Gauged Axions

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Gauged Axions

• Claudio Coriano
• Physics Department
• University of Salento, INFN Lecce

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Outline I will describe the general features of
anomalous models which are characterized by the
presence of gauged axions in their spectra.
These models have been studied in the context of
intersecting branes, but can have a rather
general (and independent) origin, if the
decoupling of chiral fermions from an anomaly
free theory, which takes to these models, follows
a specific path. (Guzzi, C.C., 2009) In this
sense, the lagrangeans that I will describe are
rather general and summarize all the basic
features of a universality class of models
which provide a generalization of the
Peccei-Quinn theory.

1. The PQ axion
2. Gauged axions and anomalous U(1)s
3. Gauged axions from intersecting branes
4. Gauged axions from decoupled fermions

• Local and non-local versions of the anomaly
  cancellation mechanism.
• Conformal and gauge anomalies.

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Nikos Irges
INFN Lecce, Roberta Armillis, Marco
Guzzi Luigi Delle Rose Antonio Mariano Simone
Morelli
Irges, Kiritsis, C.C. 2005 (Crete)
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1) Stuckelberg axions and the effective action
of anomalous Abelian models. 1. A Unitarity
analysis of the Higgs-axion mixing. JHEP
0707008,2007. 68 pp 2) Stuckelberg Axions and
the Effective Action of Anomalous Abelian Models
2. A SU(3)C x SU(2)W x U(1)Y x U(1)B model and
its signature at the LHC. 72 pp Nucl.Phys.B789133
-174,2008. 3) Trilinear Anomalous Gauge
Interactions from Intersecting Branes and
the Neutral Currents Sector. 68pp. Published
in JHEP 0805015,2008. with Armillis, Guzzi
4) Unitarity Bounds for Gauged Axionic
Interactions and the Green-Schwarz Mechanism.
50pp.Published in Eur.Phys.J.C55629-652,2008.
with Guzzi and Morelli
5) Axions and Anomaly-Mediated Interactions
The Green-Schwarz and Wess-Zumino Vertices at
Higher Orders and g-2 of the muon. Lecce) . Aug
2008. 52pp. Published in JHEP 0810034,2008, with
Armillis, Guzzi and Morelli
6) An Anomalous Extra Z Prime from Intersecting
Branes with Drell-Yan and Direct Photons at the
LHC. Sep 2008. 46pp.Published in
Nucl.Phys.B81415679,2009. With Armillis, Guzzi
and Morelli
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7) A Light Supersymmetric Axion in an Anomalous
Abelian Extension of the Standard Model. 46 pp.
(2008) Phys. Rev. D 2009, with Guzzi, Mariano and
Morelli
8) Axions from Intersecting Branes and
Decoupled Chiral Fermions at the Large Hadron
Collider. Claudio Coriano, Marco Guzzi .
e-Print arXiv0905.4462 hep-ph, with M. Guzzi
9 ) Anomalous U(1) Models in Four and Five
Dimensions and their Anomaly Poles. Roberta
Armillis, Claudio Coriano, Luigi Delle Rose,
Marco Guzzi .. e-Print arXiv0905.0865 hep-ph
, with Armillis, Guzzi and Delle Rose
Connection between gauge and conformal anomalies
in these models 10) Conformal Anomalies and
the Gauge Contributions To the Gravitational
effective action Armillis, Delle Rose, C.C.,
to appear
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.Plenty of U(1)s also in anomaly-free
constructions
The question is if we find extra neutral
currents at the LHC how do we discover if a
different mechanism of anomaly cancelation is at
work?
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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)..
corresponding to a certain class of vacua in
string theory These models are the object
of an intense scrutiny by many groups
working on intersecting branes. See. E.
Kiritsis review on Phys. Rep. These analysis
focused on general (mostly geometrical) features
of these models. One has to be careful though
these axions are not necessarily physical fields.
First identification of a physical Axion in
these models in the non-supersymmetric case is
in (Irges, Kiritsis, C.C., 2005). The physical
axion was called The Axi Higgs and the model
Minimal Low Scale Orientifold Model (MLSOM). In
the supersymmetric case, the construction Needs
a special form of superpotential, typical of the
NMSSM. The model is called the USSM-A (Mariano,
Irges, Guzzi, C.C.) Another SUSY extension is in
Anastasopoulos,Fucito, Lionetto, Racioppi,
Stanev. based on previous formulations by
Zagermann and Coll.
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Standard Model Anomalies
As we have mentioned, one of the most interesting
realizations of the class of anomalous theories
contining anomalous U(1)s are obtained from
intersecting branes.
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Widths are small for small coupling
(Faraggi, Guzzi, C.C., PRD 2008)
We need extra information in order to capture the
nature of the Extra Z prime (if it exists).
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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
pp -gt lepton anti-lepton
Excellent statistics. Theoretical error larger
than exp.
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Withs are quite small g has to be O(1)
Guzzi, Morelli, C.C.
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CANDIA, can be downloded
www.le.infn.it/candia
NNLO evolution in x-space
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• Gauged axions are naturally associated to
  anomalous symmetries.
• We can consider U(1) extensions of the Standard
  Model and compensate the
• anomalous variation of the effective action with
  Wess Zumino counterterms
• SIGNATURES at the LHC
• New trilinear gauge interactions
• Anomalous Extra Z primes
• One gauged axion
• In the supersymmetric case (UMSSM-A)
• We have axions and neutralinos as possible dark
  matter candidates.
• These models provide an extension of the (NMSSM)
  with an anomalous
• U(1) symmetry, a Stuckelberg multiplet, possible
  kinetic mixing etc.

