1 RS model with small curvature and dilepton production at the LHC Alexander Kisselev Institute for High Energy Physics Protvino, Russia The XIIth International School-Seminar The Actual Problems of Microworld Physics Gomel, Belarus, July 22 August 2, 2013 Plan of the talk Flat extra dimensions (EDs) Warped ED with small curvature (RSSC model) Kaluza-Klein (KK) excitations massive gravitons Contribution from s-channel virtual gravitons Dilepton production at the LHC Conclusions 2 Flat extra dimensions 3 G. Nordstrm (1914): T. Kaluza (1921), H. Mandel (1926): 5D vector theory = electromagnetism + scalar gravity Trajectory of charged particle = geodesic in 5-dimensional Riemann space with metric: 4 EDs: Brief History A. Einstein, P. Bergmann (1938), B.V. Bargman (1941): Generalization of Kaluza-Klein theory: periodicity in 5-th coordinate O. Klein (1926), V.A. Fock (1926): Trajectory of charged particle = geometrical line in 5-dimensional Riemann space with metric: 5 (Bergmann, Einstein, and Bargmann on Princeton Campus) Yu.B. Rumer (1956 ): Quantum mechanics = 5-dimensional optics See also F. Klein (1891 ): Single-sides surface can be embeded in D-dimensional space (Klein bottle) 6 Why spatial (i.e. space-like) EDs? Metric tensor (D=5) Massless particle in five dimensions (Lorentz invariance holds): No tachyons Spatial extra dimension 7 World sheets of open (left) and closed (right) strings propagating in the space-time Superstrings: D= EDs must be compactified: Strings lead to existence of EDs Closed strings propagate in the bulk Open strings propagate with ends at x = const for different winding 6 internal compact dimensions = (p-3) longitudinal + (9-p) transverse 9 String propagation in EDs String theories contain D(irichlet)-branes Planck scale Gauge coupling String action Upon compactification of EDs (S 4-dim S eff ): Rescaled volumeDdimensional Planck scale 10 String scale String coupling hierarchy relation: Warped ED with small curvature 11 ED with Small Curvature (RSSC Model) Background AdS 5 metric r c is radius of ED Points (x,y) and (x,y) are identified + periodicity orbifold S 1 /Z 2 12 Poincar invariance in x direction is Minkowski tensor 13 Circle S 1 defined by y = y + 2 R is subject to Z 2 identification y = - y, becoming a line segment S 1 /Z 2 with two fixed points y=0 and y = R At every point of 4-dimensional space-time there exists orthogonal dimension compactified on circle of radius R SM fields are confined to TeV brane SM Planck brane TeV brane Gravity Gravity lives in all dimensions (bulk) 14 Five-dimensional action Einstein-Hilberts equations 15 gravity action brane actions Reduced scales Non-zero elements of curvature tensor 5-dimensional scalar curvature Equations for background metric 16 Solution of E-Hs equations (A.K., arXiv: ) Original RS model: (Randall & Sundrum, 1999) 17 Warp factor (y)+ r c y 2r c -r c 0 r c r c 18 Curvature: Radius of curvature: In between the branes (0 < y < r c ) Warp factor: Five-dimensional scalar curvature: Original RS model: 19 AdS 5 space-time Massive KK gravitons 20 Gravitational 5-dimensional field Transverse-traceless gauge General coordinate transformation 21 Kaluza-Klein (KK ) gravitons Scalar massless field (x) radion 22 Interaction Lagrangian on TeV brane massive radionStabilization mechanism (Goldberger & Wise, 1999) 23 RS model Series of massive resonances (Randall & Sundrum, 1999) Graviton masses (J 1 (x n ) = 0) Hierarchy relation RSSC model Narrow low-mass resonances with small mass splitting (Giudice et al., 2004, Petrov & A.K., 2005) 24 Graviton masses Hierarchy relation Spectrum is similar to that in ADD model Negligible relative corrections to Newton law Newtons potential between test masses No