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EXTRA DIMENSIONS IN PARTICLE PHYSICS. Ferruccio Feruglio. EPS conference – Aachen, July 2003. SET-UP. brane. in the 1 st part of this talk. bulk. length. length. volume. only gravity is admitted to the bulk (few exceptions). KK modes

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## EXTRA DIMENSIONS IN PARTICLE PHYSICS

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**EXTRA DIMENSIONS**IN PARTICLE PHYSICS Ferruccio Feruglio EPS conference – Aachen, July 2003**SET-UP**brane in the 1st part of this talk bulk length length volume only gravity is admitted to the bulk (few exceptions) KK modes graviton momentum along ED is quantized in units of 1/R. To the 4D observer, gravitons come in infinite copies with 4D masses n/R (=a tower) warped geometry branes can carry some energy density and, by the laws of GR, they may warp the space-time geometry.**particles**full space-time metric in D = 4+ contains KK modes 4D graviton and its radion one combination of specifies the volume of the extra space e.g. = 1 much as other particles, specifying the shape of the ES or the fluctuations of the brane, can be present (not covered by this review…)**General motivation**unification of gravity with other fundamental interactions Kaluza-Klein (1919-1926), still valid today. String theories, candidates for a unified description of all interactions, are formulated in D = 10 (or D = 11) specific motivations 1. Hierarchy problem 2. ``little’’ hierarchy problem 3. flavour problem 4. problems of conventional GUTs 5. cosmological constant**HIERARCHY PROBLEM**(L=0 here) there is only one fundamental scale in D=4+ dimensions all KK gravitons contribute Arkani-Hamed, Dimopoulos, Dvali Antoniadis only the 4D graviton zero mode contributes 4D gravity is weak because the graviton wave functions is diluted in a big volume. . Now we should explain why**excluded: R ~ Sun-Earth distance**of special interest: sizeable deviations from Newton law clearly allowed KK graviton states can be produced - at colliders - in processes of astrophysical and/or cosmological relevance**Sub-mm tests of gravity**we expect degeneracy of the 1st KK level wavelength of the 1st KK mode EOT-WASH ex/0202008 Further improvements are an experimental challenge! important: deviations in this range are expected also in other scenarios (more on this later on…)**FLAVOUR I: and LED**LED provide a nice argument for the smallness of masses: standard Yukawa couplings to a singlet fermion who lives in the bulk originates from Dienes, Dudas, Gherghetta, Arkani-Hamed,Dimopoulos, Dvali, March-Russell, Barbieri, Creminelli, Strumia can we test this idea? if some states are sufficiently light (not unconceivable: R ~ 0.02 mm) then, few might take part in oscillations but large mixing angles between and are excluded (SN1987A) oscillations into disfavoured by both atmospheric and solar data effects subdominant, if present**reviews: Cheung; Hewett, Spiropulu;**Sanders this conf. Collider bounds on LED: 1 KK graviton production in association with a or a jet rescued by the very large phase space single KK production combined 95% CL limits on from LEP and Tevatron Giudice, Strumia 2 virtual graviton exchange sensitive to UV physics: divergent amplitudes already at the tree-level for parametrized in terms of effective operators (or computed in string theory)**energy-momentum tensor**d=8 (tree-level) d=6 (one-loop) Y is C-even and singlet under all gauge and global symmetries (flavour universal); Chang, Lebedev, Loinaz, Takeuchi No more d8 operators from fermion-gauge boson sectors alone Giudice, Strumia present 95% CL limits dilepton (LEP) diphoton (Tevatron) (Hera) cut-off scale contact interaction (LEP) dijet, Drell-Yan (Tevatron) (Hera) If, naively, then Y gives the strongest bound on remember GIM where otherwise**Limits on from astrophysics (in TeV)**Hannestad, Raffelt they are the strongest limits on fundamental scale bounds rapidly soften for higher They rely on the (essentially) gapless spectrum of KK gravitons**cosmology reminder**The universe has a standard evolution up to temperatures of order above the cooling proceeds mainly by bulk graviton production (instead of standard adiabatic expansion) =2 barely consistent with BBN such a low makes inflation and baryogenesis problematic both astrophysical and cosmological problems are eliminated if the spectrum of KK gravitons has a sufficient gap for instance evades all the astrophysical bounds of present hottest astrophysical object**How can we make ?