claudio corianò università del salento infn, lecce
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The Search for EXTRA Z’ at the LHC. Claudio Corianò Università del Salento INFN, Lecce. QCD@work 2007, Martina Franca. Summary: Searching for some extra neutral interactions at the Large Hadron Collider involves a combined effort from two sides: - PowerPoint PPT PresentationTRANSCRIPT
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”?