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Home , Matter

The of The ultimate goal (for some at least...)

A consistent view of the world AGE-OLD Questions

What are the fundamental constituents which comprise the ?

How do they interact?

What holds them together?

Who will win the World Championship? AGE-OLD Questions

What are the fundamental constituents which comprise the universe?

How do they interact?

What holds them together?

Who will win the World Championship? AGE-OLD Questions

What are the fundamental constituents which comprise the universe?

How do they interact?

What holds them together?

Who will win the World Championship? AGE-OLD Questions

What are the fundamental constituents which comprise the universe?

How do they interact?

What holds them together? circa 425 BC

Earth Fire Air “The periodic table.”

Sidney Harris Periodic Table circa 425 BC

Earth Water Fire Air “The periodic table.”

Sidney Harris Periodic Table circa 425 BC

Earth Water Fire Air “The periodic table.”

Sidney Harris Periodic Table circa 425 BC

Earth Water Fire Air “The periodic table.”

Sidney Harris Periodic Table circa 425 BC

Earth Water Fire Air “The periodic table.”

Compact Easy to remember Fits on a T-shirt Periodic Table circa 425 BC

Earth Water Fire Air “The periodic table.”

Compact Easy to remember Sidney Harris Fits on a T-shirt Periodic Table circa 425 BC

Earth Water Fire Air “The periodic table.”

Compact Easy to remember Sidney Harris

Fits on a T-shirt Physics Beyond the Standard Model? The Higgs field? Unification

Earth : Since the four elements can Water transform into each other, it is reasonable to assume that Fire there is only one fundamental substance Air and the four elements are “The periodic table.” just different manifestations Compact of it! Easy to remember Fits on a T-shirt Periodic Table circa 1900

Dimitri Mendeleev (1834-1907) Periodic Table circa 1900

Dimitri Mendeleev (1834-1907)

66 elements! The Standard Model and Beyond PredictionsAtoms Event simulations Challenge The Standard Model: matter (1)

✦ At the atomic scale, matter is composed of :! ! ✤ A core: the nucleus, made of! ★ ( )!

★ ( )! ! ✤ Peripheral ( )

✦ Naively, protons and neutrons are composed objects:! ! ✤ : two up and one down

✤ : one up quarks and two down quarks! ! ! ! !

✦In , they are dynamical objects:! ! ✤ Made of many interacting quarks and ! (see later)

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 3 The Standard Model and Beyond PredictionsAtoms Event simulations Challenge The Standard Model: matter (1)

✦ At the atomic scale, matter is composed of atoms:! ! ✤ A core: the nucleus, made of! ★ Protons ( )!

★ Neutrons ( )! ! ✤ Peripheral electrons ( )

✦ Naively, protons and neutrons are composed objects:! ! ✤ Proton: two up quarks and one

✤ Neutron: one up quarks and two down quarks! ! ! ! !

✦In reality, they are dynamical objects:! ! ✤ Made of many interacting quarks and gluons! (see later)

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 3 The Standard Model and ElementaryBeyond PredictionsMatter Constituents Event simulations I Challenge The Standard Model: matter (2)

✦ Elementary matter constituents! ! ! ! ! ✤ Up quarks! ! ! ✤ Down quarks! } ! Protons and neutrons Nucleus ! ! ! Atoms ✤ Electrons }

The ✦ Neutrons can be converted to protons: the beta decay

Sidney Harris

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 4 The Standard Model and ElementaryBeyond PredictionsMatter Constituents Event simulations II Challenge The Standard Model: matter (3)

✦ Elementary matter constituents: we have three families

✤ Three up-type quarks! ★ Up ( u )! ★ Charm ( c )! ★ To p ( t )! ✤ Three down-type quarks! ★ Down ( d )! ★ Strange ( s )! ★ Bottom ( b )! ✤ Three ! ★ ( ⌫ e )! ★ ( ⌫ µ )! ★ ( ⌫ ⌧ )! ✤ There charged ! ★ Electron ( e )! ★ Muon ( µ )! ★ Tau ( ⌧ ) The only differences are the ! All other properties are identical

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 5 The Standard Model and BeyondFour fundamental Predictions Interactions Event simulations Challenge The Standard Model: interactions

!✦ ! ✤ Interactions between charged (quarks, charged leptons)! ✤ Mediated by massless

!✦ Weak interactions! ✤ Interactions between all matter fields! ✤ Mediated by massive weak W- and Z-bosons

!✦ Strong interactions! ✤ Interactions between colored particles (quarks)! ✤ Mediated by massless gluons g ✤ Responsible for binding protons and neutrons within the nucleus

!✦ ! ✤ Not included in the Standard Model

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 6 The Standard Model and Beyond The Predictions Higgs Event simulations Challenge The last pieces: the

✦ The masses of the particles! ✤ Elegant to introduce them !

