Searching for Anomalous Extra Z at the LHC

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Searching for Anomalous Extra Z at the LHC

• Claudio Coriano
• Universita del Salento
• INFN, Lecce

Based on work in collaboration with N. Irges
(Crete), M.Guzzi (Lecce), S. Morelli (Lecce), R.
Armillis (Lecce) Olympia, April 2008
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original formulation with Irges and E.
Kiritsis On the effective theory of low scale
orientifold string vacua. Introduction of the
Axi-Higgs Nucl.Phys.B 746, 2006.
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Stuckelberg Axions and the Effective Action of
Anomalous Abelian Models Windows over a new
Low energy Axion hep-ph/0612140, Irges, C.C.,
Phys. Lett. B, 2007 2. A Unitarity analysis of
the Higgs-axion mixing. hep-ph/0701010 Irges,
Morelli, C.C., JHEP 2007 3.A SU(3) x SU(2) x
U(1)Y x U(1)B model and its signature at the
LHC hep-ph/0703127, Irges, Morelli, C.C., Nucl.
Phys B 2008 4.Trilinear gauge interactions..
M. Guzzi, R. Armillis, S. Morelli, JHEP 2008 5.
Unitarity Bound for anomalous gauge
interactions and the GS mechanism, Guzzi,
Morelli, C.C., EPJ C 2008
Plus work in prgress with Nikos Irges
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OUTLINE Searching for some extra neutral
interactions at the Large Hadron Collider
involves a combined effort from two sides 1)
Precise determination of the signal, which should
allow also a discrimination of any specific
model compared to other models 2) Precise
determination of the SM background. at a hadron
collider this is a very difficult enterprise
even with the best intentions (NNLO
QCD) Extra Zs come from many extensions of
the Standard Model However, some of these U(1)
are anomalous, and invoke a mechanism of
cancelation of the anomalies that requires an
axion. What is the effective field theory of
these U(1)s and how can they, eventually, be
found?
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Goal to study the effective field theory of a
class of brane models containing a gauge
structure of the form
SM x U(1) x U(1) x U(1)
SU(3) x SU(2) x U(1)Y x U(1).. from which
the hypercharge is assigned in a given string
construction, corresponding to a certain class
of vacua in string theory (Minimal Low Scale
orientifold Models). These models are
the object of an intense scrutiny by
many groups working on intersecting branes.
Antoniadis, Kiritsis, Rizos,
Tomaras Antoniadis, Leontaris, Rizos Ibanez,
Marchesano, Rabadan, Ghilencea, Ibanez, Irges,
Quevedo See. E. Kiritsis review on Phys. Rep.
Blumenhagen, Kors, Lust, Stieberger
recent work by G. Leontaris and Coll.
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Simplified approach 1) these neutral
interactions and the corresponding anomalous
generators decouple at LHC energies we wont
see anything. Then string theory predictions
simply overlap with those coming from the
large array of U(1)s We dont need to worry
about the axion, and its mixing with the
remaining scalars of the SM. Complete
approach 2) We dont decouple the anomalous
U(1) completely, The anomalous generators are
kept Interesting implications for ANOMALOUS
GAUGE INTERACTIONS with hopes to detect an
anomalous U(1)
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Gluon sector
Irges, Morelli, C.C.
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ALTERNATIVE MECHANISMS OF ANOMALY CANCELATION
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What is the anomaly cancelation mechanism at the
LHC Fermion charge assignment (anomaly
free) Wess-Zumino (anomalous) physical axion
(axion-like particle) Green Schwarz
(physical/unphysical axion ? Is it consistent
with unitarity?) GS involves a re-definition of
the anomalous vertices of a given theory
Wess Zumino axion
GS cancelation the problem with double poles
in supersymmetry no physical axion
Armillis, Guzzi, C.C., in preparation
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Diagrams responsible for extra double poles
Unsettled debate Adam, Bassetto, Soldati,
Andrianov,Federbush, Fosco, Montemajor
The conclusions of these papers should be
reconsidered there is a cancelation of double
poles, at least through 3-loop order (Armillis,
Guzzi, Morelli, C.C., in prep)
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1992
This paper was withdrawn.
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How do we search for extra U(1)s at the LHC ?
Golden plated process Drell-Yan lepton pair
production but also other s-channel processes
These models, being anomalous, involve
anomalous gauge interactions
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General features of the model Number of axions
Number of anomalous U(1) Two Higgs-doublets
Anomalies canceled by 1) charge assignments
CS GS These features are best illustrated in
the context of a simple model with just 1 extra
U(1)
SU(3) x SU(2) x U(1) xU(1))
SU(3) x SU(2) x U(1, Y) x U(1))
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U(1)Ax U(1)B
B gets mass by the combined Higgs-Stuckelberg
Mechanism and is chirally coupled
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shift
Stuckelberg mass
the axion is a Goldstone (if B does not gets
also its mass via ewsb)
The Stueckelberg shifts like the phase of a Higgs
field
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• These effective models have 2 broken phases
• A Stuckelberg phase
• A Higgs-Stuckelberg phase
• In the first case the axion b is a Goldstone
  boson
• in the second phase, there is a Higgs-axion
  mixing
• if the Higgs is charged under the anomalous U(1)

