Unparticle Physics JongPhil Lee Yonsei Univ Based on

Unparticle Physics Jong-Phil Lee Yonsei Univ. Based on JPL, 1009. 1730; 0911. 5382; 0901. 1020 16 Nov 2010, Yonsei Univ.

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

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H. Georgi, PRL 98; PLB 650 Unparticles U: Basic Idea Weakly interacting SM Sector Particles with definite masses Scale Inv. Sector NO particles With definite nonzero masses Unparticle ! 4

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

Phase Space of U Production Cross Section Phase Space 6

Spectral Function 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. 7

Propagators of U Cheung, Keung, Yuan, PRD 76 Grinstein, Intriligator, Rothstein, PLB 662 Scalar Unparticle Propagator Vector Unparticle Propagator 8

Fox, Rajaraman, Shirman, , PRD 76 Scale Invariance Breaking scale invariance breaking “Good Correspondence” m 0 : r. U reduces to the usual Unparticle spectral function d. U 1 : the corresponding propagator is a free particle propagator of mass m. 9

U-production via t->U+u Interaction Lagrangian Phase spaces 10

Decay rate distribution 11

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What is "Deconstruction"? Stephanov, PRD 76 Philosophy Unparticles lim S D 0 continuous sum for unparticles with mass gap D 13

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

Flat Higher Dim'l Description Massless field Lagrangian in 4+d dim Kk mode expansion 15

Scale Invariance Breaking JPL, PRD 79 Massive Lagrangian Massive propagator 16

Spectral Function Shifted 17

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Goldberg & Nath, PRL 100 Ungravity by tensor unparticles Tensor unparticle interaction Newtonian gravity modified 19

Ungravity = Fractional e. Xtra Dim(FXD) Basic Idea Unparticle lim S D 0 2 d. U-1 particles with mass gap D KK sum over Extra dim. N+1 20

Ungravity Basics Ungravity Lagrangian Spectral Function Two-Point Function 21

Ungravity Propagator Tensor Structure Grinstein, Intriligator, Rothstein, PLB 662 22

Deconstructing Ungravity JPL, 0911. 5382 Tensor Operator Decomposed (polarization tensor) Matching Tensor Structure for Deconstructed states for massive graviton Deconstructed Ungravity 23

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

Newtonian Gravity Modified Newtonian Potential 25

=? Ad. S(4+N) Ungravity= 26

Ungravity = (4+N)D Gravity JPL, 0911. 5382 (4+N)-dim’l Gravity Proposition 27

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

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U-enhanced black hole Mureika, PLB 660 Newtonian gravity modified Schwarzschild metric Geometric BH cross section Schwarzschild radius ~10 -5 fm for typical parameters 30

Vector U and Ungravity Mureika, Spallucci ar. Xiv: 1006. 4556 Vector Unparticle Interaction (Bm : baryon current) “repulsive contribution” 31

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

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

Z+graviton/U production @LHC Invariant mass spectrum of U Ask, EPJC(2009)60 Dense KK tower of large XD 34

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Basics of B-anti B mixing 36

U-contribution to Bs-anti Bs Scalar and vector unparticle couplings s- and t-channel contribution at tree level 37

Tree level calculation 38

U-contribution parametrization 39

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

Phase positive definite suppressed Unparticles cannot explain the positive cf) fs. D 41

Allowed region JPL, 1009. 1730 42

Contour for different c. S degree 43

Conclusions • Unparticles of spin 2 produce ungravity. • Ungravity modifies the Newtonian gravitational potential. • Ungravity physics is realized in Ad. S(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. 44