✤ Price to pay: a new particle, the so-called Higgs boson!

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 7 The Standard Model and Beyond The Predictions Higgs boson Event simulations Challenge The last pieces: the Higgs boson

✦ The masses of the particles! ✤ Elegant mechanism to introduce them !

✤ Price to pay: a new particle, the so-called Higgs boson! discovered in 2012

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 7 The Standard Model and Beyond Predictions Event simulations Challenge ThePeriodic Standard Table Model: circa 2017the full AD picture

✦ All the particles have been observed:! ✤ The last one: the Higgs (2012)! ✤ The next-to-last one: the (1995)

✦ Tested over 30 orders of magnitude:! ✤ from 10-18 eV ( limit)! ✤ to 10+13 eV (LHC ) Compact Easy to remember Fits on a T-shirt

The Standard Model (SM) for the strong, weak, and electromagnetic interactions

CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 8 The Standard Model of (2nd ) The Standard Model

• ... provides currently our best understanding of the world • ... is a beautiful theory, based on a few principles • ... has really weird input parameters • ... is an extremly successful theory • There are several reasons to look for theories beyond the SM

• We will now discuss some of these aspects to set the stage The beautiful SM The Beautiful SM

• QFT = QM + SR • Matter content: 3 generations of • Quarks (u,d),(s,c),(b,t) • Leptons (e,νe),(μ,νμ),(τ,ντ) • local gauge symmetry SU(3)c × SU(2)L × U(1)Y + - • 8 gluons, W , W , Z, Photon • Renormalizability • Electroweak symmetry breaking (EWSB) • Higgs boson 2 The Standard Model 2 The Standard Model 2.1 One-page Summary of the World

22.1Gauge2 The One-page The group Standard Standard Summary Model of Model the World SU(3) SU(2) U(1) Gauge group c ⇥ L ⇥ Y 2.1 One-page Summary of the World 2.1ParticleSU(3) One-page contentc SU(2)L SummaryU(1)Y of the World One page⇥ summary⇥ of the world Gauge group Particle content Gauge groupSU(3) SU(2) MatterU(1) Higgs Gauge c ⇥ L ⇥ Y + Gauge group SU(3)uc SU(2)L U(1)Y ⌫ h Particle contentL⇥ Matter⇥ L Higgs Gauge Q = 0 1 (3, 2) 1/3 L = 0 1 (1, 2)-1 H = 0 1 (1, 2)1 B (1, 1)0 0 u dL ⌫ eL h+ h Particle contentBL C Matter LB C HiggsB C Gauge Particle Q = 0 1 (3, 2) 1/3 L = 0 1 (1, 2)-1 H = 0 1 (1, 2)1 A (1, 1)0 @c A @c A 0 @ A duLR u (3, 1)-4/3 e⌫LeR (1, 1) 2 h+ h W (1, 3)0 content B CL B LC B C Q@= 0A 1 (3, 2) 1/3 L =@0 A1 (1, 2)-1 H = 0 @1 A(1, 2)1 B (1, 1)0 c c Matter c c 0 Higgs Gauge uR dR dL (3, 1(3)-4, 1/3) 2/3 eR eL⌫R (1, 1)(12, 1) 0 h W (1G, 3)0 (8, 1)0 B C B C B C @ A @ A @ A + c uuLc (3, 1) ecc ⌫L (1, 1) h W (1, 3) dR R (3, 1) 2/-43/3 ⌫RR (1, 1)2 0 G 0(8, 1)0 Q = 0 1 (3, 2) 1/3 L = 0 1 (1, 2)-1 H = 0 1 (1, 2)1 A (1, 1)0 Lagrangiandc (Lorentz(3, 1) + gauge⌫c + renormalizable)(1, 1) 0 G (8, 1) dLR 2/3 R eL 0 h 0 LagrangianB1 (LorentzC↵ ↵µ⌫ + gauge + renormalizable)B C µ 2 B C 2 = @c GAµ⌫G +...QkDQ/ [email protected] (DAµH)†(D H) µ H†@H A(H†H) +...Yk`QkH(uR)` L LagrangianuR4 (Lorentz(3, 1) +-4/ gauge3 + renormalizable)eR (1, 1) 2 4! W (1, 3)0 1 ↵ ↵µ⌫ µ 2 2 Lagrangian = G G +...Q DQ/ +...(D H)†(D H) µ H†H (H†H) +...Y Q H(u ) µ1⌫ k k µ k` k R ` (Lorentz + gauge + L 4 c ↵ ↵µ⌫ / c µ 2 4! 2 Spontaneous=dR Gµ⌫G symmetry(3+,...1)Q2/k3DQ breakingk+...(⌫DRµH)†(D (H1), 1µ) H0 †H (H†H) +...Yk`QkH(uR)`G (8, 1)0 renormalizable) L 4 4! Spontaneous symmetry breaking0 SpontaneousH H symmetry+ 1 breaking 0 p2 v Lagrangian• ! (Lorentz1 0 + gauge + renormalizable) H H0 + 1 ✓0 ◆ H H0 p+2 • 1•! ! p2v v SSB SU(2)↵ L↵µ⌫ U(1)✓ ✓◆Y◆ U(1)Q µ 2 2 = • Gµ⌫G ⇥+...Qk!DQ/ k+...(DµH)†(D H) µ H†H (H†H) +...Yk`QkH(uR)` L SU(2)4 SU(2)L LU(1)U(1)Y Y U(1)U(1)QQ 4! • • ⇥3 ⇥ !0! 1 2 + B,W ,Z and Wµ ,Wµ W ,W • B,W3 3 !,Z0 0 and W11,W22 W!++,W SpontaneousA, W symmetry,Z and breakingWµµ,Wµµ W ,W • •! ! acquire mass through! Yukawa couplings to Higgs Fermions• Fermions acquire acquire mass mass through through Yukawa couplings couplings to to Higgs Higgs • 1 0 • H H0 + • ! p2 v ✓ ◆ SU(2) U(1) U(1) • L ⇥ Y ! Q 3 0 1 2 + A, W ,Z and W ,W 3 W ,W • ! µ µ ! 3 3 Fermions acquire mass through Yukawa couplings to Higgs •

