Claudio Corianò Università del Salento INFN, Lecce

Claudio Corianò

Università del SalentoINFN, Lecce

The Search for EXTRA Z’ at the LHC

QCD@work 2007, Martina Franca

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?

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)

“Stuckelberg Axions and the Effective Action of Anomalous Abelian Models”

1. “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/0701010Irges, 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 appearApplications to 3-linear gauge interactions

Standard Model Anomalies

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

D= M4 x T2 x T2 x T2

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

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.

Gross and Jackiw 70’s

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, RizosIbanez, Marchesano, Rabadan,Ghilencea, Ibanez, Irges, QuevedoSee. 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?

(X SU(2) SU(2)) (X SU(3) SU(3))

(.YYY)

(.BBB)

(.CCC)

Extending the SM just with anomalies canceled by CS contributions

Vanishing only for SM

In the MLSOM some are vanishing after sum over thefermions

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

Momentum shifts in the loop generate linear terms in the independent momenta

redistribute the anomaly. Their sum is fixed

CS contribution

Non-local contributionits variation under B-gauge transformations is local

A is massless

A, vector-like

B, C axial

Chern-Simons contributions

It is possible to show that one needs both CS and GS interaction, Irges, Tomaras, C.C.

Stuckelberg mass

the axion is a Goldstone

shift

The Stueckelberg shifts like the phase of a Higgs field

Number of axions=number of anomalous U(1)’sanomalous

Higgs

b, c are Stuckelberg axions

physical axionGoldstone boson

Rotation into the Axi-Higgs

Mass of the anomalous gauge boson B = Stuckelberg mass + electroweak mass

Stuckelberg mass term Axion-gauge field interactions, dimension 5

Anomalous effective action

These effective models have 2 broken phases 1) A Stuckelberg phase 2) 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)

Physical axion

Goldstone boson

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 ofD’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

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

The SU(3)xSU(2)xU(1)xU(1) Modelkinetic

L/R fermion

Stueckelberg

CS

Higgs-axion mixing

GS

Higgs doublets

Irges, Kiritsis, C.

Gauge sector

The neutral sector shows a mixing between W3, hypercharge and the anomalous gauge boson, B

The Higgs covariant derivatives responsible for the gauge boson mixing together with the Stueckelberg terms

No v/M corrections on firstrow

SM-like

1/M

O(M)

Decoupling as v/M--->0

Fermion interactions of the extra Z’

Fermionic sector

CP even

CP odd

CP odd Sector. Where the physical axion appears

2 GoldstonesWe 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

GS Axions

1 physical axion, The Axi-Higgs

N Nambu-Goldstone modes

Some properties of the axi-Higgs: Yukawa couplings

Induces the decay of the Axi-Higgs, similar to Higgs decay

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

Direct coupling to gauge fields

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

Associated production g g--> H Z, now with the additionalscalars

Associated Production

Pure QCD contributions

Parton distributions

Hard scatterings

New physics

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

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

Factorization Theorems

LO, 70’s

Gribov-LipatovAltarelli ParisiDokshitzer

NLO, 80’s

Floratos, Ross, Sachrajda,

Curci,FurmanskiPetronzio

High precisio determination of the renormalization/factorization scale dependence of the pdf’s

Cafarella, Guzzi, C.C., NPB 2006

Truncated, Singlet and non-singlet

Exact , non singlet

Solved by CANDIA (Cafarella, Guzzi, C.C.)

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.

600 GeV

400 GeV, 14 TeV

QCD “error” around 2-3 %

Reduction by 60 %

Guzzi, Cafarella, C.

Cafarella, Guzzi, C.C. Anastasiou Dixon, Melnikov and Petriello

Rapidity distributions of the DY lepton pair

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 aAxi-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

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)’)

B gets mass by the combined Higgs-Stuckelberg Mechanism and is chirally coupled

U(1)Ax U(1)B

Bouchiat, Iliopoulos, Meyer. Gauge independence of the S-matrix. Work in a specific gauge and select the phase

CS interaction

GS

Irges, Morelli, C.C.

Gauge independence in the Stuckelberg phase

Gauge independence in the H-S phase

Checks in the fermionic sector.

These are the typical classes of diagrams one needs to worry about.

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

The VERY MINIMAL MODEL

2 Higgs doublets

The neutral sector shows a mixing between W3, hypercharge and the anomalous gauge boson, B

The Higgs covariant derivatives responsible for the gauge boson mixing together with the Stueckelberg terms

V/M drives the breaking

vu, vd << M

No v/M corrections on firstrow

SM-like

1/M

O(M)

CP even

CP odd

Decoupling as v/M--->0

Fermion interactions of the extra Z’

Fermionic sector

CP odd Sector. Where the physical axion appears

2 GoldstonesWe 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

GS Axions

1 physical axion, The Axi-Higgs

N Nambu-Goldstone modes

Some properties of the axi-Higgs: Yukawa couplings

Induces the decay of the Axi-Higgs, similar to Higgs decay

3-linear interactions of the gauge fields

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

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

The detection of Extra Z’ in this framework

LO, 70’s

Gribov-LipatovAltarelli ParisiDokshitzer

NLO, 80’s

Floratos, Ross, Sachrajda,

Curci,FurmanskiPetronzio

with M. Guzzi and A. Cafarella (Demokritos)

Counterterms of BYY

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

Generalized CS

Valence quark sector

Gluon sector

The structure of the anomalous amplitude

Z photon photon

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 for1) Charge asymmetries 2) Forward Backward asymmetries To discriminate among the possible models and say thatthere 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”?