Anomalous U(1) ΄ s, Chern-Simons couplings and the Standard Model

1. Alessandria, 15 December 2006 Anomalous U(1)΄s, Chern-Simons couplings and the Standard Model • Pascal Anastasopoulos • (INFN, Roma “Tor Vergata”) Work in collaboration with: Massimo Bianchi, Emilian Dudas, Elias Kiritsis.

2. Content of this lecture • Anomalous U(1)΄s are a generic prediction of all open string models (possible candidates to describe Standard Model). • The anomaly is cancelled via Green-Schwarz-Sagnotti mechanism, and the anomalous U(1)΄s become massive. • However, generalized Chern-Simons couplings are necessary to cancel all the anomalies. • These Chern-Simons terms provide new signals that distinguish such models from other Z΄-models. • Such couplings may have important experimental consequences.

3. Anomalous U(1)΄s Consider a chiral gauge theory: If , the U(1) is anomalus and gauge symmetry is broken due to the 1-loop diagram: Therefore under : To cancel the anomaly we add an axion: which also transforms as: , therefore: and the anomaly is cancelled.

4. Anomalous U(1)΄s are massive • The axion which mixes with the anomalous U(1)΄s is a bulk field emerging from the twisted RR sector. • The term that mixes the axion with the U(1) gives mass to the gauge boson and breaks the U(1) symmetry: • The UV mass can be computed from a string 1-loop diagram.

5. Limits of the open 1-loop diagrams RR-fields The mass is the UV contact term: Antoniadis Kiritsis Rizos UV limit The β-function IR limit The convergent part provides the threshold corrections. Antoniadis Bachas Dudas, Bianchi Trevigne, Anastasopoulos Bianchi Sarkissian Stanev (To appear) Antoniadis Bachas Dudas

6. Anomalous U(1)΄s and F-I terms • The masses of the anomalous U(1)s are proportional to the internal volumes. If D the brane where the U(1) is attached and P the O-pane where the axion is localized: D-brane O-plane • There are D-term like potentials of the form: where s is a bulk modulus. In SUSY models, they are the chiral partners of the axions. If we are on the O-pane, and the global U(1) symmetry remains intact. Poppitz

7. Presence of non-anomalous U(1)΄s Consider now the presence of an additional non-anomalous U(1) .By definition, this means that: However, there might be mixed anomalies due to the traces: Diagrams of the following type: break the gauge symmetries:

8. The need of Chern-Simons terms ? To cancel the anomalies we add axions as before: However, the axionic transformation does not cancel all the anomalies. The above action is -gauge invariant. We need non-invariant terms: Generalized Chern – Simons.

9. Chern-Simons terms We need non-invariant terms: the variation the variation Now, a combination of the axionic and the GCS-terms cancel the anomalies: To cancel the anomalies we obtain: The anomalies fix the coefficients of the GCS-terms in the effective action.

10. The General Case Consider the general Lagrangian: It is easy to show that: E ~

11. General Anomaly Cancellation Requiring: under and , the anomaly cancellation conditions are: Special Cases: • No fermions. • Only one anomalous U(1).

12. String Computation of GCS The GCS-terms are:

13. An example: The Z Orientifold 6 We compactify the 6 extra dimensions: 2 2 2 4D T T T we identify points: After tadpole cancellation, the gauge group and the massless spectum are:

14. Gauge group: U(6)×U(6)×U(4)| ×U(6)×U(6)×U(4)| 9 5 An example: The Z Orientifold 6 • In this model, there are six U(1)΄s. • Among them, 4 are anomalous and 2 non-anomalous. • However, 5 become massive and 1 remains massless. (due to higher dimensional anomalies) Ibanez Marchesano Rabadan, Antoniadis Kiritsis Rizos, Anastasopoulos

15. An example: The Z Orientifold 6 Therefore, if where: Chern-Simons terms are necessary. This is a generic property of all orientifold models. is not zero, we do need generalised GCS-terms to cancel all the anomalies: Eijj ~

16. Heavy Fermions • GCS-terms are also a prediction of an anomaly-free chiral gauge theory with heavy and light fermions (after SSB). • Denoting the heavy mass-insertion with ( × ): example: ~ ~

17. SU(3)×SU(2)×U(1) Y SU(3)×SU(2)×U(1)×U(1) ×U(1) ×U(1)΄ 3 2 Phenomenological implications • A typical D-brane description of the Standard Model (Top Down or Bottom Up): Standard Model • There are three more abelian gauge bosons. • These U(1)΄s are anomalous. Aldazabal Ibanez Marchesano Quevedo Rabadan Uranga, Cvetic Shiu, Blumenhagen Honecker Kors Lust Ott, Antoniadis Dimopoulos Kiritsis Tomaras Rizos, Schellekens et al..

18. (m,-1| n,+1) - SU(m) x U(1) m (Antisym ,+2) m D-branes & Gauge Groups Adjoint U(m) (m,+1| n,+1) m n Set of representations: Adjoints, bifundamentals, antisymmetric & symmetric. m n

19. A low string scale model • Higgses are charged under Y and PQ but not under B and L. • After EW symmetry breaking, both Y and PQ are spontaneously broken. • Two origins for masses: • The UV mass matrix of the anomalous U(1)s: ~ Ms . • The Higgs mechanism: vH~ 100-200 GeV. Antoniadis Tomaras Kiritsis Rizos

20. Z-Z΄ Mixings • We go to the photon basis: • The coefficients are:

21. CS Couplings and LHC • Consider the various anomaly canceling GCS-terms : • Some terms are zero on-shell. • Therefore, new signals may be visible in LHC, like: Coriano Irges Kiritsis

22. Conclusions • Anomalous U(1)΄s are a generic prediction of orientifold vacua. • If the string scale is low (few TeV region) such gauge bosons become the tell-tales signals of such vacua. • Anomaly related Chern Simons-like couplings produce new signals that distinguish such models from other Z΄-models. • Such signals may be visible in LHC.