Searching for Anomalous Extra Z’ at the LHC

1. Searching for Anomalous Extra Z’ at the LHC Claudio Coriano’ Universita’ del Salento INFN, Lecce Based on work in collaboration with N. Irges (Crete), M.Guzzi (Lecce), S. Morelli (Lecce), R. Armillis (Lecce) Olympia, April 2008

2. original formulation with Irges and E. Kiritsis “On the effective theory of low scale orientifold string vacua”. Introduction of the Axi-Higgs Nucl.Phys.B 746, 2006.

3. “Stuckelberg Axions and the Effective Action of Anomalous Abelian Models” “Windows over a new Low energy Axion” hep-ph/0612140, Irges, C.C., Phys. Lett. B, 2007 2. A Unitarity analysis of the Higgs-axion mixing. hep-ph/0701010 Irges, Morelli, C.C., JHEP 2007 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., Nucl. Phys B 2008 4.”Trilinear gauge interactions..” M. Guzzi, R. Armillis, S. Morelli, JHEP 2008 5. “Unitarity Bound for anomalous gauge interactions and the GS mechanism”, Guzzi, Morelli, C.C., EPJ C 2008 Plus work in prgress with Nikos Irges

4. OUTLINE 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?

5. 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)….. • from which the hypercharge is assigned in a given string • construction, corresponding to a certain class of vacua • in string theory (Minimal Low Scale orientifold Models). • 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. • Blumenhagen, Kors, Lust, Stieberger • recent work by G. Leontaris and Coll.

6. Simplified approach: 1) these neutral interactions and the corresponding anomalous generators decouple at LHC energies: we won’t see anything. Then: string theory 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)

7. Gluon sector Irges, Morelli, C.C.

8. ALTERNATIVE MECHANISMS OF ANOMALY CANCELATION

9. What is the anomaly cancelation mechanism at the LHC Fermion charge assignment (anomaly free) Wess-Zumino (anomalous) + physical axion (axion-like particle) 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 GS cancelation: the problem with double poles in supersymmetry: no physical axion Armillis, Guzzi, C.C., in preparation

10. Diagrams responsible for extra double poles Unsettled debate: Adam, Bassetto, Soldati, Andrianov,Federbush, Fosco, Montemajor The conclusions of these papers should be reconsidered: there is a cancelation of double poles, at least through 3-loop order (Armillis, Guzzi, Morelli, C.C., in prep)

11. 1992 This paper was withdrawn.

12. How do we search for 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”

13. General features of the model Number of axions = Number of anomalous U(1) Two Higgs-doublets Anomalies canceled by 1) charge assignments + CS + GS These features are best illustrated in the context of a simple model with just 1 extra U(1) SU(3) x SU(2) x U(1, Y) x U(1)’) SU(3) x SU(2) x U(1) xU(1))

14. U(1)Ax U(1)B B gets mass by the combined Higgs-Stuckelberg Mechanism and is chirally coupled

15. shift Stuckelberg mass the axion is a Goldstone (if B does not gets also its mass via ewsb) The Stueckelberg shifts like the phase of a Higgs field

16. 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

17. One can add an additional potential which includes the Stuckelbergs axions PQ breaking potentials give mass to the Axi-Higgs. This is due to the “competition” between of ewsb (v) and the extra PQ breaking potential. It can be driven to be quite small.

18. Chern Simons Interactions. They appear in some special situations. In multiple Z’ models (Z1,Z2,Z3) where the partial anomalies can be distributed among the 3 anomalous vertices WZ CS interaction Bouchiat, Iliopoulos, Meyer Amplitudes. Gauge independence of the S-matrix. Work in a specific gauge and select the phase Irges, Morelli, C.C.

19. One can start with a symmetric distribution Of the anomaly and then correct by Chern-Simons interactions. Z gamma gamma does not have any CS term

20. These have been computed R= product of rotation matrices, theta’s=chiral asymmetry of the fermion spectrum respect to the anomalous U(1)’s Armillis, Guzzi, C.C., JHEP 2008 Typical anomaly diagram

21. The CS terms, in this case, take part in the defining Slavnov-Taylor identities of the model in the presence Of anomalous contributions and aFF coupling Armillis, Guzzi, C.C., 2007

22. 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

23. Checks in the fermionic sector. These are the typical classes of diagrams one needs to worry about.

24. Compared to a Peccei-Quinn axion, the new axion is gauged For a PQ axion a: m = C/fa, while the aFF interaction is also suppressed by : a/fa FF with fa = 10^9 GeV In the case of these models, the mass of the axion and its gauge interactions are unrelated the mass is generated by the combination of the Higgs and the Stuckelberg mechanisms combined The interaction is controlled by the Stuckelberg mass (M1) The axion shares the properties of a CP odd scalar

25. In WZ anomaly cancelation: The axion can be massless (light) or massive. However, in the simplest formulation of the theory, there is a unitarity bound, one needs higher dimensional operators (Irges, C.C.) The Stuckelberg mass term in the lagrangean is crucial for having a physical massless axion. The axion could be the result of a “partial decoupling of a heavy fermion” (Irges, C.C., PLB 2007). In the GS case: no physical axion, at least in the supersymmetric case.

26. One or two axions? with Guzzi and Morelli

28. ONE CAN INTEGRATE OUT THE AXION IN THE WZ CASE. WE WOULD OBTAIN A THEORY DIFFERENT FROM GS EXTRA INTERACTIONS COMPARED TO GS

30. 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

31. The VERY MINIMAL MODEL 2 Higgs doublets

32. The Higgs covariant derivatives responsible for the gauge boson mixing together with the Stueckelberg terms V/M drives the breaking vu, vd << M The neutral sector shows a mixing between W3, hypercharge and the anomalous gauge boson, B

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

34. CP even CP odd

35. CP odd Sector. Where the physical axion appears 2 Goldstones We need to identify the goldstones of the physical gauge bosons Axi-Higgs projection vanishes

36. 1 physical axion, The Axi-Higgs GS Axions N Nambu-Goldstone modes

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

38. 3-linear interactions of the gauge fields

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

40. M. Guzzi, S. Morelli, C.C : axi-higgs decay into 2 photons

41. The detection of Extra Z’ in this framework

42. NNLO Drell-Yan is sensitive to the anomaly inflow 2-loop technology (master integrals and such well Developed tools) You need to add a new class of Contributions, usually neglected for anomaly-free models

43. Factorization Theorems

44. 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

45. Precision QCD: NNLO effects within 3% in Drell-Yan

47. 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

48. QCD “error” around 2-3 % 600 GeV 400 GeV, 14 TeV Reduction by 60 % Guzzi, Cafarella, C.

49. Anomaly Effects in Extra Z’ models: Drell-Yan is resonant Double prompt photon production is non-resonant and non-unitary (in the WZ case) Bouchiat-Iliopoulos-Meyer amplitudes (BIM amplitudes) The WZ mechanism does not protect the theory from the non-unitary behaviour of these amplitudes Guzzi, Morelli, C.C., 2008 The anomaly erases the pole This diagrams is IR UV finite: the amplitude takes the Dolgov-Zakharov form

50. 2-photon processes New anomalous contributions in 2-photons