Phenomenological Issues in Beyond the Standard Model

Home , Weak hypercharge

• The Structure of the Standard Model

• The MSSM

• Testing the Standard Model

• Neutrino Physics

• Beyond the MSSM

TASI (June 2, 2003) Paul Langacker (Penn) The Structure of the Standard Model

Remarkably successful gauge theory of the microscopic interactions.

1. The Standard Model Lagrangian

2. Spontaneous Symmetry Breaking

3. The Gauge Interactions (a) The Charged Current (b) QED (c) The Neutral Current (d) Gauge Self-interactions

4. Problems With the Standard Model

(See “Structure Of The Standard Model,” hep-ph/0304186)

TASI (June 2, 2003) Paul Langacker (Penn) Gauge Transformations

Φ → Φ0 ≡ UΦ i 0 −1 −1 A~µ · L~ → A~ µ · L~ ≡ UA~µ · LU~ + (∂µU) U g U = eiβ~·L~ where Φ is an n component representation vector for fermions or spin-0, Li is the n×n dimensional representation matrix for the ith generator (i = 1, ··· ,N), βi (i = 1, ··· ,N) is an arbitrary diﬀerentiable real function of space and time, and Aµ are N Hermitian gauge ﬁelds.

TASI (June 2, 2003) Paul Langacker (Penn) The Standard Model Lagrangian

Group: SU(3)×SU(2)×U(1)

0 Gauge couplings: gs (QCD); g, g (electroweak)

Generators: SU(3) (QCD): Li, i = 1, ··· , 8 SU(2): T i, i = 1, 2, 3 U(1): Y (weak hypercharge)

Gauge bosons:

i SU(3) (QCD): Gµ, i = 1, ··· , 8 i SU(2): Wµ, i = 1, 2, 3 U(1): Bµ

TASI (June 2, 2003) Paul Langacker (Penn) Quarks/leptons:

1 Chiral Projections: ψL(R) ≡ 2(1 ∓ γ5)ψ (Chirality = helicity up to O(m/E)) L-doublets:

u0 ν0 q0 = m l0 = m mL d0 mL e−0 m L m L

0 0 −0 0 R-singlets: umR, dmR, emR, (νmR) (F ≥ 3 families; m = 1 ··· F = family index; 0 = weak eigenstates (deﬁnite SU(2) rep.), mixtures of mass eigenstates (ﬂavors); quark color indices 0 α = r, g, b suppressed (e.g., umαL). )

ϕ+ Higgs: Complex scalar doublet ϕ = ϕ0

TASI (June 2, 2003) Paul Langacker (Penn) 3 U(1)Q: Electric charge generator Q = T + Y

1 1 1 Yq = ,Yl = − ,Yψ = qψ,Yϕ = + L 6 L 2 R 2

Lagrangian: L = LSU(3) + LSU(2)×U(1)

TASI (June 2, 2003) Paul Langacker (Penn) Quantum Chromodynamics (QCD)

1 i iµν X α β LSU(3) = − FµνF + q¯rαi D6 β qr 4 r

F 2 term leads to three and four-point gluon self-interactions.

i i i j k Fµν = ∂µGν − ∂νGµ − gsfijk Gµ Gν

i is ﬁeld strength tensor for the gluon ﬁelds Gµ, i = 1, ··· , 8., gs = QCD gauge coupling constant. No gluon masses.

Structure constants fijk (i, j, k = 1, ··· , 8), deﬁned by

i j k [λ , λ ] = 2ifijkλ where λi are the Gell-Mann matrices.

TASI (June 2, 2003) Paul Langacker (Penn) τ i 0 λi = , i = 1, 2, 3 0 0  0 0 1   0 0 −i  λ4 =  0 0 0  λ5 =  0 0 0  1 0 0 i 0 0  0 0 0   0 0 0  λ6 =  0 0 1  λ7 =  0 0 −i  0 1 0 0 i 0  1 0 0  λ8 = √1 0 1 0 3   0 0 −2

The SU3 (Gell-Mann) matrices.

TASI (June 2, 2003) Paul Langacker (Penn) α β Quark interactions given by q¯rαi D6 β qr th qr = r quark ﬂavor; α, β = 1, 2, 3 are color indices; Gauge covariant derivative

α i i Dµβ = (Dµ)αβ = ∂µδαβ + igs Gµ Lαβ, for triplet representation matrices Li = λi/2.

TASI (June 2, 2003) Paul Langacker (Penn) Quark color interactions:

Diagonal in ﬂavor uβ

gs i Oﬀ diagonal in color −i λ γµ @ 2 αβ §¤§¤i§¤ ¦¥¦¥¦¥ @ Gµ I@ @ Purely vector (parity conserving) uα @

Bare quark mass allowed by QCD, but forbidden by the chiral symmetry of LSU(2)×U(1) (generated by spontaneous symmetry breaking)

Additional ghost and gauge-ﬁxing terms

2 θgs i ˜iµν ˜iµν Can add (unwanted) CP-violating term Lθ = 32π2 FµνF , F ≡ 1 µναβ i 2 Fαβ

TASI (June 2, 2003) Paul Langacker (Penn) QCD now very well established

• Short distance behavior (asymptotic freedom)

• Conﬁnement, light hadron spectrum (lattice)

• Approximate global SU(3)L×SU(3)R symmetry and breaking (π, K, η are pseudogoldstone bosons)

• Unique ﬁeld theory of strong interactions

TASI (June 2, 2003) Paul Langacker (Penn) The Electroweak Sector

L = L + L + L + L SU2×U1 gauge ϕ f Yukawa

Gauge part 1 i µνi 1 µν Lgauge = − F F − BµνB 4 µν 4 Field strength tensors

Bµν = ∂µBν − ∂νBµ i i j k Fµν = ∂µWν − ∂νWµ − gijkWµWν

0 g(g ) is the SU2 (U1) gauge coupling; ijk is the totally antisymmetric symbol

Three and four-point self-interactions for the Wi

B and W3 will mix to form γ, Z

TASI (June 2, 2003) Paul Langacker (Penn) Scalar part µ † Lϕ = (D ϕ) Dµϕ − V (ϕ) ϕ+ where ϕ = . Gauge covariant derivative: ϕ0

i 0 ! τ i ig Dµϕ = ∂µ + ig W + Bµ ϕ 2 µ 2 where τ i are the Pauli matrices

Three and four-point interactions between the gauge and scalar ﬁelds

TASI (June 2, 2003) Paul Langacker (Penn) Higgs potential V (ϕ) = +µ2ϕ†ϕ + λ(ϕ†ϕ)2

Allowed by renormalizability and gauge invariance

Spontaneous symmetry breaking for µ2 < 0

Vacuum stability: λ > 0.

