Measuring a Light (Dark Matter) Neutralino Mass at the ILC Herbi - PowerPoint PPT Presentation

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 Neutralino Mass Mixing Matrix in ( ˜ B, ˜ H 1 , ˜ H 2 ) basis   M 1 0 − M z cos β sin θ w M z sin β sin θ w 0 M 2 M z cos β cos θ w − M z sin β cos θ w   M 0 =   − M z cos β sin θ w M z cos β cos θ w 0 µ     M z sin β sin θ w − M z sin β cos θ w µ 0 χ 0 • What do we know about the Mass of ˜ 1 ?

Experimental Search at LEP > • Chargino Search: M ˜ 1 > 94 GeV ⇒ | µ | , M 2 ∼ 100 GeV χ ± • Higgs search: tan β > ∼ 1 . 5 > 3 tan 2 θ w M 2 M 1 = 5 • Assume: ⇒ M 1 ∼ 50 GeV > • Insert into Neutralino Mass Matrix: ⇒ M ˜ ∼ 46 GeV χ 0 1 • Now drop above assumption on M 1 , M 2

Massless Neutralino M 2 M 2 Z sin(2 β ) s 2 w • Set det( M 0 )=0 ⇒ M 1 = µM 2 − M 2 Z sin(2 β ) c 2 w • Choose: { M 2 , µ, tan β } ∃ M 1 : M χ 0 1 = 0 ⇒ • Some fine-tuning required M 1 ≈ M 2 Z sin(2 β ) s 2 � � � � 10 150 GeV w ≈ 2 . 5 GeV µ tan β µ • = ⇒ M χ 0 1 = 0 consistent in MSSM

M χ 0 1 = 0 consistent with all lab data • Invisible Z 0 –width • e + e − − → χ 0 1 χ 0 1 γ • e + e − − Z 0 → q ¯ → χ 0 2 χ 0 χ 0 2 → Z 0 χ 0 1 ; 1 ; q • Precision Observables ( δ Γ inv , δ Γ Z , M W , δa µ , EDM ′ s) • Monojets • Rare Meson Decays • Supernova Cooling > • Dark Matter: Lee–Weinberg bound: M χ 0 ∼ 6 GeV 1 < Cowsik–McClellan bound: M χ 0 ∼ 0 . 7 eV 1

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

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 − e − χ 0 ˜ 1 R χ 0 + s–channel 1 e + e + e + ˜ R χ 0 1 • Measure e ± energies = ⇒ determine M χ 0 1 > • Earlier work by Uli Martyn (DESY): M χ 0 ∼ 95 GeV 1 • How well does this work for light neutralinos?

Electron Energy Distribution Lepton Energy; m Χ � 96 GeV 2000 1500 1000 500 0 0 50 100 150 200 • Electron energy distribution is flat, with sharp cut–offs: E ± eR = 143 GeV and √ s = 400 GeV • Here chosen: SPS1a: M ˜

Simple Kinematics • θ 0 : angle between � p ( e ) in slepton rest–frame and � p (˜ e ) M 2 √ s   � 1 − 4 M 2 χ 0 ˜ e 1 . E e =  1 −  (1 + β ˜ e cos θ 0 ) , β ˜ e =   M 2 4 s e ˜ • Max/Min Electron energy: E ± for cos θ 0 = ± 1 • Solve for the SUSY Masses � E + E − � e = √ s 1 − E + + E − M ˜ , M χ 0 1 = M ˜ √ s/ 2 e E + + E − • Measure E + and E − : thus determine M χ 0 1

Neutralino Mass Sensitivity M 2 √ s   � 1 − 4 M 2 χ 0 ˜ e 1 . E ± =  1 −  (1 ± β ˜ e ) , β ˜ e =   M 2 4 s e ˜ • Detailed ILC study by Uli Martyn for heavy neutralinos: ∆ M χ 0 1 < 0 . 2% M χ 0 1 M 2 χ 0 1 • E ± depends on = ⇒ Expect less sensitivity for: M 2 ˜ e M χ 0 1 ≪ M ˜ or as M χ 0 1 − → 0 e

Lepton Energy; m Χ � 10 GeV 2000 1500 1000 500 0 0 50 100 150 200 Lepton Energy; m Χ � 5 GeV 2000 1500 1000 500 0 0 50 100 150 200

Work in Progress: Simple Simulation • Do not consider full detector simulation. Instead simplified analysis. e + µ + e − µ − • Consider ˜ R ˜ R – and ˜ R ˜ R –Production e + e − • ˜ R ˜ R dominant • √ s = 500 GeV • Beam polarisations ( P e − , P e + ) = (+80% , − 60%) √ • Include Beam Strahlung: √ s < √ s s ′ − → This smears out the E ± –edges

Further Details of Simulation • Approximate detector resolutions � � 1 1 · 10 − 4 GeV − 1 ∆ = (tracker) p T ∆ E 0 . 166 = ⊕ 0 . 011 (ECAL) � E E/ GeV • 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.

Fit Functions � erf( E − ˆ �  E − 1 E < ˆ √ ) + 1 : E −  2 σ −  2   1 f − ( E ) = � � erf( E − ˆ E − 1 E > ˆ  ) + 1 : E − √  2 σ −  2  2 � �  erfc( E − ˆ E − 1 E < ˆ √ ) : E −  2 σ −  2   1 f + ( E ) = � erfc( E − ˆ � E − 1 E > ˆ  ) : √ E −  2 σ −  2  2 � x 2 0 e − t 2 dt erf( x ) = √ π erfc( x ) = 1 − erf( x ) • σ 1 � = σ 2 because of asymmetric beam strahlung

Results • Reproduced detailed detector study by Uli Martyn at M χ 0 1 ≈ 96 GeV and √ s = 400 GeV to within ± 30% • Used this as a systematic error for our analysis of light neutralinos

precision (GeV) precision (GeV) ~ ~ + + - + e e e e s = 500 GeV → 1.2 1.2 R R -1 L = 250 fb 1 1 0.8 0.8 0 0 1 1 ∼ ∼ χ χ m m 0.6 0.6 m = 200 GeV ~ e R 0.4 0.4 0.2 0.2 m = 100 GeV ~ e R 0 0 0 0 10 10 20 20 30 30 40 40 50 50 m m (GeV) (GeV) ∼ ∼ 0 0 χ χ • √ s = 500 GeV 1 1 � L dt = 250 fb − 1 • Integrated Luminosity:

Summary & Conclusions • A massless neutralino is consistent with all data • For M ˜ e R = 100 GeV can measure M χ 0 1 down to less than 1 GeV • For M ˜ e R = 200 GeV can measure M χ 0 1 down to about 2 GeV • Implications for Dark Matter

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95% CL contours 95% CL contours 100 12 10 80 8 60 m χ 0 1 m χ 0 1 6 40 4 20 2 0 0 142.0 142.5 143.0 143.5 144.0 142.4 142.6 142.8 143.0 143.2 143.4 m ˜ m ˜ e R e R