3 The Higgs mechanism

• The Higgs potential: V =μ2 ϕ†ϕ + λ (ϕ†ϕ)2 • = Ground state = Minimum of V:

2 • If μ >0 (): ϕmin = 0 (no symmetry breaking)

2 2 1/2 • If μ <0: ϕmin = ±v = ±(-μ /λ) These two minima in one dimension correspond to a continuum of minimum values in SU(2). The point ϕ = 0 is now unstable.

• Choosing the minimum (e.g. at +v) gives the vacuum a preferred direction in isospin → spontaneous symmetry breaking

• Perform perturbation around the minimum Higgs self-couplings In the SM, the Higgs self-couplings are a consequence of the Higgs potential after expansion of the Higgs field H~(1,2)1 around the vacuum expectation value which breaks the ew symmetry:

2 2 1 2 2 ⌘ 3 ⌘ 4 V = µ H†H + ⌘(H†H) m h + m h + h H ! 2 h 2 h 4 r 2 2 2 2 Note: v=246 GeV is fixed by the with: mh =2⌘v ,v = µ /⌘ precision measures of GF

In order to completely reconstruct the Higgs potential, on has to: h h • Measure the 3h-vertex: via a measurement of Higgs pair production h ⌘ SM = m 3h 2 h r h h h • Measure the 4h-vertex: more difficult, not accessible at the LHC in the high-lumi h Higgs self-couplings In the SM, the Higgs self-couplings are a consequence of the Higgs potential after expansion of the Higgs field H~(1,2)1 around the vacuum expectation value which breaks the ew symmetry:

2 2 1 2 2 ⌘ 3 ⌘ 4 V = µ H†H + ⌘(H†H) m h + m h + h H ! 2 h 2 h 4 r 2 2 2 2 Note: v=246 GeV is fixed by the with: mh =2⌘v ,v = µ /⌘ precision measures of GF

In order to completely reconstruct the Higgs potential, on has to: h h • Measure the 3h-vertex: via a measurement of Higgs pair production h ⌘ SM = m 3h 2 h r h h h • Measure the 4h-vertex: more difficult, not accessible at the LHC in the high-lumi phase h Higgs self-couplings In the SM, the Higgs self-couplings are a consequence of the Higgs potential after expansion of the Higgs field H~(1,2)1 around the vacuum expectation value which breaks the ew symmetry:

2 2 1 2 2 ⌘ 3 ⌘ 4 V = µ H†H + ⌘(H†H) m h + m h + h H ! 2 h 2 h 4 r 2 2 2 2 Note: v=246 GeV is fixed by the with: Measuringmh =2⌘ vthe,v 3h-couplings:= µ /⌘ precision measures of GF major goal for the high-lumi phase at the LHC In order to completely reconstruct the Higgs potential,The Higgson has particleto: is just the h h • Measure the 3h-vertex:messenger! via a measurement of Higgs pair production h ⌘ SM = m 3h Need2 toh reconstruct the potential r h h h • Measure the 4h-vertex: more difficult, not accessible at the LHC in the high-lumi phase h 3 3 µ µ µ µ iψ¯ γ ∂ ψ iψ¯ ′ γ ∂ ψ ′ iψ¯ γ ∂ ψ iψ¯ ′ γ ∂ ψ ′ SM = ℓ µ ℓ + ℓ µ ℓ + qi µ qi + qi µ qi Not so compact L ′ ′ ℓ=e,µ,τ ℓ =ν ,ν ,ν i q=u,c,t i q =d,s,b ! !e µ τ ! ! ! ! 1 + + µ ν ν µ 1 µ ν ν µ (∂ W ∂ W )(∂ W − ∂ W − ) (∂ Z ∂ Z )(∂ Z ∂ Z ) −2 µ ν − ν µ − − 4 µ ν − ν µ − 8 anymore 1 1 1 (∂ A ∂ A )(∂µAν ∂ν Aµ) (∂ Ga ∂ Ga)(∂µGaν ∂ν Gaµ)+ ∂ h∂µh −4 µ ν − ν µ − − 4 µ ν − ν µ − 2 µ a=1 3 ! 3 λℓv λqv λq′ v ψ¯ℓψℓ ψ¯q ψq ψ¯q′ ψq′ − √ − √ i i − √ i i ℓ=e,µ,τ 2 i q=u,c,t 2 i q′=d,s,b 2 ! ! ! ! ! 2 2 gv + µ 1 gv µ 1 2 2 W W − Z Z 2m h − 2 µ − 2 2cosθ µ − 2 − $ W % " # & ' g µ 2 5 µ 5 + ψ¯ℓγ (4 sin θW 1+γ )ψℓZµ + ψ¯ℓ′ γ (1 γ )ψℓ′ Zµ 4cosθW ⎛ − − ⎞ ℓ=e,µ,τ ℓ′=ν ,ν ,ν ! !e µ τ ⎝ 3 3 ⎠ g µ 8 2 5 µ 4 2 5 ψ¯ γ θ γ ψ Z ψ¯ ′ γ θ γ ψ ′ Z + qi (1 sin W ) qi µ + qi ( sin W 1+ ) qi µ 4cosθW − 3 − 3 − , i q=u,c,t i q′=b,s,b - ! ! ! ! g µ 5 + µ 5 + ψ¯ γ (1 γ )ψ W + ψ¯ γ (1 γ )ψ W − √ νℓ − ℓ µ ℓ − νℓ µ 2 2 ,ℓ=e,µ,τ ℓ=e,µ,τ - ! ! 3 3 g 5 + 5 ′ ¯ µ ′ ¯ ′ µ + ⎛ Vqq ψqγ (1 γ )ψq W + V ∗ ′ ψq γ (1 γ )ψq W −⎞ √ − i µ qq i − i µ 2 2 i q=u,c,t i q=u,c,t ⎜! q′!=d,s,b ! q′!=d,s,b ⎟ ⎜ ⎟ ⎝ ⎠ µ 2 µ 1 µ +gem ψ¯ℓγ ψℓAµ + ψ¯q γ ψq Aµ ψ¯q′ γ ψq′ Aµ − 3 i i − 3 i i , ℓ=e,µ,τ q=u,c,t q′=d,s,b - 3 !8 ! 3 8 ! µ a a µ a a g ψ¯ γ ψ G T ψ¯ ′ γ ψ ′ G T + s qj qi µ ij + qj qi µ ij , i,j a q=u,c,t i,j a q′=d,s,b - ! ! ! 3 ! ! 3! λℓ λq λq′ ψ¯ℓψℓh ψ¯q ψq h ψ¯q′ ψq′ h − √ − √ i i − √ i i ℓ=e,µ,τ 2 i q=u,c,t 2 i q′=d,s,b 2 ! µ +!ν ! + ν µ ! !+µ ν ν +µ +igem ∂µAν W − W + ∂µWν W − A + ∂µWν−W A ∂µAν W − W + µ ν +ν µ − 0∂µWν W − A ∂µWν−W A − µ− +ν + ν µ +µ ν ν +µ +ig cos θ ∂ Z W − W + ∂ W W − Z + ∂ W −W Z ∂ Z W − W W µ ν µ ν 1 µ ν − µ ν g2v g2v 0+ µ ν +ν µ + µ µ 3 ∂µWν W − Z ∂µWν−W Z + Wµ W − h + 2 ZµZ h λvh − − 2 4cos θW − 2 + µ µ + µ ν 2 2 + µ µ + µ ν +gem Wν W − AνA Wµ W − AνA1 + g cos θW Wν W − ZνZ Wµ W − ZνZ 2 −+ µ ν + ν µ + ν µ − +g cos0 θW sin θW 2Wµ W − ZνA W1µ W − AνZ 0 Wµ W − A Zν 1 2 − 2 − 2 g µ +0 +ν +µ +ν g + µ 2 g1 µ 2 λ 4 + Wµ−W − Wν W Wµ−W Wν−W + Wµ W − h + 2 ZµZ h h 2 − 4 8cos θW − 4 8 8 g 0 g2 1 s f abc(∂ Gaν ∂ Ga )GµbGνc s f abcf adeGb Gc GµdGνe − 2 µ − ν µ − 4 µ ν a,b,c a,b,c ! d,e,f!