Quartic self-interactions

TASI (June 2, 2003) Paul Langacker (Penn) Fermion part (F families)

F X 0 0 ¯0 0 LF = q¯mLi Dq6 mL + lmLi Dl6 mL m=1 0 0 ¯0 0 0 0 +u ¯mRi Du6 mR + dmRi Dd6 mR +e ¯mRi De6 mR

L-doublets u0 ν0 q0 = m l0 = m mL d0 mL e−0 m L m L R-singlets 0 0 −0 umR, dmR, emR

Diﬀerent (chiral) L and R representations lead to parity violation (maximal for SU(2))

Fermion mass terms forbidden by chiral symmetry

0 Can add gauge singlet νmR for Dirac neutrino mass term

TASI (June 2, 2003) Paul Langacker (Penn) Gauge covariant derivatives 0 0 ig i i g 0 Dµq = ∂µ + τ W + i Bµ q mL 2 µ 6 mL 0 0 ig i i g 0 Dµl = ∂µ + τ W − i Bµ l mL 2 µ 2 mL 0 2 0 0 Dµu = ∂µ + i g Bµ u mR 3 mR 0 0 g 0 Dµd = ∂µ − i Bµ d mR 3 mR 0 0 0 DµemR = (∂µ − ig Bµ) emR Read oﬀ W and B couplings to fermions

g i 1−γ5 0 1∓γ5 −i τ γµ −ig yγµ @ 2 2 @ 2 §¤§¤§i¤ §¤§¤§¤ ¦¥¦¥¦¥ @ ¦¥¦¥¦¥ @ Wµ I@ Bµ I@ @ @ @ @

TASI (June 2, 2003) Paul Langacker (Penn) Yukawa couplings (couple L to R

F X u 0 0 d 0 0 −LYukawa = Γmnq¯mLϕu˜ mR + Γmnq¯mLϕdnR m,n=1 e ¯0 0 ν ¯0 0 + ΓmnlmnϕenR (+ΓmnlmLϕν˜ mR) + H.C.

Γmn are completely arbitrary Yukawa matrices, which determine fermion masses and mixings

d, e terms require doublet ϕ = + mL ϕ

0 with Yϕ = 1/2 ϕ Γmn @ @ ϕ I@ @ u (and ν) terms require doublet nR @ Φ0 Φ = with Y = −1/2 Φ− Φ

TASI (June 2, 2003) Paul Langacker (Penn) 0† In SU(2) the 2 and 2∗ are similar ⇒ ϕ˜ ≡ iτ 2ϕ† = ϕ −ϕ− 1 transforms as a 2 with Yϕ˜ = −2 ⇒ only one doublet needed.

Does not generalize to SU(3), most extra U(1)0, supersymmetry, etc ⇒ need two doublets.

(Does generalize to SU(2)L×SU(2)R×U(1) )

TASI (June 2, 2003) Paul Langacker (Penn) Spontaneous Symmetry Breaking

Gauge invariance implies massless gauge bosons and fermions

Weak interactions short ranged ⇒ spontaneous symmetry breaking for mass; also for fermions

Color conﬁnement for QCD ⇒ gluons remain massless

Allow classical (ground state) expectation value for Higgs ﬁeld

v = h0|ϕ|0i = constant

∂µv 6= 0 increases energy, but important for monopoles, strings, domain walls

TASI (June 2, 2003) Paul Langacker (Penn) Minimize V (v) to ﬁnd v and quantize ϕ0 = ϕ − v

SU(2)×U(1) : introduce Hermitian basis

1 ! ϕ+ √ (ϕ1 − iϕ2) ϕ = = 2 , ϕ0 √1 (ϕ − iϕ 2 3 4

† where ϕi = ϕi .

4 ! 4 !2 1 X 1 X V (ϕ) = µ2 ϕ2 + λ ϕ2 2 i 4 i i=1 i=1

is O4 invariant.

w.l.o.g. choose h0|ϕi|0i = 0, i = 1, 2, 4 and h0|ϕ3|0i = ν 1 1 V (ϕ)→V (v) = µ2ν2 + λν4 2 4

TASI (June 2, 2003) Paul Langacker (Penn) For µ2 < 0, minimum at

V 0(ν) = ν(µ2 + λν2) = 0 1/2 ⇒ ν = −µ2/λ

SSB for µ2 = 0 also; must consider loop corrections

0 ϕ→√1 ≡ v ⇒ the generators L1, L2, and L3 − Y 2 ν 1 i τ i 1 spontaneously broken, L v 6= 0, etc (L = 2 ,Y = 2I)

1 0 Qv = (L3 + Y )v = v = 0 ⇒ U(1) unbroken ⇒ 0 0 Q SU(2)×U(1)Y →U(1)Q

TASI (June 2, 2003) Paul Langacker (Penn) Quantize around classical vacuum • Kibble transformation: introduce new variables ξi for rolling modes 1 P i i 0 ϕ = √ ei ξ L 2 ν + H • H = H† is the Higgs scalar • No potential for ξi ⇒ massless Goldstone bosons for global symmetry • Disappear from spectrum for gauge theory (“eaten”) • Display particle content in unitary gauge

P i i 1 0 ϕ→ϕ0 = e−i ξ L ϕ = √ 2 ν + H

+ corresponding transformation on gauge ﬁelds

TASI (June 2, 2003) Paul Langacker (Penn) Rewrite Lagrangian in New Vacuum

Higgs covariant kinetic energy terms

0 2 † µ 1 g i i g 0 (Dµϕ) D ϕ = (0 ν) τ W + Bµ + H terms 2 2 µ 2 ν 2 2 +µ − MZ µ → M W W + Z Zµ W µ 2 + H kinetic energy and gauge interaction terms

Mass eigenstate bosons: W, Z, and A (photon)

1 W ± = √ (W 1 ∓ iW 2) 2 3 Z = − sin θW B + cos θW W 3 A = cos θW B + sin θW W

TASI (June 2, 2003) Paul Langacker (Penn) Masses

gν ν M p 2 02 W MW = ,MZ = g + g = ,MA = 0 2 2 cos θW

(Goldstone scalar transformed into longitudinal components of W ±,Z)

0 Weak angle: tan θW ≡ g /g

√ 2 2 Will show: Fermi constant GF / 2 ∼ g /8MW , where GF = 1.16639(2)×10−5 GeV −2 from muon lifetime

Electroweak scale

√ −1/2 ν = 2MW /g ' ( 2GF ) ' 246 GeV

TASI (June 2, 2003) Paul Langacker (Penn) 2 Will show: g = e/ sin θW , where α = e /4π ∼ 1/137.036 ⇒ √ 1/2 (πα/ 2GF ) MW = MZ cos θW ∼ sin θW

2 Weak neutral current: sin θW ∼ 0.23 ⇒ MW ∼ 78 GeV , and MZ ∼ 89 GeV (increased by ∼ 2 GeV by loop corrections)

Discovered at CERN: UA1 and UA2, 1983

Current:

MZ = 91.1876 ± 0.0021

MW = 80.449 ± 0.034

TASI (June 2, 2003) Paul Langacker (Penn) The Higgs Scalar H

Gauge interactions: ZZH,ZZH2,W +W −H,W +W −H2

1 0 ϕ→√ 2 ν + H

µ † Lϕ = (D ϕ) Dµϕ − V (ϕ) 2 1 2 2 µ+ − H = (∂µH) + M W W 1 + 2 W µ ν 2 1 2 µ H + M Z Zµ 1 + − V (ϕ) 2 Z ν

TASI (June 2, 2003) Paul Langacker (Penn) Higgs potential:

V (ϕ) = +µ2ϕ†ϕ + λ(ϕ†ϕ)2 µ4 λ → − − µ2H2 + λνH3 + H4 4λ 4

Fourth term: Quartic self-interaction Third: Induced cubic self-interaction Second: (Tree level) H mass-squared, √ p 2 MH = −2µ = 2λν

TASI (June 2, 2003) Paul Langacker (Penn) No a priori constraint on λ except vacuum stability (λ > 0 ⇒ 0 < MH < ∞), but > t quark loops destabilize vacuum unless MH ∼ 115 GeV > > Strong coupling for λ ∼ 1⇒MH ∼ 1 TeV Triviality: running λ should not diverge below scale Λ at which theory breaks down ⇒

