1. Jong-Phil Lee Yonsei Univ. 16 Nov 2010, Yonsei Univ. Based on JPL, 1009.1730; 0911.5382;0901.1020

2. 2 Unparticles Brief Flat higher dim’l deconstruction Ungravity Fractional eXtra Dimension (FXD) Unparticle and Bs-anti Bs Conclusions

3. 3

4. 4 H. Georgi, PRL98; PLB650 SM Sector Scale Inv. Sector Weakly interacting Particles with definite masses NO particles With definite nonzero masses Unparticle!

5. 5 energy MUMU UU BZ SM Dimensional transmutation Scale inv. emerges. MWMW ; EWSB ; scale inv. breaking Banks-Zaks( BZ ) Theory Massless fermionic gauge theory With an infrared-stable fixed point. matching

6. 6 Production Cross Section Phase Space

7. 7 Two-point function Spectral density function Fixed by scale inv. Normalization factor Unparticles with d U look like a Non-integral number of massless particles.

8. 8 Grinstein, Intriligator, Rothstein, PLB662 Cheung, Keung, Yuan, PRD76 Scalar Unparticle Propagator Vector Unparticle Propagator

9. 9 Fox, Rajaraman, Shirman,, PRD76 scale invariance breaking “Good Correspondence”   0 :  U reduces to the usual Unparticle spectral function d U  1 : the corresponding propagator is a free particle propagator of mass m.

10. 10 Interaction Lagrangian Phase spaces

11. 11

12. 12

13. 13 Stephanov, PRD76 Philosophy lim S   0 Unparticle s particles with mass gap  continuous sum for unparticles

14. 14 Assume that the scale invariance is slightly broken; continuous ldiscrete l In general, Matching in the limit D-->0 Spectral function Propagator

15. 15 Massless field Lagrangian in 4+d dim Kk mode expansion

16. 16 JPL, PRD 79 Massive Lagrangian Massive propagator

17. 17

18. 18

19. 19 Goldberg & Nath, PRL 100 Newtonian gravity modified Tensor unparticle interaction

20. 20 Basic Idea lim S   0 Unparticle particle s with mass gap  KK sum over Extra dim. 2d U - 1 N+1

21. 21 Ungravity Lagrangian Spectral Function Two-Point Function

22. 22 Ungravity Propagator Tensor Structure Grinstein, Intriligator, Rothstein, PLB662

23. 23 for massive graviton Tensor Operator Decomposed Matching Tensor Structure for Deconstructed states Deconstructed Ungravity (polarization tensor) JPL, 0911.5382

24. 24 Arkani-Hamed et al., PRL 84 AdS(4+N) metric KK Decomposition Reparametrizaion for which

25. 25 Newtonian Potential

26. 26

27. 27 (4+N)-dim’l Gravity Proposition JPL, 0911.5382

28. 28 Intermediate States Have Vanishing Mass? Does Fn Satisfy the Matching Condition? Newtonian Potential Modification For large L>>r

29. 29

30. 30 Schwarzschild radius Schwarzschild metric Newtonian gravity modified Geometric BH cross section ~10 -5 fm for typical parameters Mureika, PLB660

31. 31 Mureika, Spallucci arXiv:1006.4556 (Bm : baryon current) Vector Unparticle Interaction “repulsive contribution”

32. 32 Extremal Condition (1)M>Me : Massive object. Two-horizon BH. (2)M=Me : Critical object. Single horizon. Extremal BH. (3)M<Me : “naked-singularity” Horizons As M goes down, the two horizons approach to each other. Inner & outer Horizons exist.

33. 33 cf) Hawking temp. for Schwarzschild BH in D-dim Weak coupling phase Strong coupling phase

34. 34 Ask, EPJC(2009)60 Invariant mass spectrum of U Dense KK tower of large XD

35. 35

36. 36

37. 37 Scalar and vector unparticle couplings s- and t-channel contribution at tree level

38. 38

39. 39

40. 40 Unitarity constraint In the literature, people usually put d S =d V But this is NOT true. f S is suppressed by a factor of f V is suppressed by

41. 41 suppressed positive definite cf) Unparticles cannot explain the positive f s D

42. 42 JPL, 1009.1730

43. 43 degree

44. 44 Unparticles of spin 2 produce ungravity. Ungravity modifies the Newtonian gravitational potential. Ungravity physics is realized in AdS(4+N)-dim’l gravity. Ungravity can be understood in the context of fractional extra dimensions. Scalar unparticles contribute predominantly to the Bs-(anti Bs) mixing, and can naturally explain its negative phase. The LHC might see evidences of unparticles.

46. 2010 LHC Workshop @ Korea (Konkuk Univ) Jong-Phil Lee(Yonsei Univ.) 46 1234567890-= qwertyuiop[]\ asdfghjkl;’ zxcvbnm,./` !@#$%^&*()_+ QWERTYUIOP{}| ASDFGHJKL:” ZXCVBNM<>?~

47. 2010 LHC Workshop @ Korea (Konkuk Univ) Jong-Phil Lee(Yonsei Univ.) 47 D 0000 and D 00 have opposite sign: D 0000 ~(-h 00 ) 2 ; D 00 ~-h 00