astrophysical bounds for > 10 MeV 25 For instance, can be realized only for AdS 5 Metric vs. Flat Metric with One Compact ED AdS 5 Metric vs. Flat Metric with One Compact ED solar distance (d is number of flat EDs) - strongly disfavored by astrophysical bounds RSSC model is not equivalent to ADD model with one ED of the size 26 Hierarchy relation in flat EDs Limiting case of hierarchy relation for warped metric 27 (D=4+d) means s-channel KK gravitons 28 Virtual s-channel KK Gravitons Scattering of SM fields mediated by graviton exchange Scattering of SM fields mediated by graviton exchange Energy region: Processes: Virtual s-channel KK Gravitons Parton sub-processes: 29 Matrix element for dilepton production where Tensor part of graviton propagator Energy-momentum tensor Zero width approximation (Giudice et al., 2005) (imaginary part only) 30 Widths of KK gravitons S(s) can be calculated analytically by using formula (m n = z n,1 ) where (A.K, 2006) 31 Is mass splitting small enough for mass distribution to be continuous? relevant KK numbers At 32 At the same time, for s > 3M 5 zero width result is reproduced ( resonances overlap) Suppose spectrum is a series of narrow resonances V.A. Matveev, R.M. Muradian and A.N. Tavkhelidze, JINR P (Dubna, 1969), SLAC TRANS-009: JINR R (June, 1969) S.D. Drell and T.M. Yan, SLAC-PUB-0755 (June, 1970), Phys. Rev. Lett. 25 (1970) 316, errata Phys. Rev. Lett. 25 (1970) 902 Dilepton production (Drell-Yan process) 33 Dilepton Production in Warped ED Differential cross section where 34 Weak logarithmic dependence on energy comes from PDFs d( grav ): no dependence on curvature 35 (fixed x ) Virtual graviton contributions quark-antiquark annihilation gluon-gluon fusion (absent in SM at tree level) 36 Dimuon production Pseudorapidity cut: || 2.4 Efficiency: 85 % K-factor: 1.5 for SM background 1.0 for signal 37 (A.K., JHEP, 2013) Graviton contributions to the process pp +- + X (solid lines) vs. SM contribution (dashed line) for 7 TeV 38 Graviton contributions to the process pp +- + X (solid lines) vs. SM contribution (dashed line) for 14 TeV 39 Ratio of the gravity induced cross section to the SM cross section for 14 TeV (solid lines) and 7 TeV (dashed lines) 40 Graviton contribution to the process pp +- + X (solid curves) vs. contribution from zero widths gravitons (dashed curves, multiplied by 10 3 ) for 14 TeV 41 Dielectron production Pseudorapidity (CMS) cuts: || 1.44, 1.57 || 2.4 Efficiency: 85 % K-factors: 1.5 for SM background 1.0 for signal 42 (A.K., arXiv: ) Graviton contributions to the process pp e+e- + X (solid lines) vs. SM contribution (dashed line) for 8 TeV 43 Graviton contributions to the process pp e+e- + X (solid lines) vs. SM contribution (dashed line) for 13 TeV 44 Statistical significance Number of events with p t > p t cut 45 Interference SM-gravity contribution is negligible Lower bounds on M 5 at 95% level Statistical significance for the process pp e + e - + X as a function of 5 -dimensional reduced Planck scale and cut on electron transverse momentum for 7 TeV (L=5 fb -1 ) and 8 TeV (L=20 fb -1 ) 46 Statistical significance for the process pp e + e - + X as a function of 5 -dimensional reduced Planck scale and cut on electron transverse momentum for 13 TeV (L=30 fb -1 ) 47 Angular distribution has term ~(cos) 4 How to discriminate gravity effects from other beyond SM contributions? Relation between diphoton and Drell-Yan process cross sections 48 Conclusions 49 Conclusions In the RSSC model, curvature is small, ~ GeV, with M 5 ~ 1-10 TeV Mass spectrum is similar to that in the ADD model with one ED At fixed x = 2p t / s, ratio d( grav )/d( SM ) is proportional to (s/ M 5 ) 3 Gravity cross sections weakly depend on , provided