−1/2 19 O(200) GeV, Λ ∼ MP = GN ∼ 10 GeV MH < O(750) GeV, Λ ∼ 2MH

+ − ∗ > Experimental bound (LEP 2), e e →Z →ZH ⇒ MH ∼ 114.5 GeV at 95% cl Hint of signal at 115 GeV

Indirect (precision tests): MH < 215 GeV, 95% cl MSSM: much of parameter space has standard-like Higgs with MH < 130 GeV

TASI (June 2, 2003) Paul Langacker (Penn) Theoretical MH limits, Hambye and Riesselmann, hep-ph/9708416

TASI (June 2, 2003) Paul Langacker (Penn) < + − Decays: H→¯bb dominates for MH ∼ 2MW (H→W W ,ZZ dominate when allowed because of larger gauge coupling) Production: LEP: Higgstrahlung (e+e−→Z∗→ZH) Tevatron, LHC: GG-fusion (GG→H via top loop), WW fusion (WW →H), or associated production (qq¯ →WH,ZH)

TASI (June 2, 2003) Paul Langacker (Penn) First term in V : vacuum energy

h0|V |0i = −µ4/4λ

No eﬀect on microscopic interactions, but gives negative contribution to cosmological constant

50 |ΛSSB| = 8πGN |h0|V |0i| ∼ 10 |Λobs|

Require ﬁne-tuned cancellation

Λcosm = Λbare + ΛSSB

Also, QCD contribution from SSB of global chiral symmetry

TASI (June 2, 2003) Paul Langacker (Penn) Yukawa Interactions

F X 0 u ν + H 0 −LYukawa → u¯mLΓmn √ umR + (d, e) terms + H.C. m,n=1 2 0 u u 0 =u ¯L (M + h H) uR + (d, e) terms + H.C.

0 0 0 0 T uL = u1Lu2L ··· uFL is F -component column vector √ u u u M is F ×F fermion mass matrix Mmn = Γmnν/ 2 (need not be Hermitian, diagonal, symmetric, or even square)

u u u h = M /ν = gM /2MW is the Yukawa coupling matrix

TASI (June 2, 2003) Paul Langacker (Penn) Diagonalize M by separate unitary transformations AL and AR ((AL = AR) for Hermitian M)   mu 0 0 u† u u u AL M AR = MD =  0 mc 0  0 0 mt

2 is diagonal matrix of physical masses of the charge 3 quarks. Similarly

d† d d d AL M AR = MD e† e e e AL M AR = MD eν† ν ν ν (AL M AR = MD)

(may also be Majorana masses for νR)

† Find AL and AR by diagonalizing Hermitian matrices MM and † † † 2 M M, e.g., ALMM AL = MD

TASI (June 2, 2003) Paul Langacker (Penn) Mass eigenstate ﬁelds

u† 0 T uL = AL uL = (uL cL tL) u† 0 T uR = AR uR = (uR cR tR) d† 0 T dL,R = AL,RdL,R = (dL,R sL,R bL,R) e† 0 T eL,R = AL,ReL,R = (eL,R µL,R τL,R) ν† 0 T νL,R = AL,RνL,R = (ν1L,R ν2L,R ν3L,R)

e† 0 (For mν = 0 or negligible, deﬁne νL = AL νL, so that νi ≡ νe, νµ, ντ are the weak interaction partners of the e, µ, and τ .)

TASI (June 2, 2003) Paul Langacker (Penn) Typical estimates: mu = 5.6 ± 1.1 MeV, md = 9.9 ± 1.1 MeV, ms = 199 ± 33 MeV, mc = 1.35 ± 0.05 GeV, mb ∼ 4.7 GeV, mt = 174.3 ± 5.1 GeV

Implications for global SU(3)L×SU(3)R of QCD

These are current quark masses. Mi = mi + Mdyn, Mdyn ∼ ΛMS ∼ 300 MeV from chiral condensate h0|qq¯ |0i= 6 0

2 mb,t are pole masses; others, running masses at 1 GeV

TASI (June 2, 2003) Paul Langacker (Penn) Yukawa couplings of Higgs to fermions

X gmi LYukawa = ψ¯i −mi − H ψi 2M i W

Coupling gmi/2MW is ﬂavor diagonal and small except t quark < + − H→¯bb dominates for MH ∼ 2MW (H→W W ,ZZ dominate when allowed because of larger gauge coupling) Flavor diagonal because only one doublet couples to fermions ⇒ fermion mass and Yukawa matrices proportional Often ﬂavor changing Higgs couplings in extended models with two doublets coupling to same kind of fermion (not MSSM)

Stringent limits, e.g., tree-level Higgs contribution to KL − KS −6 −1 mixing (loop in standard model) ⇒hds¯ /MH < 10 GeV

TASI (June 2, 2003) Paul Langacker (Penn) Phenomenological Issues in Beyond the Standard Model

• The Structure of the Standard Model

• Testing the Standard Model

• Neutrino Physics

• Beyond the MSSM

(First lecture available at dept.physics.upenn.edu/∼pgl/tasi1.pdf)

TASI (June 3, 2003) Paul Langacker (Penn) The Structure of the Standard Model

Remarkably successful gauge theory of the microscopic interactions.

1. The Standard Model Lagrangian

2. Spontaneous Symmetry Breaking

3. The Gauge Interactions (a) The Charged Current (b) QED (c) The Neutral Current (d) Gauge Self-interactions

4. Problems With the Standard Model

(See “Structure Of The Standard Model,” hep-ph/0304186)

TASI (June 3, 2003) Paul Langacker (Penn) The Weak Charged Current

Fermi Theory incorporated in SM and made renormalizable

W -fermion interaction g L = − √ J µ W − + J µ†W + 2 2 W µ W µ

Charge-raising current

F µ† X 0 µ 5 0 0 µ 5 0 JW = ν¯mγ (1 − γ )em +u ¯mγ (1 − γ )dm m=1  e−   d  µ 5 − µ 5 = (¯νeν¯µν¯τ )γ (1 − γ )  µ  + (¯u c¯ t¯)γ (1 − γ )V  s  . τ − b

TASI (June 3, 2003) Paul Langacker (Penn) Ignore ν masses for now

Pure V − A⇒ maximal P and C violation; CP conserved except for phases in V

u† d V = AL AL is F ×F unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix from mismatch between weak and Yukawa interactions

Cabibbo matrix for F = 2

cos θ sin θ V = c c − sin θc cos θc

sin θc ' 0.22 ≡ Cabibbo angle Good zeroth-order description since third family almost decouples

TASI (June 3, 2003) Paul Langacker (Penn) CKM matrix for F = 3 involves 3 angles and 1 CP -violating phase

(after removing unobservable qL phases) (new interations involving qR could make observable)

  Vud Vus Vub V =  Vcd Vcs Vcb  Vtd Vtd Vtd

Extensive studies, especially in B decays, to test unitarity of V as probe of new physics and test origin of CP violation

Need additional source of CP breaking for baryogenesis

TASI (June 3, 2003) Paul Langacker (Penn) Eﬀective zero- range 4-fermi interaction (Fermi theory)

For |Q| MW , neglect Q2 in W propagator

GF −Lcc = √ J µ J † eﬀ 2 W W µ

Fermi constant 2 GF g 1 √ ' = 2 2 2 8MW 2ν

2 5 −1 GF mµ −5 −2 Muon lifetime τ = 192π3 ⇒ GF = 1.16639(2)×10 GeV √ Weak scale ν = 2h0|ϕ0|0i ' 246 GeV

