The Higgs: elusive, illusive, delusive.pdf  Theoretical HighEnergy ...
Higgs
elusive, illusive, delusive
Quantum Universe 1, 21 April 2011, RuG
Sijbrand de Jong
Radboud University Nijmegen
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
1
Intro SM
QU1, RuG, 20/4/2011 (SdJ ) 2
Tuesday, April 26, 2011
Measurement Fit O meas −O fit /σ meas
0 1 2 3
Δα (5) had
(m Z
) 0.02758 ± 0.00035 0.02768
m Z [GeV] 91.1875 ± 0.0021 91.1874
Γ Z [GeV] 2.4952 ± 0.0023 2.4959
σ 0 had
[nb] 41.540 ± 0.037 41.479
R l
20.767 ± 0.025 20.742
A 0,l 0.01714 ± 0.00095 0.01645
A fb
SM successes
A l (P τ ) 0.1465 ± 0.0032 0.1481
R b
0.21629 ± 0.00066 0.21579
R c
0.1721 ± 0.0030 0.1723
A 0,b fb
0.0992 ± 0.0016 0.1038
A 0,c fb
0.0707 ± 0.0035 0.0742
A b
0.923 ± 0.020 0.935
A c
0.670 ± 0.027 0.668
A l (SLD) 0.1513 ± 0.0021 0.1481
sin 2 θ lept eff
(Q fb
) 0.2324 ± 0.0012 0.2314
m W [GeV] 80.399 ± 0.023 80.379
Γ W [GeV] 2.085 ± 0.042 2.092
m t [GeV] 173.3 ± 1.1 173.4
July 2010
0 1 2 3
QU1, RuG, 20/4/2011 (SdJ ) 3
Tuesday, April 26, 2011
SM fermion masses
Electroweak interaction: left handed doublets
right handed singlets
split masses in doublets: Higgs doublet to connect LR
⎛ ⎞
e + R(ϕ  ϕ 0 )
υe
⎝ e  ⎠L
dynamic symmetry breaking by vacuum expectation value
⎛ ⎞
e + R(0 v+H)
υe
⎝ e  ⎠L
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
4
Weak boson cross section unitary
e +
W +
υ
e  W 
e +
W
γ
+
+ E 2 divergent
e  W 
e +
W +
+
Z
E divergent
e  W 
e +
W +
+
H
log(E) divergent
e  W 
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
5
quantum corrections
fermion loop ~mf 2
Higgs correction ~log(MH)
Quantum Field Theory:
Everything depends
on everything else
running coupling constant
running masses
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
6
SM Higgs boson perturbativity and stability
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SM Higgs boson properties
★ mass limited by perturbativity and stability
★ Turns up as log(MH) in quantum corrections
★ Couples proportional to mass:
• preferably produced by heavy particles
• decays into heaviest particles kinematically available
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
8
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QU1, RuG, 20/4/2011 (SdJ ) 9
Tuesday, April 26, 2011
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SM successes
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QU1, RuG, 20/4/2011 (SdJ ) 10
Tuesday, April 26, 2011
Direct SM Higgs boson searches at LEP
19892000
L3
Aleph
Opal
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
Delphi
Energy pb 1
Z peak 162
>189 GeV 2461
>206 GeV 536
>208 GeV 32
11
muon
OPAL detector
photon
electron
QU1, RuG, 20/4/2011 (SdJ ) 12
Tuesday, April 26, 2011
Direct SM Higgs boson production at LEP
Easy background
Irreducible
background
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
13
Direct SM Higgs boson search channels at LEP
ττ qq
8%
υυ bb
19%
ll bb
6%
qq bb
66%
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
14
Higgs boson limit combination statistical method
test statistic (discriminator): LLR(MH) = 2 log ⎛
⎝
p(data  s+b)
p(data  b)
⎠ ⎞
The observation is: LLRobs
Determine what to expect for LLR with “toy experiments”
for both hypotheses: PDF(LLR  b), PDF(LLR  s+b)
confidence levels: 1CLb = p(LLRLLRobs  s+b)
To correct for small # events being
s+b
obs
b
unlikely for both hypothese,
modified frequentist: CLs=CLs+b/CLb
1CLb
CLs+b
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
15
Higgs boson limit from LEP statistical method
N
p(data  η) = ∏ (1/nk!)(ηsk+bk) n k
e (ηs k+b k )
×
k=1
Poisson statistics
nk
∏ (ηskSk(xjk;mH)+bkBk(xjk))/(ηsk+bk;mH)
j=1
η 1 for s+b, 0 for b discriminating variables statistics
N number of search channels
nk number of candidates in channel k
xjk (discriminating) variable(s) for candidate j in channel k
sk, bk total number of signal, background events in channel k
Sk, Bk PDFs for (discriminating) variable(s) in signal, background
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
16
2 ln(Q)
50
40
30
LEP
20
10
0
10
20
30
Observed
Expected for background
Expected for signal plus background
106 108 110 112 114 116 118 120
m H
(GeV/c 2 )
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Tuesday, April 26, 2011
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Tuesday, April 26, 2011
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QU1, RuG, 20/4/2011 (SdJ ) 20
Tuesday, April 26, 2011
Higgs boson searches at Tevatron
19892011
CDF
D0
(1992)
9.55 fb 1
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21
Dzero detector
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Higgs boson production and decay at Tevatron
pb
Hard
Easy
Higgs boson searches at Tevatron
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
23
SM Higgs boson search channels at Tevatron
Low Mass: WH → lυbb
ZH → llbb
ZH → υυbb
H → ττ
H → γγ
High Mass: H →WW → lυlυ, µυτ(had)υ, lυ qq
WH→WWW→ l ± l ± , l ± l ± X,
ZH →ZWW → lllX, l ± l ± X,
l=e,µ
l=e,µ,τ
l=e,µ
l=e,µ,τ
l=e,µ
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
24
Higgs boson limit derivation at Tevatron
Modified frequentist as for LEP
BUT, with nuisance parameters:
Extra Gaussian constraints
★ to clamp background predection to observed data
★ outside the expected signal region
Checked with Bayesian method (overall 1% agreement)
QU1, RuG, 20/4/2011 (SdJ )
25
Tuesday, April 26, 2011
SM Higgs boson limits at Tevatron
LLR
15
10
LLR b
!1 !
