CP-violating Loop E ects in the Higgs Sector of the MSSM · Mh1 is the mass of the lightest neutral...

CP-violating Loop Effects in the Higgs Sector of the

MSSM

Karina Williams, in collaboration with Georg Weiglein, Oliver Brein, PhilipBechtle and Sven Heinemeyer

IPPP, University of Durham

14th December 2007

Karina Williams (IPPP) Higgs Sector of the CP-violating MSSM 14th December 2007 1 / 26

Supersymmetry

Supersymmetry is a symmetry connecting bosons and fermions.

Solves ‘naturalness’ problem - cancellation of quadratic divergences.

Exact supersymmetry: particles and sparticles have the same mass.

Sparticles have not been observed - SUSY is broken.

Softly broken SUSY - quadratic divergences still cancel.


Minimal Supersymmetric Standard Model

Minimum number of superpartners

2 Higgs Doublets

No assumption about SUSY breaking mechanism - all terms that break SUSYsoftly are added to Lagrangian

Has more than 100 free parameters (in addition to those in the SM)

Gives unification of gauge couplings

Conserves R Parity - SUSY particles can not decay in to only SM particles -lightest SUSY particle is a Dark Matter Candidate

Predicts that the lightest Higgs Mass < 140 GeV - within the reach of theLHC

Higgs mass is given in terms of other parameters - lightest Higgs mass will bea good electroweak precision observable - can be exploited by the LHC andILC.


The complex Minimal Supersymmetric Standard Model

Often complex phases in the MSSM are taken to be zero for simplicity. Includingcomplex phases causes the tree level neutral Higgs h, H , A (which are CPeigenstates) to mix to form h1, h2, h3.This CP violation leads to some interesting phenomenology

a new source of CP violation to explain the matter-antimatter asymmetry inthe universe

the possibility of a low mass for the lightest Higgs without conflicting withLEP results

CPX scenario - chosen to maximise the effect of complex phases. We use

MSUSY = 500 GeV, µ = 2000 GeV, |M3| = 1000 GeV,M2 = 200 GeV

|Aon−shell

t,b| = 900 GeV (|AMS

t,b| = 1000 GeV)

φAt= φAb

= φM3= π

2

mt = 170.9 GeV (174.3 GeV)

(brackets show values used in original analysis)


Analysis of LEP results by LEP Higgs Working GroupExclusions in the CPX scenario (from hep-ex/0602042)

1

10

0 20 40 60 80 100 120 140

1

10

mH1 (GeV/c2)

tanβ

Excludedby LEP

TheoreticallyInaccessibleCPX

(c)

Mh1 is the mass of the lightest neutral Higgs and tan β is the ratio of vacuumexpectation values.

One of the areas that could not be excluded at 95 % CL by the LEP HiggsWorking Group is Mh1 ∼ 45 GeV and tan β ∼ 6.


h2 → h1 + h1 Decay Width

In this region, the h2 → h1 + h1 decay width is very important.

However, at the time, there was no reliable Feynman-diagrammatic result for thisdecay width.

Here, we show results for Γ(ha → hbhb), which include

propagator corrections, which use self-energies from the program FeynHiggs

full 1-loop vertex corrections


Propagator CorrectionsWe use DR renormalisation for the Higgs field ren. constants

Therefore, diagrams with external Higgs bosons need finite wave functionrenormalisation factors (involving the renormalised Higgs self-energies)contained in the 3 × 3 matrix Z.

For example, for a vertex function involving an external Higgs h1

Γh1f f = Zai Γi =√

Zh

(

Γhf f + ZhH ΓHf f + ZhAΓAf f

)

h1

f

f

=√

Zh (h

f

f

+ h H

f

f+ h A

f

f

)



0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

4 5 6 7 8 9 10 15

Γ(h 2

→h 1

+h 1

)/G

eV

tanβ

Mh1=30 GeV

Tree

Tree level vertex

Finite wave functionrenormalisation factors areincluded by

Γh2h1h1 = Z1kZ1j Z2iΓtree

ijk

h2

h1

h1



0

0.05

0.1

0.15

0.2

0.25

4 5 6 7 8 9 10 15

Γ(h 2

→h 1

+h 1

)/G

eV

tanβ

Mh1=30 GeV

Yukawa ApproxTree

Yukawa approximation in

vertex

m4t terms only

zero incoming momentum:p2 = 0

h2

h1

h1

t

tt

h2

h1

h1

tA

tB

tC

h2

h1

h1

tA

tB

h2

h1

h1

tAtB

where tA, tB , tC = t1, t2.