Excellent description of β, K, hyperon, heavy quark, µ, and τ − − − decays, νµe→µ νe, νµn→µ p, νµN→µ X

TASI (June 3, 2003) Paul Langacker (Penn) Full theory probed:

(−) ± e p→ ν eX at high energy (HERA) Electroweak radiative corrections (loop level) ¯ MKS − MKL, kaon CP violation, B ↔ B mixing (loop level)

TASI (June 3, 2003) Paul Langacker (Penn) Quantum Electrodynamics (QED)

Incorporated into standard model

Lagrangian:

0 gg µ 3 L = − J (cos θW Bµ + sin θW W ) pg2 + g02 Q µ

Photon ﬁeld:

3 Aµ = cos θW Bµ + sin θW Wµ

0 Positron electric charge: e = g sin θW , where tan θW ≡ g /g

TASI (June 3, 2003) Paul Langacker (Penn) Electromagnetic current:

F µ X 2 1 J = u¯0 γµu0 − d¯0 γµd0 − e¯0 γµe0 Q 3 m m 3 m m m m m=1 F X 2 µ 1 µ µ = u¯mγ um − d¯mγ dm − e¯mγ em 3 3 m=1

Flavor diagonal: Same form in weak and mass bases because ﬁelds which mix have same charge

Purely vector (parity conserving): L and R ﬁelds have same charge

TASI (June 3, 2003) Paul Langacker (Penn) Spectacularly successful: Many low energy tests (e.g., cesium hfs, e anomalous magnetic moment, etc., to few ×10−8) −16 mA < 2×10 eV Muon g − 2 sensitive to new physics. Anomaly? Running α(Q2) observed High energy well-measured

TASI (June 3, 2003) Paul Langacker (Penn) The Weak Neutral Current

Prediction of SU(2)×U(1)

p 2 02 g + g µ 3 L = − J − sin θW Bµ + cos θW W 2 Z µ g µ = − JZZµ 2 cos θW

Neutral current process and eﬀective 4-fermi interaction for |Q| MZ

TASI (June 3, 2003) Paul Langacker (Penn) Neutral current:

µ X 0 µ 0 ¯0 µ 0 0 µ 0 0 µ 0 JZ = u¯mLγ umL − dmLγ dmL +ν ¯mLγ νmL − e¯mLγ emL m 2 µ − 2 sin θW JQ X µ µ µ µ = u¯mLγ umL − d¯mLγ dmL +ν ¯mLγ νmL − e¯mLγ emL m 2 µ − 2 sin θW JQ

Flavor diagonal: Same form in weak and mass bases because ﬁelds which mix have same charge

GIM mechanism: c quark predicted so that sL could be in doublet to avoid unwanted ﬂavor changing neutral currents (FCNC) at tree and loop level Parity violated but not maximally: ﬁrst term is pure V −A, second is V

TASI (June 3, 2003) Paul Langacker (Penn) 2 2 Eﬀective 4-fermi interaction for |Q | MZ:

NC GF µ −L = √ J JZµ eﬀ 2 Z

Coeﬃcient same as WCC because

2 2 02 GF g g + g √ = 2 = 2 2 8MW 8MZ

WNC discovered 1973: Gargamelle at CERN, HPW at FNAL

Tested in many processes: νe→νe, νN→νN, νN→νX; e↑ ↓D→eX; atomic parity violation; e+e−, Z-pole reactions

WNC, W , and Z are primary test/prediction of electroweak model

TASI (June 3, 2003) Paul Langacker (Penn) Gauge Self-Interactions

Three and four-point interactions predicted by gauge invariance

Indirectly veriﬁed by radiative corrections, αs running in QCD, etc.

Strong cancellations in high energy amplitudes would be upset by anomalous couplings

Tree-level diagrams contributing to e+e−→W +W −

TASI (June 3, 2003) Paul Langacker (Penn) TASI (June 3, 2003) Paul Langacker (Penn) TASI (June 3, 2003) Paul Langacker (Penn) The Z, the W , and the Weak Neutral Current

• Primary prediction and test of electroweak uniﬁcation

• WNC discovered 1973 (Gargamelle, HPW)

• 70’s, 80’s: weak neutral current experiments (few %) – Pure weak: νN, νe scattering – Weak-elm interference in eD, e+e−, atomic parity violation

• W , Z discovered directly 1983 (UA1, UA2)

TASI (June 3, 2003) Paul Langacker (Penn) • 90’s: Z pole (LEP, SLD), 0.1%; lineshape, modes, asymmetries

• LEP 2: MW , Higgs, gauge self-interactions

• Tevatron: mt, MW

• 4th generation weak neutral current experiments

• Implications – SM correct and unique to zeroth approx. (gauge principle, group, representations)

– SM correct at loop level (renorm gauge theory; mt, αs, MH) – TeV physics severely constrained (uniﬁcation vs compositeness) – Precise gauge couplings (gauge uniﬁcation)

TASI (June 3, 2003) Paul Langacker (Penn) The LEP/SLC Era

• Z Pole: e+e− → Z → `+`−, qq,¯ νν¯

– LEP (CERN), 2×107Z0s, unpolarized (ALEPH, DELPHI, L3, OPAL); 5 SLC (SLAC), 5 × 10 , Pe− ∼ 75 % (SLD)

• Z pole observables

– lineshape: MZ, ΓZ, σ – branching ratios ∗ e+e−, µ+µ−, τ +τ − ∗ qq,¯ cc,¯ b¯b, ss¯ ∗ νν¯ ⇒ Nν = 2.986 ± 0.007 if mν < MZ/2

– asymmetries: FB, polarization, Pτ , mixed – lepton family universality

TASI (June 3, 2003) Paul Langacker (Penn) The Z Lineshape

Basic Observables: e+e−→ff¯ (f = e, µ, τ, s, b, c, hadrons) (s = 2 ECM ) 2 sΓZ σf (s) ∼ σf 2 2 2 2 s ΓZ (s − MZ) + 2 MZ (plus initial state rad. corrections)

Peak Cross Section:

12π Γ(e+e−)Γ(ff¯) σf = 2 2 MZ ΓZ

TASI (June 3, 2003) Paul Langacker (Penn) Partial Widths:

3 Cf GF MZ 2 2 Γ(ff¯) ∼ √ |g¯V f | + |g¯Af | 6 2π

(plus mass, QED, QCD corrections; C` = 1,Cq = 3;g ¯V,Af = eﬀective coupling (includes ew)).