LLR b
!2 !
LLR b
LLR s+b
LLR obs
Tevatron RunII Preliminary
= 5.9 fb
1
5
Text
0
5
100 110 120 130 140 150 160 170 180 190 200
m H (GeV)
July 19, 2010
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Tuesday, April 26, 2011
26
95% CL Limit / SM
SM Higgs boson limits at Tevatron
1
DØ Preliminary, L=4.38.2 fb
SM Higgs Combination
Text
Observed
Expected
Expected !1!
Expected !2!
1
Standard Model = 1.0 DØ Exclusion
)
130 140 150 160 170 180 190 200
March 7, 2011
2
m H (GeV/c )
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Tuesday, April 26, 2011
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SM Higgs boson limits at Tevatron
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Tuesday, April 26, 2011
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SM Higgs boson prospects at Tevatron
QU1, RuG, 20/4/2011 (SdJ )
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select events with
CDF bump
exactly 1 lepton (e,mu) with pT>20 GeV
missing ET>25 GeV and
exactly 2 jets > 30 GeV
PT jj >40 GeV
M(l,ET)>30 GeV
similar to WH selection,
except no btags
~4pb !
arXiv:1104.0699v1
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Higgs boson searches at the LHC
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Higgs boson searches at the LHC
]
]
1
Total Integrated Luminosity [pb
35
30
25
20
15
10
5
Total Integrated Luminosity [pb
1
ATLAS Online Luminosity
60
50
40
30
20
10
LHC Delivered
ATLAS Recorded
1
Total Delivered: 28.8 pb
1
Total Recorded: 26.8 pb
ATLAS Online Luminosity
LHC Delivered
ATLAS Recorded
1
Total Delivered: 48.1 pb
1
s = 7 TeV
Total Recorded: 45.0 pb
2010:
delivered 48 pb 1
recorded 45 pb 1
0
24/03 19/05 14/07 08/09 03/11
Day in 2010
s = 7 TeV
0
25/02 04/03 11/03 18/03 25/03 01/04 08/04 15/04
Day in 2011
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Higgs boson searches at the LHC
QU1, RuG, 20/4/2011 (SdJ )
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Higgs boson searches at the LHC
QU1, RuG, 20/4/2011 (SdJ )
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Higgs boson prospects at the LHC
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22
20
18
16
14
2
Direct searches $!
LEP 95% CL
= 2ln(Q)
Tevatron 95% CL
LHC: H% WW only. Average neglects correlations
G fitter SM
MOR 11
4#
12
10
8
Max Baak,
Moriond 15/3/2011
3#
6
4
2
0
115 GeV < Theory uncertainty
mH < 137 GeV
Fit including theory errors
2#
Fit excluding theory errors
1#
100 150 200 250 300
M H
[GeV]
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SM Higgs boson combining it all
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Beyond SM: No Higgs
e +
W +
υ
e  W 
e +
W
γ
+
+ E 2 divergent
e  W 
e +
W +
+
Z
E divergent
e  W 
!
