Claudio Corianò Università del Salento INFN, Lecce

1. The Search for EXTRA Z’ at the LHC Claudio Corianò Università del Salento INFN, Lecce QCD@work 2007, Martina Franca

2. 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 Z’s” 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?

3. Simplified approach: 1) these neutral interactions and the corresponding anomalous generators decouple at LHC energies: we won’t see anything. Then predictions simply “overlap” with those coming from the “large array” of U(1)’s We don’t need to worry about the axion, and its mixing with the remaining scalars of the SM. Complete approach: 2) We don’t 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)

4. “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

6. Standard Model Anomalies

7. work in progress with Alon Faraggi, Marco Guzzi and Alessandro Cafarella

10. D= M4 x T2 x T2 x T2

12. Irges, Kiritsis, C.C. “On the effective theory of low-scale Orientifold vacua”, Nucl. Phys. B, 2005

13. 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.

14. Gross and Jackiw 70’s

15. 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?

16. Extending the SM just with anomalies canceled by CS contributions (.YYY) (.BBB) (.CCC) (X SU(2) SU(2)) (X SU(3) SU(3))

17. Vanishing only for SM In the MLSOM some are vanishing after sum over the fermions

19. 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

20. CS contribution Non-local contribution its variation under B-gauge transformations is local A is massless

21. 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.

22. shift Stuckelberg mass the axion is a Goldstone The Stueckelberg shifts like the phase of a Higgs field

23. Number of axions=number of anomalous U(1)’s anomalous Higgs b, c are Stuckelberg axions physical axion Goldstone boson

24. Rotation into the Axi-Higgs Mass of the anomalous gauge boson B = Stuckelberg mass + electroweak mass

26. Anomalous effective action Stuckelberg mass term Axion-gauge field interactions, dimension 5

27. 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

28. 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 D’Hoker 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 don’t seem, at this time, to explained by this low energy construction Armillis, Guzzi, C.C. work in progress

30. 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

31. 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

32. Gauge sector

33. 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

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

35. Fermionic sector Fermion interactions of the extra Z’ Decoupling as v/M--->0

36. CP even CP odd

37. 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

38. 1 physical axion, The Axi-Higgs GS Axions N Nambu-Goldstone modes

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

41. Moving to the broken phase, the axion has to be rotated into its physical component, the Axi-Higgs and the Goldstones

42. Direct coupling to gauge fields

43. M. Guzzi, S. Morelli, C.C., in progress: axi-higgs decay into 2 photons

44. Associated Production Associated production g g--> H Z, now with the additional scalars

45. New physics Hard scatterings Pure QCD contributions Parton distributions

46. 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

47. 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

48. Factorization Theorems

49. LO, 70’s Gribov-Lipatov Altarelli Parisi Dokshitzer NLO, 80’s Floratos, Ross, Sachrajda, Curci, Furmanski Petronzio

50. High precisio determination of the renormalization/factorization scale dependence of the pdf’s Solved by CANDIA (Cafarella, Guzzi, C.C.) Truncated, Singlet and non-singlet Exact , non singlet Cafarella, Guzzi, C.C., NPB 2006