The Search for Extra Z’ and an extended Higgs sector in Effective U(1) Models

from Branes

Claudio Corianò

Dipartimento di Fisica Univ. di Lecce, INFN Lecce

The search for Extra neutral components at the LHC is an important goal We are currently selecting the kinds of processes on which we hope to be able to say something and contribute to this workshop by combining (whenever possible) NNLO QCD studies with studies of new physics.(Cafarella, Guzzi, Morelli, C.C.)

High Precision QCD (NNLO) pursued by various people, is useful, at least for some basic processes, DY for instance, we need new ideas to test.

impact of scaling violations on the pdf’s (study is quite involved: errors on the pdf’s, issues related to the choice of a suitable scale in the evolution, tests of benchmarks - Marco Guzzi’s talk-)

Objective: having Drell-Yan under control at NNLO, fine tuning XSIEVE, etc., comparisonswith PEGASUS, interface with VRAP, and so on (will be done soon).

How to organize the search for EXTRA Z’ in such a way that it covers also other possibilities, is sufficiently general, etc.

• We will try a general analysis (here an experimental input is welcomed) • But also: how to find some signatures for specific models. Then we can’t just stop at DY, but we need to look closely at other sectors as well, the Higgs sector, for instance. but we need to look closely at other sectors as well, the Higgs sector, for instance.

Directions:

Minimal Low Scale Orientifold Model: Summarizes a basic set of properties of a class of string vacua, derived from Brane Theory

(Irges, Kiritsis, C.C., to appear on Nucl. Phys. B) ,

I will illustrate some of its features next. In this class of models there are some very specific signatures:

-Constraints on couplings, masses of the additional Z’s, etc (Stuckelberg/ Green Schwarz extensions),

1) Higgs-Axion Mixing (Z’--> gamma gamma, Zgg vertex, associated

W/Z production with scalars)

2) DY

Other Questions:

-What about GUT’s? Is there also something specific that we can say about EXTRA U(1)’s.

• Theories with extra dimensions predict a gravity scale close to the electroweak scale, say 1 TeV, which can be accessed at future colliders (even the LHC). Gravitational and Supersymmetric effects should appear at some stage if the gravity scale is indeed low

In brane models the type of gauge interactions

that appears aro those of U(N) type.

U(N)=SU(N)x U(1).

The pattern is very different compared to stuandard GUT’s

Extra Dimensional Theories

Extra Dimensional models are based on the idea that we live on a BRANE (a domain wall) immersed in a bigger space. String theories live in D=10= 9(space) +1(time) spacetime dimensions. ED models assume a spacetime structure in which p coordinates describe the brane and (9- p) are the remaining “extra” space coordinates.

These extra coordinates are characterized by a compactification radius R which can be of a millimeter (the extra dimensional space is called: the bulk).

Gravity can go into the bulk (ED) Matter stays on the brane. The Planck scale we are used to (MPlanck)is not the true scale for gravity.

There can be, additionally, “Kaluza Klein dimensions” Example: D=10 = 9 +1 = (3 +1) + (Nkk) + nNkk= Kaluza-Klein dimensions D= 4 + n n= number of extra dimensions. We can have up to n=6 extra dimensions (Nkk=0)

The scale of gravity is lowered (M *) << MPlanck

Gravity becomes strong as soon as we reach M*, which is the true scale for gravity. It can be of the order of the electroweak scale (say M* = 1 TeV) .

Gravitational effects which ordinarily occur for very large masses, say 1.5 times the solar mass, are now possible at an equivalent energy E > M*

gravity

EM

Str

engt

h

r

…

1/m*

Gravity Becomes Stronger

D= M4 x T2 x T2 x T2

U(3,a)xU(2,b)XU(1,c)xU(1,d)=SU(3)xSU(2)xU(1,a))xU(1,b))xU(1,c))xU(1,d)

U(1,a)xU(1,b)xU(1,c)xU(1,d)=U(1,Y)xU(1)xU(1)xU(1)

The lagrangean is not gauge invariant and renormalizability does not hold

Observe that we can cure the gauge variation in 2 possible ways

1) Introducing a direct (gauge variant) direct interaction between the gauge bosons whose variation cancels the anomaly

2) Or we can introduce an additional field (compensator field), one or more, say b,c (axions) and let them shift linearly under the gauge transformations to remove the FF unwanted terms 3) Both (?)

