hep-ph/0607106, with M. Carena (FNAL), E. Pontón (Columbia) and C. Wagner (ANL)
Randall-Sundrum for a theorist A dream come true !! Solid motivation: Solution to the gauge hierarchy problem Suggestive theory of flavor: Fermion masses hierarchical with FCNC naturally absent for light fermions Insight on strongly coupled theories: AdS/CFT
Higgs
Randall-Sundrum for an experimentalist Hold your horses, boy!!
The devil is in the details:
Strong Z and W mixing with their KK modes: T too large Large flavor violation for heavy fermions ... maybe too large? Bounds from EW precision observables sends new physics at the verge (or well beyond it) of LHC reach But: New ideas protect EW precision observables, allowing KK modes with masses
Outline Fields in models with extra dimensions Phenomenology of Randall-Sundrum:
Masses
Bounds on the KK scale
Couplings
Gauge boson mixing: T parameter Heavy fermions: Zbb coupling Light fermion coupling to KK gauge bosons: S parameter New Ideas: Custodial protection of T and Zbb
How far can we get? One-loop corrections to T and Zbb
Global fit to Electroweak precision observables Phenomenology Conclusions
Fields in Extra Dimensions Fields living in higher dimensional compact spaces can be decomposed in normal (Kaluza-Klein) modes:
(Quantized) momentum in the extra dimension corresponds to 4D mass for the Kaluza-Klein modes:
Interactions are given by overlaps of the wave functions:
Phenomenology of RS: masses
Goal: Study phenomenology
Boundary conditions:
: Massless zero mode
masses and couplings
Chiral fermions Unbroken gauge symmetries
: No zero mode
Broken gauge symmetries
In Randall-Sundrum the Kaluza-Klein scale is given by:
Spectrum: couplings Light KK modes are localized towards the IR brane with small, almost constant, tails toward the UV brane Strong KK coupling to the Higgs
Gauge boson zero modes are flat (4D gauge invariance)
Fermion zero modes can be (exponentially) localized anywhere: Light fermions far from the IR (Higgs) Third generation near the IR: Important effects
Spectrum: couplings (continued) Fermion zero mode couplings to the gauge boson KK modes depend on the fermion localization: Constant for light fermions (near the UV brane) Zero for delocalized fermions Highly enhanced for heavy fermions (near IR brane)
The bads of the old RS: T parameter Gauge KK modes are localized near the IR brane
Large mixing with the Z and W zero modes through the Higgs
Large T parameter
The bads of the old RS: Zbb coupling Top (bottom) zero modes are localized near the IR brane
Large gauge and Yukawa couplings to GB and fermion KK modes
Large anomalous Zbb coupling
The bads of the old RS: S parameter Light fermions are localized near the UV brane
Constant (non-zero) couplings to Gauge Boson KK modes
Can be reabsorbed into a (moderate) S parameter
light fermions
New Ideas: custodial symmetry The T parameter is protected in the SM (at tree level) by a global SU(2)R custodial symmetry Custodial protection of Randall-Sundrum:
Agashe, Delgado, May, Sundrum JHEP (03)
Bulk Gauge Symmetry: Broken by boundary conditions (-,+) to the SM on the UV brane
What about Zbb? New KK modes [SU(2)R gauge bosons and new fermions] also affect the anomalous coupling of the b quark to the Z The correction depends on the fermion quantum numbers: The simplest choice doesn’t work: large Zbb corrections If we have
then Zbb coupling is protected
by the custodial symmetry:
Mixing with fermion KK modes affecting Zbb naturally reduced
Agashe, Contino, Da Rold, Pomarol ph/0605341
What about Zbb?
Custodial protection of T and Zbb is crucial to have light KK excitations
Fermion Quantum Numbers The simplest option is bidoublets under
The Higgs is also a bidoublet with
How low can we get? Tree level corrections to the T parameter and Zbb anomalous coupling are tiny (no constraints) The S parameter forces
However, one-loop corrections can be important: Bidoublets contribute negatively to T Singlets contribute positively to T (need light singlets) Light fermion KK modes with strong couplings induce large one loop corrections to the Zbb coupling
T parameter at one loop
Light, strongly coupled
Large corrections to Zbb coupling UV
singlet localization
IR
Global Fit to Electroweak Observables Han, Skiba PRD(05); Han PRD(06)
We have performed a global fit to all relevant electroweak precision observables including: All tree-level effects at leading order in
Leading one loop effects: S and T parameters and Zbb We compute the
as a function of the localization parameter
of the fermion zero modes:
Zbb coupling and the S parameter are the most restrictive observables when the light fermions are near the UV brane Loss of universality when light fermions near the IR brane
Result of the global fit
Example of model that saturates the bound:
IR
light families
UV
Phenomenology Fermionic spectrum:
Three light quarks (with charge 5/3, 2/3 and -1/3) that do not mix Two charge 2/3 quarks that mix (strongly) with the top
Heavier modes with masses Top mixing with vector-like quarks induces anomalous couplings
Conclusions
New ideas based on custodial symmetry get the RandallSundrum model back in the game for the LHC One loop effects are important: Tension between the T parameter and Zbb coupling Realistic models with can be constructed and typically have light quarks that mix strongly with the top. Exciting phenomenology at the LHC Light new fermions and gauge bosons: Anomalous top couplings: up to 10-20% corrections Future work: Collider phenomenology Flavor Physics