2 2 m 2 λℓv 3λq v gv gv 2 gem = g sin θW ,v = − (m < 0,λ> 0),mℓ = ,mq = ,mW = ,mZ = ,mh = √ 2m λ √2 √2 2 2cosθW − The weird SM Input parameters

• The SM Lagrangian has 26 input parameters (of course not all are equally important)

• They need to be fixed in order to make predictions • The values and patterns of these parameters are quite bizarre! The Flavor Puzzle The charged masses are very hierarchical, extending over 5 orders of magnitude

up-type down-type leptons Charged fermion masses

9 8.2 7,5 6.6 6.1 6.2 6 5.0 5.0 4,5 3.7 3.3 t b τ log(m/keV) 3 2.7 c s μ u d e 1,5

0 1st generation 2nd generation 3rd generation The Flavor Puzzle Things get even worse when we include neutrino masses! 12Why ...14 the neutrino orders mass of ismagnitude! so small ?" Why the Whyneutrino the neutrino mass is mass so small is so ?small" ?"

& m ) 3 )( # & 1 # $ ! ( $ 12 ! $ & m&) 3!)( m )#3 )( & # 1& #1 # % m top$ quark$ )( " % !'(103 ! " $ $ ! $ ! ( $ 12 ! 12 ! m top%quarkm top )( quark% )( "'103 % '"103 " o#0%M,) % "

0'7) o#0%M,) o#0%M,) 2)

H 0'7)

-"3$(',) 2) 0'7) d&'M(Q,M.=)x0'0A&70=))))))))))))))))))))))))))) H 2) -"3$(',) H -"3$(',) \""U,0Q)+"/40'&,+) O"--U+0''=)E0+('7=)\-0',M.)d&'M(Q,M.=)x0'0A&70=))))))))))))))))))))))))))) \""U,0Q)+"/40'&,+)d&'M(Q,M.=)x0'0A&70=)))))))))))))))))))))))))))O"--U+0''=)E0+('7=)\-0',M.) \""U,0Q)+"/40'&,+) O"--U+0''=)E0+('7=)\-0',M.)

2 2

2 d0,,)*"wp/ d0,,)*"wp/ mq mq Z:)Q")&'3#$)+ )0'7)+Z:)Q")&'3#$)+*+ !])0'7)+)&,)#,"72=)Y)*+$(3)&,)#,"72=) d0,,)*"wp/ mmq ! !] Y) $(3 m" ! " Z:)Q")&'3#$)+!])0'7)+J_)Y)*+$(3)&,)#,"72=) m" ! Q")A"$)+m j)JIJ_)Q")A"$)+O"w) !j)JI O"w) mN Q")A"$)+!N j)JIJ_)O"w) mN ! ! 3 ! ! 2 ! 3 ! 3 2 ! 2

F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?") F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?")F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?")%"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/01('h))) %"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/01('h)))A"'"%01(')%"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/01('h))) 58)6%"7&$0$()U)53%&-)HIJH) J]^) A"'"%01(')A"'"%01(') 58)6%"7&$0$()U)53%&-)HIJH)58)6%"7&$0$()U)53%&-)HIJH) J]^) J]^) The Flavor Puzzle

Quark and mixingThe Flavor Puzzle parameters are quite different! Quark and Lepton Mixing Parameters Quark Mixings Leptonic Mixings

0.976 0.22 0.004 0.85 0.54 0.16 V 0.22 0.98 0.04 U 0.33 0.62 0.72 CKM 3 PMNS 3 ⇠ 20.007 0.04 1 ⇠ 2 0.40 0.59 0.70 4 5 4 5

K.S. Babu (OSU) Probing Flavor Dynamics at the LHC 4/38 Corrections

• Quantum corrections have to be considered (otherwise some predictions very rough!)

