Introduction to universal extra dimensions (UEDs) Mitsuru Kakizaki (ICRR, University of Tokyo) May 10, KEK Refs: Original idea: Appelquist, Cheng, Dobrescu, PRD67 (2000) Second KK particle physics: MK, Matsumoto, Sato, Senami, hep-ph/ UED vs SUSY at CLIC: Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ Pedagogical introduction to UED models Comparison of UED and SUSY phenomenology Pedagogical introduction to UED models Comparison of UED and SUSY phenomenology UED cosmology and astrophysics Dr. Matsumoto’s talk Probing extra dimensions at linear collidersProf. Raychaudhuri’s talk

May 10, 2005Mitsuru Kakizaki2 Large extra dimensions Warped extra dimensions Today’s topic [Arkani-hamed, Dimopoulos, Dvali PLB 429 (1998) 263] [Randall, Sundrum PRL 83 (1999) 3370] 1. Motivation etc. Extra-dimension scenarios provide new views of various problems Hierarchy problem: Fermion mass hierarchy Existence of dark matter [Arkani-hamed, Schmaltz PRD 61 (2000)] Universal extra dimensions (UEDs) [Appelquist, Cheng, Dobrescu, PRD67 (2000) ] The Lightest Kaluza-Klein particle (LKP) in UED models is an excellent candidate for dark matter due to Kaluza-Klein (KK) parity [Servant, Tait, NPB 650 (2003) 391]

May 10, 2005Mitsuru Kakizaki3 Study at linear colliders is mandatory UED SUSY R parity stabilizes the LSP Kinematics of 1st KK modes resembles that of superparticles with degenerate mass KK parity stabilizes the LKP Attention to spins of new particles and second KK modes Superparticle mass 1st KK mode mass UED is similar to SUSY  SUSY breaking mass SM SUSY Same spin Different spin

May 10, 2005Mitsuru Kakizaki4 Contents 1.Motivation 2.Universal extra dimensions (UEDs) 3.UED vs SUSY 4.Summary

May 10, 2005Mitsuru Kakizaki5 2. Universal extra dimensions For definiteness, we concentrate on one-extra dimensional cases in this talk Idea: All SM particles propagate compact spatial extra dimensions [Appelquist, Cheng, Dobrescu, PRD67 (2000) ] Dispersion relation: Momentum along the extra dimension  Mass in four-dimensional viewpoint For compactification with radius, Mass spectrum for is quantized Momentum conservation in the extra dimension Conservation of KK number in each vertex

May 10, 2005Mitsuru Kakizaki6 Parameters in UED models c.f. minimal SUGRA: : Cutoff scale : Size of extra dimension : Higgs boson mass Kaluza-Klein expansion (Fourier expansion): Parameters in UED models are completely specified in terms of the SM parameters and Only three free parameters in minimal UED model: Zero modes are identified with SM fields

May 10, 2005Mitsuru Kakizaki7 Minimal UED Conservation of KK parity [+ (--) for even (odd) ] The lightest KK particle (LKP) is stable c.f. R-parity and the LSP in SUSY models Reflection sym. under Experimental limit on is weaker than other extra-dimensional models: Electroweak precision tests Single KK particle cannot be produced { Dark matter In 5D spacetime, spinor representation has 4 complex components  Chiral fermions in 4D e.g. Dirac Chiral

May 10, 2005Mitsuru Kakizaki8 Particle contents in minimal UED Electroweak symmetry breaking effects are suppressed for higher KK modes There appear infinite towers of KK modes with quantum numbers identical to SM particles KK level New particles: Massless Massive (Mass ) Dirac Gauge boson Fermion (SU(2) L ) Real scalar Scalar (SU(2) L ) SM particles: (Mass ) Dirac Chiral Complex scalar

May 10, 2005Mitsuru Kakizaki9 Interactions in UED models e.g. gauge interaction of fermion: KK expansion 5D Couplings in UED models are determined by corresponding SM ones 4D For SM KK