0

0.05

0.1

0.15

0.2

0.25

4 5 6 7 8 9 10 15

Γ(h 2

→h 1

+h 1

)/G

eV

tanβ

Mh1=30 GeV

FullYukawa Approx

TreeFull 1-loop

Includes

SM fermions and theirsuperpartners

neutralinos and charginos

vector, neutral Higgs,charged Higgs and Goldstonebosons

Faddeev-Popov ghosts


h2 → h1 + h1 Decay Width - varying Mh1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

15 20 25 30 35 40 45 50 55

Γ(h 2

→h 1

+h 1

)/G

eV

Mh1

tβ=6

FullYukawa Approx

Tree

Above Mh1 = 52GeV ,

Mh2 < 2Mh1

so decay is not allowed.


h2 → h1 + h1 Decay Width - varying Arg(At)

0.01

0.1

1

10

2 3 4 5 6 7 8 9 10 20

Γ(h 2

→h 1

+h 1

)/G

eV

tanβ

Mh1=30 GeV

ϕAt = 0.9 π/2

ϕAt = 1.0 π/2

ϕAt = 1.1 π/2

Γ(h2 → h1 + h1) is stronglydependent on Arg(At ).


Ingredients

Neutral Higgs MassesI using neutral Higgs self-energies from FeynHiggsI has full phase dependence at order αtαs (arXiv:0710.4891)

Γ(ha → hbhb), includingI finite wave ren. factors in ZI full 1-loop vertex corrections (with the option of h1, h2, h3 in loops)

Γ(ha → bb), includingI finite wave ren. factors in ZI SM QCD correctionsI SUSY QCD corrections - resummation includes full M3 phase dependenceI full 1-loop vertex corrections (with the option of h1, h2, h3 in loops)I QED corrections

Γ(ha → τ+τ−), includingI finite wave ren. factors in ZI full 1-loop vertex corrections (with the option of h1, h2, h3 in loops)I QED corrections

Contribution of other neutral Higgs decay channels are taken from FeynHiggs

Effective couplings of neutral Higgs bosons to Z bosons


Contribution to the h2 → h1 + h1 Branching Ratio

0

0.05

0.1

0.15

0.2

0.25

4 5 6 7 8 9 10 15

Γ(h 2

→h 1

+h 1

)/G

eV

tanβ

Mh1=30 GeV

0

0.05

0.1

0.15

20 30 40 50

Γ(h 2

→h 1

+h 1

)/G

eV

Mh1

tβ=6

20 40 60 80 100 120Mh1

2

3

4 5 6 7 8 9

10

20

30

40

tanβ

0

0.2

0.4

0.6

0.8

1

Colour: Br(h2→h1+h1)


Comparing to the LEP Higgs predictions

The theoretical prediction for each channel is compared to the experimentalprediction for that channel at LEP.

2

3

4

5 6 7 8 9

10

20

30

40

20 40 60 80 100 120

tanβ

Mh1

Channel with the highest statisticalsensitivity:� = h1Z → bbZ

� = h2Z → bbZ

� = h2Z → h1h1Z → bbbbZ

� = h2h1 → bbbb

� = h2h1 → h1h1h1 → bbbbbb

� = other channels


New LEP Higgs exclusions for the CPX scenario

2

3

4

5 6 7 8 9

10

20

30

40

20 40 60 80 100 120

tanβ

Mh1

2

3

4

5 6 7 8 9

10

20

30

40

20 40 60 80 100 120

tanβ

Mh1

Channel with the highest statisticalsensitivity

Exclusion region at 95 % CL

� = h1Z → bbZ

� = h2Z → bbZ


� = h2h1 → bbbb



green = excludedwhite = unexcluded


Program HiggsBoundsTakes, as input,

neutral Higgs massesnormalised e+e− → hiZ and e+e− → hjhi cross sectionshi → bb, hi → τ τ and hj → hihi branching ratios

and compares these to the cross section limits from the LEP Higgs searches.

generalised to models with any number of neutral Higgs - can be used tocheck any theoretical model against the LEP Higgs resultsa web version and downloadable version will be made publically availablesoon to include Tevatron data


Summary

Presented results for ha → hb + hc decay width, which include 1-loop vertexcorrections.

Concentrated on the example of Γ(h2 → h1 + h1) in the CPX scenario,showed these new corrections can increase the decay width by factor of 50.

Looked at the implications of these new corrections to constraints on themass of the lightest Higgs mass Mh1 in the CPX scenario. The resultsconfirm the existence of a ‘hole’ in the LEP coverage at Mh1 ∼45. To coverthis hole, we’ll need to wait for results from the LHC (possibly) or ILC.

Discussed the new program HiggsBounds, which will allow physicists tocompare their Higgs sector predictions with the LEP and Tevatron limits.


The End

Will the LHC get enough evidence to finally track down aHiggs Boson or could a very light Higgs still escape

detection?