At tree level:

1 1 2 g¯Af = ± , g¯V f = ± − 2sin θW qf 2 2

2 2 MW 1 where sin θW ≡ 1 − 2 is the weak angle, ±2 is the weak MZ − isospin (+ for (u, ν), − for (d, e )), and qf is the electric charge

TASI (June 3, 2003) Paul Langacker (Penn) LEP averages of leptonic widths

Γ ± e 83.92 0.12 MeV

Γµ 83.99 ± 0.18 MeV

Γ τ 84.08 ± 0.22 MeV

Γ¡ ± l 83.98 0.09 MeV

1000

800

] 600

m£ = 91 188 ± 2 MeV GeV Z [

¢ ± m 400 mt = 174.3 5.1 GeV

200

83.5 84 84.5

Γ¡ [ ] l MeV TASI (June 3, 2003) Paul Langacker (Penn) Z-Pole Asymmetries

• Eﬀective axial and vector couplings of Z to fermion f

√ g¯Af = ρf t3f

√ h 2 i g¯V f = ρf t3f − 2¯sf qf

2 where s¯f the eﬀective weak angle,

2 2 s¯f = κf sW (on − shell) 2 2 =κ ˆf sˆZ ∼ sˆZ + 0.00029 (f = e)(MS ),

ρf , κf , and κˆf are electroweak corrections, qf = electric charge, t3f = weak isospin

TASI (June 3, 2003) Paul Langacker (Penn) 0 • A = Born asymmetry (after removing γ, oﬀ-pole, box (small), Pe−)

0f 3 forward − backward : A ' AeAf FB 4

0e 0µ 0τ 0` (AFB = AFB = AFB ≡ AFB→ universality)

A + A 2z 0 τ e1+z2 τ polarization : Pτ = − 2z 1 + Aτ Ae1+z2

(z = cos θ, θ = scattering angle)

− 0 e polarization (SLD) : ALR = Ae

0FB 3 mixed (SLD) : A = Af LR 4

2¯gVF g¯Af Af ≡ 2 2 g¯VF +g ¯AF

TASI (June 3, 2003) Paul Langacker (Penn) The Z Pole Observables: LEP and SLC (01/03)

Quantity Group(s) Value Standard Model pull

MZ [GeV] LEP 91.1876 ± 0.0021 91.1874 ± 0.0021 0.1 ΓZ [GeV] LEP 2.4952 ± 0.0023 2.4972 ± 0.0011 −0.9 Γ(had) [GeV] LEP 1.7444 ± 0.0020 1.7436 ± 0.0011 — Γ(inv) [MeV] LEP 499.0 ± 1.5 501.74 ± 0.15 — Γ(`+`−) [MeV] LEP 83.984 ± 0.086 84.015 ± 0.027 — σhad [nb] LEP 41.541 ± 0.037 41.470 ± 0.010 1.9 Re LEP 20.804 ± 0.050 20.753 ± 0.012 1.0 Rµ LEP 20.785 ± 0.033 20.753 ± 0.012 1.0 Rτ LEP 20.764 ± 0.045 20.799 ± 0.012 −0.8 AFB(e) LEP 0.0145 ± 0.0025 0.01639 ± 0.00026 −0.8 AFB(µ) LEP 0.0169 ± 0.0013 0.4 AFB(τ ) LEP 0.0188 ± 0.0017 1.4

TASI (June 3, 2003) Paul Langacker (Penn) Quantity Group(s) Value Standard Model pull

Rb LEP/SLD 0.21664 ± 0.00065 0.21572 ± 0.00015 1.1 Rc LEP/SLD 0.1718 ± 0.0031 0.17231 ± 0.00006 −0.2 Rs,d/R(d+u+s) OPAL 0.371 ± 0.023 0.35918 ± 0.00004 0.5 AFB(b) LEP 0.0995 ± 0.0017 0.1036 ± 0.0008 −2.4 AFB(c) LEP 0.0713 ± 0.0036 0.0741 ± 0.0007 −0.8 AFB(s) DELPHI/OPAL 0.0976 ± 0.0114 0.1037 ± 0.0008 −0.5 Ab SLD 0.922 ± 0.020 0.93476 ± 0.00012 −0.6 Ac SLD 0.670 ± 0.026 0.6681 ± 0.0005 0.1 As SLD 0.895 ± 0.091 0.93571 ± 0.00010 −0.4 ALR (hadrons) SLD 0.15138 ± 0.00216 0.1478 ± 0.0012 1.7 ALR (leptons) SLD 0.1544 ± 0.0060 1.1 Aµ SLD 0.142 ± 0.015 −0.4 Aτ SLD 0.136 ± 0.015 −0.8 Ae(QLR) SLD 0.162 ± 0.043 0.3 Aτ (Pτ ) LEP 0.1439 ± 0.0043 −0.9 Ae(Pτ ) LEP 0.1498 ± 0.0048 0.4 QFB LEP 0.0403 ± 0.0026 0.0424 ± 0.0003 −0.8

TASI (June 3, 2003) Paul Langacker (Penn) • LEP 2

– MW , ΓW , B (also hadron colliders)

– MH limits (hint?) – WW production (triple gauge vertex) – Quartic vertex – SUSY/exotics searches

• Other: atomic parity (Boulder); νe; νN (NuTeV); MW , mt (Tevatron)

TASI (June 3, 2003) Paul Langacker (Penn) Non-Z Pole Precision Observables (1/03)

Quantity Group(s) Value Standard Model pull mt [GeV] Tevatron 174.3 ± 5.1 174.4 ± 4.4 0.0 MW [GeV] LEP 80.447 ± 0.042 80.391 ± 0.018 1.3 MW [GeV] Tevatron /UA2 80.454 ± 0.059 1.1 2 gL NuTeV 0.30005 ± 0.00137 0.30396 ± 0.00023 −2.9 2 gR NuTeV 0.03076 ± 0.00110 0.03005 ± 0.00004 0.6 Rν CCFR 0.5820 ± 0.0027 ± 0.0031 0.5833 ± 0.0004 −0.3 Rν CDHS 0.3096 ± 0.0033 ± 0.0028 0.3092 ± 0.0002 0.1 Rν CHARM 0.3021 ± 0.0031 ± 0.0026 −1.7 Rν¯ CDHS 0.384 ± 0.016 ± 0.007 0.3862 ± 0.0002 −0.1 Rν¯ CHARM 0.403 ± 0.014 ± 0.007 1.0 Rν¯ CDHS 1979 0.365 ± 0.015 ± 0.007 0.3816 ± 0.0002 −1.0

TASI (June 3, 2003) Paul Langacker (Penn) Quantity Group(s) Value Standard Model pull νe gV CHARM II −0.035 ± 0.017 −0.0398 ± 0.0003 — νe gV all −0.041 ± 0.015 −0.1 νe gA CHARM II −0.503 ± 0.017 −0.5065 ± 0.0001 — νe gA all −0.507 ± 0.014 0.0 QW (Cs) Boulder −72.69 ± 0.44 −73.10 ± 0.04 0.8 QW (Tl) Oxford/Seattle −116.6 ± 3.7 −116.7 ± 0.1 0.0 103 Γ(b→sγ) BaBar/Belle/CLEO 3.48+0.65 3.20 ± 0.09 0.5 ΓSL −0.54 ττ [fs] direct/Be/Bµ 290.96 ± 0.59 ± 5.66 291.90 ± 1.81 −0.4 4 (3) + − 10 ∆αhad e e /τ decays 56.53 ± 0.83 ± 0.64 57.52 ± 1.31 −0.9 9 α 10 (aµ − 2π ) BNL/CERN 4510.64 ± 0.79 ± 0.51 4508.30 ± 0.33 2.5

TASI (June 3, 2003) Paul Langacker (Penn) Anomalies, Things to Watch

b • AFB = 0.0995(17) is 2.4σ below expectation of 0.1036(8)

– Rb = 0.21664 ± 0.00065 (SM: 0.21572 ± 0.00015, agrees at 1.1σ)

– Ab = 0.922 ± 0.020 (SM: 0.93476 ± 0.00012 agrees at −0.6σ)

– Compensation of L and R couplings (Rb) – 5% eﬀect, but ∼ 25% in κ → probably tree level aﬀecting third family – New physics possibilities include Z0 with non-universal couplings, or bR mixing with BR in doublet with charge −4/3

– New physics or ﬂuctuation/systematics lead to smaller MH

TASI (June 3, 2003) Paul Langacker (Penn) TASI (June 3, 2003) Paul Langacker (Penn) • aµ = (gµ − 2)/2

