1. Claudio Corianò Università del Salento INFN, Lecce
The Search for EXTRA Z’ at the LHC
Claudio Corianò
Università del Salento
INFN, Lecce
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/ , Irges, C., to appear on Phys. Lett. B
2. A Unitarity analysis of the Higgs-axion mixing.
hep-ph/
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/ , 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
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. Irges, Kiritsis, C. 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. Solved by CANDIA (Cafarella, Guzzi, C.C.)
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

52. 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

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

55. Rapidity distributions of the DY lepton pair
Cafarella, Guzzi, C.C.
Anastasiou Dixon, Melnikov and Petriello

56. Conclusions
The possibility of discovering extra Z’ at the LHC
Is realistic,
They are common in GUT’s and string inspired models.
Anomalous U(1)’s are important for a variety of reasons.
They may play a considerable role in the flavour sector
Froggatt-Nielsen (Ramond, Irges),
But predict also new 3-linear gauge interactions and a
Axi-Higgs.
Precision QCD necessary to discriminate them
at the LHC. Z gamma gamma and Drell-Yan the best place
to loo at them.
Anomalies also can be due to partial decoupling of a heavy
Fermion, leaving at low energy a gauged axion

57. General features of the model
Number of axions = Number of anomalous U(1)
Two Higgs-doublets
(we have found that it is necessary to have full Higgs-axion mixing in order to have
a unitary model)
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) xU(1))
SU(3) x SU(2) x U(1, Y) x U(1)’)

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

60. GS
CS interaction
Bouchiat, Iliopoulos, Meyer. Gauge independence of the
S-matrix. Work in a specific gauge and select the phase
Irges, Morelli, C.C.

61. Gauge independence in the Stuckelberg phase
Gauge independence in the H-S phase

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

63. 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

64. The VERY MINIMAL MODEL
2 Higgs doublets

65. V/M drives the breaking
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

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

67. CP even
CP odd

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

69. 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

70. 1 physical axion,
The Axi-Higgs
GS Axions
N Nambu-Goldstone modes

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

72. 3-linear interactions of the gauge fields

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

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

75. The detection of Extra Z’ in this framework

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

80. with M. Guzzi and A. Cafarella (Demokritos)

82. U(1,Y ) x U(1,B)
Counterterms of BYY

84. Impose the BRS invariance of the gauge fixed action, having removed the bB mixing

85. Generalized CS

86. Valence quark sector
Gluon sector

87. The structure of the anomalous amplitude

89. Z photon photon

90. Conclusions and Open Issues
New 3-linear gauge interactions at the LHC
due to the different cancelation mechanism
Question: if a new resonance in DY, for instance
Is found, are we going to have enough statistics to
resolve the type of resonance, that is
once the resonance is found, can we look for
1) Charge asymmetries
2) Forward Backward asymmetries
To discriminate among the possible models and say that
there is an inflow?
If we integrate part of the fermion specrum we get a
WZ term. How do we know that the anomalous theory is
Just a result of “partial decoupling”?