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
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Beyond SM: No Higgs
e +
W +
υ
e  W 
e +
W
γ
+
+ E 2 divergent
e  W 
e +
W +
+
Z
E divergent
e  W 
e +
W +
+
H
Composite Higgs
e  W 
weak: deviating Br
strong (technicolor):
multihiggs production
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
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Beyond SM: No Higgs
e +
W +
υ
e  W 
e +
W
γ
+
+ E 2 divergent
e  W 
e +
W +
+
Z
E divergent
e  W 
Z Z
+
W’
W’ and Z’ bosons
W 
W 
W’ and Z’ should
be discovered at
LHC energy scale
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
40
Beyond SM: Many Higgs
e +
W +
υ
e  W 
e +
W
γ
+
+ E 2 divergent
e  W 
e +
W +
+
Z
E divergent
e  W 
e +
W +
+
H
no divergence
e  W 
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
41
h
A
Gauge particles
H ±
MSSM:
> 100 parameters
MSugra:
4.5 parameters
SQuarks
~ ~ ~
~ ~ ~
~ ~ ~
~ ~ ~
SLeptons
A~
h~
χ~
0 2
~
χ~
0 1 ~ ~
~
~ ~
χ
~ ±
~ 1
Higgsino
fermion
χ ± 2
H ±
χ 0 3
Gauginos
Charginos
χ~
0 4
Gluinos
Neutralinos
QU1, RuG, 20/4/2011 (SdJ ) 42
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⎛
⎜
⎝
⎛
⎜
⎝
2 Higgs Doublet Model (2HDM) properties
tan(β)=vu/vd
tan(α)
Up
Down
vu
vd
⎛ϕ u
+
⎜
⎝
ϕ u
0
⎛ϕ d
+
⎜
⎝
ϕ d
0
W
H ±
Z
A
⎧
⎨
⎩
h
H
in general 2 free parameters:
tan(β) & mA
or tan(β) & mh
or mh & mA
In MSSM more constraint
lightest
often SM like
(not always)
heaviest
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
43
⎛
⎜
⎝
⎛
⎜
⎝
SUSY 2 Higgs Doublet Model properties
tan(β)=vu/vd
tan(α)
Up
Down
vu
vd
⎛ϕ u
+
⎜
⎝
ϕ u
0
⎛ϕ d
+
⎜
⎝
ϕ d
0
W
H ±
Z
A
⎧
⎨
⎩
h
H
Higgs masses function of other
SUSY parameters:
1 st order mh
e +
e 
~sin(βα)
SUSY Higgs searches at LEP
Z
Z*
h
e +
e 
~cos(βα)
Z*
A e +
Z*
H +
h e  H 
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
45
SUSY Higgs limits from Tevatron
~tan 2 (β)
b
b
h,A
for large tan 2 (β)
similar h and A production
123!
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SUSY Higgs: beware non SM behaviour
Fermiofobic Higgs: H→γγ
D*
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QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
47
But acceleration not nearly
as big as SM predicts !
VEV in
expanding
space
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
48
Canonical Quantization Path Integral
V(ϕ)
µ 2 0
v +v
ϕ
Expand
around
minimum
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Tuesday, April 26, 2011
Expanding around classical minimum gives:
IMAPP: Ronald Kleiss & collaborators
complex and nonconvex effective potential (=sum 1PI Greenʼs functions)
In general effective potential must be convex
(Symanzik & Iliopoulos et al. & Haymaker et al.)
For path integral approach:
this is indeed the case,
=
∫Dφ φ e iS(φ)/ħ
∫Dφ e iS(φ)/ħ
and there is a huge discrepancy with canonical quantization !
Euclidean lattice calculations conform this picture (G.J. Besjes, MSc thesis)
QU1, RuG, 20/4/2011 (SdJ ) 50
Tuesday, April 26, 2011
What if:
QU1, RuG, 20/4/2011 (SdJ ) 51
Tuesday, April 26, 2011
Canonical Quantization Path Integral !
Convex
V(ϕ)
µ 2 0
Potential
solves:
 vacuum
expansion
problem
 part of dark
energy
problem
v +v
ϕ
Phenomenological
implications
QU1, RuG, 20/4/2011 (SdJ )
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Tuesday, April 26, 2011
Higgs and non commutative geometry
(Chamseddine, Connes, Marcolli)
IMAPP: Walter van Suijlekom
& collaborators
spectral triple: A matrices on
H Hilbert space of spinors L 2 (M,S)⊗Mn(C)
D Dirac operator on H: γ µ ∂µ
Spectral action: count number of states of D on H up to
cutoff Λ
SΛ(D) = ∑fk ak(D 2 /Λ 2 )
= (Λ 2 ) 2 f0 (1/4π 2 ) ∫M √g dx + Λ 2 f2 (1/4π 2 ) (1/12) ∫M R√g dx +
f4 (1/4π 2 ) (1/360) ∫M [R µ ;µ +(5/4)R 2 2RµνR µν (7/4)RµνρσR µνρσ √g dx + ...
EinsteinHilbert Action if Λ 2 f2/24π 2 =1/8πG ⇒ Λ ~ Plank energy
Local symmetries incorporated by D DA=D+a[D,b], a,b∈ A
QU1, RuG, 20/4/2011 (SdJ )
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53
Higgs and non commutative geometry
IMAPP: Walter van Suijlekom
& collaborators
Standard Model: A= C I ⊕ IH ⊕ M3(C) I (cf. U(1)⊗SU(2)⊗SU(3))
(btw: A= C I ⊕ IH ⊕ IH ⊕ M3(C) I gives also υmaj seesaw mass terms)
relations between couplings: g 32
=g 22
=(5/3)g 1
2
, g 32
f0=π 2 /2
Note: NO unification !
predicts Higgs mass at 168 GeV
Now attempting to include SUSY...
QU1, RuG, 20/4/2011 (SdJ )
Tuesday, April 26, 2011
54
Higgs
elusive: Yes, but probably not for much longer
illusive: Probably not
delusive: There is reason to be suspicious
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