Claudio Corian

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The Search
for EXTRA Z at the LHC

• Claudio Corianò
• Università del Salento
• INFN, Lecce

QCD_at_work 2007, Martina Franca
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Summary 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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Simplified approach 1) these neutral
interactions and the corresponding anomalous
generators decouple at LHC energies we wont
see anything. Then 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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• Stuckelberg Axions and the Effective Action of
• Anomalous Abelian Models
• Windows over a new Low energy Axion
• hep-ph/0612140, Irges, C., to appear on Phys.
  Lett. B
• 2. A Unitarity analysis of the Higgs-axion
  mixing.
• hep-ph/0701010
• Irges, Morelli, C.C., to appear on JHEP
• 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.
• 4. M. Guzzi, R. Armillis, S. Morelli, to appear
• Applications to 3-linear gauge interactions

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Standard Model Anomalies
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work in progress with Alon Faraggi, Marco Guzzi
and Alessandro Cafarella
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D M4 x T2 x T2 x T2
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Irges, Kiritsis, C.C. On the effective theory
of low-scale Orientifold vacua, Nucl. Phys. B,
2005
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Possibility of direct Chern Simons
interactions. The interpretation of these
interactions is subtle they are gauge variant,
but force the anomaly diagrams to take a
specific form. In that sense they are physical.
An alternative way to introduce these
interactions is to impose external Ward
identities on the the theory to preserve gauge
invariance in the effective action. EFFECTIVE
ACTION tree level anomalous triangle diagrams
axions.
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Gross and Jackiw 70s
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Goal The study the effective field theory of a
class of 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 to be anomaly free 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. The analysis is however quite general
What happens if you to have an anomalous U(1)
at low energy? What is its signature?
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Extending the SM just with anomalies canceled by
CS contributions
(.YYY)
(.BBB)
(.CCC)
(X SU(2) SU(2))
(X SU(3) SU(3))
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Vanishing only for SM
In the MLSOM some are vanishing after sum over
the fermions
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Momentum shifts in the loop generate linear terms
in the independent momenta
redistribute the anomaly. Their sum is fixed
These two invariant amplitudes correspond to CS
interactions and can be defined by external Ward
Identities. In the Standard Model one chooses
CVC, but this is not necessary because of
traceless conditions on the anomalies
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CS contribution
Non-local contribution its variation under
B-gauge transformations is local
A is massless
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Chern-Simons contributions
A, vector-like B, C axial
It is possible to show that one needs both CS and
GS interaction, Irges, Tomaras, C.C.
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shift
Stuckelberg mass
the axion is a Goldstone
The Stueckelberg shifts like the phase of a Higgs
field
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Number of axionsnumber of anomalous U(1)s
anomalous
Higgs
b, c are Stuckelberg axions
physical axion
Goldstone boson
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Rotation into the Axi-Higgs
Mass of the anomalous gauge boson B
Stuckelberg mass electroweak mass
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Anomalous effective action
Stuckelberg mass term
Axion-gauge field interactions, dimension 5
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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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There is an overlap between these models and
Those obtained by decoupling of a chiral fermion
due to large Yukawa couplings (Irges, C.C.
Windows over a new lower energy axion,
PLB) Some connection also to older work
of DHoker and Farhi, Preskill. The Stuckelberg
field (b) is just the phase of a Higgs that
survives at low energy. The theory is left
anomalous, the fermions are left in a reducible
representation Only the CS interactions dont
seem, at this time, to explained by this low
energy construction Armillis, Guzzi, C.C. work
in progress
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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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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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Gauge sector
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The Higgs covariant derivatives responsible for
the gauge boson mixing together with the
Stueckelberg terms
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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Fermionic sector
Fermion interactions of the extra Z
Decoupling as v/M---gt0
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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
These have to vanish
You need some rotations among the gapless
excitations to identify the goldstones
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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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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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Direct coupling to gauge fields
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M. Guzzi, S. Morelli, C.C., in progress
axi-higgs decay into 2 photons
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Associated Production
Associated production g g--gt H Z, now with the
additional scalars
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New physics
Hard scatterings
Pure QCD contributions
Parton distributions
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How do we search for anomalous 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
2 jet events
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NNLO Drell-Yan is sensitive to the anomaly inflow
2-loop technology (master integrals and such well
Developed) 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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LO, 70s Gribov-Lipatov Altarelli
Parisi Dokshitzer
NLO, 80s Floratos, Ross, Sachrajda, Curci, Fur
manski Petronzio
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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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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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Rapidity distributions of the DY lepton pair
Cafarella, Guzzi, C.C. Anastasiou Dixon,
Melnikov and Petriello
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Conclusions The possibility of discovering
extra Z at the LHC Is realistic, They are
common in GUTs and string inspired models.
Anomalous U(1)s are important for a variety of
reasons. They may play a considerable role in
the flavour sector Froggatt-Nielsen (Ramond,
Irges), But predict also new 3-linear gauge
interactions and a Axi-Higgs. Precision QCD
necessary to discriminate them at the LHC. Z
gamma gamma and Drell-Yan the best place to
loo at them. Anomalies also can be due to
partial decoupling of a heavy Fermion, leaving
at low energy a gauged axion
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General features of the model Number of axions
Number of anomalous U(1) Two Higgs-doublets
(we have found that it is necessary to have full
Higgs-axion mixing in order to have a unitary
model) 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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GS
CS interaction
Bouchiat, Iliopoulos, Meyer. Gauge independence
of the S-matrix. Work in a specific gauge and
select the phase
Irges, Morelli, C.C.
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Gauge independence in the Stuckelberg phase
Gauge independence in the H-S phase
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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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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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Fermionic sector
Fermion interactions of the extra Z
Decoupling as v/M---gt0
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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
These have to vanish
You need some rotations among the gapless
excitations to identify the goldstones
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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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LO, 70s Gribov-Lipatov Altarelli
Parisi Dokshitzer
NLO, 80s Floratos, Ross, Sachrajda, Curci, Fur
manski Petronzio
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with M. Guzzi and A. Cafarella (Demokritos)
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U(1,Y ) x U(1,B)
Counterterms of BYY
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Impose the BRS invariance of the gauge fixed
action, having removed the bB mixing
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Generalized CS
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Valence quark sector
Gluon sector
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The structure of the anomalous amplitude
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Z photon photon
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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?