XXXVI th Recontres de Moriond Very High Energy Phenomena in the Universe 22 January 2001 Ephraim Fischbach Department of Physics Purdue University, West Lafayette, IN Extra Dimensions, New Forces, and Non-Newtonian Gravity

22 January 2001Purdue University Department of Physics Overview Was Newton Really Right? –Tests of 1/r 2 law –Tests of the equivalence principle –Importance of scale Motivations for Non-Newtonian Gravity –New light quanta  new forces –Unification and extra dimensions Experimental Tests –Problems with short-distance experiments –The “iso-electronic” effect –The Purdue AFM experiment Outlook

22 January 2001Purdue University Department of Physics Summary of Newtonian Gravity Newtonian GravityNon-Newtonian Gravity a)independent of the nature of m 1 (Equivalence Principle) b)varies as 1/r 2 doesn’t vary as 1/r 2 * not independent of 1 or 2 * * Evidence for either of these would point to a new fundamental force in nature. m1m1 m2m2 r

22 January 2001Purdue University Department of Physics Summary of Newtonian Gravity a)independent of the nature of m 1 (Equivalence Principle) b)varies as 1/r 2 m1m1 m2m2 r

22 January 2001Purdue University Department of Physics Non-Newtonian Gravity doesn’t vary as 1/r 2 * not independent of 1 or 2 * * Evidence for either of these would point to a new fundamental force in nature. m1m1 m2m2 r

22 January 2001Purdue University Department of Physics Mini-Review #1 The existence of ultra-light particles can produced long- range fields which behave somewhat like gravity The presence of such fields would show up as apparent deviations from the predictions of Newtonian gravity 1/r 2 violations equivalence principle violations To search for such violations, experiments must be carried out over many distance scales Newtonian gravity is OK down to ~ 1mm. Below ~ 1 mm we know relatively little about the behavior of Newtonian gravity

22 January 2001Purdue University Department of Physics Theory of New Forces A new force can arise from the exchange of a light quantum with appropriate properties scalar(J P = 0 + ) vector (J P = 1 - )  p, e, n, (  , …) scalar vector Bulk Matter = Range =  /  c if  = eV/c 2  = 200 m

22 January 2001Purdue University Department of Physics Long-Range Forces Over Sub-mm Scales Various mechanisms lead to potentials with and inverse power law behavior n=2 2-photon exchange; 2-scalar exchange n=3 2-pseudoscalar exchange n=4 n=5 -exchange; 2-axion exchange Also: String Theory Models … Such forces can best be detected in experiments where the interacting bodies are very close to each other, as in the Casimir Effect Problems –How to separate out the new forces from the known electromagnetic effects –Forces are intrinsically small –V(r)  1/r

22 January 2001Purdue University Department of Physics Numerical Estimates It is convenient to introduce an energy scale set by the usual Newtonian constant G 4. This is the Plank mass M Pl  M 4 M 4  M Pl = (  c/G 4 ) 1/2 = 2.18  g = 1.22  GeV/c 2 In natural units (  = c = 1 ) M 4 2 = 1/G 4 The analog of the Plank mass in higher dimensions is called M 4+n When expressed in terms of M 4 and M 4+n the previous result G 4 = G 5 /4R generalizes to This forms the basis for current experiments

22 January 2001Purdue University Department of Physics How Big is M 4+n ? How big is n ? 1)The usual Plank mass M 4 and the associated length scale  /M 4 c  cm are the scales at which gravitational interactions become comparable in strength to other interactions, and hence can be unified with these interactions 2)It would be nice if this happened at a smaller energy scale  bigger length scale. A natural choice is ~ 1 TeV = eV where supersymmetry breaks down 3)This can happen in some string theories with extra spatial dimensions if ordinary matter is confined to 3-dimensional walls (“branes”), and only gravity propagates in the extra dimensions

22 January 2001Purdue University Department of Physics How Big is M 4+n ? How big is n ? 4)In such theories M 4+n  1 TeV by assumption We then solve: n = 1  R(1)  2  cm NO GOOD !!  n = 2  R(2)  0.2 = 2 mm OK !! n = 3  R(3)  9  cm ?? (10 19 GeV) 2 (1 TeV) n+2

22 January 2001Purdue University Department of Physics Mini-Review #2 The gravitational force in a space with n extra spatial dimensions varies as To avoid a conflict with known gravity tests one must arrange things such that any new force law show up only at very short scales. This can be achieved using additional compact spatial dimensions. The size of R(n) of these extra dimensions is governed by the relation

22 January 2001Purdue University Department of Physics Motivation for Short-Distance Gravity Selected References: N. Arkani-Hamed, S. Dimopoulos, & G. Dvali, Phys. Rev. D59, (1999) A. Kehegias and K. Sfetsos, Phys. Lett. B472, 39 (2000) L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999) J. Garriga and T. Tanaka, Phys. Rev. Lett. 84, 2778 (2000)