Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 248.882 LHC PhysicsExperimental Methods and MeasurementsExtra Dimension Searches at the LHC[Lecture 24, May 05, 2009]C.Paus, LHC Physics: Extra Dimension Searches at the LHC 2Organization Project 3●make sure to hand in very soon Conference●Higgs Analysis update is not yet ready●read the README it contains all relevant info●e-mail to the course list (Si Xie, [email protected], is our local expert!)●please make sure to ask your questions early!‘09The Physics Colloquium Series Thursday, May 7 at 4:15 pm in room 10-250Kip ThorneCalifornia Institute of Technology"The Warped Side of Our Universe"SpringFor a full listing of this semester’s colloquia, please visit our website at web.mit.edu/physicsColloquium SeriesPhysicsC.Paus, LHC Physics: Extra Dimension Searches at the LHC 4Lecture Outline Extra dimension searches at the LHC●theory introduction●some selected models of extra dimensions●large extra dimensions●warped extra dimensions●experimental signatures and searches●reach of the LHC Mini Black Holes●what are they?●how to detect them at LHCC.Paus, LHC Physics: Extra Dimension Searches at the LHC 5Kaluza-Klein Theory Standard Model unifies electromagnetic and weak forces and includes the strong force as well●uses: SU(3) x SU(2) x U(1) symmetry group●does not say anything about gravity●gravitational force much too small, 35 orders of magnitude* reminds me of the Higgs mechanism solving the mass problem Integration of gravity into Standard Model●1921 Kaluza GR in 5 spacetime dimensions●the resulting equations can be split into●Einstein's field equations (GR)●Maxwell's equations for the EM field●and an extra scalar field, radion*●1926 Klein proposed extra dimension to be real and just curled up in circle of small radiusT.KaluzaO.KleinC.Paus, LHC Physics: Extra Dimension Searches at the LHC 6Kaluza-Klein Theory Theory: fifth dimension represented●by U(1) circle group●can be replaced with general Lie group (many extra dim.)●generalization called Yang-Mills theory, gauge theories, though here we are in general treating curved spacetime●for realistic Kaluza-Klein theories the SU(3) x SU(2) x U(1) Standard model has to be generated... but it is theoretically not very appealing (fermions are introduced artificially)●string theories or M-theories deal with this more coherentlyC.Paus, LHC Physics: Extra Dimension Searches at the LHC 7Kaluza-Klein TheoryConsequence of the fifth dimension●particle (graviton) moving along 5th dimension returns to initial position●explains naturally smallness of gravitational force●graviton travels mostly in dimensions we do not observe●we notice only small fraction of its force●one dimension implies circle size of the universe (very noticeable)●several additional dimensions drop circle sizes to atom sizes (unnoticeable)●motion in all dimensions are overlaid and nothing changes●as long as the 5th dimension stays small●standing waves on 5th dimensions can form: E = n h c / R●h – Planck constant, c – speed of light●R – radius of extra dimension, n – any integer●energy spectrum called Kaluza-Klein towers (particles?)C.Paus, LHC Physics: Extra Dimension Searches at the LHC 8Kaluza-Klein Theory Compact? What does that mean?●extra dimensions are constrained....●we cannot see them therefore they have to be compact●serious constraints on extra dimensions originate from this requirement●a circle is compact as it allows particles to travel without leaving their position as long as the circle is small enough●compactification: theory is built using for example 10 dimensions of which 6 have to be compactified to establish our 4 dimensional spacetimeC.Paus, LHC Physics: Extra Dimension Searches at the LHC 9String Theory with Extra Dimensions Large extra dimensions (Arkani-Hamed, Dimopoulos and Dvali: PL B426:263 (1998))●gravity becomes strong at the TeV scale●compactification on a δ-torus (flat geometry)boundary conditions cause periodic wave functionsKaluza Klein modes (towers) of the graviton Mn2 = M02 + δ2/R2real Planck mass: mD = MPlanck,4+δ MPlanck,42 = (MPlanck,4+δ)2+δ x Rδex. MD = 1TeV, means R ~1mm (for δ=2)Kaluza Klein modes give an extra contribution to every SM process (should be pretty small) graviton couples to any massive particleC.Paus, LHC Physics: Extra Dimension Searches at the LHC 10Large Extra DimensionsC.Paus, LHC Physics: Extra Dimension Searches at the LHC 11Constraints On Large Extra Dimensions From particle data booklet 2002: G.F.Guidice, J.March-Russelcareful: n is what I call δ beforeC.Paus, LHC Physics: Extra Dimension Searches at the LHC 12String Theory with Extra DimensionsWarped metric (Randall, Sundrum: PRL 83:3370 (1999))●gravity is strong on the Plank brane●compactification through warped metric●warped distance would make our perception of gravity weak while strong at Plank scale (on Plank brane)distances shrink with ygraviton resonances in 4D with:C.Paus, LHC Physics: Extra Dimension Searches at the LHC 13Searches for Extra Dimensions Large extra dimensions●direct graviton production: single jet and missing pT (gg→gG, ..)L.Vacavant, I.Hinchliffe (J. Phys. G: Nucl. Part. Phys. 27 (2001) 1839-1850)Atlas experimentC.Paus, LHC Physics: Extra Dimension Searches at the LHC 14Searches for Extra Dimensions Large extra dimensions: direct graviton searchStolen from B.Laforge: Moriond QCD 2002 presentation on extra dimension:http://moriond.in2p3.fr/QCD/2002/thursday/pm/laforge.pptC.Paus, LHC Physics: Extra Dimension Searches at the LHC 15Searches for Extra Dimensions Extra dimensions at TeV level●fermions: open string excitations with ends stuck to brane●gauge bosons though could also propagate in the bulk●search for Kaluza-Klein resonances of Z, etc.or search for compactification mass in all data with likelihood techniquedirectlyG. Azuelos, G. Polesello (Les Houches 2001 Workshop Proceedings)C.Paus, LHC Physics: Extra Dimension Searches at the LHC 16Searches for Extra Dimensions Direct Search for graviton resonances (warped ED)●generic search for any model with narrow gravitonC.Paus, LHC Physics: Extra Dimension Searches at the LHC 17Searches for Extra Dimensions Direct Search for graviton resonances (warped ED)●generic