A New Problem ofVirtual Kaluza-Klein graviton exchanges
Tokyo Metropolitan U.
Haruka Namatame

実験理論共同研究会 「LHCが切り拓く新しい物理」
2009/4/02

Motivation”To probe ADD model at LHC”
Virtual Kaluza-Klein graviton exchange processes↑massive particle· Analysises have performed
without the decay width !
But： Z boson exchange process

KK

Diverge at⇒Why can these cross section get a finite value ?

“ Large Extra Dimension Scenario”
A model by Arkani-Hamed, Dimopoulos and Dvali
Phys.Lett.B429,263 (1998)

Momenta inextra dimensions :/RGraviton

SM particles are confinedon 3D space

2πR Direction of extraD

yMomenta in extra dimensions
are not conserved !

Aproach to“Gauge Hierarchy Problem”

Kaluza-Klein gravitons· Infinite number of massive gravitons
exist in ADD model !

＝~Only one KK“ordinary weak gravity”⇒~Many KK“strong gravity”

·Degeneracy of KK gravitons=
Ex number of KK gravitons〜of which mass is 100 GeV·Decay width of KK gravitons
Main decay channels areKK！

Collider Signatures of the ADD model
Virtual Kaluza-Klein graviton exchange processes

J.L.Hewett,
Phys. Rev. Lett. 82, 4765 (1999)

KK

T. Han, J. D. Lykken and R. J. Zhang,Phys. Rev. D 59, 105006 (1999)· On-shell KK gravitons must be in the intermediate state⇒Resonance effect is important

We should analyse these processes
with the decay width of KK gravitons !

“ Toy Model”
KK gravitons: real scalar, mass isLight Fermion: real scalar, massless/R

Simplify
KK

The process in ADD model

The process in toy model

2-body scattering via KK gravitons⇒

·In caseδ ＞ ２Strongly depend on the cutoff α
Not depend on δ (the number of extra dimensions)Leading term is constant ! (not depend on)

KK graviton productions

Hard to believe this as a physical result !

HintsNarrow-width approximation· In a process (a particle X is in intermediate state)
X can be on-shell in intermediate state）
width of X is enough small （Fullprocess⇒On-shell X
production

Decay channelof X

XCut!
XFull process⇒XProduction

Decay

· In case of the toy model (or ADD model)
can be on-shell in intermediate state
width ofis enough small (But ! （)）«1»1

Discussion
Why is the approximation not good ?
· Cancellation of on-shell contributions(only for 2-body scattering)⇒«· Interferences between KK graviton
which have same mass⇒»

· Cancellation of on-shell contributions

Canceled out for any

Cut offm

· Interferences between KK graviton
which have same mass
The effect of interferences between
which have same mass is unphysical !

・in case of
only one particle⇒⇒

・in case ofN particles

⇒ N×2
⇒ N ×

This is not the quantum effect !

· In case of 2-body scattering via KK gravitons
A contribution from KK gravitonsof which mass isis dominant· In case of KK graviton productions
A contribution from KK gravitonsof which mass isis dominantContribution from on-shell KK gravitons

Conclusion
The cross section of virtual KK exchange process
can be huge or small unphysically· This problem is a kind of over counting

Double counting of phase spase in extra dimensions· If there is no double counting,the problem does not appear· An origin of this problem is the explicit breakingof translational symmetry in extra dimensions⇒ We need to consider some properties of brane dynamics

Thank you !
ありがとうございましたBuck up

Signature of ADD at ATLAS
MissingSignature of ADD at ATLAS

KK

Dominant terms
All of each 4 terms
are sameOrdinaryquantum corrections

Dominant terms
All of each 4 terms
are sameOrdinaryquantum corrections

Dominant terms
All of each 4 terms
are same