Modifying the Higgs mechanism for U(1) interactions

You can cure anomalies by (a FF) interactions using a suitable set of axions.

Then: if string theory predicts several U(1)’s and we are not necessarily bound to introduce a breaking at some large (super heavy scale, say a GUT scale) Via a Higgs system, then we should look for alternative ways to render the U(1)’s massive

This comes fore free: The Stuckelberg trick.

(gauge field)-axion mixing

We can generate a mass for U(1)_B through a combined Higgs-Stuckelberg mechanism

Summary: 1) b FF for anomaly cancelation

2) matter term (b) for U(1)_B

Question: are the axions just Nambu-Goldstone modes

In the presence of an anomalous fermionic spectrum ?

No. One axion becomes physical and mixes with the Higgs sector: the axi-Higgs (Irges, Kiritsis, CC)

is this all ?

Chern Simons Interactions

Irges , Tomaras,C.C.

Are there perhaps CS interactions in the Standard Model and we have not seen them? effects in Z gg and Z gamma gamma…

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

(.YYY)

(.BBB)

(.CCC)

In the Standard Model, cancelation of the anomalies needs the imposition of the defining Ward identities on the anomaly diagram. Two invariant amplitudes a1, a2 are divergent and there is no regularization scheme that can make them finite. By imposing WI on 3-point functions we re-express a1 and a2 in terms of a3,…a6, which are finite.

In other words: in the presence of chiral couplings the

Feynman rules are not sufficient to fix the theory.

Hagiwara, Peccei and Zeppenfeld

Axions aI2 Higgses, AAF Chern Simons interactions Stuckelberg terms for the anomalous U(1)’s

To this lagrangean we add dimension-5 aFF operators for an anomaly free theory at 1-loopThe fermion spectrum is, therefore: anomalous How do we extract an anomaly free hypercharge?

Axion couplings dimension 5

CS interactions in the exact phase

SU(3) X SU(2) X U(1)x U(1) X…..U(1)

Axions aI2 Higgses, AAF Chern Simons interactions Stuckelberg terms for the anomalous U(1)’s

To this lagrangean we add dimension-5 aFF operators for an anomaly free theory at 1-loopThe fermion spectrum is, therefore: anomalous How do we extract an anomaly free hypercharge?

(G0,A0) come from the CP-odd part (Im Hu,Im Hd)

The counting is 14 (gauge) + 8 (Higgs) + 3 axions------> 20 (gauge) + 5 (Higgs) + 3 axions Broken generators: 4 + 3 -1(em)=6 ---------> 6 NG modes = G+, G0, a1,a2,a3 Therefore when there is no mixing in the potential the axions are NG modes.

Two cases: axions not in the scalar potential

We need to determine MI, the masses of the U(1) GAUGE BOSONS

Rotation from the hypercharge basisto the physical basis (mass eigenstates)

Masses of the physical eigenstates

Ibanez Model (Ibanez, Marchesano and Rabadan)

Charges in the brane basis In terms of the charges of SU(3) xSU(2)x U(1)_y xU(1)’

Guzzi, Irges, C.C.

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

Associated Production

Irges, Kiritsis, C.C.

• Unification models– Based on GUTS, some popular extensions are those including SO(10) and E6– E6SO(10) x U(1)SU(5)xU(1)x U(1)SMxU(1)ß

Models with anomalous U(1)’s from the Brane construction

Antoniadis, Kiritsis, Rizos, TomarasAntoniadis, Leontaris, RizosIbanez, Marchesano, Rabadan,Ghilencea, Ibanez, Irges, QuevedoSee. E. Kiritsis’ review on Phys. Rep.Nikos Irges + E. Kiritsis talks at this meeting

Conclusions

We can study an entire class of models based on the brane construction

These model are peculiar (and general, with universal features) because of a specific mechanism of anomaly cancelations (Green.Schwarz)

1) The Higgs sector has an Axi-Higgs ( Irges, Kiritsis, C.)The phenomenology is different from usual GUT-based models

2) Stuckelberg mechanism 3) Direct Chern Simons Interactions absent in the Standard Model

NUMERICAL WORK: Zgg vertex, Z gamma gamma, Drell-Yan…