Goldstone boson
Physical axion
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One can add an additional potential which
includes the Stuckelbergs axions
PQ breaking potentials give mass to the
Axi-Higgs. This is due to the competition
between of ewsb (v) and the extra PQ breaking
potential. It can be driven to be quite small.
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Chern Simons Interactions. They appear in some
special situations. In multiple Z models
(Z1,Z2,Z3) where the partial anomalies can be
distributed among the 3 anomalous vertices
WZ
CS interaction
Bouchiat, Iliopoulos, Meyer Amplitudes. Gauge
independence of the S-matrix. Work in a specific
gauge and select the phase
Irges, Morelli, C.C.
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One can start with a symmetric distribution Of
the anomaly and then correct by Chern-Simons
interactions. Z gamma gamma does not have any CS
term
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These have been computed
R product of rotation matrices, thetaschiral
asymmetry of the fermion
spectrum respect
to the anomalous U(1)s
Armillis, Guzzi, C.C., JHEP 2008
Typical anomaly diagram
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The CS terms, in this case, take part in the
defining Slavnov-Taylor identities of the model
in the presence Of anomalous contributions and
aFF coupling
Armillis, Guzzi, C.C., 2007
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Check of gauge independence in the 2 phases (3
loop)
In the Stuckelberg phase cured by the axion b
In the HS phase cured by the Goldstone GB
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Checks in the fermionic sector.
These are the typical classes of diagrams one
needs to worry about.
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Compared to a Peccei-Quinn axion, the new axion
is gauged For a PQ axion a m C/fa,
while the aFF interaction is also suppressed
by a/fa FF with fa 109 GeV In
the case of these models, the mass of the axion
and its gauge interactions are unrelated the
mass is generated by the combination of the Higgs
and the Stuckelberg mechanisms combined The
interaction is controlled by the Stuckelberg mass
(M1)

