Supersymmetry IV. Hitoshi Murayama (Berkeley) PiTP 05, IAS

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1 Supersymmetry IV Hitoshi Murayama (Berkeley) PiTP 05, IAS

2 Plan Mon: Non-technical Overview what SUSY is supposed to give us Tue: From formalism to the MSSM Global SUSY formalism, Feynman rules, soft SUSY breaking, MSSM Wed: SUSY breaking how to break SUSY, mediation mechanisms Thu: SUSY at colliders basic reactions, signatures, and how do we know it is SUSY? Fri: SUSY as a telescope supersymmetry breaking, GUT, string

3 e+e- Linear Collider

4 Large Hadron Collider (LHC) proton-proton collider 14TeV energy (cf. Fermilab) Under construction at CERN, Geneva Turn on in 2007 Finally reaching the energy Fermi told us about in 1933!

5 CMS

Higgs at ATLAS Robust discovery Signal significance 100 10 H $ %% tth (H $ bb) H $ ZZ (*) $ 4l H $ WW (*) $ l&l& qqh $

6 Higgs at ATLAS Robust discovery Signal significance H $ %% tth (H $ bb) H $ ZZ (*) $ 4l H $ WW (*) $ l&l& qqh $ qqww (*) qqh $ qq'' Total significance!ldt = 30 fb "1 (no K-factors) ATLAS 5# m H (GeV/c 2 )

7 Supersymmetry Tevatron/LHC will discover supersymmetry! L dt = 1, 10, 100, 300 fb m 1/2 (GeV) CMS TH! h 2 = 0.4! h 2 = 1 g(3000) ~ miss E T (100 fb -1 ) q(2000) ~ q(1500) ~ g(1500) ~ A 0 = 0, tan! = 35, µ > 0 miss E T (300 fb -1 ) g(2000) ~ miss E T (10 fb -1 ) miss E T (1 fb -1 ) g(1000) ~ h(123) g(2500) ~ q(2500) ~ -1 one one one M l (GeV) " R Can do many precision measurements at LHC O1 S5 one 200 q(500) ~ h(110) EX! h 2 = 0.15 g(500) ~ q(1000) ~ cosmologically plausible region Fermilab reach: < 500 GeV M! " 0 (GeV) m 0 (GeV)

8 New physics looks alike missing ET, multiple jets, b-jets, b _ b t W b W q _ q l W l W _ b q l l _ q (like-sign) leptons g~ g~ g~ q~ ~ b ~ q W _ q b ~ _ b W l ~ l l l 0 ~ l l 0 P 8 0 P 8 0 P 8 0 t _ t t _ t W b b W _ b W W _ b l q l _ l q q _ q l 4th generation SUSY technicolor +Universal extra dimension, little Higgs with T-parity

9 9

10 Task Why do we live in a cosmic superconductor? We can eliminate many possibilities at LHC But new interpretations necessarily emerge Race will be on: theorists coming up with new interpretations experimentalists excluding new interpretations A loooong process of elimination Crucial information is in details Reconstruct the theory from measurements

Need absolute confidence for a major discovery As an example, supersymmetry New-York Times level confidence still a long way to Halliday-Resnick level confidence We have learned

11 Need absolute confidence for a major discovery As an example, supersymmetry New-York Times level confidence still a long way to Halliday-Resnick level confidence We have learned that all particles we observe have unique partners of different spin and statistics, called superpartners, that make our theory of elementary particles valid to small distances.

