BSM Theory: The SM and Beyond Patrick PaDDy Fox Topics to (try to) - - PowerPoint PPT Presentation

Patrick “PaDDy” Fox

BSM Theory: The SM and Beyond

!2

Topics to (try to) cover

• Review of the SM its “Bugs and Features”
• Case study in BSM: SUSY
• General BSM
• Dark Matter at Colliders and in the Cosmos
• Model Building in the LHC era
• Conclusions

dR dER = NT ρ mχ Z vmax

vmin

d3vf(v(t))dσ|v| dER

• -..-.

..-..

!3

The Standard Model

+ Gauge principle

Dµ = @µ + igsT aAa

µ + ig2

j 2 W j

µ + ig1Y Bµ.

!3

The Standard Model

+ Gauge principle

Dµ = @µ + igsT aAa

µ + ig2

j 2 W j

µ + ig1Y Bµ.

Particle Fever

!4

L = L0 + L1 + L2 + L3 + L4 + L5 + L6 + . . .

The Standard Model

L0 = Λ4

The cosmological constant…hard to measure @LHC

L1 = µ3Φ

Need a gauge singlet scalar, none in SM.

L2 = ±µ2|H|2

Mass term of SM Higgs

L3 = µ ξη

Fermion mass term. Sterile neutrinos? Gauge kinetic terms, fermion kinetic terms, Higgs self- coupling, Yukawa couplings

L4 = −1 4FµνF µν + ¯ Q / DQ + |DµH|2 − λ|H|4 + yHQU c + . . .

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L = L0 + L1 + L2 + L3 + L4 + L5 + L6 + . . .

The Standard Model

L0 = Λ4

The cosmological constant…hard to measure @LHC

L1 = µ3Φ

Need a gauge singlet scalar, none in SM.

L2 = ±µ2|H|2

Mass term of SM Higgs

L3 = µ ξη

Fermion mass term. Sterile neutrinos? Gauge kinetic terms, fermion kinetic terms, Higgs self- coupling, Yukawa couplings

L4 = −1 4FµνF µν + ¯ Q / DQ + |DµH|2 − λ|H|4 + yHQU c + . . .

Come back to these later

The Standard Model

The SM contains 18 physical parameters, the Lagrangian contains many more e.g.

!5

Y ij

u QiU c j H + Y ij d QiDc j e

H

Yu,d

3 × 3 C matrix ⇒ 2 × 18 params

:

The quark kinetic terms ( etc. ) have broken to

¯ Q / DQ

U(3)3

U(1)B

27 gens. / →1 gens

Can make 26 field redefinitions to alter parameters

36 − 26 = 10

6 quark masses, 3 angles and 1 phase of CKM

The Standard Model

What are the 18 physical parameters? How do we explain them?

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g1, g2, g3

(α, sin θW , αS)

hHi ⌘ v, λh

me,µ,τ

mu,d,c,s,b,t

  c12c13 s12c13 s13eiδ −s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13 s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ c23c13  

VCKM

θQCD, mνe,νµ,ντ , VP MNS

3 2 3 6 4 1+3+4

(Depends on neutrino mass model)

= 18

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Bugs and Features

Gauge coupling unification 1 generation of SM matter fits into , of SU(5) SM + N fits into of SO(10)

d dtα1

i

= − bi 2π

are bi = (b1, b2, b3) = (−33/5, −1, 3) 10 19 6 7).

coefficients are bi = (b1, b2 , bi = (−41/10, 19/6, 7).

5 10 15 10 20 30 40 50 60

log10HmêGeVL a-1

SU(3)

b = 11 3 N − 2 3 X

fermions

C(rf) − 1 3 X

bosons

C(rb).

SU(2)

U(1)[g1 = p 5/3g0]

¯ 5 10

16

SM MSSM

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Bugs and Features

Gauge coupling unification

5 10 15 10 20 30 40 50 60

log10HmêGeVL a-1

Hint for what new physics? Many possible combinations of weak scale states give good unification e.g. MSSM, NMSSM, 6 Higgs doublets,

5 10 15 20 25 5

• 2 N2 N1

2 2 4 N2 N3 1015 GeV 1019 GeV

[Giudice, Romanino, ph/0406088]

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Bugs and Features

Gauge coupling unification

5 10 15 10 20 30 40 50 60

log10HmêGeVL a-1

Hint for what new physics? Many possible combinations of weak scale states give good unification e.g. MSSM, NMSSM, 6 Higgs doublets,

5 10 15 20 25 5

• 2 N2 N1

2 2 4 N2 N3 1015 GeV 1019 GeV

[Giudice, Romanino, ph/0406088]

P r e d i c t i

• n

s ? N e w s t a t e s a t w e a k s c a l e w i t h S M c h a r g e N e w s t a t e s a t G U T s c a l e — p r

• t
• n

d e c a y !

