GGI and INFN

Galileo Galilei Institute for Galileo Galilei Institute for Theoretical physics

GGI is coordinated by CSN4 (INFN theory Committee) Agreement between INFN and Florence University (October 2004) Location: old Physics building in Arcetri

The GGI Launching Committee has been appointed by Roberto Petronzio (INFN President) on November 2004 with the following membership: David Gross, Giuseppe Marchesini, Alfred Mueller, Giorgio Parisi and Gabriele Veneziano (chair). The repost was prepared by December 2004 (see www.fi.infn.it/GGI)

Two workshops per year; each WS lasts 2-3 months with about 20 guests at each time; guests are invited to stay about one month (with reasonable per-diem)

Area of interest: Theoretical particle physics (in a broad sense) -theory of quantum fields and strings, -phenomenology of the and beyond, -astro/cosmo-particle physics, -statistical field theory and complex systems.

Area broader than all other European similar Institutes but narrower than KITP Galileo Galilei Institute for Theoretical physics

Advisory Committee: Riccardo Barbieri, Marcello Ciafaloni, Paolo Di Vecchia, Alfred Mueller, Giorgio Parisi, Gabriele Veneziano (chair)

Scientific Committee: Roberto Casalbuoni, Gia Dvali, Michelangelo Mangano, Giuseppe Marchesini (chair), Guido Martinelli, Eliezer Rabinovici, , Antonio Riotto, Augusto Sagnotti

Local Committee: Andrea Cappelli, Stefano Catani, Stefania De Curtis, Daniele Dominici, Domenico Seminara, Marco Tarlini

Coordinator: Giuseppe Marchesini, CSN4 President

Deputy Coordinator: Roberto Casalbuoni, Physics Department, Florence

Workshop Organizers: During the WS 3-4 Organizes are present all the time

Visits of Graduate Students are encouraged Galileo Galilei Institute for Theoretical physics

February 2005: Call for Workshop proposal

April 2005: proposals submitted 1. Advancing Collider Physics: from Twistors to Monte Carlos 2. String and M theory approaches to particle physics and cosmology 3. New Directions Beyond the Standard Model in FT and String Theory 4. Astroparticle and Cosmology 5. Flavour Physics in the LHC era 6. High Density QCD 7. Low-dimensional quantum field theories and applications 8. Complex Systems

April 2005: selections of 2006 Workshops

Spring 2006: New Directions Beyond Standard Model in Field and String Theory Autumn 2006: Astroparticle and Cosmology Galileo Galilei Institute for Theoretical physics

First Workshop May 2, 2006 - Jun 30, 2006

New Directions Beyond the Standard Model in Field and String Theory

Organizers: C. Angelantonj, E. Dudas, T. Gherghetta, A. Pomarol

The main topics of the workshop include:

● Electroweak symmetry breaking.

● Supersymmetric models and breaking.

● String vacua and model building.

● Warped compactifications and holography.

● Modifications of gravity and cosmological implications. Galileo Galilei Institute for Theoretical physics

Second Workshop Aug 28, 2006 - Nov 10, 2006: Astroparticle and Cosmology

Organizers: C. Baccigalupi, K. Enqvist, E. Kolb, J. Lesgourgues

The main topics of the workshop include:

● Models for the Early Universe

● Dark Matter and Dark Energy

● CMB, Large Scale, Cosmological Parameters From Asymptotic Freedom to LHC

Giuseppe Marchesini Milan-Bicocca University and INFN-Milan

● pre 1972: the quest for “elementary particles” in strong interactions

● QCD and Asymptotic Freedom

● an example of LHC perturbative study

● perspective Pre 1972: long road to point-like

1 QED the only successful Quantum field theory: (ge 2)=0.001159652187(4) 2 − µ Point-like objects and interaction: ψ(x), Aµ(x) and jµ(x) A (x) · Vacuum polarisation (virtual e+e− pairs): α = e2/4π~c depends on distance Q−1

2 dα 1 2 1 1 Q = α + α(Q) , α(me) dQ2 3π 1 Q2 137 ··· ⇒ ≃ 137 ln 2 ≃ − 3π me

1 Vacuum polarization from charge of spin s = 2 gives susceptibility (N.Nielsen, R.Hughes 1981)

1 2 χ ( 1)2s +(2s)2 = < 0 ǫ> 1 (screening) ∼ − −3  −3 ⇒

Charge diverges at very short distance 10−250 cm

Landau 1954: QED not a well defined theory, quantum field theory inconsistent Strong interactions (pre 1972): long road to point-like

S-matrix theory: deals only with “physical” observed hadrons which are composite

Flavour quantum numbers, Duality: asymptotic behaviour and hadron spectrum

1964 Gell-Mann and Zweig: hadron spectroscopy explained by quarks with flavour quantum numbers with approximate symmetry − colour quantum numbers (needed for spin-statistics) with exact SU(3) symmetry − Late 1960 Feynman suggests: diffraction explained by point-like interaction

