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8. Beyond the Standard Model8.1 Recapitulation of the Standard Model8.2 Grand Unified Theories (GUT)8.3 Supersymmetry (SUSY)8.4 Minimal Supersymmetric Standard Model (MSSM)8.5 MSSM phenomenology8.6 Experimental SUSY searches
Brief overview of supersymmetry and its phenomenology
Particle Physics
Beyond the Standard Model Recapitulation of the Standard Model
Components of the Standard Model
fermions(uLdL
),
(cLsL
),
(tLbL
),
uR, dR, cR, sR, tR, bR(νe
e−L
),
(νµ
µ−L
),
(ντ
τ−L
),
e−R, µ−R, τ−R
gauge bosons
SU(3)c × SU(2)L ×U(1)Yelm.: γweak: W±,Z 0
strong: gluons
Higgs
additional scalar weak-isospin doublet with weak hypercharge YH = 12 :
SU(2)L × U(1)YSSB−→ U(1)elm Φ(x) =
(0
1√2ρ(x)
)
Particle Physics
Beyond the Standard Model Recapitulation of the Standard Model
Problems of the Standard Model
I many parameters
I SM describes about 4 % of the matter in the universe only
I hierarchy problem
MSM ∼ 102GeV MPlanck ∼ 1019GeV
I Higgs mass corrections
−|λf |2
8π2Λ2UV + . . . +
λs16π2
Λ2UV (1)
I mass-less neutrinos in contradiction to observed neutrino oscillations
I no underlying symmetry for baryon number conservation
Particle Physics
Beyond the Standard Model Grand Unified Theories (GUT)
Grand unification - SU(5)
I 3 gauge groups in SM⇒ 3 couplings as “free” parameters
I running couplings approach each other for M ∼ 1014 GeV
I unification into 1 group containing the SM gauge groups possible?⇒ only 1 parameter
I smallest such group (Georgi, Glashow, 19??):
SU(5) ⊃ SU(3)× SU(2)× U(1)
I fermion decomposition into SU(3),SU(2):
5 = (1, 2) + (3, 1) = (νe, e−) + dL (2)
10 = (1, 1) + 3, 1) + (3, 2) = eL+ + uL + (uL,dL) (3)
I gauge bosons (N2 − 1 = 24):
24 = (8, 1) + (1, 3) + (1, 1) + (3, 2) + (3, 2) (4)
Particle Physics
Beyond the Standard Model Grand Unified Theories (GUT)
Predictions from SU(5) unification
I weak mixing angle: sin2 θW ∼ 0.2
I quark charges:
Qd =1
3Qe− Qu = −2Qu (5)
I proton decay:consider p→ π0e+ in analogy to weak interaction
GG√2
=g2G
8M2X
(6)
⇒ Γ(p→ π0e+) ∝ G 2Gm
5p ∝
m5p
M4X
(7)
⇒ τp ∼ 1030y (8)
but experimental limit τp→π0e+ > 1034y
Particle Physics
Beyond the Standard Model Supersymmetry (SUSY)
Towards supersymmetry
I trivial cancellation of Higgs mass correctionsif we postulate pairs of fermions and bosons→ supersymmetry
I introduce operator Q, s.t.
Q |fermion〉 = |boson〉 Q |boson〉 = |fermion〉 (9)
Observations:
I Q† also a symmetry generator
I Q, Q† fermionic operators with S = 12
I decomposition into supermultiplets:∣∣Ω′⟩ = αQ |Ω〉+ βQ† |Ω〉 (10)
Beyond the Standard Model Supersymmetry (SUSY)
Supermultipletsconsider members of a given supermultiplets
I [Q,P2] = [Q†,P2] = 0 ⇒ equal masses
I [Q,G ] = [Q†,G ] = 0 for G any generator of a gauge group⇒ same elm. charge, weak isospin, colour
I Nbosons = Nfermions
we get
I scalar supermultiplet:
Weyl fermion (S =1
2)↔ complex scalar (S = 0) (11)
I vector supermultiplet:
Weyl fermion (S =1
2)↔ boson (S = 1) (12)
implies identical gauge transf. for left-/right-handed components
I (gravitational supermultiplet)
Particle Physics
Beyond the Standard Model Minimal Supersymmetric Standard Model (MSSM)
Minimal Supersymmetric Standard Model (MSSM)fermions
I construct a minimal SUSY model which contains the SM particles
I SM fermions must be in scalar supermultiplets
I scalar quarks → squarks:(uLdL
),
(cLsL
),
(tLbL
),
uR, dR, cR, sR, tR, bRI scalar leptons → sleptons:(
νe
e−L
),
(νµ
µ−L
),
(ντ
τ−L
),
e−R, µ−R, τ−RI chiral index refers to handedness of the fermionic parter,
e.g. only (uL, dL) couple to W
Particle Physics
Beyond the Standard Model Minimal Supersymmetric Standard Model (MSSM)
Minimal Supersymmetric Standard Model (MSSM)Higgs
I S = 0 ⇒ scalar supermultiplet
I two supermultiplets needed to avoid anomalies⇒ extend SM Higgs sector
I introduce two weak isospin doublets with Y = ±12 :
(H+u ,H
0u) (H0
d ,H−d ) (13)
I then supersymmetric higgsinos:
(H+u , H
0u) (H0
d , H−d ) (14)
I el. weak symmetry breaking more complicated because of two Higssdoublets . . .
Particle Physics
Beyond the Standard Model Minimal Supersymmetric Standard Model (MSSM)
Minimal Supersymmetric Standard Model (MSSM)gauge bosons
I SM gauge bosons must be in vector supermultiplets:
W+, W 0, W−︸ ︷︷ ︸winos
, B0︸︷︷︸bino
gauginos (15)
I mixing of W 0, B0 to photino γ and zino Z 0
I gluons: 8 gluinosI because of el. weak symmetry breaking mixing:
I neutralinos:
H0u, H
0d , W
0, B0 −→ χ01, χ
02, χ
03, χ
04
I charginos
H+u , W
+, −→ χ+1 , χ
+2
H+u , W
+, −→ χ+1 , χ
+2
Particle Physics
Beyond the Standard Model MSSM phenomenology
R-parity conservation
I introduce new quantum number
PR = (−1)3(B−L)+2S (16)
which is conservedI no mixing between particles and sparticlesI lightest SUSY particle (lsp) must be stableI proton decay, e.g.:
forbidden
Particle Physics
Beyond the Standard Model MSSM phenomenology
MSSM phenomenology
I if SUSY was exact ⇒ equal masses in supermultiplets
I contradicts lack of experimental evidence for SM states
I SUSY must be brokensoft SUSY breaking, not unique
LMSSM = LSUSY + Lsoft (17)
I number of SUSY operators can be increased (here: 1)
⇒ many viable MSSM scenarios possible and proposed
Particle Physics
Beyond the Standard Model MSSM phenomenology
MSSM scenarios
Figure: SUSY scenarios
Particle Physics
Beyond the Standard Model Experimental SUSY searches
Experimental SUSY searches
Problem Too many SUSY scenarios to check one specific prediction
Instead look for signatures which deviate from SM predictions andcan be explaeined by SUSY,e.g. jets and missing ET
e.g. ATLAS:
Particle Physics