– More sensitive than ae to new physics exp −10 – BNL (2002) + other: aµ = 11659203(8)×10 – Hadronic light by light has settled down, but considerable Had uncertaintly from aµ exp SM −10 + − Had – aµ − aµ = (26 ± 11)×10 (2.6σ) (using e e data for aµ ) →1.1σ (using τ decay data) – New: radiative correction error should reduce discrepancy √ – New physics? Supersymmetry: (m ˜ ∼ 55 GeV tan β)

TASI (June 3, 2003) Paul Langacker (Penn) The Anomalous Magnetic Moment of the Muon

gµ − 2 aµ ≡ 2

SM QED Had EW −10 aµ = aµ + aµ + aµ = 11659177(7)×10

α α2 aQED = + 0.765857376(27) µ 2π π α3 α4 +24.05050898(44) + 126.07(41) π π α5 +930(170) = 11658470.57(0.29)×10−10 π

TASI (June 3, 2003) Paul Langacker (Penn) Had Had Had aµ = aµ (vp)1+2 + aµ (ll) = (692(6) − 10.0(0.6) + 8.6(3.2)) ×10−10

EW −10 aµ (2 loop) = 15.1(0.4)×10

– More sensitive than ae to new physics exp −10 – BNL (2002) + other: aµ = 11659203(8)×10 – Hadronic light by light has settled down, but considerable Had uncertaintly from aµ exp SM −10 + − Had – aµ − aµ = (26 ± 11)×10 (2.6σ) (using e e data for aµ ) →1.1σ (using τ decay data) √ – New physics? Supersymmetry: (m ˜ ∼ 55 GeV tan β)

TASI (June 3, 2003) Paul Langacker (Penn) (5) • ∆αhad(MZ) – Hadronic contribution to running of α up to Z-pole 2 – Largest theory uncertainty in MZ − sˆZ had – Closely related to aµ – Recent progress using improved QCD calculations (high energy part) and precise BES data

TASI (June 3, 2003) Paul Langacker (Penn) • NuTeV (−) (−) ν µN→ ν µX (−) ∓ ν µN→µ X

– Little c threshold uncertaintly 2 – sW = 0.2277(16), 3.0σ above SM value 0.2228(4) 2 ∗ gL = 0.3001(14) is 2.9σ below expected 0.3040(2) 2 ∗ gR = 0.0308(11) is 0.7σ above expected 0.0300(0) – Possible QCD eﬀects: Large isospin breaking is sea; large s¯ − s asymmetry; nuclear shadowing; NLQCD – Possible exotic eﬀects: designer Z0; ν mixing with heavy neutrino (CKM universality?)

TASI (June 3, 2003) Paul Langacker (Penn) weak mixing angle scale dependence in MS−bar scheme 0.25

0.245

0.24 NuTeV W θ

2 MSSM £ old QW(APV)

sin ¢ 0.235 QWEAK E158

new QW(APV)

¤ Z−pole

0.23

0.225

0.001 0.01 0.1 1¡ 10 100 1000 Q [GeV] TASI (June 3, 2003) Paul Langacker (Penn) Fit Results (06/02) (Erler, PL)

+49 MH = 86−32 GeV,

mt = 174.2 ± 4.4 GeV,

αs = 0.1210 ± 0.0018, −1 αˆ(MZ) = 127.922 ± 0.020 2 sˆZ = 0.23110 ± 0.00015, χ2/d.o.f. = 49.0/40(15%)

TASI (June 3, 2003) Paul Langacker (Penn) • mt = 174.2 ± 4.4 GeV

+9.9 – 174.0−7.4 GeV from indirect (loops) only (direct: 174.3 ± 5.1)

- - 't, b $ 't $

§¤§¤§¤§¤ §¤§¤§¤§¤ §¤§¤§¤+§¤ §¤§¤§¤+§¤ ¦¥¦ZZ¥¦¥¦¥ t, b ¦¥¦¥¦¥¦¥ ¦¥¦W¥¦¥¦¥ b ¦¥¦W¥¦¥¦¥ & % & %

TASI (June 3, 2003) Paul Langacker (Penn) • αs= 0.1210 ± 0.0018

– Higher than world average αs = A ¡ 0.1172(20) (Hinchliﬀe (PDG) A ¡ q A G ¡ q¯ 2001), because of τ lifetime A ¡ A ¡ A §¤§¡¤ ¦A¥¦¥¡ A ¡ – insensitive to oblique new physics A¡ ¤ §¥ ¦¤ §¥Z – very sensitive to non-universal ¦¤ §¥ ¯ ¦¤ new physics (e.g., Zbb vertex) §¥ ¦

TASI (June 3, 2003) Paul Langacker (Penn) +49 • Higgs mass MH= 86−32 GeV

> – direct limit (LEP 2): MH ∼ 114.4 (95%) GeV < < – SM: 115 (vac. stab.) ∼ MH ∼ 750 (triviality) H ' $

§¤§¤§¤§¤§¤§¤§¤§¤§¤§¤ < ¦¥¦ZZ¥¦¥¦¥¦¥¦¥¦¥¦¥¦¥¦¥ – MSSM: MH ∼ 130 GeV (150 in extensions)

– indirect: ln MH but signiﬁcant ∗ fairly robust to new physics (except S < 0, T > 0) ∗ however, strong AFB(b) eﬀect ∗ MH < 215 GeV at 95%, including direct

TASI (June 3, 2003) Paul Langacker (Penn) 1000

¥ Γ σ Z, had, Rl, Rq asymmetries ¦ ν scattering

500 MW

§ all data ¨ 90% CL 200

100 [GeV] H M

50 excluded

¢ £ ¤ 100 120¡ 140 160 180 200

mt [GeV] TASI (June 3, 2003) Paul Langacker (Penn) 80.6

direct (1σ) indirect (1σ) all (90% CL) 80.5

80.4 [GeV] W M

80.3 100

200

400

800 MH [GeV]

80.2

¢ £ ¤ ¥ 150 160¡ 170 180 190 200 m [GeV] TASI (June 3, 2003)t Paul Langacker (Penn) Phenomenological Issues in Beyond the Standard Model

• The Structure of the Standard Model

• Testing the Standard Model

• Neutrino Physics

• Beyond the MSSM

(Second lecture available at dept.physics.upenn.edu/∼pgl/tasi2.pdf)

TASI (June 5, 2003) Paul Langacker (Penn) The Structure of the Standard Model

Remarkably successful gauge theory of the microscopic interactions.

1. The Standard Model Lagrangian

2. Spontaneous Symmetry Breaking

3. The Gauge Interactions (a) The Charged Current (b) QED (c) The Neutral Current (d) Gauge Self-interactions

4. Problems With the Standard Model

(See “Structure Of The Standard Model,” hep-ph/0304186)

TASI (June 5, 2003) Paul Langacker (Penn) Neutrino Preliminaries

• Weyl fermion – Minimal (two-component) fermionic degree of freedom c – ψL ↔ ψR by CPT

• Active Neutrino (a.k.a. ordinary, doublet) – in SU(2) doublet with charged lepton → normal weak interactions c – νL ↔ νR by CPT

• Sterile Neutrino (a.k.a. singlet, right-handed) – SU(2) singlet; no interactions except by mixing, Higgs, or BSM c – NR ↔ NL by CPT – Almost always present: Are they light? Do they mix?