12 Multiple Wavebands in Astronomy antennae galaxy = collision of galaxies

13 Telescopes vs Accelerators aim need telescopes accelerators probe deeper better resolution better mirrors, CCD higher energy better image full understanding better exposure multiple probes larger telescopes, more time visible, radio, X-ray, infrared, UV, gamma more powerful beams (luminosity) protons, electrons, neutrinos

Linear Collider Electron-positron collider e, e + point-like with no structure Well-understood environment Linear instead of ring to avoid synchrotron loss Super-high-tech machine Accelerate the beam

14 Linear Collider Electron-positron collider e, e + point-like with no structure Well-understood environment Linear instead of ring to avoid synchrotron loss Super-high-tech machine Accelerate the beam over >15km Focus beam down to a few nanometers and make them collide electron sources (HEP and x-ray laser) e - damping ring linear accelerator aux. positron and 2nd electron source e - x-ray laser positron source electron-positron collision high energy physics experiments linear accelerator 33 km International Linear Collider (ILC) positron preaccelerator damping ring e +

15 ILC elementary particles well-defined energy, angular momentum uses its full energy LHC p p can produce particles democratically can capture nearly full information ILC e + e -

16 LHC vs ILC (oversimplified) total energy 14TeV TeV usable energy a fraction full beam proton (composite) electron (point-like) signal rate high low noise rate very high low analysis specific modes nearly all modes events lose info along the beams capture the whole status under construction needs to finish design

17 Reconstruct Lagrangian from data Specify the fields mass spin Klein-Gordon, Dirac, Majorana, gauge SU(3)xSU(2)xU(1) quantum numbers mixing of states Specify their interactions SU(3)xSU(2)xU(1) quantum numbers determine gauge interactions Yukawa couplings trilinear and quartic scalar couplings

18 Reconstruct Lagrangian from data Specify the fields mass spin Klein-Gordon, Dirac, Majorana, gauge SU(3)xSU(2)xU(1) quantum numbers mixing of states Specify their interactions SU(3)xSU(2)xU(1) quantum numbers determine gauge interactions Yukawa couplings trilinear and quartic scalar couplings

19 mass

20 EPH!"#$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% &'()*+,+-%%%./0)1234%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 54167/%.8 531%67/%.8,5167/%98 *5-%67/%98 &J H!4--I>%%%%%% -!%%%% %%%%%%%4--I>H H!4--I>%%%%%% :;)*%%%<585%=>?5 - J%%%% %%%%%%%4--I>H H!4--I>%%%%%% %%%%%%%4--I>H H!,--I>%%%%%% %<585%=>?5 - A% H!4--I>%%%%%% :;)*%%%<585%=>?5 - J %%%%%%%4--I>H

21 Two-body kinematics In the CM frame of two particles of mass m 1 and m 2 ( ) s E 1 = 1 + m2 1 2 s m2 2 s ( ) s E 2 = 1 + m2 2 2 s m2 1 s s p 1 = p 2 = 1 2(m2 1 + m2 2 ) 2 s + (m2 1 m2 2 )2 s 2

22 ~ μ μχ 0 s 4 ( In the smuon rest frame In the lab frame γ µ = E µ m µ = ˆp µ = m µ 2 s 2m µ muon momentum in the lab frame p µ = m µ 2 1 m2 χ 0 m 0 µ Therefore, the muon energy is ) ( 1 m2 χ 0 m 0 µ ) (1 β µ ) < E µ < dσ de µ ( 1 m2 χ 0 β µ = m 2 µ ) (1,sin ˆθ,0,cos ˆθ) 1 4m2 µ s (γ µ + γ µ β µ cos ˆθ,sin ˆθ,0,γ µ cos ˆθ + γ µ β µ ) s 4 ( 1 m2 χ 0 m 0 µ dσ d cos ˆθ = constant ) (1 + β µ ) d d E

23 ~ μ μχ W W E miss ~ ~ R R lepton energy E l [GeV] fit to the kinetic distribution m µ = ± 0.3 GeV m χ 0 = 71.9 ± 0.1 GeV

24 LHC/LC synergy

25 Reconstruct Lagrangian from data Specify the fields mass spin Klein-Gordon, Dirac, Majorana, gauge SU(3)xSU(2)xU(1) quantum numbers mixing of states Specify their interactions SU(3)xSU(2)xU(1) quantum numbers determine gauge interactions Yukawa couplings trilinear and quartic scalar couplings

