Light Higgs Boson / No Fine-Tuning Radiative Symmetry Breaking Per-Mille

Central arguments : X Higgs sector : light Higgs boson / no ﬁne-tuning radiative symmetry breaking

per-mille prediction of elw mixing angle

maximal symmetry of fermions bosons ⊕ local susy gravity ⇒ candidate particle for Cold dark Matter

Central diﬃculty X: X micoscopic mechanism generating susy breaking

Deﬁning property : X pairing fermions bosons : matter forces ⇔ ⇔ cancellation of quad divergencies in loops ⇒ stable extrapolation from electroweak scale to Planck scale :

connect particle physics with gravity 1 Unification of the Coupling Constants in the SM and the minimal MSSM i i α α 60 60 1/α 1/ 1/ 1 MSSM 50 50

40 40 α 1/ 2 30 30

20 20

10 10 α 1/ 3 0 0 0 5 10 15 0 5 10 15 10log Q 10log Q

X X 1A 1. Minimal SUSY Spectrum

Particle SM stat spin SUSY Partner stat spin mix

lepton `R, `L F 1/2 slepton `˜R, `˜L B 0

quark qR, qL F 1/2 squark q˜R, q˜L B 0 gluon g B 1 gluino g˜ F 1/2 ,3 ,3 elw bosons W B 1 wino w˜ F 1/2 charginoX : χ˜1,2 ˜ 0 elw bosons B B 1 bino b F 1/2 neutralino : χ˜1,2,3,4 Higgs bosons H B 0 higgsinos h˜ F 1/2 /mix graviton G B 2 gravitino G˜ F 3/2

Mass estimate for LE SUSY :X M˜ M/√α 1 TeV ∼ ∼

X 2 2. Characteristics

[1] Lagrangian: L = Lsusy + Lsoft

Lsusy = gauge + matter/gauge + superpotential

Lsoft = mass terms + bi/trilinear scalar couplings

[2] identity : gauge = Y ukawa couplings : ff˜V˜ = ff V

[3] R parity conservation : Rp = 1 for SM/SUSY particles − X production in pairs ⇒ X lightest SUSY particle [LSP] stable ⇒ [4] Majorana character of ino fields − [5] Mixings :X V˜ H˜ H V˜ H˜ H : gaugino - higgsino mix XX [charginos/neutralinos] → h i f˜f˜H f˜f˜ H X : sfermionL - sfermionR mix [sfermion1,2 : t,˜ ˜b, τ˜] → h i X 3 Charginos X 0 M2 √2MW cos β 1 @ √2MW sin β µ A

Neutralinos X M1 0 MZ cβ sW MZ sβ sW 0 − 1 0 M M c c M s c B 2 Z β W Z β W C B − C B MZ cβ sW MZ cβ cW 0 µ C B − − C B C @ MZ sβ sW MZ sβ cW µ 0 A − −

2 2 3 2 2 Sfermions X M + m + (I Qf s )c2β M mf (Af µ cot / tan β) 0 L u/d f − w Z − 1 2 2 2 2 mf (Af µ cot / tan β) M + m + Qf s c2β M @ − R u/d w Z A

X 3A determine experimentally : masses, mixings, couplings extract theoretically XXX: gaugino masses M1,2 higgsino parameter µ

scalar mass parameters M˜ Higgs mixing tan β

Production at LHC main mechanisms : squarks/gluinos : qq¯ q˜q˜¯ – gauge / Yukawa cplgs → qq q˜q˜ – Yukawa cplgs → gg g˜g˜ – gauge cplgs → gq g˜q˜ – gauge / Yukawa cplgs → etc

XX X diagrams / cross sections at parton level

hadron level : folded with parton luminosities X 4 squark / gluino production :

X 4A squark / gluino production :

XX X 4B Higher-orderX super-QCD corrections : 5A

stabilize dependence on renormalization / factorization scales

corrections under control / positive : X K = σNLO/σLO 1.5 ∼

X XHigher-order super-QCD corrections : 5B

stabilize dependence on renormalization / factorization scales

corrections under control / positive : X K = σNLO/σLO 1.5 ∼

X direct non-color particle production : elw super-Compton X: gq χ˜q˜ → modulated Drell-Yan : qq¯ χ˜χ˜ → qq¯ `˜`˜ → typical cross sections : X X X

X X 6 Cascade decays : X SPS1a chain : 7

0 0 X q˜L q + χ˜ q + (``˜ ) q + `` + χ˜ X BR = 30/10/100% → 2 → → 1

X X production of charginos/neutralinos/sleptons

Search technique : missg transv momentum pp pmiss + X → T due to escaping LSP pp pmiss + X → T -7 LHC Point 5 10

-8 10

-9 10

-10 10 (mb/400 GeV) eff -11 /dM

σ 10 d

-12 10

-13 10 0 1000 2000 3000 4000

Meff (GeV) X XXXXXXXXXXXXXXX Mass reach of LHC : XXXXXXXXXXXXXXXXX A = 0 , tanβ = 35 , µ > 0 3 years, high lumi (3000 fb 1400 ~ g (GeV) (3000) -1 1/2 ) X X Mq˜,g˜ 2.5 to 3 GeV m 1 year, high lumi (100 fb h(123) ≤ 1200

