RS model with small curvature and dilepton production at the LHC

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, July22 – August 2, 2013

2. 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

3. Flat extra dimensions

4. EDs: Brief History G. Nordström (1914): 5D vector theory = electromagnetism + scalar gravity T. Kaluza (1921), H. Mandel (1926): Trajectory of charged particle = geodesic in 5-dimensional Riemann space with metric:

5. O. Klein (1926), V.A. Fock (1926): Trajectory of charged particle = geometrical line in 5-dimensional Riemann space with metric: A. Einstein, P. Bergmann (1938), B.V. Bargman (1941): (Bergmann, Einstein, and Bargmann on Princeton Campus) Generalization of Kaluza-Klein theory: periodicity in 5-th coordinate

6. 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)

7. Why spatial (i.e. space-like) EDs? Metric tensor (D=5) Massless particle in five dimensions (Lorentz invariance holds): Spatial extra dimension No tachyons

8. Strings lead to existence of EDs Superstrings: D=10 World sheets of open (left) and closed (right) strings propagating in the space-time 6 EDs must be compactified:

9. String propagation in EDs 6 internal compact dimensions = (p-3) longitudinal + (9-p) transverse Open strings propagate with ends at x┴ = const for different windingω Closed strings propagate in the bulk String theories contain D(irichlet)-branes

10. String scale • String coupling • Planck scale • Gauge coupling String action Upon compactification of EDs (S → 4-dim Seff): Rescaled volume D–dimensional Planck scale hierarchy relation:

11. Warped ED with small curvature

12. ED with Small Curvature (RSSC Model) Background AdS5 metric Points (x,y) and (x,–y) are identified + periodicity orbifold S1/Z2 rc is radius of ED Poincaré invariance in xμ direction ημνis Minkowski tensor

13. At every point of 4-dimensional space-time there exists “orthogonal” dimension compactified on circle of radius R Circle S1 defined by y = y + 2 πR is subject to Z2 identification y = - y, becoming a line segment S1/Z2 with two fixed points y=0 and y = πR

14. Gravity lives in all dimensions (bulk) Gravity Planck brane TeV brane SM SM fields are confined to TeV brane

15. Five-dimensional action gravity action brane actions Reduced scales Einstein-Hilbert’s equations

16. Non-zero elements of curvature tensor 5-dimensional scalar curvature Equations for background metric

17. Solution of E-H’s equations (A.K., arXiv:1306.5402) Warp factor Original RS model: (Randall & Sundrum, 1999)

18. σ(y)+ κπrc κπrc y -πrc πrc 2πrc 0

19. In between the branes (0 < y < πrc ) AdS5 space-time Five-dimensional scalar curvature: Curvature: Radius of curvature: Warp factor: Original RS model:

20. Massive KK gravitons

21. Gravitational 5-dimensional field General coordinate transformation Transverse-traceless gauge

22. Kaluza-Klein (KK ) gravitons Interaction Lagrangian on TeV brane Scalar massless field Φ(x) – radion Stabilization mechanism (Goldberger & Wise, 1999) massive radion

23. RS model (Randall & Sundrum, 1999) Hierarchy relation Graviton masses (J1(xn) = 0) Series of massive resonances

24. RSSC model (Giudice et al., 2004, Petrov & A.K., 2005) Hierarchy relation Graviton masses Narrow low-mass resonances with small mass splitting Spectrum is similar to that in ADD model

25. Newton’s potential between test masses Negligible relative corrections to Newton law No astrophysical bounds forκ > 10 MeV

26. AdS5 Metric vs. Flat Metric with One Compact ED RSSC model is not equivalent to ADD model with one ED of the size For instance, can be realized only for (d is number of flat EDs) solar distance - strongly disfavored by astrophysical bounds

27. Hierarchy relation in flat EDs (D=4+d) Limiting case of hierarchy relation for warped metric means

28. s-channel KK gravitons

29. Virtual s-channel KK Gravitons Virtual s-channel KK Gravitons Scattering of SM fields mediated by graviton exchange Processes: Parton sub-processes: Energy region:

30. Matrix element for dilepton production Tensor part of graviton propagator where Energy-momentum tensor Zero width approximation (Giudice et al., 2005) (imaginary part only)

31. Widths of KK gravitons S(s) can be calculated analytically by using formula (mn = zn,1κ) (A.K, 2006) where

32. Is mass splitting small enough for mass distribution to be continuous? Suppose ( resonances overlap) relevant KK numbers At the same time, for √s > 3M5 zero width result is reproduced spectrum is a series of narrow resonances At

33. Dilepton production (Drell-Yan process) V.A. Matveev, R.M. Muradian and A.N. Tavkhelidze,JINR P2-4543 (Dubna, 1969), SLAC TRANS-009: JINR R2-4543(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

34. Dilepton Production in Warped ED Differential cross section where

35. Weak logarithmic dependence on energy comes from PDFs (fixed x┴) dσ(grav): no dependence on curvature κ

36. Virtual graviton contributions quark-antiquark annihilation gluon-gluon fusion (absent in SM at tree level)

37. Dimuon production (A.K., JHEP, 2013) Pseudorapidity cut: |η| ≤ 2.4 Efficiency: 85 % K-factor: 1.5 for SM background 1.0 for signal

38. Graviton contributions to the process pp → μ+μ- + X (solid lines) vs. SM contribution (dashed line) for 7 TeV

39. Graviton contributions to the process pp → μ+μ- + X (solid lines) vs. SM contribution (dashed line) for 14 TeV

40. Ratio of the gravity induced cross section to the SM cross section for 14 TeV (solid lines) and 7 TeV (dashed lines)

41. Graviton contribution to the process pp → μ+μ- + X (solid curves) vs. contribution fromzero widths gravitons (dashed curves, multiplied by 103) for 14 TeV

42. Dielectron production (A.K., arXiv:1306.5402) Pseudorapidity (CMS) cuts: |η| ≤ 1.44, 1.57 ≤ |η| ≤ 2.4 Efficiency: 85 % K-factors: 1.5 for SM background 1.0 for signal

43. Graviton contributions to the process pp → e+e- + X (solid lines) vs. SM contribution (dashed line) for 8 TeV

44. Graviton contributions to the process pp → e+e- + X (solid lines) vs. SM contribution (dashed line) for 13 TeV

45. Number of events with pt > ptcut Interference SM-gravity contribution is negligible Statistical significance Lower bounds on M5 at 95% level

46. Statistical significance for the process pp → e+e- + X as a function of 5-dimensional reducedPlanck scale and cut on electron transverse momentum for 7 TeV (L=5 fb-1) and 8 TeV (L=20 fb-1)

47. Statistical significance for the process pp → e+e- + X as a function of 5-dimensional reducedPlanck scale and cut on electron transverse momentum for 13 TeV (L=30 fb-1)

48. How to discriminate gravity effects from other beyond SM contributions? Relation between diphoton and Drell-Yan process cross sections Angular distribution has term ~(cosθ)4

49. Conclusions

50. Conclusions • In the RSSC model, curvature κis small, • κ ~ 0.1-10 GeV, with M5 ~ 1-10 TeV • Mass spectrum is similar to that in the ADD model with one ED • At fixed x┴ = 2pt /√s, ratio dσ(grav)/dσ(SM) is proportional to (√s/ M5 )3 • Gravity cross sections weakly depend on κ, provided κ << M5 • Account of KK graviton widths is a crucial point for calculations • LHC search limits on M5 are: • ● 6.35 TeV, for 7+8 TeV, L = 5 fb-1 + 20 fb-1 ● 8.95 TeV, for 13 TeV, L = 30 fb-1