The axion shares the properties of a CP odd scalar
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In WZ anomaly cancelation The axion can be
massless (light) or massive. However, in the
simplest formulation of the theory, there is a
unitarity bound, one needs higher dimensional
operators (Irges, C.C.) The Stuckelberg mass term
in the lagrangean is crucial for having a
physical massless axion. The axion could be the
result of a partial decoupling of a heavy
fermion (Irges, C.C., PLB 2007). In the GS
case no physical axion, at least in the
supersymmetric case.
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One or two axions?
with Guzzi and Morelli
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ONE CAN INTEGRATE OUT THE AXION IN THE WZ CASE.
WE WOULD OBTAIN A THEORY DIFFERENT FROM GS
EXTRA INTERACTIONS COMPARED TO GS
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The SU(3)xSU(2)xU(1)xU(1) Model
kinetic
Higgs doublets
L/R fermion
CS
GS
Higgs-axion mixing
Irges, Kiritsis, C.
Stueckelberg
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The VERY MINIMAL MODEL
2 Higgs doublets
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The Higgs covariant derivatives responsible for
the gauge boson mixing together with the
Stueckelberg terms
V/M drives the breaking
vu, vd ltlt M
The neutral sector shows a mixing between W3,
hypercharge and the anomalous gauge boson, B
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No v/M corrections on first row
SM-like
1/M
O(M)
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CP even
CP odd
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CP odd Sector. Where the physical axion appears
2 Goldstones We need to identify the goldstones
of the physical gauge bosons
Axi-Higgs projection vanishes
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1 physical axion, The Axi-Higgs
GS Axions
N Nambu-Goldstone modes
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Some properties of the axi-Higgs Yukawa
couplings
Induces the decay of the Axi-Higgs, similar to
Higgs decay
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3-linear interactions of the gauge fields
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Moving to the broken phase, the axion has to be
rotated into its physical component,
the Axi-Higgs and the Goldstones
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M. Guzzi, S. Morelli, C.C axi-higgs decay into
2 photons
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The detection of Extra Z in this framework
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NNLO Drell-Yan is sensitive to the anomaly inflow
2-loop technology (master integrals and such well
Developed tools) You need to add a new class of
Contributions, usually neglected for
anomaly-free models
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Factorization Theorems
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High precisio determination of the
renormalization/factorization scale dependence of
the pdfs
Solved by CANDIA (Cafarella, Guzzi, C.C.)
Truncated, Singlet and non-singlet
Exact , non singlet
Cafarella, Guzzi, C.C., NPB 2006
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Precision QCD NNLO effects within 3 in
Drell-Yan
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Neutral current sector Why it is important and
how to detect it at the LHC
Guzzi, Cafarella, C.C.
To discover neutral currents at the LHC, we need
to know the QCD background with very high
accuracy. Much more so if the resonance is in
the higher-end in mass (5 TeV). NNLO in the
parton model
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QCD error around 2-3
600 GeV
400 GeV, 14 TeV
Reduction by 60
Guzzi, Cafarella, C.
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Anomaly Effects in Extra Z models Drell-Yan is
resonant Double prompt photon production is
non-resonant and non-unitary (in the WZ case)
Bouchiat-Iliopoulos-Meyer amplitudes (BIM
amplitudes) The WZ mechanism does not protect
the theory from the non-unitary behaviour of
these amplitudes
Guzzi, Morelli, C.C., 2008
The anomaly erases the pole This diagrams is IR
UV finite the amplitude takes the
Dolgov-Zakharov form
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2-photon processes
New anomalous contributions in 2-photons
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with Armillis, Guzzi, Morelli,
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2 methods for anomaly cancelation Wess-Zumino
Green Schwarz
Green-Schwarz vertex pole subtractions on the
anomalous lines
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New anomalous corrections
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Untarity bound in the WZ case gluon-gluon to
gama gamma
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M_1 is approximately the mass of the extra Z.
Unitarity bound for axion-like particles.
Obtained from a parton level Analysis. Should be
generalized at hadron level
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The two formulations are the WZ and the GS
mechanisms for anomaly cancelation. Then, if we
believe in the results from axial QED The GS
mechanism fails to be unitary because of the
extra double Poles. On the other hand also the
WZ mechanism fails to be unitary, but in a
different way some amplitudes grow quadratically
with energy
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Unitarity bound for axion-like particles (Guzzi,
Morelli, C.C.)
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Armillis, Guzzi, Morelli, C.C, in preparation
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Drell Yan anomalous (partial) (Madrid Model,
Ibanez et al, MLSOM)
MLSOM versus anomaly Free U(1)s
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Armillis, Guzzi, Morelli, C.C.
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Withs are quite small G has to be O(1)
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Conclusions and Open Issues New 3-linear gauge
interactions at the LHC due to the different
cancelation mechanism Question if a new
resonance in DY, for instance Is found, are we
going to have enough statistics to resolve the
type of resonance, that is once the resonance is
found, can we look for 1) Charge asymmetries 2)
Forward Backward asymmetries To discriminate
among the possible models and say that there is
an inflow? If we integrate part of the fermion
specrum we get a WZ term. How do we know that
the anomalous theory is Just a result of
partial decoupling?