• UV divergences appear • of Lagrangian parameters and fields • This leads to running parameters • Scale-dependence governed by renormalization group equations (RGEs) ASYMPTOTIC FREEDOMAsymptotic Freedom

• Gross, Wilczek (’73); Politzer (’73) Renormalization of UV-divergences: Running coupling constant as := αs/(4π)

1 a (µ)= s 2 2 β0 ln(µ /Λ )

0.4 Non-abelian gauge theories: αs(µ) NLO, MSbar 0.35 upper: αs(MZ)=0.121 negative beta-functions αs(MZ)=0.1187 0.3 lower: αs(MZ)=0.1165 das 2 α (M )=0.118 = β0a + ... 0.25 s Z d ln µ2 − s 0.2 where β = 11 C 2 n 0.15 0 3 A − 3 f

0.1 2 asympt. freedom: as for µ 1 10 10 µ (GeV) ⇒ ↘ ↗ • Nobel Prize 2004

I. Schienbein (LPSC Grenoble) Masses in pQCD Oct. 27, 2011 6 / 74 The Standard Model and Beyond Predictions Event simulations Challenge

Proton-ProtonHadron collisions colliders at(1) the LHC

✦The master formula for colliders! ! 1 ! = dPS(n)dx dx f (x ) f (x ) M 2 F a b a/p a b/p b | fi| ! ab Z ✤ We sum over all protonX constituents (a and b here)! ! ✤ We include the parton (the f-function)! ! ! ! a ! ! b ! ! They represent the probability of having a parton a inside the proton carrying a fraction xa of the proton momentum!

Also need parton densities as an input! CERN summer studentCan program not 2015 - (yet)MADGRAPH be calculated Guillaumein lattice Chalons & BenjaminQCD Fuks - August 2015 - 24 The successful SM The Succesful SM

• All the elementary matter particles (quarks, charged leptons, neutrinos) postulated by the SM have been discovered • All the gauge bosons (gluons, W+, W -, Z, photon) predicted by the SU(3)cxSU(2)LxU(1)Y gauge symmetry have been discovered • A -0 particle compatible with the SM Higgs boson has been discovered • No other particles have been found (so far) • The SM is the best-tested theory in the history of ! A very large number of precision measurements have been compared to SM computations at the (multi-)loop level and no evidence for BSM physics has emerged (neither in direct searches nor indirectly due to loop effects) The Succesful SM

• All the elementary matter particles (quarks, charged leptons, neutrinos) postulated by the SM have been discovered • All the gauge bosons (gluons, W+, W -, Z, photon) predicted by the SU(3)cxSU(2)LxU(1)Y gauge symmetry have been discovered • A spin-0 particleAmerica compatible first! with the SM Higgs boson has been discovered • No other particlesThe fermions have been have found been (so far) • The SM is the best-testeddiscovered intheory the USA in the history of science! A very large number of precision measurements have been compared to SM computations at the (multi-)loop level and no solid evidence for BSM physics has emerged (neither in direct searches nor indirectly due to loop effects) The Succesful SM

• All the elementary matter particles (quarks, charged leptons, neutrinos) postulated by the SM have been discovered • All the gauge bosons (gluons, W+, W -, Z, photon) predicted by the SU(3)cxSU(2)LxU(1)Y gauge symmetry have been discovered • A spin-0 particle compatible with the SM Higgs boson has been discovered • No other particles have been found (so far) • The SM is the best-tested theory in the history of science! A very large number of precision measurements have been compared to SM computations at the (multi-)loop level and no solid evidence for BSM physics has emerged (neither in direct searches nor indirectly due to loop effects) The Succesful SM

• All the elementary matter particles (quarks, charged leptons, neutrinos) postulated by the SM have been discovered • All the gauge bosons (gluons, W+, W -, Z, photon) predicted by the SU(3)cxSU(2)LxU(1)Y gauge symmetry have been discovered • A spin-0 particle compatible with the SM Higgs boson has been discovered • No other particles have been found (so far) • The SM is the best-tested theory in the history of science! A very large number of precision measurements have been compared to SM computations at the (multi-)loop level and no solid evidence for BSM physics has emerged (neither in direct searches nor indirectly due to loop effects) The Succesful SM

• All the elementary matter particles (quarks, charged leptons, neutrinos) postulated by the SM have been discovered • All the gauge bosons (gluons, W+, W -, Z, photon) predicted by the SU(3)cxSU(2)LxU(1)Y gauge symmetry have been discovered • A spin-0 particle compatible with the SM Higgs boson has been discovered • No other particlesEurope have beensecond! found (so far) • The SM is the best-tested theory in the history of science! The bosons have been A very large number of precision measurements have been compared to SM computationsdiscovered at in the (multi-)loop level and no solid evidence for BSM physics has emerged (neither in direct searches nor indirectly due to loop effects) The Succesful SM

• All the elementary matter particles (quarks, charged leptons, neutrinos) postulated by the SM have been discovered • All the gauge bosons (gluons, W+, W -, Z, photon) predicted by the SU(3)cxSU(2)LxU(1)Y gauge symmetry have been discovered • A spin-0 particle compatible with the SM Higgs boson has been discovered • No other particles have been found (so far) • The SM is the best-tested theory in the history of science! A very large number of precision measurements have been compared to SM computations at the (multi-)loop level and no solid evidence for BSM physics has emerged (neither in direct searches nor indirectly due to loop effects) The Succesful SM

