Unparticle Physics

Jong-Phil Lee Yonsei Univ.

16 Nov 2010, Yonsei Univ.

Based on JPL,1009.1730; 0911.5382;0901.1020

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Outlook

•Unparticles Brief

•Flat higher dim’l decon-

struction

•Ungravity

•Fractional eXtra Dimension

(FXD)

•Unparticle and Bs-anti Bs

•Conclusions

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UNPARTICLES

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Unparticles U: Basic Idea H. Georgi, PRL98; PLB650

SM Sec-tor

Scale Inv.

Sector

Weakly interacting

Particles with definite masses

NO particles With definite nonzero masses

Unpar-ticle!

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Effective Theory for Uenergy

MU

LU

BZ

SM

Dimensionaltransmutation

Scale inv. emerges.

MW; EWSB; scale inv. breaking

Banks-Zaks(BZ) The-oryMassless fermionic gauge theoryWith an infrared-stable fixed point.

matching

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Phase Space of UProduction Cross Section

Phase Space

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Spectral FunctionTwo-point function

Spectral density functionFixed by scale inv.

Normalization factorUnparticles with dU look like a Non-integral number of massless particles.

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Propagators of UGrinstein, Intriligator, Rothstein, PLB662

Cheung, Keung, Yuan, PRD76

Scalar Unparticle Propagator

Vector Unparticle Propagator

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Scale Invariance BreakingFox, Rajaraman, Shirman,, PRD76

scale invariance breaking

“Good Correspondence”

m0 : rU reduces to the usual Unparticle spectral function

dU1 : the corresponding propagator is a free particle propagator of mass m.

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U-production via t->U+uInteraction Lagrangian

Phase spaces

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Decay rate distribution

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HIGHER DIMEN-SIONAL

DECONSTRUCTION

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What is "Deconstruction"?Stephanov, PRD76

Philosophy

lim S D 0

Unparti-cles

particles with mass gap D

continuous sum for unparticles

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How to deconstructAssume that the scale invariance is slightly broken;

continuous l discrete l

In general,

Matching in the limit D-->0

Spectral function

Propagator

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Flat Higher Dim'l DescriptionMassless field Lagrangian in 4+d dim

Kk mode expansion

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Scale Invariance BreakingJPL, PRD 79

Massive Lagrangian

Massive propagator

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Spectral Function Shifted

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UNGRAVITY &EXTRA DIMENSION

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Ungravity by tensor unparticlesGoldberg & Nath, PRL 100

Newtonian gravity modified

Tensor unparticle interaction

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Ungravity = Fractional eXtra Dim(FXD)

Basic Idea

lim S D 0

Unparti-cle

parti-cles with mass gap D

KK sum overExtra dim.

2dU-1 N+1

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Ungravity BasicsUngravity Lagrangian

Spectral Function

Two-Point Function

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Ungravity PropagatorUngravity Propagator

Tensor Structure Grinstein, Intriligator, Rothstein, PLB662

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Deconstructing Ungravity

for massive graviton

Tensor Operator Decomposed

Matching

Tensor Structure for Deconstructed states

Deconstructed Ungravity

(polarization tensor)

JPL, 0911.5382

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Gravity in AdS(4+N)Arkani-Hamed et al., PRL 84

AdS(4+N) metric

KK Decomposition

Reparametrizaion

for which

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Newtonian Gravity ModifiedNewtonian Potential

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Ungravity=?AdS(4+N)

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Ungravity = (4+N)D Gravity(4+N)-dim’l Gravity

Proposition

JPL, 0911.5382

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Some RemarksIntermediate States Have Vanishing Mass?

Does Fn Satisfy the Matching Condition?

Newtonian Potential Modification

For large L>>r

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RELATED ISSUES

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U-enhanced black hole

Schwarzschild radius

Schwarzschild metric

Newtonian gravity modified

Geometric BH cross section

~10-5 fm for typical parameters

Mureika, PLB660

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Vector U and UngravityMureika, Spallucci

arXiv:1006.4556

(Bm : baryon current)

Vector Unparticle Interaction

“repulsive contribution”

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Extremal Black Hole

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 & outerHorizons exist.

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Hawking Temperature

cf) Hawking temp. for Schwarzschild BH in D-dim

Weak coupling phase

Strong coupling phase

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Z+graviton/U production @LHCAsk,

EPJC(2009)60

Invariant mass spectrum of U Dense KK tower of large XD

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UNPARTICLE AND BS-ANTI BS

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Basics of B-anti B mixing

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U-contribution to Bs-anti Bs

Scalar and vector unparticle couplings

s- and t-channel contribution at tree level

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Tree level calculation

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U-contribution parametrization

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Discussions

Unitarity constraint

In the literature, people usually put

dS =dV

But this is NOT true.

fS is suppressedby a factor of

fV is suppressed by

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Phase

suppressed

positive definite

cf)

Unparticles cannot explain the positive fsD

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Allowed regionJPL, 1009.1730

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Contour for different cS

degree

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Conclusions

•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.