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Wess-Zumino case. Trilinear gauge interaction
CS terms
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Excellent domain 4-fermion processes
LO
NLO
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The Peccei-Quinn axion
Peccei and Quinn ? U(1)PQ symmetry the axion as a
pseudo Goldstone boson The mass and the coupling
of the axion to photons depend on the SAME scale
fa
Astrophysical constraint linked to the stellar
evolution
Cosmological constraint given by the dark energy
amount
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Solution of the strong CP problem
Total lagrangean axion theta term
Anomalous contribution due to U(1)_PQ
Axion field is driven by the instanton potential
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The gauged axion
We obtain a gauged axion by promoting the
U(1)PQ global symmetry to a local one
The mass and the coupling of the gauged axion are
independent. This may allow to evade the
constraints from CAST and other experiments
and/or astrophysical bounds
However The presence of an axion-like particle
is an indication of of a different mechanism of
anomaly cancelation at work. At field theory
level we have two possible versions of this
mechanism 1) a local subtraction via a
Wess-Zumino term 2) a nonlocal subtraction
(subtraction of an anomaly pole)
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One or two axions?
with Guzzi and Morelli
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anomaly cancellation mechanism(s) 1) Fermion
charge assignment (anomaly free) 2) Wess-Zumino
(anomalous) physical axion (axion-like
particle) 3) 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
Subtraction of an anomaly pole
Armillis, Guzzi, C.C., Armillis, Delle Rose,
Guzzi, C.C.
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This cancellation is identical only for special
kinematics
BIM amplitudes.
Use these amplitudes to detect The non-unitary
behaviour of the theory
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Re-defined vertex
Redefined BIM amplitude. It is zero only for
on-shell scattering of massless gauge bosons
Digrammatic expansion
The re-definition removes the anomaly pole from
the vertex. In the UV this is always possible,
but is an over subtraction in the IR
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Description with two axions
This description renders the lagrangean local
but at a costt
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The cost a ghost
Negative kinetic energy term
(Federbush)
Similar results in the case of the conformal
anomaly
Two pseudoscalars to re-express the conformal
anomalous contribution in Gravity (Giannotti and
Mottola, PRD 2009). In this case the authors
claim consistency of this reformulation, wth the
two field interpreted as collinear fermion
antifermion states. I believe that these local
formulations always have a ghost in the
spectrum.
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Is there a way to unitarize the amplitude? Yes,
but at a cost.
The example
The subtraction, however, is well defined in the
UV, but leaves, In some cases an infrared pole
coupled In the infrared. (Armillis, Delle Rose,
Guzzi, C.C.)
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Similar situation in gravity
To see the poles (the virtual axion) you need to
keep all the terms in the effective Action
Armillis, Delle Rose, C.C.
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1/m captures the correct physics
Euler Heisenberg
In the anomalous case this is not true any longer
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But there is neverthless a pole
The extra terms are given In our paper Armillis
et al
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Gravity same story (Conformal anomaly)
Riegert
The anomaly pole is here
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Linearized gravity
Mottola, Giannotti, 2009
Anomaly poles from the loops of TJJ
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Specify the realization of the anomaly
cancellation mechanism
Pole subtraction
Wess Zumino Asymptotic axion
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The effective actions in the two cases are rather
different.
The only actions which have been studied so far
are of type 1). (MLSOM) They involve WZ terms and
are characterized by a unitarity bound which is
strongly sensitive on the coupling of the
anomalous U(1) (anomalous) symmetry. In
general, each anomalous U(1) symmetry requires an
axion which acquires a kinetic term via a
Stuckelberg mass term for the corresponding
anomalous gauge boson
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The MLSOM
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Counterterms can be fixed using BRST invariance.
JHEP 2008
Armillis, Guzzi, CC
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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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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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Some properties of the axi-Higgs Yukawa