26 Spin

27 Spin production angle distribution well above the threshold: θ (1+cosθ) 2 spin 1/2 spin 0 θ sin 2 θ

28 ALEPH DALI Run=15768 Evt=5906

29 New particle has spin 1/2 θ (1+cosθ) 2 1+cos 2 θ θ sin 2 θ (1-cosθ) 2

30 ALEPH DALI Run=9063 Evt=7848

31 New particle has spin ALEPH N/N 3jets Corrected Data 1992 Vector Gluon, LO Vector Gluon, LO + Fragment. Scalar Gluon, LO Scalar Gluon, LO + Fragment Z (x 2 -x 3 )/

32 EPH!"#$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% &'()*+,+-%%%./0)1234%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 54167/%.8 531%67/%.8,5167/%98 *5-%67/%98 &J H!4--I>%%%%%% -!%%%% %%%%%%%4--I>H H!4--I>%%%%%% :;)*%%%<585%=>?5 - J%%%% %%%%%%%4--I>H H!4--I>%%%%%% %%%%%%%4--I>H H!,--I>%%%%%% %<585%=>?5 - A% H!4--I>%%%%%% :;)*%%%<585%=>?5 - J %%%%%%%4--I>H

33 Smuon production e + e µ + µ (µ + χ 0 1)(µ χ 0 1) once masses known, you can solve kinematics up to a two-fold ambiguity muon momenta measured: neutralino momenta: neutralino mass constraint: smuon mass constraint: momentum conservation: p µ 1,2 = (E 1,2, p 1,2 ) ( ) q µ s 1,2 = 2 E 1,2, q 1,2 ( s q 2 1,2 = Now know Know q 1 up to a two-fold ambiguity 2 ( s 2 E 1,2 ) 2 m 2 χ ) 2 ( p 1 + q 1 ) 2 = m 2 µ p 1 q 1 q 2 2 = ( p 1 + p 2 + q 1 ) 2 = ( p 1 + p 2 ) 2 + q p 1 q p 2 q 1 p 2 q 1 q 1, p 1 q 1, p 2 q 1

34 Smuon has spin 0 θ ~ ~ R R (1+cosθ) 2 false solution θ cos R ~ sin 2 θ

35 Spin threshold behavior non-relativistic limit: L, S separately conserved θ S-wave m=100 GeV spin 1/2 θ spin 0 P-wave E CM m µ = ± 0.09 GeV m χ 0 = 71.9 ± 0.05 GeV

36 Reconstruct Lagrangian from data Specify the fields mass spin Klein-Gordon, Dirac, Majorana, gauge SU(3)xSU(2)xU(1) quantum numbers mixing of states Specify their interactions SU(3)xSU(2)xU(1) quantum numbers determine gauge interactions Yukawa couplings trilinear and quartic scalar couplings

37 gauge quantum numbers

38 polarization Use polarized electron beam can ignore m Z2 s e R couples only to B μ e L couples to B μ +W μ 0 e R e B f _ f (g 2 Y f ) 2 e L B +W f e _ f (g 2 Y f +g 2 I 3f ) 2 /4

39 Reconstruct Lagrangian from data Specify the fields mass spin Klein-Gordon, Dirac, Majorana, gauge SU(3)xSU(2)xU(1) quantum numbers mixing of states Specify their interactions SU(3)xSU(2)xU(1) quantum numbers determine gauge interactions Yukawa couplings trilinear and quartic scalar couplings

40 Disentangle mixings

41 gauginos, higgsinos charged ones charginos ( )( ) ( W H d ) M 2 2mW sinβ W + 2mW cosβ µ H + u neutral ones neutralinos M 1 0 m Z s W c β m Z s W s β ( B, W 0, H d, 0 H u) 0 0 M 2 m Z c W c β m Z c W s β m Z s W c β m Z c W c β 0 µ m Z s W s β m Z c W s β µ 0 B W 0 H d 0 H u 0

42 e + e χ + 1 χ 1 ( χ 0 1l ± ν l )( χ 0 1q q )

43 e + e χ 0 2 χ 0 2 ( χ 0 1l + l )( χ 0 1l + l )

