Large Extra Dimensions and the Minimal Length

Large extra dimensions lower the Planck scale to values soon accessible. Motivated by String Theory, the models of large extra dimensions predict a vast number of new effects in the energy range of the lowered Planck scale, among them the production of TeV-mass black holes and gravitons. But not only is the Planck scale the energy scale at which effects of modified gravity become important. String Theory as well as non-commutative quantum mechanics suggest that the Planck length acts as a minimal length in nature, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime. Within the extra dimensional scenario, the minimal length effects thus become important in the same energy range in which the effective extra dimensional models predict new physics. We examine a model which includes the minimal length into the extra dimensional extension of the Standard Model. To appear in the Proceedings of the conference Physics@LHC, Vienna, Austria, July 2004. 1 The Minimal Length Scale It was in the 5th century b.c. that Demokrit postulated a smallest particle out of which matter is build. He called it an “atom”. In Greek, the prefix “a” means “not” and the word “tomos” means cut. Thus, atomos or atom means uncuttable or undividable. 2500 years later, we know that not only the atom is dividable, but also is the atomic nucleus. The nucleus is itself a composite of neutrons and protons and further progress in science has revealed that even the neutrons and protons have a substructure. Is there an end to this or will the quarks and gluons turn out to be non-fundamental too? An answer to this can not be given yet, but judging from one of the most promising candidates for an unified theory – String Theory – there is indeed a smallest possible resolution of spacetime[1]. This is not surprising since the success of String Theory is due to the very reason that the extension of strings is finite. The scale for this expected minimal length is given by the string scale which is close to the Planck-scale lp. ∗[email protected]