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PHENO SYMPOSIUM, Madison, WI, May, 10 th , 2010 Measuring a Light (Dark Matter) Neutralino Mass at the ILC Herbi Dreiner Universit at Bonn & SCIPP, University of California, Santa Cruz . MSSM Neutralino Mixing W 3 , MSSM

SLIDE 1

PHENO SYMPOSIUM, Madison, WI, May, 10th, 2010

Measuring a Light (Dark Matter) Neutralino Mass at the ILC

Herbi Dreiner

Universit¨ at Bonn & SCIPP, University of California, Santa Cruz .

SLIDE 2

MSSM Neutralino Mixing

MSSM Neutralino Mass Mixing Matrix in ( ˜

B, ˜ W 3, ˜ H1, ˜ H2) basis M0 =

    

M1 −Mz cos β sin θw Mz sin β sin θw M2 Mz cos β cos θw −Mz sin β cos θw −Mz cos β sin θw Mz cos β cos θw µ Mz sin β sin θw −Mz sin β cos θw µ

    

What do we know about the Mass of ˜

χ0

1?

SLIDE 3

Experimental Search at LEP

Chargino Search:

M˜

χ±

1 > 94 GeV

⇒ |µ|, M2

>

∼ 100 GeV

Higgs search: tan β >

∼ 1.5

Assume:

M1 = 5

3 tan2 θw M2

⇒ M1

>

∼ 50 GeV

Insert into Neutralino Mass Matrix:

⇒ M˜

χ0

>

∼ 46 GeV

Now drop above assumption on M1, M2

SLIDE 4

Massless Neutralino

Set det(M0)=0

⇒ M1 = M2M2

Z sin(2β)s2 w

µM2 − M2

Z sin(2β)c2 w

Choose: {M2, µ, tan β}

⇒ ∃ M1 : Mχ0

1 = 0

Some fine-tuning required

M1 ≈ M2

Z sin(2β)s2 w

µ ≈ 2.5 GeV

tan β 150 GeV µ

⇒ Mχ0

1 = 0 consistent in MSSM

SLIDE 5

Mχ0

1 = 0 consistent with all lab data

Invisible Z0–width
e+e− −

→ χ0

1χ0 1γ

e+e− −

→ χ0

2χ0 1;

χ0

2 → Z0χ0 1;

Z0 → q¯ q

Precision Observables (δΓinv, δΓZ, MW , δaµ, EDM′s)
Monojets
Rare Meson Decays
Supernova Cooling
Dark Matter: Lee–Weinberg bound:

Mχ0

>

∼ 6 GeV Cowsik–McClellan bound: Mχ0

<

∼ 0.7 eV

SLIDE 6

Publications

A Supersymmetric solution to the KARMEN time anomaly
D. Choudhury, HD, P. Richardson, Subir Sarkar
Phys. Rev. D61:095009,2000; e-Print: hep-ph/9911365
Supernovae and light neutralinos: SN1987A bounds on supersymmetry revisited

HD, C. Hanhart, U. Langenfeld, D.R. Phillips

Phys. Rev. D68:055004,2003; e-Print: hep-ph/0304289
Discovery potential of radiative neutralino production at the ILC

HD, O. Kittel, U. Langenfeld

Phys. Rev. D74:115010,2006; e-Print: hep-ph/0610020
Mass Bounds on a Very Light Neutralino

HD, S. Heinemeyer, O. Kittel, U. Langenfeld, A.M. Weber, G. Weiglein Eur.Phys.J.C62,2009; e-Print: arXiv:0901.3485

Rare Meson Decays to a Light neutralino

HD, S. Grab, D. Koschade, M. Kr¨ amer, U. Langenfeld, B. O’Leary

Phys. Rev. D80:035018,2009

SLIDE 7

Measuring a Light Neutralino Mass at the ILC

Work in progress with Bonn group: John Conley, HD, Peter Wienemann, Karina Williams

Consider the process:

e− e+ χ0

1 ˜ e−

R

˜ e+

R

e− e+ χ0

1 χ0

1 + s–channel

Measure e± energies =

⇒ determine Mχ0

Earlier work by Uli Martyn (DESY): Mχ0

>

∼ 95 GeV

How well does this work for light neutralinos?

