Jong-Phil Lee Yonsei Univ. 16 Nov 2010, Yonsei Univ. Based on JPL, 1009.1730; 0911.5382;0901.1020.
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Transcript of Jong-Phil Lee Yonsei Univ. 16 Nov 2010, Yonsei Univ. Based on JPL, 1009.1730; 0911.5382;0901.1020.
Unparticle Physics
Jong-Phil Lee Yonsei Univ.
16 Nov 2010, Yonsei Univ.
Based on JPL,1009.1730; 0911.5382;0901.1020
2
Outlook
•Unparticles Brief
•Flat higher dim’l decon-
struction
•Ungravity
•Fractional eXtra Dimension
(FXD)
•Unparticle and Bs-anti Bs
•Conclusions
3
UNPARTICLES
4
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!
5
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
6
Phase Space of UProduction Cross Section
Phase Space
7
Spectral FunctionTwo-point function
Spectral density functionFixed by scale inv.
Normalization factorUnparticles with dU look like a Non-integral number of massless particles.
8
Propagators of UGrinstein, Intriligator, Rothstein, PLB662
Cheung, Keung, Yuan, PRD76
Scalar Unparticle Propagator
Vector Unparticle Propagator
9
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.
10
U-production via t->U+uInteraction Lagrangian
Phase spaces
11
Decay rate distribution
12
HIGHER DIMEN-SIONAL
DECONSTRUCTION
13
What is "Deconstruction"?Stephanov, PRD76
Philosophy
lim S D 0
Unparti-cles
particles with mass gap D
continuous sum for unparticles
14
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
15
Flat Higher Dim'l DescriptionMassless field Lagrangian in 4+d dim
Kk mode expansion
16
Scale Invariance BreakingJPL, PRD 79
Massive Lagrangian
Massive propagator
17
Spectral Function Shifted
18
UNGRAVITY &EXTRA DIMENSION
19
Ungravity by tensor unparticlesGoldberg & Nath, PRL 100
Newtonian gravity modified
Tensor unparticle interaction
20
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
21
Ungravity BasicsUngravity Lagrangian
Spectral Function
Two-Point Function
22
Ungravity PropagatorUngravity Propagator
Tensor Structure Grinstein, Intriligator, Rothstein, PLB662
23
Deconstructing Ungravity
for massive graviton
Tensor Operator Decomposed
Matching
Tensor Structure for Deconstructed states
Deconstructed Ungravity
(polarization tensor)
JPL, 0911.5382
24
Gravity in AdS(4+N)Arkani-Hamed et al., PRL 84
AdS(4+N) metric
KK Decomposition
Reparametrizaion
for which
25
Newtonian Gravity ModifiedNewtonian Potential
26
Ungravity=?AdS(4+N)
27
Ungravity = (4+N)D Gravity(4+N)-dim’l Gravity
Proposition
JPL, 0911.5382
28
Some RemarksIntermediate States Have Vanishing Mass?
Does Fn Satisfy the Matching Condition?
Newtonian Potential Modification
For large L>>r
29
RELATED ISSUES
30
U-enhanced black hole
Schwarzschild radius
Schwarzschild metric
Newtonian gravity modified
Geometric BH cross section
~10-5 fm for typical parameters
Mureika, PLB660
31
Vector U and UngravityMureika, Spallucci
arXiv:1006.4556
(Bm : baryon current)
Vector Unparticle Interaction
“repulsive contribution”
32
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.
33
Hawking Temperature
cf) Hawking temp. for Schwarzschild BH in D-dim
Weak coupling phase
Strong coupling phase
34
Z+graviton/U production @LHCAsk,
EPJC(2009)60
Invariant mass spectrum of U Dense KK tower of large XD
35
UNPARTICLE AND BS-ANTI BS
36
Basics of B-anti B mixing
37
U-contribution to Bs-anti Bs
Scalar and vector unparticle couplings
s- and t-channel contribution at tree level
38
Tree level calculation
39
U-contribution parametrization
40
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
41
Phase
suppressed
positive definite
cf)
Unparticles cannot explain the positive fsD
42
Allowed regionJPL, 1009.1730
43
Contour for different cS
degree
44
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.