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FINALLYA REALISTIC
HIGGSLESS MODEL
Guido MarandellaUniversity of California, Davis
G. Cacciapaglia, C. Csáki, GM, J, Terning, hep-ph/0607146
Santa Fe - June 24 2006
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OUTLINE
Review about Higgsless models
Main challenges
The third generation: top mass and Zbb
New realization of the custodial symmetry
Summary
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Why do we need the Higgs ?
• Break the ElectroWeak symmetry
• Fermion masses
• Unitarize the WW scattering
All this can be achieved through extra dimensions
HIGGSLESS MODELS
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Why do we need the Higgs ?
• Break the ElectroWeak symmetry -> BC
• Fermion masses -> BC
• Unitarize the WW scattering -> KK gauge bosons
All this can be achieved through extra dimensions
(C. Csaki, C. Grojean, J. Hubisz, H. Murayama, L. Pilo, Y. Shirman, J. Terning)
HIGGSLESS MODELS
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Attempts to build realistic Higgsless models face two main challanges already at tree-level
• ElectroWeak Precision Data (S-parameter)
• Top mass without spoiling Zbb
HIGGSLESS MODELS
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HIGGSLESS MODELS
SU(2)L x SU(2)R x U(1)X
SU(2)L x U(1)Y SU(2)D x U(1)X
The setup
UV IRAdS5
Embedding fermions
Chiral spectrum with different BC
Left-handedRight-handed
! =!
!"
"!:! :
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For massless fermions ( under SU(2)L x SU(2)R x U(1)X )
BC (UV,IR)
give a LH zero mode living in and a RH zero mode living in
HIGGSLESS MODELS
!L!R
!L = (2,1)Y , !R = (1,2)Y
= (-,-)
= (-,-)
= (+,+)= (+,+)
!R
!L
!L
!R
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Where do fermions live ?
Bulk mass terms
HIGGSLESS MODELS
Sm =!
d5x
"R
z
#5 $cL
R!̄L!L +
cR
R!̄R!R
%
IRUV
cL = !cR = 1/2
cL > 1/2 (cR < !1/2)
cL < 1/2 (cR > !1/2)
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Three KK towers of neutral gauge boson.
Before EWSB
W3L (+,+), BY (+,+), B2 (-,+)
Corrections to precision observables
HIGGSLESS MODELS
make it ≃ 0
f
f̄
Z
B(k), B(k)2 ,W (k)
3L
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S-parameter
(G. Cacciapaglia, C. Csaki, C. Grojean and J. Terning, hep-ph/0409126)
HIGGSLESS MODELS
1/R = 10-8 GeV, 1/R’ = 280 GeV
0.4 0.5 0.6 0.7c
-0.005
0.005
0.01
0.015
0.02
0.025
0.03
U
0.4 0.5 0.6 0.7c
-8
-6
-4
-2
S
0.4 0.5 0.6 0.7c
0.02
0.04
0.06
0.08
0.1
T
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The third generation is special due to the heaviness of the top quark
Big Dirac mass on the TeV brane
TOP MASS AND Zbb
M (!L"R+!R"L )
!(1,2)1/6R =
!!R
"R
"!(2,1)1/6
L =!
!L
"L
"
!L =!
!tL
!bL
", "L =
!"tL
"bL
".....
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Boundary conditions on the TeV brane
It is not possible to get arbitrarily high mass. For MR’->∞ the BC become
So the top is a KK excitation: its mass is set by 1/R’ ≃ 300 GeV
The bottom mass is suppressed with a big kinetic terms localized on the Planck brane
TOP MASS AND Zbb
!R = "L = 0
!R = !MR! !L!L = MR! !R
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To have Zbb ok we need cL ≃ 0.46, i.e. the bottom
wave function almost flat. But
M has to be ≃ 1/R’ to get the top mass
The coupling of the LH bottom to the Z modified
TOP MASS AND Zbb
is a LH bottom quark with Y = -1/3 !
!R = !MR! !L
!R =!
!tR
!bR
"!bR
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TOP MASS AND Zbb
0.1 0.2 0.3 0.4cL
!0.2
0
0.2
0.4
0.6
0.8
"gZbb !gSM
Z
b
b!
b
b!
