensions make concrete predictions that can be tested at the LHC

References N. Arkani-Hamed, S. Dimopoulos, G. Dvali, “The Hierarchy Problem and New Dimensions at a Millimeter”, hep-ph/9803315 R. Bryan, “Are the Dirac particles of the Standard Model dynamically confined states in a higher-dimensional flat space? ”, hepph/9904218