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Gauge coupling unification

log10HmêGeVL a-1

X,Y lead to proton decay, generate dim-6 operator

g2

X

M 2

X

(¯ uγµd) (¯ eγµu)

Γ ∼ ✓ gX M 2

X

◆2 m5

p × NP

τ ∼ 1032(24)yr

Use Avogadro’s number to our advantage

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Gauge coupling unification

log10HmêGeVL a-1

X,Y lead to proton decay, generate dim-6 operator

g2

X

M 2

X

(¯ uγµd) (¯ eγµu)

Γ ∼ ✓ gX M 2

X

◆2 m5

p × NP

τ ∼ 1032(24)yr

Use Avogadro’s number to our advantage

SuperK

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Bugs and Features

Fermion masses, and mixings

e Μ Τ d s b u c t

Mass (GeV) 1 10 100 10−1 10−2 10−3

Chiral symmetry What explains this hierarchy? Technically natural

δmf ∼ g2 16π2 mf log ✓ Λ mf ◆

SM has no tree-level FCNC’s BSM physics probed indirectly for FCNC searches See Jure Zupan’s lectures

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Bugs and Features

Fermion masses, and mixings

e Μ Τ d s b u c t

Mass (GeV) 1 10 100 10−1 10−2 10−3

Neutrinos?

Chiral symmetry What explains this hierarchy? Technically natural

δmf ∼ g2 16π2 mf log ✓ Λ mf ◆

SM has no tree-level FCNC’s BSM physics probed indirectly for FCNC searches See Jure Zupan’s lectures

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Fermion masses, and mixings

Λ ≥ 100 TeV

Λ ≥ 1000 − 10000 TeV

BSM physics must have a carefully controlled flavour structure e.g. MFV

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Bugs and Features

(see A. Shukraft lectures ) Neutrino masses-another window to high scales? Not present in the SM, but observed in Nature

yLHN

Dirac?

y ∼ 10−12

Lepton number Majorana? L5 = 1

Λ (LH) (LH)

Lepton number

Λ ∼ 1014 GeV

Only dim-5 op….already observed? Neutrino model building

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Dial “N” for neutrino

yLHN + MNN → y2 M (LH) (LH)

0νββ

See-saw mechanism, new states at high scale Low energy observable

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Dial “N” for neutrino

yLHN + MNN → y2 M (LH) (LH)

L3

L5

{

{

0νββ

See-saw mechanism, new states at high scale Low energy observable

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Bugs and Features

Strong CP problem

L4 ⊃ ✓QCDGa

µνGa αβ✏µναβ

Dim-4 term violates CP (like E.B) Leads to neutron electric dipole moment

dn ≤ 10−26e cm

dn ∼ θ egA (4πfπ)2 mumd mu + md log m2

n

m2

π

∼ θ × 10−16e cm

Massless up quark? (probably not) Symmetry protection? e.g. Peccei-Quinn, Nelson-Barr





 

        

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Bugs and Features

Hierarchy (Naturalness) problem

L2 = ±µ2|H|2

Why is so much smaller than ?

μ

MGUT, MPl

Unlike fermions (and gauge bosons) no symmetry protects scalar mass parameter 1.Nature is fine-tuned (anthropics?) 2.The SM has no high scales (gravity?, unification?) 3.New dynamics/symmetries keeps mass scale low

!16

Bugs and Features

Hierarchy (Naturalness) problem

L2 = ±µ2|H|2

Why is so much smaller than ?