• All the elementary matter particles (quarks, charged leptons, neutrinos) postulated by the SM have been discovered • All the gauge bosons (gluons, W+, W -, Z, photon) predicted by the SU(3)cxSU(2)LxU(1)Y gauge symmetry have been discovered • A spin-0 particle compatible with the SM Higgs boson has been discovered • No other particles have been found (so far) • The SM is the best-tested theory in the history of science! A very large number of precision measurements have been compared to SM computations at the (multi-)loop level and no solid evidence for BSM physics has emerged (neither in direct searches nor indirectly due to loop effects) Cross sections at the LHC in comparison to the SM Standard model observables

15 Cross sections at the LHC in comparison to the SM Standard model observables

15 CKM angles EW parameters

running αS

Z0 width top and W mass anom. magnetic moment (g-2) Higgs effective potential SM

self-consistency of SM: the Higgs-Top miracle

( ) 2( † )2 =ln 2 2 • consider self coupling of Higgs λ t (from λ/ ϕ ϕ )witht Λ /Q0

• coupling runs:

2 4π dλ(t) 2 4 = λ y + ... 3 dt − t 4 4 λλ2 yt g

if λ term, i s λ˙ λ2 t • ∼ →

λ(Q0) λ(Λ)= 2 1 3/(4π ) λ(Q0) t − 2 2 2 2 8π v = 2λ(v)v = M < ⇒ H 3ln(Λ2/v2)

Adrian Signer, May 2014 – p. 9/27 Higgs effective potential SM self-consistency of SM: the Higgs-Top miracle plot: [Spencer-Smith. 1405.1975]

˙ 4 if yt term dominant i.e. large top mass λ y • ∼− t ! 4 4 2 3 4 2 3 v yt Λ vacuum stability: λ(Λ)=λ(Q0) y t > 0 = M > ln • − 4π2 t ⇒ H 2π2v2 v2

for MH 125 GeV and Mt 173 GeV the SM seems to be consistent up to very • ∼ 9 ∼ 14 high ΛUV 10 10 GeV is this a coincidence ?? ∼ −

Adrian Signer, May 2014 – p. 10/27 Problems of the Standard Model There are also problems...

• Observational problems Earth/Sky • Conceptional problems • Theoretical problems • Naive/Aesthetical/Religious problems Observational problems Problems on “earth”

• Real problems with laboratory based experiments

• Neutrino oscillations It is by now well-established that neutrinos oscillate which is only possible if at least two neutrinos are massive. Now, in the original SM, neutrinos are massless particles... Motivation Specific Example All Models Small Groups Why Are We Not HappyThe With SM the Standard with Model? massive neutrinos

(i) Too many free parameters The Standard Model

Gauge sector: 3 couplings g 0, g, g3 3 Quark sector: 6 masses, 3 mixing angles, 1 CP phase 10 Particles Spin SU(3)C SU(2)L U(1)Y

Lepton sector: 6 masses, 3 mixing angles and 1-3 phases 10 uL 1 1 Q = 2 323 dL Higgs sector: Quartic coupling and vev v 2 3c 4 1 4 uR 2 31 3 ✓ parameter of QCD 1 c 1 ≠2 dR 2 313 Motivation Specific Example All Models Small Groups 26 ‹L 1 L = 2 12-1 Why Are We Not Happy With the Standard Model? eL 3c 4 1 ‹R 2 1 1 0 c 1 eR 2 112 (ii) StructureAkın of Wingerter, gauge symmetry LPSC Grenoble Tribimaximal Mixing From Small Groups + H = 0 1 2 1 0 ? ? ? ? 3 4 SU(3)c SU(2)L U(1)Y SU(5) SO(10) E6 E8 – ⇥ ⇥ ⇢ ⇢ ⇢ ⇢ Gµ 1 810 a Why 3 di↵erent coupling constants g 0, g, g3? Wµ 1 130 Bµ 1 110

(iii) Structure of family multiplets

? (3,2)1/3 +(3,1)-4/3 +(1,1)-2 +(3,1)2/3 +(1,2)-1 +(1,1)0 = 16 Q u¯ e¯ dL¯ ⌫¯ Fits nicely into the 3/20 16-plet of SO(10)

Akın Wingerter, LPSC Grenoble Tribimaximal Mixing From Small Groups Problems in the “sky”

• The SM does not provide a candidate for (if DM is made of particles) • is unexplained • The amount of CP-violation in the SM is not sufficient to explain the matter- in the universe/ asymmetry of the universe (BAU) Conceptual problems Internal consistency

