Transcript Document

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., comparisons
with 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.
1) We will try a general analysis (here an experimental input is welcomed)
2) 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.
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.
Extra Dimensional Theories
• 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 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) + n
Nkk= 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 Becomes Stronger
Strength
EM
…
gravity
1/m*
r
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…
(.YYY)
(.BBB)
(.CCC)
(X SU(2) SU(2))
(X SU(3) SU(3))
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 aI
2 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-loop
The 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 aI
2 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-loop
The fermion spectrum is, therefore: anomalous
How do we extract an anomaly free hypercharge?
Two cases: axions not in the scalar potential
(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.
Rotation from the hypercharge basis
to the physical basis (mass eigenstates)
We need to
determine
MI, the
masses of
the U(1)
GAUGE
BOSONS
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
Associated production g g--> H Z, now with the additional
scalars
Irges, Kiritsis, C.C.
•
Unification models
–
–
Based on GUTS, some popular extensions are those including SO(10) and
E6
E6SO(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, Tomaras
Antoniadis, Leontaris, Rizos
Ibanez, Marchesano, Rabadan,
Ghilencea, Ibanez, Irges, Quevedo
See. 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…