May 10, 2005Mitsuru Kakizaki10 Compactification  5-dimensional Lorentz invariance Orbifolding  translational invariance in the 5th dimension Radiative corrections generate KK mass splitting Radiative corrections to mass spectra of KK modes [Cheng, Matchev, Schmaltz, PRD66, (2002)] One-loop corrected masses of 1st KK modes c.f. SUSY: Universal soft mass at cutoff scale Mass splitting at weak scale Tree level masses spectrum of 1st KK modes

May 10, 2005Mitsuru Kakizaki11 LHC: [Cheng, Matchev, Schmaltz PRD 66 (2002) ] Signals of 1st KK modes are similar to those of superparticles Discovery reach for minimal UED: 3. UED vs SUSY Future colliders is promising for distinguishing UED and SUSY (UED is called “Bosonic supersymmetry”) Observation of effects caused by second KK modes Determination of spins of new particles

May 10, 2005Mitsuru Kakizaki12 Contrasting SUSY and UED at CLIC (Multi-TeV collider) [Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ] missing energy > 2.5 TeV transverse energy < 150 GeV event sphericity > 0.05 missing trans. energy > 50 GeV Event seletion: SM background: (small polar angle) MSSM parameters are adjusted to reproduce UED kinematics Comparison of with in UED in SUSY UED parameters: Missing Rad. cor.

May 10, 2005Mitsuru Kakizaki13 Angular distribution and spin measurements : Spin 1/2 : Spin 0 : signal + background : signal UED: SUSY: at Factor [From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]

May 10, 2005Mitsuru Kakizaki14 Discrimination of UED from SUSY Cross section for resonance Including beamstrahlung Photon energy spectrum in c.f. SUSY: at threshold region, no sharp peak due to resonance [From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]

May 10, 2005Mitsuru Kakizaki15 4. Summary LHC would not distinguish UED from SUSY models Study at linear colliders is mandatory Attention to Spins of new particles Effects caused by second KK particles Remarkable features of UED models: Towers of KK modes with spins identical to corresponding SM particles Small number of free parameters Excellent dark matter candidate: LKP

May 10, 2005Mitsuru Kakizaki16 Backup slides

May 10, 2005Mitsuru Kakizaki17 Radiative corrections KK number violating couplings pair production is naturally enhanced by -resonance in the s-channel Second KK particle physics Signal of 2 lepton + large missing energy is expected to have large cross section and be almost background free (2nd KK mode mass) (1st KK mode mass) [MK, Matsumoto, Sato, Senami, hep-ph/ ] e.g.

May 10, 2005Mitsuru Kakizaki18 Threshold singularity Threshold cross section for KK quarkonium at linear collider Precise determination of parameters is possible [MK, Matsumoto, Okada, Yamashita, …] KK quarkonium KK quarkonium cross section for small decay width Energy of bound state:

May 10, 2005Mitsuru Kakizaki19 Higgs mass vs 1/R [Appelquist, Yee, PRD 67 (2003) ] KK modes of top-bottom quark doublet  T negative For large Higgs mass, SM Higgs and KK Higgs  S positive KK quarks and KK HIggs  T positive Combined analysis

May 10, 2005Mitsuru Kakizaki20 Collider signatures at LHC The discovery reach: Signals of 1st KK modes are similar to those of superparticles The discovery reach: Signals of 1st KK modes are similar to those of superparticles [Cheng, Matchev, Schmaltz PRD66 (2002) ] Discovery reach Decay chains of 1st KK modes

May 10, 2005Mitsuru Kakizaki21 One-loop corrected masses of 1st KK modes [From Cheng, Matchev, Schmaltz PRD66 (2002) ]

May 10, 2005Mitsuru Kakizaki22 Muon energy spectrum [From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]

May 10, 2005Mitsuru Kakizaki23 Threshold scan Cross section for [From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]

May 10, 2005Mitsuru Kakizaki24 Radiative return to [From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ] Photon energy spectrum in