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
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.
“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/0701010Irges, 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
OUTLINESearching 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?
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, RizosIbanez, Marchesano, Rabadan,Ghilencea, Ibanez, Irges, QuevedoSee. E. Kiritsis’ review on Phys. Rep.
Blumenhagen, Kors, Lust, Stieberger recent work by G. Leontaris and Coll.
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)
Gluon sector
Irges, Morelli, C.C.
ALTERNATIVE MECHANISMS OF ANOMALY CANCELATION
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
Armillis, Guzzi, C.C., in preparationin supersymmetry: no physical axion
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)
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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”
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) 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
Stuckelberg mass
the axion is a Goldstone (if B does not gets also its mass via ewsb)
shift
The Stueckelberg shifts like the phase of a Higgs field
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
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.
One can add an additional potential which includes the Stuckelbergs axions
Bouchiat, Iliopoulos, Meyer Amplitudes. Gauge independence of the S-matrix. Work in a specific gauge and select the phase
CS interaction
WZ
Irges, Morelli, C.C.
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
One can start with a symmetric distributionOf the anomaly and then correct by Chern-Simons interactions. Z gamma gamma does not have any CS term
These have been computed
Armillis, Guzzi, C.C., JHEP 2008
Typical anomaly diagram
R= product of rotation matrices, theta’s=chiral asymmetry of the fermion spectrum respect to the anomalous U(1)’s
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
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
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
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.
with Guzzi and Morelli
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One or two axions?
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ONE CAN INTEGRATE OUT THE AXION IN THE WZ CASE. WE WOULD OBTAIN A THEORY DIFFERENT FROM GS
EXTRA INTERACTIONSCOMPAREDTO GS
The SU(3)xSU(2)xU(1)xU(1) Modelkinetic
L/R fermion
Stueckelberg
CS
Higgs-axion mixing
GS
Higgs doublets
Irges, Kiritsis, C.
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
CP odd Sector. Where the physical axion appears
2 GoldstonesWe need to identify the goldstones of the physical gauge bosons
Axi-Higgs projection vanishes
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
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
Factorization Theorems
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.)
Precision QCD: NNLO effects within 3%in Drell-Yan
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.
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
2-photon processes
New anomalous contributions in 2-photons
with Armillis, Guzzi, Morelli,
2 methods for anomaly cancelation
Wess-Zumino Green Schwarz
Green-Schwarz vertex: pole subtractions on the anomalous lines
New anomalous corrections
Untarity bound in the WZ case: gluon-gluon to gama gamma
Unitarity bound for axion-like particles. Obtained from a parton level Analysis. Should be generalized at hadron level
M_1 is approximately the mass of the extra Z’.
The two formulations are the WZ and the GS mechanisms for anomaly cancelation. Then, if we believe in the results from axial QED The GS mechanism fails to be unitary because of the extra double Poles. On the other hand also the WZ mechanism fails to be unitary, but in a different way: some amplitudes grow quadratically with energy
Unitarity bound for axion-like particles (Guzzi, Morelli, C.C.)
Armillis, Guzzi, Morelli, C.C, in preparation
Drell Yan anomalous (partial) (Madrid Model, Ibanez et al, MLSOM)
MLSOM versus anomaly Free U(1)’s
Armillis, Guzzi, Morelli, C.C.
Withs are quite smallG has to be O(1)
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”?
