1. Gauged Axions Claudio Coriano’ Physics Department University of Salento, INFN Lecce

2. 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 5Local and non-local versions of the anomaly cancellation mechanism. Conformal and gauge anomalies.

3. INFN Lecce, Roberta Armillis, Marco Guzzi Luigi Delle Rose Antonio Mariano Simone Morelli Nikos Irges Irges, Kiritsis, C.C. 2005 (Crete)

4. 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 pp Nucl.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

5. 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

6. ….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?

7. 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.

8. 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.

9. (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).

10. 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.

11. Withs are quite small g has to be O(1) Guzzi, Morelli, C.C.

12. CANDIA, can be downloded www.le.infn.it/~candia NNLO evolution in x-space

13. 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.

14. Wess-Zumino case. Trilinear gauge interaction CS terms

15. Excellent domain: 4-fermion processes LO NLO

16. 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 f a Astrophysical constraint linked to the stellar evolution Cosmological constraint given by the dark energy amount

17. 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

18. 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 term 2) a nonlocal subtraction (subtraction of an anomaly pole)

19. with Guzzi and Morelli One or two axions?

20. 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.

21. This cancellation is identical only for special kinematics BIM amplitudes. Use these amplitudes to detect The non-unitary behaviour of the theory

22. 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

23. Description with two axions This description renders the lagrangean local but at a costt

24. 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.

25. 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.)

26. 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.

27. Euler Heisenberg 1/m captures the correct physics In the anomalous case this is not true any longer

28. But there is neverthless a pole The extra terms are given In our paper Armillis et al

30. Gravity: same story (Conformal anomaly) Riegert The anomaly pole is here

31. Linearized gravity Mottola, Giannotti, 2009 Anomaly poles from the loops of TJJ

32. Specify the realization of the “anomaly cancellation mechanism” Pole subtraction Wess Zumino Asymptotic axion

33. 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

34. The MLSOM

35. Counterterms can be fixed using BRST invariance. Armillis, Guzzi, CC JHEP 2008

36. The SU(3)xSU(2)xU(1)xU(1) Model kinetic L/R fermion Stueckelberg CS Higgs-axion mixing GS Higgs doublets Irges, Kiritsis, C.

37. No v/M corrections on first row SM-like 1/M O(M)

38. CP even CP odd

39. Some properties of the axi-Higgs: Yukawa couplings Induces the decay of the Axi-Higgs, similar to Higgs decay

40. GS Axions 1 physical axion, The Axi-Higgs N Nambu-Goldstone modes

41. 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

42. 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

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

44. Same behaviour for a varying Tan-beta

45. CP-odd sector in the WZ mechanism (MLSOM) SU(3) x SU(2) x U(1)_Y x U(1)_B

46. 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

47. Difference of the Higgs charges under the anomallous U(1)_B WZ counterterms fixed in terms of charge difference Guzzi, C.C.

48. The Madrid model is a special case of this general approach

51. The dependence on the charge assignments truly small

52. 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.

54. 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.)

55. 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.

56. The WZ terms come from the chiral transformation that removes the phase of the Higgs Guzzi, C.C.

57. WZ terms generated by chiral redefinition

58. Supersymmetric Extensions 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) Stuckelberg multiplet Anastasopoulos, Lionetto, Fucito, Racioppi, Stanev, the axino is part of the neutralino mass matrix

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

60. Axion-neutralino interactions

61. Neutralino has an axino component beside the usual gauginos and singlino

62. The neutralino mass depends on the Stuckelberg mass M_St

63. 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