The Higgs: elusive, illusive, delusive.pdf - Theoretical High-Energy ...

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The Higgs: elusive, illusive, delusive.pdf - Theoretical High-Energy ...

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

4 3 %1!"#2

65)

6))

05)

$%M%#

$%M%0#

%7"89:8;=9%;+:@A

%B9


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


'

&

G219*#!"!

F:,B59*270,5E867E9

!# !#&@#!>!!!$&

*H.4*.II+

E

%

!>!#%A#!>!!!"#

6701>*1BC*D

SM successes

# *38E8

!" #

$

#

"

!

./0123,3 45,16(67859

$! "!!

$!!

( )

*!+,-"

QU1, RuG, 20/4/2011 (SdJ ) 9

Tuesday, April 26, 2011


DEBF,)"'"

* 1

,,!-./"

!"#&

!"#%

456),789,8,@A>.B#C

456',789,:4;

2!#,34

SM successes

!"#$

!"

* +

,!-./"

''% $"" '"""

'&" '(& )""

* 0

,,!-./"

QU1, RuG, 20/4/2011 (SdJ ) 10

Tuesday, April 26, 2011


Direct SM Higgs boson searches at LEP

1989-2000

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: 1-CLb = p(LLRLLRobs | s+b)

To correct for small # events being

s+b

obs

b

unlikely for both hypothese,

modified frequentist: CLs=CLs+b/CLb

1-CLb

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 )

QU1, RuG, 20/4/2011 (SdJ ) 17

Tuesday, April 26, 2011


QU1, RuG, 20/4/2011 (SdJ ) 18

Tuesday, April 26, 2011


QU1, RuG, 20/4/2011 (SdJ ) 19

Tuesday, April 26, 2011


'

&

G219*#!"!

F:,B59*270,5E867E9

!# !#&@#!>!!!$&

E

%

!>!#%A#!>!!!"#

6701>*1BC*D # *38E8

!" #

$

#

"

!

./0123,3 45,16(67859

$! "!!

$!!

( )

*!+,-"

QU1, RuG, 20/4/2011 (SdJ ) 20

Tuesday, April 26, 2011


Higgs boson searches at Tevatron

1989-2011

CDF

D0

(1992)

9.55 fb -1

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

21


Dzero detector

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

22


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

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

26


95% CL Limit / SM

SM Higgs boson limits at Tevatron

-1

DØ Preliminary, L=4.3-8.2 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 )

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

27


SM Higgs boson limits at Tevatron

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

28


SM Higgs boson prospects at Tevatron

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

29


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 b-tags

~4pb !

arXiv:1104.0699v1

QU1, RuG, 20/4/2011 (SdJ )

30

Tuesday, April 26, 2011


Higgs boson searches at the LHC

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

31


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

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

32


Higgs boson searches at the LHC

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

33


Higgs boson searches at the LHC

QU1, RuG, 20/4/2011 (SdJ )

Tuesday, April 26, 2011

34


Higgs boson prospects at the LHC

/)

012$3452$6!78(91:;92

)+

)*

A

@

-

!"#!$ H4$I9(9154


SM Higgs boson combining it all

"!

2

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]

QU1, RuG, 20/4/2011 (SdJ )

36

Tuesday, April 26, 2011


SM Higgs boson combining it all

4 3 %1!"#2

65)

6))

$%S%#

$%S%0#

%G";:;H9:A8A:I%H+


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

38


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

39


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

Tuesday, April 26, 2011








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(β-α)

SUSY Higgs searches at LEP

Z

Z*

h

e +

e -

~cos(β-α)

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!

,--

7-

L&D21CM3#N;3#OO#@C&:E+E32C>I#G#,P0K"P"#Q=

K&D21CL3#M;3#NN#@C&:E+E32C>I#G#,O0H"O"#P=

+ J #+29I##GH"--#%&'

+ J #+29I##GH"--#%&'#

#K,

#H,

123!

,--

7-

M&D21CI3#N;3#OO#@C&:E+E32C>K#G#,P0L"P"#Q=

L&D21CI3#M;3#NN#@C&:E+E32C>K#G#,O0H"O"#P=

3I#+E9E3JK##GH"--#%&'

3I#+E9E3JK##GH"--#%&'#

#L,

#H,

0-

6-

/-

89):;


SUSY Higgs: beware non SM behaviour

Fermiofobic Higgs: H→γγ

D*

EF!>5$G9:9BH5IJ!KC-!'0

"!!&!"'0&

-

*+

304$56$7!89:9;

$;$7!89:9;

@83!>5$79;9AB

$;$7!89:9;!!!*!4C7C

$;$7!89:9;!!!-!4C7C

'

$!#!12"(

*+

*

*++ *+, **+ **, *-+ *-, *.+ *., */+ */, *,+

!"#$%& ) ('

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

QU1, RuG, 20/4/2011 (SdJ )

49

Tuesday, April 26, 2011


Expanding around classical minimum gives:

IMAPP: Ronald Kleiss & collaborators

complex and non-convex 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 )

52

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

cut-off 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 + ...

Einstein-Hilbert 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 )

Tuesday, April 26, 2011

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 see-saw 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

QU1, RuG, 20/4/2011 (SdJ ) 55

Tuesday, April 26, 2011


QU1, RuG, 20/4/2011 (SdJ ) 56

Tuesday, April 26, 2011


QU1, RuG, 20/4/2011 (SdJ ) 57

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