couplings
Induces the decay of the Axi-Higgs, similar to
Higgs decay
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1 physical axion, The Axi-Higgs
GS Axions
N Nambu-Goldstone modes
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The Stuckelberg are NOT necessarily physical
fields. Their nature is identified after
electroweak symmetry breaking When the anomalous
gauge boson acquires an additional Mass
correction due to the Higgs vev
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(Guzzi, Morelli, C.C.)
Unitarity Bounds
Bouchiat-Iliopoulos-Meyer amplitudes (BIM
amplitudes) The WZ mechanism does not protect
the theory from the non-unitary behaviour of
these amplitudes
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Unitarity bound in the WZ case gluon-gluon to
gamma gamma
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Same behaviour for a varying Tan-beta
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CP-odd sector in the WZ mechanism (MLSOM)
SU(3) x SU(2) x U(1)_Y x U(1)_B
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Models can be built without any string
construction. Phenomenologically The specific
charges are not relevant (Guzzi, C.C.)
Combine axion countertemrs (Cs) Anomaly
cancellation conditions And gauge invariance to
fix the model
We obtain 10 eqs. That allows a clas sof charge
assignments
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Difference of the Higgs charges under the
anomallous U(1)_B
WZ counterterms fixed in terms of charge
difference
Guzzi, C.C.
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The Madrid model is a special case of this
general approach
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The dependence on the charge assignments truly
small
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The axi-Higgs couples significantly to the
quarks. The decay is fast, The mass is a free
parameter. For a GeV mass no dark matter, too
short lived, more Higgs-like. Has to be very
light to be dark Matter, to suppress
kinematically its decay.
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Lifetime as a function of tanBeta
In Intersecting brane models a GeV axion is not
dark matter. But a very light Axion can be dark
matter. If, instead the axion is produced by a
mechanism of Higgs-Fermion chiral decoupling,
the coupling of the axion to the light (Standard
Model) fermions is missing or suppressed -----gt
no tringle diagram, only pointlike interactions,
Which is pretty small. (Guzzi, C.C.)
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Can we have a GeV axion that works like dark
matter? Yes axion as the phase of a Higgs
(decoupling of a fermion) (Guzzi, C.C., 2009)
Notice that this decoupling is DIFFERENT from
DHoker Farhi (large Yukawa couplings). Here we
require a decoupled Higgs (large vev of an extra
Higgs) The phase of the Higgs survives as a
(quasi) massless mode.
Integrate out the heavy chiral fermion.
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The WZ terms come from the chiral transformation
that removes the phase of the Higgs
Guzzi, C.C.
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Guzzi, C.C.
WZ terms generated by chiral redefinition
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Supersymmetric Extensions
Anastasopoulos, Lionetto, Fucito, Racioppi,
Stanev, the axino is part of the neutralino
mass matrix
Stuckelberg multiplet
We need a specific superpotential. For instance,
in the MSSM one does not obtain a physical
axion We have succeded with the inclusion of one
extra single (similar to the NMSSM)
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The physical axion is a linear combination of the
CP odd Higgs, the Stuckelberg and the bosonic
component of the scalar singlet superfield S
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Axion-neutralino interactions
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Neutralino has an axino component beside the
usual gauginos and singlino
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The neutralino mass depends on the Stuckelberg
mass M_St
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Conclusions Gauged Axions are an interesting
avenue for physics BSM They can be framed in a
completely supersymmetric scenario The issue of
anomaly cancellation and its realization in terms
of local operators remains open. In a local
formulation these theories predict a new (gauged)
Axion, an anomalous extra Z prime. In the
supersymmetric case two forms of dark matter.
The issue of the UV completion of anomalus
theories (FROM A FIELD THEORY FRAMEWORK) remains
still open. Similar features appear in gravity,
in the trace anomaly, for instance. We are
starting to discover the physical implications
of anomalies using more dynamics than geometry.
How to imbed these formulations in more
sophisticated theories such as gauged
supergravities remain open. Soon or later,
these formulations have to be described By
effective actions either of MLSOM-type or of the
USSM-A