Warped extra dimensions
The hierarchy problem can also be solved by considering only one extremely small new compact dimension with a warped geometry of curvature к « MPl where only gravity propagates (Randall and Sundrum, 1999). This setup, called minimal Randall-Sundrum (RS), is composed of a five-dimensional bulk with one compacti- fied dimension, and two four-dimensional branes, called SM and gravity branes. In these conditions, the Planck scale is redshifted for SM brane observers and becomes MD = MPe-knR. For kR ~ 12, i.e., R = 10-32 cm, MD ~ 1 TeV, which solve the hierarchy problem.
Experimental consequences are very different from the ADD case: KK graviton masses are not regularly spaced but given by mn = xnke-knR, where xn are the roots of Bessel functions. Only the first excitation, G(1), with a narrow width k/MPl < 1, is generally accessible at the LHC. Its coupling to SM particles is proportional to 1/(MPle-knR) and therefore much stronger than for the ADD model. As a consequence, the main experimental evidence is a narrow peak in the diboson (Fig. 8.18 (c)) or dilepton (Fig. 8.19 (a)) invariant mass. For k/MPl = 0.02, G(1) masses below 2.7 TeV are excluded (ATLAS Coll., 2014).
Since solving the hierarchy problem requires only the Higgs to be close to the SM brane, the minimal RS can be modified by allowing SM fields to propagate also in the bulk (Davoudiasl et al., 2000). This has the extra advantage of explaining the SM Yukawa coupling hierarchies by the position of the SM fields in the bulk. All SM
Fig. 8.19 Warped extra dimension searches at LHC: (a) dielectron resonance; (b) tt resonance. For the figure in color, please see the online version of the lectures.
fields create KK towers which are constrained to have below than 2-3 TeV for the first excitation (Hewett and Spiropulu, 2002). A particularly interesting search comes from the KK gluon (gKK) decaying to tt which provides an enhancement at high mass of the tt invariant mass spectrum, as shown in Fig. 8.19(b) for the all hadronic channel(CMS Coll., 2013g). Combining all sensitive tt decay channels, gKK masses are excluded below 2.5 TeV CMS Coll. (2013) getting close to the upper part of the allowed region. In these RS-bulk models, the cross-section of gg ^ G(1) ^ WW(ZZ) is driving the G(1) hunt, motivating a search for ZZ or WW resonances (CMS Coll., 2012d, 2014). However, presently, no mass limit beyond 500 GeV can be put on G(1) when 0.04 < k/Mpi < 0.1.