TASI (June 5, 2003) Paul Langacker (Penn) • Dirac Mass

– Connects distinct Weyl spinors (usually active to sterile): (mDν¯LNR + h.c.)

– 4 components, ∆L = 0 νL 6 v = hφi

1 h – ∆I = 2 → Higgs doublet m = hv NR D – Why small? LED? HDO? 6

TASI (June 5, 2003) Paul Langacker (Penn) • Majorana Mass

– Connects Weyl spinor with itself: 1 c 2(mT ν¯LνR + h.c.) (active); 1 ¯ c 2(mSNLNR + h.c.) (sterile) – 2 components, ∆L = ±2 – Active: ∆I = 1 → triplet or νL 6 νL 6 seesaw @@ @@ @@ @@ – Sterile: ∆I = 0 → singlet or c ν νL ? bare mass R 6

• Mixed Masses – Majorana and Dirac mass terms

– Seesaw for mS mD

– Ordinary-sterile mixing for mS and mD both small and comparable (or mS md (pseudo-Dirac))

TASI (June 5, 2003) Paul Langacker (Penn) CDHSW • 3 ν Patterns CHORUS NOMAD

– Solar: LMA (SNO, 100 KARMEN2 NOMAD LSND CHORUS Kamland) Bugey BNL E776

2 −5 −4 SuperK – ∆m ∼ (10 − 10 ) CHOO 2 PaloVerde eV for LMA 10–3 Z

] LMA

2 2 – Atmospheric: ∆mAtm ∼ −3 2 KamLAND 3×10 eV , near- SMA [eV maximal mixing 2 –6

m 10 ∆

– Reactor: Ue3 small LOW νe↔νX νµ↔ντ ν ↔ν 10–9 e τ νe↔νµ

VAC

10–12 10–4 10–2 100 102 tan2θ – Mixings: let ν ≡ √1 (ν ± ν ): ± 2 µ τ

ν3 ∼ ν+

ν2 ∼ cos θ ν− − sin θ νe

ν1 ∼ sin θ ν− + cos θ νe

3 2 1 2 1 3

– Hierarchical pattern – Inverted quasi-degenerate pattern

∗ Analogous to quarks, ∗ ββ0ν if Majorana charged leptons ∗ SN1987A energetics ∗ ββ0ν rate very small (if Ue3 6= 0)? ∗ May be radiative unstable

TASI (June 5, 2003) Paul Langacker (Penn) – Degenerate patterns ∗ Motivated by CHDM (no longer needed)

∗ Strong cancellations needed for ββ0ν if Majorana ∗ May be radiative unstable

TASI (June 5, 2003) Paul Langacker (Penn) • 4 ν Patterns

2 2 – LSND: ∆mLSND ∼ 1 eV – Z lineshape: 2.986(7) active ν’s lighter than MZ/2 → fourth sterile νS

– 2 + 2 patterns – 3 + 1 patterns

2 + 2 3 + 1

• Pure (νµ − νs) excluded for atmospheric by SuperK, MACRO

• Pure (νe − νs) excluded for solar by SNO, SuperK

• More general admixtures possible, but very poor global ﬁts

TASI (June 5, 2003) Paul Langacker (Penn) Problems with the Standard Model

Lagrangian after symmetry breaking:

X miH L = Lgauge + LHiggs + ψ¯i i 6∂ − mi − ψi ν i

g µ − µ† + µ g µ − √ JW Wµ + JW Wµ − eJQAµ − JZZµ 2 2 2 cos θW

Standard model: SU(2)×U(1) (extended to include ν masses) + general relativity

Mathematically consistent, renormalizable theory

Correct to 10−16 cm

TASI (June 5, 2003) Paul Langacker (Penn) However, too much arbitrariness and ﬁne-tuning (O(20) parameters, not including ν masses/mixings, which add at least 7 more, and electric charges)

• Gauge Problem – complicated gauge group with 3 couplings

– charge quantization (|qe| = |qp|) unexplained – Possible solutions: strings; grand uniﬁcation; magnetic monopoles (partial); anomaly constraints (partial)

• Fermion problem – Fermion masses, mixings, families unexplained – Neutrino masses, nature? – CP violation inadequate to explain baryon asymmetry – Possible solutions: strings; brane worlds; family symmetries; compositeness; radiative hierarchies. New sources of CP violation.

TASI (June 5, 2003) Paul Langacker (Penn) • Higgs/hierarchy problem

2 2 – Expect MH = O(MW ) – higher order corrections: 2 2 34 δMH/MW ∼ 10 Possible solutions: supersymmetry; dynamical symmetry breaking; large extra dimensions; Little Higgs

• Strong CP problem

θ 2 ˜ – Can add 32π2 gsF F to QCD (breaks, P, T, CP) −9 – dN ⇒ θ < 10 −3 – but δθ|weak ∼ 10 – Possible solutions: spontaneously broken global U(1) (Peccei- Quinn) ⇒ axion; unbroken global U(1) (massless u quark); spontaneously broken CP + other symmetries

TASI (June 5, 2003) Paul Langacker (Penn) • Graviton problem – gravity not uniﬁed – quantum gravity not renormalizable 50 124 – cosmological constant: ΛSSB = 8πGN hV i > 10 Λobs (10 for GUTs, strings) – Possible solutions: ∗ supergravity and Kaluza Klein unify ∗ strings yield ﬁnite gravity. ∗ Λ?

TASI (June 5, 2003) Paul Langacker (Penn) The Two Paths: Unification or Compositeness • The Bang – unification of interactions – grand desert to unification (GUT) or Planck scale – elementary Higgs, supersymmetry (SUSY), GUTs, strings

– possibility of probing to MP and very early universe – hint from coupling constant uniﬁcation – tests ∗ light (< 130 − 150 GeV) Higgs (LEP 2, TeV, LHC) ∗ absence of deviations in precision tests (usually) ∗ supersymmetry (LHC)

∗ possible: mb, proton decay, ν mass, rare decays ∗ SUSY-safe: Z0; seq/mirror/exotic fermions; singlets – variant versions: large dimensions, low fundamental scale, brane worlds

TASI (June 5, 2003) Paul Langacker (Penn) • The Whimper – onion-like layers – composite fermions, scalars (dynamical sym. breaking) – not like to atom → nucleus +e− → p + n → quark – at most one more layer accessible (LHC) – rare decays (e.g., K → µe) ∗ severe problem ∗ no realistic models – eﬀects (typically, few %) expected at LEP & other precision observables (4-f ops; Zb¯b; ρ0; S, T, U) – anomalous VVV , new particles, future WW → WW – recent variant: Little Higgs

TASI (June 5, 2003) Paul Langacker (Penn) Beyond the MSSM

(aka, what to look for in string constructions)

Even if supersymmetry holds, MSSM is unlikely to be the full story

Most of the problems of standard model remain (hierarchy of electroweak and Planck scales is stabilized but not explained)

µ problem introduced

Could be that all new physics is at GUT/Planck scale, but there could be remnants surviving to TeV scale

TASI (June 5, 2003) Paul Langacker (Penn) Extreme example: Fundamental scale MF ∼ 1 − 100 TeV √ 18 M¯ P l = 1/ 8πGN ∼ 2.4 × 10 GeV −δ Assume δ extra dimensions with volume Vδ MF

¯ 2 2+δ 2 MP l = MF Vδ MF

(Introduces new hierarchy problem) Black holes, graviton emission at colliders!