SLIDE 8

Electron Energy Distribution

50 100 150 200 500 1000 1500 2000

Lepton Energy; mΧ96 GeV

Electron energy distribution is flat, with sharp cut–offs: E±
Here chosen: SPS1a: M˜

eR = 143 GeV and √s = 400 GeV

SLIDE 9

Simple Kinematics

θ0: angle between

p(e) in slepton rest–frame and p(˜ e) . Ee = √s 4

  1 −

M2

χ0

M2

˜ e

   (1 + β˜

e cos θ0) ,

β˜

e =

1 − 4M2

˜ e

s

Max/Min Electron energy: E± for cos θ0 = ±1
Solve for the SUSY Masses

M˜

e = √s

E+E−

E+ + E− , Mχ0

1 = M˜

e

1 − E+ + E−

√s/2

Measure E+ and E−: thus determine Mχ0

SLIDE 10

Neutralino Mass Sensitivity

. E± = √s 4

  1 −

M2

χ0

M2

˜ e

   (1 ± β˜

e) ,

β˜

e =

1 − 4M2

˜ e

s

Detailed ILC study by Uli Martyn for heavy neutralinos:

∆Mχ0

Mχ0

< 0.2%

E± depends on

M2

χ0

M2

˜ e

= ⇒ Expect less sensitivity for: Mχ0

1 ≪ M˜

e

r as

Mχ0

1 −

→ 0

SLIDE 11

50 100 150 200 500 1000 1500 2000

Lepton Energy; mΧ10 GeV

50 100 150 200 500 1000 1500 2000

Lepton Energy; mΧ5 GeV

SLIDE 12

Work in Progress: Simple Simulation

Do not consider full detector simulation. Instead simplified analysis.
Consider ˜

e−

R ˜

e+

R – and ˜

µ−

R ˜

µ+

R –Production

e−

R ˜

e+

R dominant

√s = 500 GeV
Beam polarisations (Pe−, Pe+) = (+80%, −60%)
Include Beam Strahlung: √s

− → √ s′ < √s This smears out the E±–edges

SLIDE 13

Further Details of Simulation

Approximate detector resolutions

∆

pT

1 · 10−4 GeV−1 (tracker) ∆E E = 0.166

E/GeV

⊕ 0.011 (ECAL)

Smear electron energy according to minimum of the two
For muons always choose momentum resolution
This further smoothes out the edges
We then fit the edges using basically the convolution of a Gaussian

and an upward or downward step function.

SLIDE 14

Fit Functions

f−(E) =

        

1 2

erf(E− ˆ

E− √ 2σ−

) + 1

E < ˆ E−

1 2

erf(E− ˆ

E− √ 2σ−

) + 1

E > ˆ E− f+(E) =

        

1 2

erfc(E− ˆ

E− √ 2σ−

)

E < ˆ E−

1 2

erfc(E− ˆ

E− √ 2σ−

)

E > ˆ E− erf(x) = 2 √π

x

0 e−t2dt

erfc(x) = 1 − erf(x)

σ1 = σ2 because of asymmetric beam strahlung

SLIDE 15

Results

Reproduced detailed detector study by Uli Martyn at Mχ0

1 ≈ 96 GeV

and √s = 400 GeV to within ±30%

Used this as a systematic error for our analysis of light neutralinos

SLIDE 16

(GeV)

χ ∼

m 10 20 30 40 50 precision (GeV)

χ ∼

m 0.2 0.4 0.6 0.8 1 1.2 = 500 GeV s

L = 250 fb

R +

e ~

R +

e ~ →

+

e = 200 GeV

e ~

m = 100 GeV

e ~

m (GeV)

χ ∼

m 10 20 30 40 50 precision (GeV)

χ ∼

m 0.2 0.4 0.6 0.8 1 1.2

√s = 500 GeV
Integrated Luminosity:

Ldt = 250 fb−1

SLIDE 17

Summary & Conclusions

A massless neutralino is consistent with all data
For M˜

eR = 100 GeV can measure Mχ0

1 down to less than 1 GeV

For M˜

eR = 200 GeV can measure Mχ0

1 down to about 2 GeV

Implications for Dark Matter

SLIDE 18

.

SLIDE 19