1969 Bjorken (and Feynman) on DIS: at short distance point-like partons-quarks

µ How to find point-like interaction? As in QED jµ(x) A (x): · promote exact colour SU(3)-symmetry to gauge symmetry gluons and QCD ⇒ 1 µν QCD Lagrangian: = ψ¯ /D m ψ Fµν F LQCD − − 4  a ψf : a = SU(3) colour index, f = flavour

mf : quark mass ab ab Dµ = ∂µ + igs Gµ , gs = strong coupling  ab  ab Fµν = ∂µGν ∂νGµ + gs[Gµ, Gν] − ab   Gµ : 8 gluons

Standard Model: SU(2) U(1) + symmetry breaking LQCD × ×

● Asymptotic Freedom: D.Gross, F.Wilczek,PhysRevLett.30(1973), H.Politzer,PhysRevLett.30(1973)

● Confinement: K.Wilson,Phys.Rev.D10(1974), S.Mandelstam,Phys.Rep.23C(76) A.Polyakov,Phys.Lett.72B(1978), G.’t Hooft,Nucl.Phys.B190(1981) QCD and Asymptotic Freedom

QCD vacuum polarisation 1 due to nf 6 virtual quark-antiquark with spin s = and gluons with spin s = 1 ≤ 2

2s 1 2 2 11 χ ( 1) +(2s) = nf + 3 > 0 ǫ< 1(anti screening) ∼ − −3  − 3 3 ⇒ − Xs

2 ~ −1 QCD coupling αs = gs/4π c decreases with distance Q :

2 Q dαs nf 2 + 3 11 = β α2 + β = − · · > 0 dQ2 − 0 s ··· 0 12π

αs(µ) 1 αs(Q) = ≃ Q2 Q2 1+β0αs(µ)ln µ2 β0 ln 2 ΛQCD

ΛQCD = 210 40MeV fundamental QCD scale ±

The discovery of Asymptotic Freedom

● 1969 Kriplovich computed β0 in SU(2) Yang-Mills. No connection to strong interaction. Landau skepticism still present

● 1972 ’t Hooft computed β0 in SU(3) Yang-Mills and wrote in a blackboard in 1972 Marseilles Conference on Yang-Mills field theory. Strong concern on EW

● 1973 D.Gross, F.Wilczek and H.Politzer computed β0 in QCD with physical interpretation and consequences (2004 Nobel)

● 1974 Caswell and Jones computed the 2-loop beta function coefficient β1

● 1980 Tarasov, Vladimirov and Zharkov computed the 3-loop coefficient β2

● 1997 van Ritbergen, Vermaseren and Larin computed the 4-loop coefficient β3

∂a α q2 = β a2 β a3 β a3 β a4 a = s ∂q2 − 0 − 1 − 2 − 3 ··· 4π 0.5 Theory Data NLO NNLO α Lattice s(Q) Deep Inelastic Scattering e+e- Annihilation 0.4 Hadron Collisions Heavy Quarkonia

Λ(5) α (Μ ) MS s Z 245 MeV 0.1210 QCD 0.3 211 MeV 0.1183 O(α 4 ) { s 181 MeV 0.1156

0.2

0.1

1 10 100 Q [GeV] DIS [pol. strct. fctn.] 250 MeV 100 GeV DIS [Bj-SR] 0.8 DIS [GLS-SR] α( ) τ-decays [LEP] q SU(3) gauge theory ν xF3 [ -DIS] 0.6 µ F2 [e-, -DIS] DIS [ep Ð> jets] DIS & pp Ð> jets QQ + lattice QCD 0.4 Υ decays + _ γ 3-loop perturbation theory e e_ F 2 e+ e [σ ] _ had 0.2 + [jets & shapes 14 GeV] e e_ + [jets & shapes 22 GeV] e e_ e+ e [jets & shapes 35 GeV] + _ σ ] e e_ [ had 0 e+ e [jets & shapes 44 GeV] 1 10 100Λ 1000 _ q/ e+ e [jets & shapes 58 GeV] pp --> bb X pp, pp --> γ X α Asymptotic fit of S σ(pp --> jets) 1.5 Γ(Z0--> had.) [LEP] _ e+ e [scaling. viol.] + _ e e [4-jet rate] pert 2 α (1+c/p ) jets & shapes 91.2 GeV 1 Lattice data jets & shapes 133 GeV )

jets & shapes 161 GeV µ ( S

jets & shapes 172 GeV α jets & shapes 183 GeV jets & shapes 189 GeV 0.5 jets & shapes 195 GeV jets & shapes 201 GeV jets & shapes 206 GeV 0 0.10 0.12 0.14 0 1 2 3 4 5 6 7 µ α s (Μ Z ) Key developments of QCD

● QCD sum rules from OPE&AF: soft physics observables from QCD vacuum parametrization

● PT calculations (exact and resummed) for all hard processes: total-inclusive, semi-inclusive distributions and exclusive (MonteCarlo)

● QCD Lattice calculations of EW parameters (flavour physics and CKM)

● Lattice calculations of QCD vacuum: confinement (monopoles, vortexes)

for Lattice QCD, see Claudio Rebbi talk here I start from an example of perturbative QCD Perturbative QCD: strategy and limitation PT calculations: quark and gluons Contradictions or predictions Physic states:hadrons ⇒ Collinear and IR divergences in general PT coefficients diverge but: ⇒ 1) Factorization of divergences: absorbed in universal factors (factorization scale)

