Download Unparticle Physics - Theoretical Particle Physics Group of Yonsei Univ.

Jong-Phil Lee
Yonsei Univ.
Based on JPL,
1009.1730; 0911.5382;0901.1020
16 Nov 2010, Yonsei Univ.
•Unparticles Brief
•Flat higher dim’l deconstruction
•Ungravity
•Fractional eXtra Dimension (FXD)
•Unparticle and Bs-anti Bs
•Conclusions
2
3
H. Georgi, PRL98; PLB650
Weakly interacting
SM Sector
Particles with
definite masses
Scale Inv.
Sector
NO particles
With definite
nonzero masses
Unparticle!
4
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
Production Cross Section
Phase Space
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Two-point function
Spectral density function
Fixed by scale inv.
Normalization factor
Unparticles with dU look like a
Non-integral number of
massless particles.
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Cheung, Keung, Yuan, PRD76
Grinstein, Intriligator, Rothstein, PLB662
Scalar Unparticle Propagator
Vector Unparticle Propagator
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Fox, Rajaraman, Shirman,, PRD76
scale invariance breaking
“Good Correspondence”
m0 : rU reduces to the usual Unparticle spectral function
dU1 : the corresponding propagator is a free particle propagator of mass m.
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Interaction Lagrangian
Phase spaces
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12
Stephanov, PRD76
Philosophy
Unparticles
lim S
D 0
continuous sum for unparticles
particles
with mass
gap D
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Assume that the scale invariance is slightly broken;
continuous l
discrete l
Spectral function
Propagator
Matching in the limit D-->0
In general,
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Massless field Lagrangian in 4+d dim
Kk mode expansion
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JPL, PRD 79
Massive Lagrangian
Massive propagator
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Goldberg & Nath, PRL 100
Tensor unparticle interaction
Newtonian gravity modified
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Basic Idea
Unparticle
lim S
D 0
2dU-1
particles
with
mass
gap D
KK sum
over
Extra dim.
N+1
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Ungravity Lagrangian
Spectral Function
Two-Point Function
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Ungravity Propagator
Tensor Structure
Grinstein, Intriligator, Rothstein, PLB662
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JPL, 0911.5382
Tensor Operator Decomposed
(polarization tensor)
Matching
Tensor Structure for Deconstructed states
for massive graviton
Deconstructed Ungravity
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Arkani-Hamed et al., PRL 84
AdS(4+N) metric
Reparametrizaion
KK Decomposition
for which
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Newtonian Potential
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JPL, 0911.5382
(4+N)-dim’l Gravity
Proposition
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Intermediate States Have Vanishing Mass?
For large L>>r
Does Fn Satisfy the Matching Condition?
Newtonian Potential Modification
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Mureika, PLB660
Newtonian gravity modified
Schwarzschild metric
Geometric BH cross section
Schwarzschild radius
~10-5 fm
for typical parameters
30
Mureika, Spallucci
arXiv:1006.4556
Vector Unparticle Interaction
(Bm
: baryon current)
“repulsive contribution”
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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”
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Weak coupling phase
Strong coupling phase
cf) Hawking temp. for
Schwarzschild BH in D-dim
33
Ask,
EPJC(2009)60
Invariant mass spectrum of U
Dense KK tower of large XD
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Scalar and vector unparticle couplings
s- and t-channel contribution at tree level
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In the literature, people usually put
dS =dV
fS is suppressed
by a factor of
But this is NOT true.
Unitarity constraint
fV is suppressed by
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positive definite
suppressed
Unparticles cannot explain the positive
cf)
fsD
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JPL, 1009.1730
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degree
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•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.
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