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An alternative realization of the custodial symmetry (K. Agashe, R. Contino, L. Da Rold, A. Pomarol, hep-ph/0605341
M. Carena, E. Ponton, J. Santiago and C. Wagner, hep-ph/0607106)
Consider a BSM sector symmetric under
broken to
C
A NEW REALIZATION
O(4) ! SU(2)L " SU(2)R " PLR
O(3) ! SU(2)V " PLR
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Z coupling to a fermion
Q is conserved, QL3 not necessarily
If ψ is a +1 eigenstate of PLR then
which implies
i.e. QL3 is protected
A NEW REALIZATION
g
cos !W
!Q3
L !Q sin2 !W
"Zµ"̄#µ"
TL = TR, T 3L = T 3
R
!QL + !QR = 0, !QL = !QR
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Promote
for the RH fields
Mass for top and bottom
A NEW REALIZATION
!L = (2,1)1/6 !" (2,2)2/3 =!
tL XL
bL TL
"
tR = (1,1)2/3 !R = (1,3)2/3 =
!
"XR
TR
bR
#
$
M1!2
tR (tL " TL) +
M3
!1!2TR (tL + TL) + bRbL
"
T3L = T3R = -1/2
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Not enough though
(Almost) constant +4/5 % deviation.
Where does it come from ?
A NEW REALIZATION
0.1 0.2 0.3 0.4cL
1.01
1.02
1.03
1.04
1.05gZ bl !bl !gSM
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On the Planck brane
SU(2)R x U(1)Y -> U(1)Y
breaks the discrete parity PLR
Suppose that there is no such breaking on the UV brane. Before EWSB all gauge bosons have a flat zero mode and the same KK tower
A NEW REALIZATION
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A NEW REALIZATION
BX
is broken on the TeV brane
are not
W 3L !W 3
R
W 3L + W 3
R
Z
b
b
(W 3L + W 3
R)(k), B(k)X
cannot occur
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However, is broken on the UV brane, so its KK tower is different from
When going to the basis
one can have
A NEW REALIZATION
BX
W 3L !W 3
R
W 3L + W 3
R
Z
b
b
!(W 3L " W 3
R)(k), B(k)X #
W 3R !BX
W 3R + BX , W 3
L
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The solution
If bL and bR are localized far apart, M3 has to be ≃ 1/R’ and a sizable component of the LH bottom
lives in bR -> modifications in Zblbl
A NEW REALIZATION
!L = (2,1)1/6 !" (2,2)2/3 =!
tL XL
bL TL
"
tR = (1,1)2/3 !R = (1,3)2/3 =
!
"XR
TR
bR
#
$
Lm = M3
!1!2TR (tL + TL) + bRbL
"
T3L = T3R = -1/2
T3L = 0, T3R = -1
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Diagramatically, before we were neglecting
which instead can be sizable if bL and bR are localized near opposite branes
A NEW REALIZATION
Z
b
b!
b
b!
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A NEW REALIZATION
!0.75 !0.7 !0.65 !0.6 !0.55 !0.5cRb
0.9
0.92
0.94
0.96
0.98
1.02
1.04
gZ bl "bl !gSM
1/R = 10-8 GeV, 1/R’ = 280 GeV, cL = 0.1
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Summarizing the configuration for zero modes
A NEW REALIZATION
UV IR
Gauge bosonsLight fermions
LH top and bottomRH top
RH bottom
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The couplings of the third generation
SUMMARY OF THE MODEL
frac. of SMZb!b̄! 1.004Zbr b̄r 0.993Zt!t̄! 0.461Ztr t̄r 1.908Wt!b̄! 0.862Wtr b̄r 3 · 10!4 gWt!b̄!
1/R = 10-8 GeV, 1/R’ = 280 GeV, cL = 0.1, cRt = 0, cRb = -0.73
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An alternative realization of the custodial symmetry allows with a discrete L-R parity
• obtain the top mass
• make Zbb deviations arbitrarily small
(Almost) flat light fermions allow an arbitrarily small S parameter.
The Higgsless model has finally a fully realistic formulation at tree level.
Loop effects to be analyzed (T-parameter ?)
CONCLUSIONS