~ g(2500) -1 ) 1000 ~ ~ q q(2000) (2500)

TH 1 year, low lumi (10 fb ~ g(2000) -1 800 )

1 month, low lumi (1 fb ~ g(1500) 600 -1 ~ q ) (1500)

~ 400 g(1000)

q ~ (1000) h (114) mass limit

~ 200 g(500) q ~ (500) S. Abdullin

0 0 500 1000 1500 2000

m0 ( GeV) 8 Exploring SUSY particles 9

[a] Mass : X edge and threshold eﬀects in cascades

0 + 0 + 0 examples : χ˜ ` `− + χ˜ and q˜L q` `− + χ˜ 2 → 1 → 1

200

1500 600 -1 -1

180 1000 400 m(Chi02) (GeV) Events/1 GeV/100 fb Events/5 GeV/100 fb 500 200 160

0 0 0 20 40 60 80 100 0 200 400 600 80 100 120

m(ll) (GeV) m(llq)max (GeV) m(Chi01) (GeV)

2 edge 2 2 2 2 2 edge : [m``] = (m 0 m` )(m` m 0 )/m` χ˜2 − R R − χ˜1 R 2 edge 2 2 2 2 2 [mq``] = (mq˜ m 0 )(m 0 m 0 )/m 0 L − χ˜2 χ˜2 − χ˜1 χ˜2

2 thrs 2 2 2 2 2 2 2 2 thrs : [mq``] = [(mq˜ + m 0 )(m 0 m` )(m` m 0 ) ...]/4m` m 0 L χ˜2 χ˜2 − R R − χ˜1 R χ˜2 rates/bkgds: LHC Mass, ideal “LHC” “LC” “LHC+LC” sens: 1 .. 5% χ˜1 179.7 dash: excluded χ˜2 382.3 – blank: not excl. χ0 ˜1 97.2 4.8 X 0 χ˜2 180.7 4.7

e˜R 143.9 4.8

e˜L 207.1 5.0

ν˜e 191.3 –

µ˜R 143.9 4.8

τ˜1 134.8 5-8

τ˜2 210.7 –

q˜L 570.6 8.7 mass diﬀerences: ˜ t1 399.5 up to 102 imprvd t˜2 586.3 g˜ 604.0 8.0 h0 110.8 0.25 A0 399.4 AAAAAAXX9A [b] Spin :Xparticle chain in SUSY equivalent to UED 10

0 0 SUSY : q˜L q + χ˜ q + (``˜ ) q + `` + χ˜ → 2 → → 1

UED : q1 q + Z1 q + (`1`) q + `` + γ1 → → →

distinction by spin angular distributions / invariant masses : ∼ 0 XX χ˜ left `− right slow 2 ⇒ ⇒ `+ leftX fast ⇒ + charge asymmetry in [q ` ] vs [q `−] :

X [c] Majorana nature of gluino :X 11

events with like-sign lepton pairs :

X X alternative : pp g˜g˜ (t˜t¯) + (t˜t¯) → → [d] Yukawa-gauge identity :

qqg = qq˜g˜ X : test in cross section for like-sign dilepton pairs

estimate 4% ∼

SUSY LHC summary : X LE SUSY discovery up to 2.5 to 3 TeV

accuracy of measurements at per-cent level

important steps in proﬁling SUSY experimentally X 12A SUSY BREAKING SCHEMES

[1] Minimal supergravity :

SUSY breaking in hidden sector transferred to eigen-world by gravitational interactions suggestive: universal soft breaking paramters ⇒ complexity of system reduced to a few basic parameters:

XX – gaugino mass parameter : M1/2 X universal at MU

10 XX – scalar mass parameter X : M0 XX ditto

XX – A trilinear coupling : A0 XX ditto 8

XX – signum (µ) [modulus: radiative SB] 6 (today) 2 CMSSM, µ > 0 XX – tan β [subst. bilin. B] χ 4 β tan = 10, A0 = 0 β tan = 10, A0 = +m1/2 tanβ = 10, A = -m typical scenarios: M1/2, M0 100 GeV 2 0 1/2 tanβ = 10, A = +2 m ∼ × 0 1/2 β tan = 10, A0 = -2 m1/2 0 focus point : M0 large 0 200 400 600 800 1000 m [GeV] XXXX 1/2 [2] Supergravity: gravitino = LSP / cdm :

(τ˜2 G˜2)4 gravitino = LSP : τ˜ τ + G˜ : m 100 GeV macro lifetime Γ − G˜ 48πG˜2τ˜3M2 → ∼ | ' P l

stable heavy track τ + Emiss → sugra coupling GN determined

[3] Split supersymmetry : very large scalar masses long gluino lifetime : ⇒ R-hadrons = bound states of [gluino+quark]

[4] Gauge mediated susy breaking :