• Without the Higgs boson (or something equivalent) the SM would be internally inconsistent at the LHC scale! • Without a Higgs the scattering of weak bosons would grow strongly with energy and violate unitarity (conservation of probability) • The Higgs had to be there! (and was found)

• The vacuum stability of the Higgs potential is another necessary condition for the internal consistency of the SM Internal consistency

• Without the Higgs boson (or something equivalent) the SM would be internally inconsistent at the LHC scale! • Without a Higgs the scattering of weak bosons would grow strongly with energy and violate unitarity (conservation of probability) • The Higgs had to be there! (and was found) • The vacuum stability of the Higgs potential is another necessary condition for the internal consistency of the SM

No internal inconsistencies so far! Conceptual ‘problems’

• The SM is ‘only’ an effective theory, it doesn’t explain ...

• effective theory means: the SM is valid up to a scale ΛUV 19 • Gravity not included, therefore ΛUV < MPl~10 GeV because at the Planck scale gravity effects have to be included

n • Error of predictions at energy scale E: O[(E/ΛUV) ] where n = 1,2,3,4,... depending on the truncation of the effective theory • Renormalisability is not considered a fundamental principle anymore, non-renormalisable operators of dimension 5,6,... can be included to reduce the theory error • Systematic approach but involved due to a large number of possible operators (global required) What is ΛUV? • Despite the phenomenal success of the SM, it is not the theory of everything (if this exists at all)

• The SM is ‘only’ an effective theory valid up to a scale ΛUV • What is ΛUV? 19 • gravity not part of SM: ΛUV < MPl~10 GeV • dark energy not part of SM: ΛUV = ?? • dark matter, matter-antimatter asymmetry: ΛUV = ?? 10 • strong CP problem: ΛUV ~ 10 GeV 10 15 • neutrino masses (seesaw): ΛUV ~ 10 ... 10 GeV • problem: ΛUV ~ ΛEW (new physics at LHC) Theoretical problems Naturalness problems I

• : Why Mew << ΛUV ?

• Naturalness problem: Why Mh << ΛUV ? A fundamental scalar is problematic!

Its mass is not protected from large radiative corrections by any symmetry. Possible solutions to the naturalness problem

• TeV-scale (a symmetry protecting the scalar)

• TeV-scale Compositeness (the scalar is not fundamental)

• Large extra-dimensions at the TeV-scale (would also solve the hierarchy problem)

All these solutions require new physics at the LHC! What if no new physics is found at the LHC?

• Would be a M A J O R (theoretical) problem!

• Fine-tuning, anthropic principle, ? • NEW classes of solutions?: Relaxion solutions, arXiv:1504.07551 • Non-LHC experiments: (nEDM, , lepton flavor violation, neutrinoless double- beta decay, ...) • New crazy ideas? Naturalness problems II

• All operators allowed by all symmetries should appear in the Lagrangian; if absent at tree level, these operators are generated at the loop level in any case • Theorists prejudice: naturally, the coefficients of the operators are of O(1) unless there is • a (broken) symmetry • the operator is loop-suppressed • Strong CP problem: There is an allowed term in the QCD Lagrangian (renormalisable, gauge invariant) which violates P, T, CP

Its coefficient is extremly suppressed (or zero). There is only an upper limit... WHY? Naturalness problems III

• The spectrum of fermion masses is not natural Aesthetics, Symmetry, Religion Aestethics, Symmetry, Religion

• Gauge symmetry SU(3) x SU(2) x U(1) • not a simple group • left-right asymmetric (maximal parity violation) • Matter content in different representations • left vs right, quarks vs leptons • Why three generations? (Why three space dimensions?) (“Who ordered that?” I. I. Rabi after muon discovery) • Wouldn’t it be a revelation to have complete unification? • one simple gauge group = one interaction • one representation for all matter = one matter type/one primary substance AttractiveFlavor in Unified Theories featuresAMinimalSO(10)Model of GUTs Gauge coupling evolution with threshold K. S. Babu, S. Khan,1507.06712

K.S. Babu (OSU) Probing Flavor Dynamics at the LHC 8/38 • Gauge coupling unification • Explanation for quantization of electric charges Conclusions Conclusions

• The SM is still in excellent shape

• We need detailed understanding of electroweak symmetry breaking (LHC, Future Linear Collider)

• Important neutrino oscillation experiments

• Low energy experiments probing the SM

• DM searches

• Ongoing searches at LHC! Never give up!

• Theory: It is to revisit the naturalness problem! Alternative ideas/approaches/explanations needed!

Maybe the SM is valid up to a very high scale. “The desert scenario”.