Effect of different approximations for Γ(h2 → h1h1) (CPX

scenario) I

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55

tanβ

Mh1

Full

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55

tanβ

Mh1

Fermion, sfermion

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55

tanβ

Mh1

Yukawa Approximation

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55

tanβ

Mh1

Full

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55

tanβ

Mh1

Fermion, sfermion

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55ta

nβ

Mh1

Yukawa Approximation


New LEP Higgs exclusions for the CPX scenario but

mt = 174.3 GeV

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55

tanβ

Mh1

4

5

6

7

8

9

10

15 20 25 30 35 40 45 50 55

tanβ

Mh1

Channel with the highest statisticalsensitivity

Is this channel excluded at 95 % CL?

� = h1Z → bbZ

� = h2Z → bbZ


� = h2h1 → bbbb



green = yeswhite = no


LEP results

from Philip Bechtle

from Alex ReadS95

Mhi

hi → bb, predicted

140120100806040200

100

10

1

0.1

0.01

predicted S95 valuesfor e+e− → hiZ →bbZ

from Philip Bechtle

from Alex ReadS95

Mhi

hi → bb, observed

140120100806040200

100

10

1

0.1

0.01

observed S95 valuesfor e+e− → hiZ →bbZ


The neutral Higgs masses in the complex MSSM

First, find the poles of the 3 × 3 propagator matrix ∆(p2), which is equivalent tosolving

∣

∣p21 − M(p2)∣

∣ = 0 where

M(p2) =

m2h − Σhh(p

2) −ΣhH(p2) −ΣhA(p2)

−ΣhH(p2) m2H − ΣHH(p2) −ΣHA(p2)

−ΣhA(p2) −ΣHA(p2) m2A − ΣAA(p2)

In general, the three solutions M2ha

are complex. The physical masses,

M2ha

= ReM2ha

and labelled by Mh1 ≤ Mh2 ≤ Mh3

Σjk (p2) were calculated using an expansion about Rep2.

Σjk (p2) = Σjk (Rep2) + i(

Imp2)

Σ′

jk(Rep2) + O(

Imp2)2

The program FeynHiggs was used for Σjk(Rep2) and Σ′jk (Rep2). In practice, the

eigenvalues of a momentum independent appoximation to M(p2) was used as astarting point for iteration.


External Higgs Bosons

Diagrams with external Higgs bosons need finite wave function renormalisationfactors, contained in the 3× 3 matrix Z.

limp2→M2

h1

− i

p2 −M2h1

(

Z · Γ2 · ZT)

hh= 1

limp2→M2

h2

− i

p2 −M2h2

(

Z · Γ2 · ZT)

HH= 1

limp2→M2

h3

− i

p2 −M2h3

(

Z · Γ2 · ZT)

AA= 1

with

Z =

√Zh

√ZhZhH

√ZhZhA√

ZHZHh

√ZH

√ZHZHA√

ZAZAh

√ZAZAH

√ZA

−Γ2(p2) is the inverse of the propagator matrix ∆(p2).


External Higgs Bosons

The components of Z are found using,

Z−1h =

∂

∂p2

„

i

∆hh(p2)

«˛

˛

˛

˛

p2=M2h1

note

Z−1H =

∂

∂p2

„

i

∆HH (p2)

«˛

˛

˛

˛

p2=M2h2

∆ii (p2) =

i

p2− m2

i + Σeff

ii (p2)

Z−1A =

∂

∂p2

„

i

∆AA(p2)

«˛

˛

˛

˛

p2=M2h3

ZhH =∆hH

∆hh

˛

˛

˛

˛

p2=M2h1

ZHh = ∆hH

∆HH

˛

˛

˛

p2=M2h2

ZAh =∆hA

∆AA

˛

˛

˛

˛

p2=M2h3

ZhA =∆hA

∆hh

˛

˛

˛

˛

p2=M2h1

ZHA = ∆HA

∆HH

˛

˛

˛

p2=M2h2

ZAH =∆HA

∆AA

˛

˛

˛

˛

p2=M2h3

where ∆ij are components of the 3 × 3 propagator matrix ∆(p2).


External Higgs BosonsFor a vertex function involving 1,2,3 external Higgs Γha

, Γhahb, Γhahbhc

respectively,

Γha= Zai Γi

Γhahb= Zbj Zai Γij

Γhahbhc= Zck Zbj Zai Γijk

For example,

Γh1f f =√

Zh

(

Γhf f + ZhH ΓHf f + ZhAΓAf f

)

h1

f

f

=√

Zh (h

f

f

+ h H

f

f+ h A

f

f

)


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CP-violating Loop E ects in the Higgs Sector of the MSSM · Mh1 is the mass of the lightest neutral...

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