**1. KK spectrum also depends on the shape of ES, not just from R Dienes 2. New relation between and due to warped geometry in RS set-up the branes carry some energy density and this warps the surrounding ST in a loose sense, since V cannot be precisely defined Randall, Sundrum if a large can be obtained with a natural KK modes are now at and astrophysical and cosmological bounds do not apply**collider phenomenology**radion KK gravitons (unevenly spaced) large anomalous coupling to gluons. At hadron colliders - production mainly through gluon fusion - decay into dijet or into ZZ if kin. allowed (similar to Higgs. Indeed radion-Higgs mixing possible) no significant bound from present data resonance enhancements at hadron colliders in Drell-Yan processes a portion of the parameter space already probed by Tevatron**Up to now**SM fields confined on a brane having vanishing width strong and e.w. interactions successfully tested only up to a part of (or all=UED) the SM fields might live in a sized ED motivations for early: SUSY breaking via compactification Antoniadis more recently: solutions to the `little’ hierarchy problem indirect evidence for a gap between the Higgs mass and the EW symmetry breaking scale EW precision tests search for new physics**`LITTLE’ HIERARCHY PROBLEM**from the solution to the `big’ hierarchy problem: finite corrections controlled by the mass of some new particle from EWPT or even lighter expected (think, for instance to the chargino in constraint MSSM) new light weakly interacting particles: not seen in either direct searches or in EWPT modest gap (factor ~ 10) can be filled 1. by a moderate fine-tuning of the parameters in the underlying theory 2. by looking to specific theories where this gap is natural in ED with • can be protected by either • SUSY or • - gauge symmetry new states are expected at the TeV scale**Pomarol, Quiros; Barbieri, Hall, Nomura; Ghilencea, Groot**Nibbelink, Nilles; Scrucca, Serone, Silvestrini, Zwirner,… 1. SUSY broken by boundary conditions on an interval of size L EWSB triggered by the top Yukawa couplings is finite and calculable in terms of 2 parameters (L,M) including two-loop corrections Barbieri, Marandella, Papucci characteristic spectrum mild experimental bounds: momentum conservation along ED preserved by gauge interactions as in UED Appelquist, Cheng, Dobrescu - no single KK mode production - no 4f operators from tree-level KK exchange**2. gauge symmetry: Higgs-gauge unification**Manton 1979 Yang-Mills theory in D>4 gauge group G 4D vector bosons 4D scalars D gauge vector bosons Example: G = SU(3) (8 independent generators) unseen unseen we can eliminate the `unseen’ by compactification on an orbifold all fields required to have a well-defined parity the `unseen’ states have no zero modes because they are odd**4D viewpoint: SU(2)xU(1) gauge symmetry + 1 Higgs doublet**Csaki, Grojean, Murayama Burdman, Nomura general problems solutions • - large corrections from branes • at y=0,L • choose the right group • e.g. Higgs embedding Y(H)=1/2 usually leads to wrong D=5: from D-terms if SUSY D6 includes Higgs self-interactions Higgs self-coupling for EWSB key feature: residual gauge symmetry absence of quadratic divergences from gauge sector (crucial) D=5 forbidden D=6 absent in specific models Von Gersdorff, Irges, Quiros realistic Yukawa couplings interactions of H are universal if minimally coupled Wilson lines**and here**we put fermions here Csaki, Grojean, Murayama Scrucca, Serone, Silvestrini invariant under both local and residual gauge transformations [however may reintroduce quadratic divergences for at 1 or 2 loops] features: • naturally light Higgs boson • KK gauge vector bosons of an extended group G • not necessarily KK replica for fermions remarkable progress towards a realistic model in the last year!