μ

MGUT, MPl

Unlike fermions (and gauge bosons) no symmetry protects scalar mass parameter 1.Nature is fine-tuned (anthropics?) 2.The SM has no high scales (gravity?, unification?) 3.New dynamics/symmetries keeps mass scale low

There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact. —Mark Twain

!17

L = |∂µφ|2 + ψi6∂ψ mfψψ yφψψ µ2 |φ|2 λ |φ|4

∆mf ∼ − y2 16π2 mf log ✓ Λ mf ◆

Hierarchy (Naturalness) problem

etc

∆µ2 ∼ λ − y2 16π2 Λ2 − y2 16π2 m2

f log Λ

mf

Scalars are sensitive to the highest scale in the theory! Expect new physics ( ) at

Λ

4π g mh

!17

L = |∂µφ|2 + ψi6∂ψ mfψψ yφψψ µ2 |φ|2 λ |φ|4

∆mf ∼ − y2 16π2 mf log ✓ Λ mf ◆

Possible solution?

Hierarchy (Naturalness) problem

etc

∆µ2 ∼ λ − y2 16π2 Λ2 − y2 16π2 m2

f log Λ

mf

Scalars are sensitive to the highest scale in the theory! Expect new physics ( ) at

Λ

4π g mh

!18

Hierarchy (Naturalness) problem

δm2

h = αtΛ2 t + αgΛ2 g + αhΛ2 h

αt = 3m2

t

4π2v2, αg = −6m2

W + 3m2 Z

16π2v2 , αh = − 3m2

h

16π2v2

SM Higgs sensitivity (how low can you go)

Di(mh) ≡

• ∂ log m2

h

∂ log Λ2

i

• = |αi|Λ2

i

m2

h

(One) Measure of fine tuning: No guaranteed discovery, unlike Higgs mechanism Should not stop us looking!!

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Hierarchy (Naturalness) problem

δm2

h = αtΛ2 t + αgΛ2 g + αhΛ2 h

αt = 3m2

t

4π2v2, αg = −6m2

W + 3m2 Z

16π2v2 , αh = − 3m2

h

16π2v2

SM Higgs sensitivity (how low can you go)

Di(mh) ≡

• ∂ log m2

h

∂ log Λ2

i

• = |αi|Λ2

i

m2

h

(One) Measure of fine tuning: d

• e

s N a t u r e No guaranteed discovery, unlike Higgs mechanism Should not stop us looking!!

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Supersymmetry…a BSM case study Bosons Fermions

SM Field SU(3) SU(2) U(1) MSSM partner Superfield qi (LH quarks) 3 2

1 6

˜ qi (LH squarks) Qi uc

i (RH top, charm, up)

¯ 3 1 − 2

3

˜ uc

i (RH stop, scharm, sup)

Uc

i

dc

i (RH bottom, strange, down)

¯ 3 1

1 3

˜ dc

i (RH sbottom, sstrange, sdown)

Dc

i

`i (LH leptons) 1 2 − 1

2

˜ `i (LH sleptons) Li ec

i (RH tau, muon, electron)

1 1 1 ˜ ec

i (RH stau, smuon, selectron)

Ec

i

hu (hd) (up-type (down-type) Higgs) 1 2

1 2

` − 1

2

´ ˜ hu “ ˜ hd ” (up-type (down-type) higgsino) Hu (Hd)

Superpartners have the same couplings as SM partners If SUSY (softly) broken they have different masses Many new interactions…>100 new parameters!

(more than) Doubling of the spectrum

gluino 8 1 0 gluino W/Z 1 3 0 Wino/Zino B/photon 1 1 0 bino/photino

Many constrained by flavour, CP-violation SUSY breaking models (GMSB, AMSB ,…) predict relations

!19

Supersymmetry…a BSM case study Bosons Fermions

SM Field SU(3) SU(2) U(1) MSSM partner Superfield qi (LH quarks) 3 2

1 6

˜ qi (LH squarks) Qi uc

i (RH top, charm, up)

¯ 3 1 − 2

3

˜ uc

i (RH stop, scharm, sup)

Uc

i

dc

i (RH bottom, strange, down)

¯ 3 1

1 3

˜ dc

i (RH sbottom, sstrange, sdown)

Dc

i

`i (LH leptons) 1 2 − 1

2

˜ `i (LH sleptons) Li ec

i (RH tau, muon, electron)

1 1 1 ˜ ec

i (RH stau, smuon, selectron)

Ec

i

hu (hd) (up-type (down-type) Higgs) 1 2

1 2

` − 1

2

´ ˜ hu “ ˜ hd ” (up-type (down-type) higgsino) Hu (Hd)

Superpartners have the same couplings as SM partners If SUSY (softly) broken they have different masses Many new interactions…>100 new parameters!

