Proton Lifetime from SU5 Unification in Extra Dimension

Proton Lifetime from SU(5) Unification in Extra Dimension hep-ph 051086 L. A. , F. Feruglio, Y. Lin, A. Varagnolo

Why extra-dimensions? • Doublet-Triplet splitting Problems with 4 D SUSY GUT: • Proton Decay from Dim=5 operators • Different orbifold parities 5 D SUSY GUT: • R symmetries FORBIDDEN D-T d=5 operators

masse 4/R KK tower (Mass spectrum of 4 D particles) 3/R ORBIFOLD (bulk with boundary conditions) 2/R 1/R 0 D-T splitting SU(5) SU(3)x. SU(2)x. U(1)

Estimate of proton lifetime Dim 5 operators for p-decay Dim=6 operator for p-decay ( X bosons exchange) Main ingredients: 1) Gauge Coupling Unification in a next-to-leading order analysis 2) Interaction gauge bosons-brane fields 3) ( flavor suppression ) 3 options for fields localization y=0 SU(5) y=p. R/2 SM

Estimate of Mc ERRORS: • Experimental input: Heavy thresholld : DCPRT 2 DHL Exp. (gaussian) dominated by a 3 Unknown (non gaussian) Susy Spectra DMAX 4 • Susy Spectra Snow. Mass Points and Slopes (SPS) • : random numbers BIG THERETICAL UNCERTAINTY (enhance for proton decay)

Proton Lifetime

Proton Lifetime

Conclusions • Proton Decay : decisive test for GUT • precise estimate for Mc • Next-to-leading order analysis with experimental and theoretical uncertainties • Flavor sector Option 0 (almost completely excluded) Option I (almost out of range) Option II (interesting for next-generation experiment) (anarchy in n sector) Dominant decay mode with flavor suppression

Branching Ratios

Yukawa Interactions (on the brane) and Fermion Masses BULK Option 0 BRANA y=0 T i, F i Option I T 1, T 2, F 1 Option II T 1, T 2 - Bulk suppression ( Cut-off scale) Minimal SU(5) mass relations T 3, F 2, F 1 - Different Relative Normalization Flavor Suppression - Bulk Mass term for T 1 Good matching of experimental data ( Cabibbo Angle)

TEXTURES Phenomenological relations: OPTION I Option I OPTION II Option II

Gauge Coupling Unification Non leading contributions (h) : Heavy thresholds (2) : 2 -loop (l) : Light thresholds K-K towers of the gauge bosons and matter hypermultiplets with (b) : SU(5) breaking effects Brane Kinetic terms for SM gauge bosons on y= p. R/2. NON UNIVERSAL SU(5) invariant component >> non symmetric one

Two-loop (Correction from gauge sector) Light thresholds j runs over Susy particles of masses mj Brane kinetic terms Theory strongly coupled at L Predictibility for gauge coupling unification HN: leading logaritmic approximation Heavy thresholds CPRT: effective lagrangian approach