2) Collinear and IR safe observables, e.g. ET = ~kit | | P -Collinear safe: ~ki,~kj parallel, then substitute with ~ki+~kj

-IR safe: ki kj then neglect ki ≪ PT coefficients finite, PT calculation possible

hadron-flow parton-flow ≃ LHC collisions and the fifth form factor

Bott,Sterman; Kidonakis,Oderla,Sterman; Bonciani,Catani,Mangano,Nason Banfi,Salam,Zanderighi; Dokshitzer&GM Example of collinear safe observable in pp-collisions with high ET -jet emission

Out-of-plane dist. Σ(ET , Kout)= dσn(ET )Θ(Kout ~ki out ) Z − | | Xn Xi

Distributions with two hard scales: ΛQCD K ET ≪ out ≪

hard parton process: p +p p +p 1 2 → 3 4

1 4 P1 = x1p1,P2 = x2p2 2 3

P3 = x3p3,P4 = x4p4 (to trigger ET )

Collinear divergences ln ET /Qµ, ln QV /Qµ parton densities (as in DIS) ⇒ + − Collinear and infrared enhancements ln ET /K radiators (as in e e ) out ⇒ Mellin-transform to factorize individual parton contribution General factorized structure

Kout ET < √S 1 4 ≪

2 3 −1 Pi = xipi Mellin variable ν K ∼ out

Σ(˜ ν, Pi )= dxiσ0( pi ) Σ˜ coll(ν, xi, pi ) (ν, pi ) { } Z { } · { } · S { } Yi 4 2 4 −Ri(ν,{pi}) Σ˜ (ν, xi, pi )= e D(xi, K ) D¯(xi, K ) coll { } · out · out iY=1 iY=1 iY=3

Collinear divergences along incoming P ,P hadrons D(xi, K ) (as in DIS) 1 2 ⇒ out + − Collinear divergences along outgoing P ,P hadrons D¯(xi, K ) (as in e e ) 3 4 ⇒ out + − Collinear enhancements (K ET ) factorize i (Sudakov factors as in e e ) out ≪ ⇒R

Soft enhancements (K ET ) factorize in fifth form factor (only in LHC) out ≪ S Fifth form factor

1 4 ˜ 2 3 Σ(ET , Kout)= dxi σ0 Σcoll (Kout,pi) Z · · S Yi

Fifth form factor resums soft enhancements S origin: in 2 2 hard matrix elements soft emission rotates colour state → sensitive to Coulomb phase it involves a strange symmetry: N (t + u)/(t u) t=(p p )2, u=(p p )2 ↔ − 1− 3 1− 4 Soft anomalous dimension gg gg →

1 t u 3 T =ln − +iπ, U =ln − +iπ s s 4 T U 2 b= − T +U

1 0 b b b b 0 4 4 N2 N2 1 b(N+1)(N−2) b(N−1)(N+2) B 0 1 0 b C B 2 2 2N2 2N2 C B C B b 000 0 0 C B N2 C B −1 C Γ= N(T +U) B C B b b 0 1 0 0 C B 4 N2−4 4 C B C B b(N+3) b(N+3) N+1 C B 0 0 0 C B 4(N+1) 4(N+2) 2N C B C B b(N−3) b(N−3) N−1 C @ 4(N−1) 4(N−2) 0 0 0 2N A

Strange symmetry for eigenvalues: b 1 ↔ N Not yet the end

Σ(˜ ν, Pi )= dxiσ0( pi ) Σ˜ coll(ν, xi, pi ) (ν, pi ) { } Z { } · { } · S { } Yi 4 2 4 −Ri(ν,{pi}) Σ˜ (ν, xi, pi )= C(αs) e D(xi, Qµ) D¯(xi, Qµ) coll { } · · · iY=1 iY=1 iY=3 with 2 C =1+ c αs(ET )+ c α (ET ) 1 2 s ··· which accounts for K ET . out ∼

Exact higher order calculations needed to compute C(αs) for all studies in SM, BSM, Higgs emission, heavy flavour emission Maltoni, Mangano, Piccinini, Isidori,....

Techniques: standard Feynman diagrams, helicity formalism, twistor space

Twistors: new development on prturbative calculations

Fourier transform of scattering amplitudes from momentum space to twistor space, work on holomorfic curves (connection with string theory)

ex Bryan Webber From AS to LHC

The quest for point-like interaction has been very successful: QCD and SM ⇒ Very successful PT results for short distance strong interactions

QCD not yet a solved theory, although PT studies are very constrained:

- Collinear+IR divergences factorize universal phenomenological soft inputs - non-convergence of PT expansion ⇒ power corrections Q−p, p = 1, 2 ⇒ ··· Key problem: confinement

’t Hooft (1974): confinement related to QCD monopoles

Lattice calculations indications: monopoles lies on low dimensional IR structures

The future development for fundamental physics: move from point-like objects to extended objects (string theory)?