(more than) Doubling of the spectrum

gluino 8 1 0 gluino W/Z 1 3 0 Wino/Zino B/photon 1 1 0 bino/photino

Many constrained by flavour, CP-violation SUSY breaking models (GMSB, AMSB ,…) predict relations

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Supersymmetry

WMSSM = YUU cQHu − YDDcQHd − YEEcLHd + µHuHd

H0

u

tR tL ˜ H0

u

tR ˜ tL ˜ H0

u

˜ tR tL

Flip two

Yukawa Gauge Gauge

!20

Supersymmetry

WMSSM = YUU cQHu − YDDcQHd − YEEcLHd + µHuHd

H0

u

tR tL ˜ H0

u

tR ˜ tL ˜ H0

u

˜ tR tL

Flip two

Yukawa Gauge Gauge

Extended Higgs sector Higgs modifications

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Supersymmetry

WMSSM = YUU cQHu − YDDcQHd − YEEcLHd + µHuHd

H0

u

tR tL ˜ H0

u

tR ˜ tL ˜ H0

u

˜ tR tL

Flip two

Yukawa Gauge Gauge

Extended Higgs sector Higgs modifications

!21

Supersymmetry New fields allow for new interactions (EFT philosophy)

W∆B,L = ijk

1 QiLjDc k + ijk 2 LiLjEc k + i 3LiHu + ijk 4 Dc i Dc jU c k .

∆L = 1

∆B = 1

∆L = 1

∆L = 1

Forbid these (RPV) operators with a parity (R-parity)

Γ ∼ κ1κ4 16π m5

p

m4

˜ q

Proton lifetime:

κ < 10−12!

LPOP 1.SM and partners don’t mix 2.SUSY states pair produced 3.Lightest parity odd particle stable (DM?)

SM → SM

BSM → −BSM

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Supersymmetry New fields allow for new interactions (EFT philosophy)

W∆B,L = ijk

1 QiLjDc k + ijk 2 LiLjEc k + i 3LiHu + ijk 4 Dc i Dc jU c k .

∆L = 1

∆B = 1

∆L = 1

∆L = 1

Forbid these (RPV) operators with a parity (R-parity)

Γ ∼ κ1κ4 16π m5

p

m4

˜ q

Proton lifetime:

κ < 10−12!

LPOP 1.SM and partners don’t mix 2.SUSY states pair produced 3.Lightest parity odd particle stable (DM?) More later….

SM → SM

BSM → −BSM

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Supersymmetry Complicated spectrum, details depend on model GMSB, Effective/Natural SUSY, Dirac gauginos…. Many, many interesting collider signatures Lightest coloured states made first, decays involve MET Compressed/Stealth spectra can hide SUSY (a little) Electroweakino sector starting to be probed (DM) SUSY is a great signal generator

h0 H0 A0 H± ˜ N1 ˜ N2 ˜ N3 ˜ N4 ˜ C1 ˜ C2 ˜ g ˜ dL ˜ uL ˜ uR ˜ dR ˜ eL ˜ eR ˜ νe ˜ t1 ˜ t2,˜ b2 ˜ b1 ˜ τ1 ˜ τ2 ˜ ντ

GMSB Natural

stopL, stopR, sbottomL higgsino gluino Wino

!23

!23

p p

• χ0

• χ±

W±

• χ0

• χ0

Z p p

• χ0

• χ±

W±

• χ0

• χ0

H

!23

p p

• χ0

• χ±

W±

• χ0

• χ0

Z p p

• χ0

• χ±

W±

• χ0

• χ0

H

q γ (W± ) g g S

• G
• S
• χ0

1 (

χ±

1 )

• qL

!23

p p

• χ0

• χ±

W±

• χ0

• χ0

Z p p

• χ0

• χ±

W±

• χ0

• χ0

H

p p ¯ ˜ t ˜ t ¯ t ˜ χ0

t ˜ χ0

p p ˜ g ˜ g ¯ t t ˜ χ0

t ¯ t ˜ χ0

p p ˜ g ˜ g ¯ t b ˜ χ+

W∗+ ˜ χ0

t ¯ b ˜ χ−

W∗− ˜ χ0

p p ˜ g ˜ g ¯ t ˜ t t ˜ χ0

t ¯ ˜ t ¯ t ˜ χ0

p p ˜ g ˜ g ¯ t ˜ t c ˜ χ0

t ¯ ˜ t ¯ c ˜ χ0

q γ (W± ) g g S

• G
• S
• χ0

1 (

χ±

1 )

• qL

!24

General BSM lessons

Top partners (fermions/bosons) Higgs sector modifications LPOPs, parity, DM, MET Extra matter in fundamental and adjoint reps. New gauge groups? Lighter, more weakly coupled particles? Resonances?