TASI (June 5, 2003) Paul Langacker (Penn) Second extreme example: time varying couplings and parameters

(Murphy et al, astro-ph/0209488)

TASI (June 5, 2003) Paul Langacker (Penn) Suggested by absorption by molecular clouds (Webb et al) Expected at some level in string/brane models in which couplings are related to moduli, which could be time varying 1 λφ µν Lelm ∼ 1 + FµνF + ··· 4 MPL However, natural scale

+43 −1 α/α˙ ∼ MPL ∼ 10 s ,

while Webb et al. results suggest

−15 −1 −66 α/α˙ ∼ 10 yr ∼ 10 MPL

May be analogous to dark energy: Type IA supernova and CMB suggest −124 4 ρvac ∼ 10 MPL 6= 0

TASI (June 5, 2003) Paul Langacker (Penn) α variation likely correlated with variations in other dimensionless couplings, mass ratios (PL, Segre, Strassler; Calmet, Fritzsch)

Will mainly consider less extreme examples of new interactions, particles at TeV scale

TASI (June 5, 2003) Paul Langacker (Penn) Uniﬁcation: from the Top Down

Bottom up: usually motivated by SM problems

Top down:

• Ambitious/promising string/M theory paradigm. However:

– many realms of perturbative and non-perturbative M theory – compactiﬁcation – dilaton/moduli

– SUSY breaking, Λcosm

TASI (June 5, 2003) Paul Langacker (Penn) • Detailed study of speciﬁc constructions:

– develop techniques – suggest new TeV-scale physics – suggest promising new directions

(M. Cvetiˇc, PL; G. Cleaver, L. Everett, J.R. Espinosa, J. Wang, G. Shiu)

• Unlikely to ﬁnd fully realistic theory soon. Studies emphasize speciﬁc features:

– fundamental scale Mfund Mpl (LED)

– SUSY breaking, Λcosm – dilaton/moduli stabilization

– semi-realistic 4D gauge theories containing MSSM (Mfund ∼ Mpl)

TASI (June 5, 2003) Paul Langacker (Penn) To GUT or not to GUT

• String → GUT → MSSM (+ extended?) or String → MSSM (+ extended?) – gauge uniﬁcation – quantum numbers for family (15-plet) – seesaw ν mass scale/leptogenesis

– mb/mτ

– large lepton mixings – other fermion mass relations – additional GUT scale; no adjoints in simple heterotic – hierarchies, e.g. doublet-triplet – proton decay

TASI (June 5, 2003) Paul Langacker (Penn) • Gauge uniﬁcation: GUTs, string theories

2 – α +s ˆZ → αs = 0.130 ± 0.010 16 – MG ∼ 3 × 10 GeV 17 – Perturbative string: ∼ 5 × 10 GeV (10% in ln MG). Exotics: O(1) corrections.

TASI (June 5, 2003) Paul Langacker (Penn) TASI (June 5, 2003) Paul Langacker (Penn) Discovery of Pluto

1781: Uranus observed by Sir William Herschel

1846: Uranus orbit anomalies → Neptune predicted (John Adams, Jean Leverrier)

1846: Neptune observed in predicted location (in Berlin)

1900’s: Further Uranus anomalies → Pluto predicted by “computers” (several possible locations)

1930: Pluto discovered in one of predicted locations (Clyde Tombaugh)

1978: Charon discovered → mPluto too small to aﬀect Uranus orbit

TASI (June 5, 2003) Paul Langacker (Penn) Direct compactiﬁcation

• String → MSSM (+ extended?) in 4D

• Constructions with SU(3) × SU(2) × U(1) and 3 families

• Usually additional surviving gauge groups – quasi-hidden non-abelian – U(1)0 (non-anomalous), often family non-universal

• Usually exotic chiral supermultiplets – standard model singlets – quarks/leptons w. non-standard SU(2)×U(1) – extra Higgs doublets

– possibly Higgs/lepton mixing (6RP )

TASI (June 5, 2003) Paul Langacker (Penn) Things to watch for

Examples of new physics which could emerge in speciﬁc constructions

TASI (June 5, 2003) Paul Langacker (Penn) Gauge uniﬁcation?

• Gauge uniﬁcation usually present in modiﬁed form (higher Kaˇc- Moody, exotics, moduli boundary conditions) – no new exotics? – complete GUT multiplets? – cancellations (accidental or otherwise)?

TASI (June 5, 2003) Paul Langacker (Penn) A TeV scale Z0?

• Motivations

– Strings, GUTs, DSB often involve extra U(1)0(GUTs require extra

ﬁne tuning for MZ0 MGUT) – String models: radiative breaking of electroweak (SUGRA or gauge mediated) often yield EW/TeV scale Z0 (unless breaking along ﬂat direction → intermediate scale) – Solution to µ problem

W ∼ hSHuHd,

S = standard model singlet, charged under U(1)0. hSi breaks 0 U(1) , µeff = hhSi (like NMSSM, but no domain walls)

TASI (June 5, 2003) Paul Langacker (Penn) • Experimental limits (precision and collider) model dependent, but 0 typically MZ0 > (500 − 800) GeV and Z − Z mixing |δ| < few×10−3

> • Models: MZ0 ∼ 10MZ by either modest tuning (Demir et al), or by secluded sector (Erler, PL, Li)

• Implications – Exotics – FCNC (especially in string models) – Non-standard Higgs masses, couplings (doublet-singlet mixing) – Non-standard sparticle spectrum – Enhanced possibility of EW baryogenesis (Kang, Liu, PL, Li)

TASI (June 5, 2003) Paul Langacker (Penn) Exotics

• L-singlets

• R-doublets

• Standard model singlets

• Extra Higgs doublets

• Fractional charges (e.g., 1/2)

• Ordinary/hidden sector mixing

• Higgs/lepton mixing

TASI (June 5, 2003) Paul Langacker (Penn) Flat directions

• Two SM singlets charged under U(1)0

02 02 2 2 2 2 g Q 2 2 2 V (S1,S2) = m |S | + m |S | + (|S | − |S |) 1 1 2 2 2 1 2

2 2 Break at EW scale for m1 + m2 > 0, at intermediate scale for 2 2 m1 + m2 < 0 (stabilized by loops or HDO)

• Small Dirac (or other fermion) masses from

ˆ !PD c S W ∼ Hˆ 2LˆLνˆ L M

• Possible cosmological implications

TASI (June 5, 2003) Paul Langacker (Penn) Family Structure/Fermions

• Differences in embeddings for third family? (Family symmetries in 4d effective field theory vs string dynamics) – Hierarchy of masses – Mixings? – FCNC

• Sources/magnitudes of CP phases. Strong CP.

• Majorana neutrino masses? Diagonal terms?

• WYSINWYG – Some particles may be composite (e.g., intersecting brane construction) – Family disappearance under vacuum restabilization

TASI (June 5, 2003) Paul Langacker (Penn) Asymptotic freedom in quasi-hidden sector

• SUSY breaking/moduli stabilization

• Motivated parametrizations of SUSY breaking

• Compositeness

• Fractional charge conﬁnement

TASI (June 5, 2003) Paul Langacker (Penn) Conclusions

• Standard Model extremely successful, but is clearly incomplete

• Most aspects tested. Precision electroweak points towards decoupling types of new physics (e.g., SUSY, uniﬁcation)

• Superstring/M theory extremely promising theoretical direction

• Need vigorous bottom-up experimental and theoretical probes to test SM/MSSM and search for alternatives

• Need vigorous top-down program to connect to experiment and suggest new TeV scale physics

• May be much beyond MSSM at TeV scale

TASI (June 5, 2003) Paul Langacker (Penn)