**FLAVOUR II**In ED we have a new tool to understand fermion mass hierarchy: geometry examples D.B. Kaplan, Arkani-Hamed, Schmaltz, Mirabelli generations are `copies’ in ED. FS broken by a non-trivial Higgs VEV Dvali, Shifman several generations may arise as independent zero modes of a single higher-dimensional fermion. Troitsky, Libanov, Nougaev, Frere Biggio, Feruglio, Masina, Perez-Victoria related to the properties of compactification mechanism unexplained in D=4!**can we test these ideas?**most stringent bounds from FCNC Del Aguila, Santiago; Delgado, Pomarol, Quiros; Lillie, Hewett,… KK modes of gauge bosons have non-constant wave functions after rotation from flavour basis to mass eigenstate basis**Sub-mm gravity (again)**all previous statements assume that some dynamics stabilizes the radion at the right scale: in explicit models of weak scale compactification (not a theorem) Chacko, Perazzi radion coupling to matter m gravity-like observable deviations from Newton’s law at 100 m even for Kolb, Servant, Tait radion becomes cosmologically `active’ if**generic problems of ED models with cut-off scale**potentially large corrections to EW observables, conflict with EWPT how can we understand approximate B and L conservation? B & L violating operators d>4 are allowed by known low-energy symmetries suggest gauge coupling unification • the running is log • high sensitive to light particle content • unification conditions at SUSY 1-loop LO 2-loop, thresholds**approximate B & L conservation**gauge coupling unification natural within `UV desert’ possible, but not a generic feature of IR desert problematic if especially if complemented by a Grand Unified picture where - particle classification clarified - unification condition automatic at**GRAND UNIFICATION AND ED**Urgent problems of conventional 4D GUTs The Problem: DT splitting • - fine-tuned in minimal models • baroque Higgs structure in non-minimal ones • usually spoiled by radiative corrections after SUSY breaking • or by non-renormalizable operators Altarelli, Feruglio, Masina p-decay Hisano, Murayama, Yanagida; Goto, Nihei minimal SUSY SU(5) predictions**both solved if G=SU(5) is broken by compactification**in SUSY version additional states and one more parity the zero modes of can be removed by appropriate parity assignment if then, for a 4D observer: SU(5) does not exist in 4D! and parities fixed from gauge sector AUTOMATIC DT SPLITTING Kawamura**p-decay**Altarelli, Feruglio Hebecker, March-Russel d=5 operators arise from a mass term such a term is forbidden by a U(1) symmetry characteristic of the bulk action and extendible to the whole theory no d=5 (and d=4) p-decay Hall, Nomura gauge coupling unification preserved Hall, Nomura Contino, Pilo, Rattazzi, Trincherini test:p-decay dominated by d=6 operators Hebecker, March-Russel Hall, Nomura uncertainties: mixing angles and c no uncertainties from SUSY breaking brane coupling**cosmological constant and ED**Two problems 1. why is nearly zero? 2. cosmic coincidence why now? (nothing to say about this here) massless graviton universally coupled to all sources 1. 4D + general covariace then vacuum energy curves our space-time this is what we measure in D>4 this is not necessarily true: can curve the ED space leaving our space flat this might occur if depends on the wavelength of the source**wavelength **coupling standard cosmology vacuum energy is the source with the largest wavelength a large does not curve our 4D space time Dvali, Gabadadze, Porrati Dvali, Gabadadze, Shifman**here ED are infinite , otherwise a**massless 4D graviton exists one testable prediction gravity modified below departure from Newton potential at the sub- mm scale expected above gravity becomes strong and should be soften e.g. by string theory (production of Regge states) The fine-tuning is not eliminated but the hierarchy becomes stable - effective field theory necessitates careful treatment Rubakov, Luty, Porrati, Rattazzi - closely related picture derivable from string theory Antoniadis, Minasian, Vanhove Sundrum Arkani-Hamed, Dimopoulos, Dvali, Gabadadze - related approaches**Laurels beckoned us, so we started out**With Nightingale towards a mountain height. While I grappled with the sheer cliffs below, She seized her prize in easy, graceful flight. What I may perhaps never ever reach, Took but a brief moment for the bird; O Heaven don't be so unjust, I plead, Grant me wings too. Let my prayer be heard. Roland von Eotvos

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