44 Model-independent parameter determination e + e - L/R! /Z s-channel Chargino/neutralino mass matrices have four parameters M 1, M 2, μ, tanβ Can measure 2+4 masses can measure 10x2 neutralino cross sections σ L,R (e + e χ 0 i χ 0 j) σ L,R (e + e χ + i χ j ) can measure 3x2 chargino cross sections depend on masses of ν e, ẽ L, ẽ R input fit " ~ + e + " ~ M GeV 152 ±1.8 GeV + # ~ e µ 316 GeV 316 ±0.9 GeV "- tanβ 3 3 ±0.7 ~ 1 e - " ~ - R 1 M GeV 78.7 ±0.7 GeV t-channel

45 Stop ( m ( t L t R) 2 Q 3 + mt 2 (A t µ cotβ)m t (At µcotβ)m t m 2 t + m2 t a) b) cos! t ~ "R -#" R "R +#" R " L +#" L polarization e - /e + 0.8/ m(stop) (GeV) " L -#" L cos! t ~ m h = 115 GeV, m t1 LHC TESLA GigaZ )( t L t R ) m t2 ~ = 180 GeV M A = 257 GeV, tan$ > 10 direct ~ [GeV] measurement at TESLA

46 Reconstruct Lagrangian from data Specify the fields mass spin Klein-Gordon, Dirac, Majorana, gauge SU(3)xSU(2)xU(1) quantum numbers mixing of states Specify their interactions SU(3)xSU(2)xU(1) quantum numbers determine gauge interactions Yukawa couplings trilinear and quartic scalar couplings

47 Interaction

48 Feynman rules Single gauge coupling constant gives all of these Feynman vertices f f ~ f A g g T a D a T a g 2 f ~ ~ f f ~ f ~ f

49 selectron production e + ~ l + R e + ~ e + R! /Z + 4 $ i=1 # ~ 0 i e - L/R l=e,!," ~ l - R e - R ~ e - R s-channel t-channel Fig.1 M sinθ [ 1 4Y 2 B 1 2cosθβ f + β 2 f + 4M2 1 /s ] Y B = g e R ẽ R B 2 g

50 gaugino coupling 1.2 ILC ratio of couplings e B = B ~ e supersymmetry e e~ rate and angular distribution of selectron production kinematic fit and threshold scans mass of the bino

51 Reconstruct Lagrangian from data Specify the fields mass spin Klein-Gordon, Dirac, Majorana, gauge SU(3)xSU(2)xU(1) quantum numbers mixing of states Specify their interactions SU(3)xSU(2)xU(1) quantum numbers determine gauge interactions Yukawa couplings trilinear and quartic scalar couplings

52 Proof of supersymmetry This way, you can show: new particle has the same gauge quantum numbers as one of the SM particle their spins differ by 1/2 it has a Yukawa coupling whose size is 2 times the known gauge coupling You have reconstructed the supersymmetric Lagrangian from data!

53 Robust search capability

54 Degenerate case (AMSB) E cm =600 GeV, L=50 fb -1 In anomaly mediation, M 2 <M 1 Standard SUSY Search chargino (wino) nearly degenerate with neutralino (wino) M (GeV) 1 + +Secondary Vertex decay products are soft and hard to see 10-1 Terminating Track Decaying to Stable Chargino Chargino Mass (GeV)

55 Big Caveat e + e - LC great as long as the new particles are there for m< s/2 What energy is enough? LHC will tell us

LHC/ILC. Hitoshi Murayama (Berkeley) SLAC SSI, 7/27/2006

LHC/ILC. Hitoshi Murayama (Berkeley) SLAC SSI, 7/27/2006 LHC/ILC Hitoshi Murayama (Berkeley) SLAC SSI, 7/27/2006 Technicolor Lykken: It doesn t look good but is not going away 2 LHC/ILC Hitoshi Murayama (Berkeley) SLAC SSI, 7/27/2006 Outline e + e - Linear Collider