SUSY breaking transferred by gauge interactions at scale 10 to 100 TeV

0 m ˜ keV long lifetime χ˜ γ + G˜ : pointing γ’s G ∼ | ⇒ 1 → `˜ ` + G˜ → and other scenarios ... 12B 4.3 EXTRA DIMENSIONS

NATURALNESS

Supersymmetry : solving naturalness / ﬁne-tuning problem in Higgs sector 2 19 X MH v 10 GeV MP l 10 GeV ∼ ∼ ∼ by applying classical criterion:

Parameter “naturally small” if in the limit 0 → symmetry of system rises

SUSY : symmetry fermions bosons ⇔ 2 2 2 δM log M /M 0 for M˜ Mt H ∼ t˜ t → t →

Extra Dimensions ADD : reduce MP lanck to (TeV) by assuming gravity strong O in 4 + δ dimensions and weak only in projection to D = 4

nat problem solved by removing unnatural parameter X 13 Landscape : disregard naturalness problem 14 parameter set one of many other scenarios and selection by probability and anthropic principle [?]

ADD SCENARIO

Gravity extended to D = 4 + δ dimensions curled up at radius Rc fundamental parameters : Planck scale : M P l ∗

compactiﬁcation radius : Rc

metric : flat

1 1 1 Newton’s law : D = 4 : V (R Rc) = GN r = 8πM 2 r ≥ P l N 1 1 1 D = 4 + δ : V (R Rc) = G r1+δ = 2+δ r1+δ ≤ ∗ 8πM∗P l

2+δ δ 2 M P l Rc = MP l δ = 2, M∗P l = 10 TeV : Rc = 1µm [large] ∗ −1 2 Rc = 10 eV [small] Radiation of gravitons : 15A qq¯ g + ΣGKK etc →

graviton KK mass : mN = N/Rc small ⇒ large number in tower of densely spaced KK gravitons ⇒ balancing weak gravity observable gravity eﬀect : ⇒

δ/2 δ+2 dσ = αs 2π √s f(xg,cos θg ) dxg d cos θg 64 Γ(δ/2) “ M∗P l ” s

Measurement [M P l, δ] : ∗ 2 params change √s ⇒

XXXX Radiation of gravitons : 15B qq¯ g + ΣGKK etc →

graviton KK mass : mN = N/Rc small ⇒ large number in tower of densely spaced KK gravitons ⇒ balancing weak gravity observable gravity eﬀect : ⇒

δ/2 δ+2 dσ = αs 2π √s f(xg,cos θg ) dxg d cos θg 64 Γ(δ/2) “ M∗P l ” s

Measurement [M P l, δ] : ∗ δ M (max) TeV M (min) TeV 2 params change √s ∗ ∗ ⇒ 2 8.8 3.8 3 6.8 4.8 4 5.8 4.9 5 5.0 5.1 RS SCENARIO 16A X – Gravity concentrated on gravity brane – spreading through 5th dimension to SM brane 2 2 2 2 with exponential fall-oﬀ : dx = exp[ 2πkRc y ] dx (πRc) dy 5 − | | 4 − fundamental parameters : Planck scale : MP l canonical 1 length of 5th dimension : Rc (M − ) O P l curvature of 5th dimension : k (MP l) O

SM scale : MSM exp[ πkRc] MP l 1 TeV for kRc 10 ∼ − ⇒ ∼ X X Signature : Kaluza-Klein gravitons : mass : M RS 1 TeV KK ≥ Bessel spaced

Params : Rc, k mass and width ⇐ AAA X RS SCENARIO 16B

– Gravity concentrated on gravity brane – spreading through 5th dimension to SM brane with exponential fall-oﬀ fundamental parameters : Planck scale : MP l canonical 1 length of 5th dimension : Rc (M − ) O P l curvature of 5th dimension : k (MP l) O

SM scale : MSM exp[ πkRc] MP l 1 TeV for kRc 10 ∼ − ⇒ ∼ XX X Signature : Kaluza-Klein gravitons : KK graviton spin = 2 qq¯ KK µµ angular distribution: → → XX spin = 2 : d2 (θ) sin2 / cos2 2θ n,m → XX spin = 1 : d1 (θ) 1 + cos2 θ n,m → AAA UED SCENARIO 17A

ED : potentially Scherk-Schwartz symmetry breaking [boundary conditions in high dims] and fermion mass hierarchy by positioning wave-functions

UED : fermions etc : KK tower over SM ﬁelds :

ψ = 1 ψ0 + 1 Σ ψN cos Ny + ψN sin Ny etc √2πR L √πR ` L R R R ´

N Masses : leading part universal : mKK = N/R N SB + loop corrections : order v/MKK

X X Vertices : connection Σ KK number = 0 mod.2

lightest KK stable cdm candidateX X X ⇒ UED SCENARIO 17B

LHC production : qq¯ q1Lq¯1L →

decay : q1L ql + γ1 ⊕ → XX

Signature : pp qq¯ + pmiss → T

resonance qq¯ γ2 µµ → → [via 00 1lp 2 00] → → → X X

UED vs. SUSY : diﬀerent mass pattern expected with certainty, i.p. N = 2

spin measurements :

[discrimination possible] UED SCENARIO 17C