gauged axions

Gauged Axions

Claudio Coriano’

Physics Department

University of Salento, INFN Lecce

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)’s3. Gauged axions from intersecting branes 4. Gauged axions from decoupled fermions

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

INFN Lecce,

Roberta Armillis, Marco GuzziLuigi Delle Rose Antonio MarianoSimone Morelli

Nikos Irges

Irges, Kiritsis, C.C. 2005 (Crete)

1) Stuckelberg axions and the effective action of anomalous Abelian models. 1. A Unitarity analysis of the Higgs-axion mixing. JHEP 0707:008,2007. 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 ppNucl.Phys.B789:133-174,2008.

3) Trilinear Anomalous Gauge Interactions from Intersecting Branes and the Neutral Currents Sector. 68pp. Published in JHEP 0805:015,2008. with Armillis, Guzzi

4) Unitarity Bounds for Gauged Axionic Interactions and the Green-Schwarz Mechanism. 50pp.Published in Eur.Phys.J.C55:629-652,2008. 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 0810:034,2008, 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.B814:15679,2009. With Armillis, Guzzi and Morelli

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: arXiv:0905.4462 [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: arXiv:0905.0865 [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

….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?

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.

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.

(Faraggi, Guzzi, C.C., PRD 2008)

Widths are small for small coupling

We need extra information in order to capture the nature of the Extra Z prime (if it exists).

Neutral current sector Why it is important and how to detect it at the LHC

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

Guzzi, Cafarella, C.C.

pp -> lepton +anti-lepton

Excellent statistics. Theoretical error larger than exp.

Withs are quite smallg has to be O(1)

Guzzi, Morelli, C.C.

CANDIA, can be downloded

www.le.infn.it/~candiaNNLO evolution in x-space

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

1) New trilinear gauge interactions 2) Anomalous Extra Z prime’s

3) 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.

Wess-Zumino case. Trilinear gauge interaction CS terms

Excellent domain: 4-fermion processes

LO

NLO

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

afg

1≈

GeVfa1010≥ GeVfa

1210≤Astrophysical constraint linked to the stellar evolution

Cosmological constraint given by the dark energy amount

eVmeV a36 1010 −− ≤≤

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

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

The “gauged” axion

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 term2) a nonlocal subtraction (subtraction of an anomaly pole)

with Guzzi and Morelli

QuickTime™ and a decompressor

are needed to see this picture.

One or two axions?

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 anomalypole

Armillis, Guzzi, C.C., Armillis, Delle Rose, Guzzi, C.C.



This cancellation is identical only for special kinematics



BIM amplitudes.

Use these amplitudes to detect The non-unitary behaviour of the theory



Redefined BIM amplitude. It is zero only for on-shell scattering of massless gauge bosons

Re-defined vertex



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

Description with two axions

This description renders the lagrangean local but at a costt

The cost: a ghost

Similar results in the case of the conformal anomaly

Negative kinetic energy term

(Federbush)

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.

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.)

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.



Euler Heisenberg





1/m captures the correct physics



In the anomalous case this is not true any longer



But there is neverthless a pole




are needed to see this picture.The extra terms are given In our paperArmillis et al

Gravity: same story (Conformal anomaly)









Riegert

The anomaly pole is here



Linearized gravity



Mottola, Giannotti, 2009



Anomaly poles from the loops of TJJ QuickTime™ and a decompressor






Specify the realization of the “anomaly cancellation mechanism”

Pole subtraction

Wess Zumino

Asymptotic axion

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

The MLSOM

Counterterms can be fixed using BRST invariance.

Armillis, Guzzi, CCJHEP 2008

The SU(3)xSU(2)xU(1)xU(1) Modelkinetic

L/R fermion

Stueckelberg

CS

Higgs-axion mixing

GS

Higgs doublets

Irges, Kiritsis, C.

No v/M corrections on firstrow

SM-like

1/M

O(M)

CP even

CP odd

Some properties of the axi-Higgs: Yukawa couplings

Induces the decay of the Axi-Higgs, similar to Higgs decay

GS Axions

1 physical axion, The Axi-Higgs

N Nambu-Goldstone modes

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

Unitarity Bounds (Guzzi, Morelli, C.C.)

Bouchiat-Iliopoulos-Meyer amplitudes (BIM amplitudes) The WZ mechanism does not protect the theory from the non-unitary behaviour of these amplitudes

Unitarity bound in the WZ case: gluon-gluon to gamma gamma



Same behaviour for a varying Tan-beta

CP-odd sector in the WZ mechanism (MLSOM)



SU(3) x SU(2) x U(1)_Y x U(1)_B





Models can be built without any string construction. Phenomenologically The specific charges are not relevant (Guzzi, C.C.)







Combine axion countertemrs (C’s) Anomaly cancellation conditions And gauge invariance to fix the model

We obtain 10 eqs. That allows a clas sof charge assignments




are needed to see this picture.Difference of the Higgs charges under the anomallous U(1)_B



WZ counterterms fixed in terms of charge difference



Guzzi, C.C.


are needed to see this picture.The Madrid model is a special case of this general approach









The dependence on the charge assignments truly small





The axi-Higgscouples 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 kinematicallyits decay.



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 -----> no tringle diagram, only pointlike interactions, Which is pretty small. (Guzzi, C.C.)

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 D’Hoker 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.





The WZ terms come from the chiral transformation that removes the phase of the Higgs





Guzzi, C.C.



Guzzi, C.C.



WZ terms generated by chiral redefinition

Supersymmetric Extensions

We need a specific superpotential. For instance, in the MSSM one does not obtain a physical axionWe have succeded with the inclusion of one extra single (similar to the NMSSM)



Stuckelberg multiplet

Anastasopoulos, Lionetto, Fucito, Racioppi, Stanev, the axino is part of the neutralino mass matrix





The physical axion is a linear combination of the CP odd Higgs, the Stuckelberg and the bosonic component of the scalar singlet superfield “S”







Axion-neutralino interactions







Neutralino has an axino component beside the usual gauginos and singlino

The neutralino mass depends on the Stuckelberg mass M_St



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

gauged axions

Documents

anomalous u1 models

anomalous u1sgauged

stuckelberg axions

presence of gauged axions

morelli5 axions

roberta armillis

su3c x su2w x u1y x

class of brane models