!24

General BSM lessons

Top partners (fermions/bosons) Higgs sector modifications LPOPs, parity, DM, MET Extra matter in fundamental and adjoint reps. New gauge groups? Lighter, more weakly coupled particles? Resonances? Composite Higgs

!24

General BSM lessons

Top partners (fermions/bosons) Higgs sector modifications LPOPs, parity, DM, MET Extra matter in fundamental and adjoint reps. New gauge groups? Lighter, more weakly coupled particles? Resonances? Composite Higgs Randall Sundrum

!24

General BSM lessons

Top partners (fermions/bosons) Higgs sector modifications LPOPs, parity, DM, MET Extra matter in fundamental and adjoint reps. New gauge groups? Lighter, more weakly coupled particles? Resonances? Little Higgs Composite Higgs Randall Sundrum

Twin Higgs

Higgs is a PNGB, and Higgs potential is O(8) symmetric

SMA × SMB × Z2 L ⊃ y QAHAU c

A + y QBHBU c B

V = −m2H†H + λ

• H†H

2

[Chacko, Goh, Harnik]

O(8) → O(7) :7 Goldstone bosons, 3 eaten by B gauge bosons

H = ✓ HA HB ◆ = eihata/f B B @ f 1 C C A

Twin Higgs

Higgs is a PNGB, and Higgs potential is O(8) symmetric

SMA × SMB × Z2 L ⊃ y QAHAU c

A + y QBHBU c B

V = −m2H†H + λ

• H†H

2

[Chacko, Goh, Harnik]

O(8) → O(7) :7 Goldstone bosons, 3 eaten by B gauge bosons

H = ✓ HA HB ◆ = eihata/f B B @ f 1 C C A

SM Higgs

Twin Higgs

Gauge and Yukawa interactions explicitly break the O(8) Mass for Higgs?

3 8π2 Λ2 ⇣ y2

AH† AHA + y2 BH† BHB

⌘ Z2 ⇒ yA = yB 3 8π2 Λ2y2H†H

Loop corrections to mass is O(8) symmetric, does not lead to quadratically divergent Higgs mass

H = ✓ HA HB ◆ = eihata/f B B @ f 1 C C A

EFT aside

Low energy degrees of freedom, non-linearly realized symm. ….

H =    h

if √ h†h sin √ h†h f

f cos

√ h†h f

   =   ih f −

1 2f

√ h†h   + . . .

˜ h ˜ h − yt

2f

ytf ˜ h ˜ h yt yt

+

12

Quadratic divergences cancel, states running in loop have no SM charge, same spin A B L ∼ y QAHU c

A + y QB

✓ f − |H|2 2f 2 ◆ U c

B

Top sector

(3 is just a number) Cancelling states not coloured: small production x-sec at LHC

To separate v and f and make the SM Higgs lie mostly in A introduce soft breaking µ2

A|HA|2

δm2

h ∼ 3ytm2 t

4π2 ✓f v ◆2 log Λv mtf hHAi = vSM ⌧ hHBi = f ⇠ 1 TeV

˜ h ˜ h − yt

2f

ytf ˜ h ˜ h yt yt

+

12

Tuning grows with f/v

∆ =

• 2δm2

h

m2

h

• −1

To separate v and f and make the SM Higgs lie mostly in A introduce soft breaking µ2

A|HA|2

δm2

h ∼ 3ytm2 t

4π2 ✓f v ◆2 log Λv mtf

f/v~3-5

hHAi = vSM ⌧ hHBi = f ⇠ 1 TeV

˜ h ˜ h − yt

2f

ytf ˜ h ˜ h yt yt

+

12

Tuning grows with f/v

∆ =

• 2δm2

h

m2

h

• −1

Higgs portal between A and B sectors

V = −m2 ⇣ H†

AHA + H† BHB

⌘ + λ ⇣ H†

AHA + H† BHB

⌘2

• Higgs mixing and corrections to Higgs pheno at v2

f 2

• Higgs invisible decay width, to light B sector stuff

[1411.3310]