Quark Mass Matrix from Dimensional Deconstruction Academia Sinica Andrea Soddu Taipei November 17,...
-
Upload
harvey-stevenson -
Category
Documents
-
view
219 -
download
2
Transcript of Quark Mass Matrix from Dimensional Deconstruction Academia Sinica Andrea Soddu Taipei November 17,...
Quark Mass Matrix from Dimensional Deconstruction
Academia Sinica
Andrea Soddu
Taipei November 17, 2004
National Taiwan University
P.Q Hung, A.S., N.-K. Tran
hep-ph/0410179
OUTLOOK
Dimensional Deconstruction
What if the world is not four dimensional ?
Deconstructing 5D QED
Deconstructing 5D SU(2)xU(1)
Fermion zero modes and Quark Mass Matrices
Numerical results
Conclusions
Possible projects
World is apparently four dimensional
Simple scenario: theory of fields living in a space-time with four extended dimensions, plus one or more additional compact dimensions
At distances large compared to the size of compact dimensions, the world appears four dimensional: gauge forces fall off like the square of the distance
The Universe may be better described by a theory with more than the conventional one time and three space coordinates at energies not yet probed
At energies corresponding to the inverse compactification size, Kaluza-Klein excitations appear with a spectrum depending on the detailed nature of the compact space
At energies much higher than the compactification scale the extra dimensions become manifest. Physics is insensitive to the compactification and the theory appears higher dimensional
Higher-dimensional field theories have dimensionful couplings and therefore require a cutoff
As energy approaches the cutoff physics becomes strongly coupled and this makes difficult to address what happens at energies above the cutoff
Dimensional (De)Construction provides a possible scenario for UV completing higher-dimensional field theories
N. Arkani-Hamed, A.G. Cohen, and H. Georgi
Dimensional Deconstruction provides a manifestly gauge invariant description of n KK modes for an SU(m) gauge theory in the bulk
C. T. Hill, S. Pokorski, and J. Wang
Dimensional Deconstruction provides at low energy a theory with a similar spectrum of particles as higher dimensional theories
A natural light axion can be obtained as a WLPNGBC. T. Hill, and K. Leibovich
U(1) gauge theory in 1+4 dim.’s periodically compactified to 1+3 dim.’s
Latticization of a U(1) gauge theory with periodic 5th dim. gives a theory in 1+3 dim.s for N copies of the U(1) gauge group
1=N+12 n n+1 N-1 N… …
invariant under
has replaced translational invariance
Good approximation in the large N case for quantities that are insensitive to short distance (UV) structure of the theory
B.C.
From the point of view of 1+3 dim.’s each is effectively a non linear model field
compactification scale
causes each to develop a common VEV
gauge transformation
is the zero mode of
tower of doubled KK modes ( massive photons )
( SM photon )
N-1 are eaten to become longitudinal modes
is a massless scalar field (WLPNGB)
At low energy the deconstructed model has the same spectrum as an higher dimensional model
The master gauge group U(1)N is broken to the diagonal subgroup U(1) by the
N-1 of the link fields are eaten, giving N-1 massive vector fields (KK modes)
One massless vector field and one massless scalar field are left
When fermions are introduced becomes massive
The mass of the field is obtained by expanding about
the minimum of its Coleman-Weinberg potential
Similar result is obtained in a non-Abelian gauge theory
has been proposed as a candidate for an axion
Moose Diagram
Moose not for “chocolate moose”
Moose is a large deer, “ELK”
Deconstructing SU(2)xU(1)
2x2 matrix
Because of the potential
develop a VEV
[SU(2)xU(1)]N is broken down to the diagonal group SU(2)xU(1)
Four zero modes are left
We are interested in the SM Chiral FermionsImpose Chiral Boundary Conditions on Fermions
One more LH d.o.f over RH for Q fieldOne more RH d.o.f over LH for U and D fields
is complex
all couplings remain real
for
for
for
for
for
for
Zero Mode Zero Eigenvalue
Zero Mode Zero Eigenvalue
Zero Mode Zero Eigenvalue
unitary (not just orthogonal)
has the same
eigenvalues as
except the zero eigenvalue
Zero Mode localized at n = 1
Zero Mode localized at n = N
C.B.C.
C.B.C.N.C.
N.C.
bigger is more localized is the zero mode w. f.
localized in n=1
localized in n=1
localized in n=N
theory space
SU(2)xU(1) is equally broken at each site n
Comment: in Higgless theories [SU(2)xU(1)]N is broken completely through the deconstruction process. The SM massive gauge bosons correspond to the lightest KK modes.
The diagonal group SU(2)xU(1) is broken down to U(1)Q by SSB
Fermion zero modes obtain mass through Yukawa interaction with a Higgs field as in the SM
R.S. Chivukula, M. Kurachi, and M. Tanabashi
zero modes are the SM particles
When a liquid is cooled down sufficiently slowly, the atoms are often able to line themselves up and form a pure crystal, state of minimum energy
Simulated Annealing Method
Assign a probability to the change
from a configuration with energy to one with energy
assign
The system always takes a downhill step
transitionno transition
The system sometimes takes an uphill step
The temperature T is reduced with a given schedule
Q, U and D localized at n=1
Q, U and D localized at n=1
Q and U localized at n=1 D localized at n=N
Q and U localized at n=1 D localized at n=N
is localized at
is delocalized lives in the bulk
new source of CP violation mediated by KK gluons
One can have CP violation with only two families
KK gluons mediate FCNC at tree level
A. Delgado, A. Pomarol, and M. Quiros
In a split fermion scenario from deconstructed modelsone can have a new source of CP violation as well One can constrain from FCNC
Conclusions
The world could have more than four dimensions
Deconstructed theories have the same low energy behavior as higher dimensional theories but gauge invariance is preserved
(De)constructed theories can offer a UV completion of higher dimensional theories
Zero mode fermions can be localized in the theory space
Realistic quark mass matrices can be constructed starting from universal Yukawa coupling
Study of split fermion scenarios from deconstruction and FCNC Generation of small Dirac neutrino masses without See-Saw
Future projects