Instantons/Sphalerons: Searching for New Physics within the Standard Model Andreas Ringwald DESY Festkolloquium Fridger Schrempp, February 19th, 2008, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 1 1. Introduction • Standard Model of electroweak (QFD) and strong (QCD) inter- actions extremely successful ⇐ Ordinary perturbation theory • There are processes inaccessible to ordinary perturbation theory [Adler ‘69; Bell,Jackiw ‘69; Bardeen ‘69] B+L/ Chirality-violating processes in QFD/QCD • Induced by topological fluctuations of non-Abelian gauge fields, in particular instantons [Belavin et al. ‘75; ‘t Hooft ‘76] A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 2 1. Introduction 4(B + L) = −6: sL • Standard Model of electroweak s L tL (QFD) and strong (QCD) inter- c b actions extremely successful L L d I b ⇐ Ordinary perturbation theory L W /Sph L d ν • There are processes inaccessible to L τ ν ordinary perturbation theory uL µ νe [Adler ‘69; Bell,Jackiw ‘69; Bardeen ‘69] 4Q5 = 6: B+L/Chirality-violating processes in uL uR QFD/QCD • Induced by topological fluctuations dL Is dR of non-Abelian gauge fields, in particular instantons sL sR [Belavin et al. ‘75; ‘t Hooft ‘76] A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY 1 – Instantons/Sphalerons: Searching for New Physics within the SM – 3 1. Introduction • Standard Model of electroweak • B + L/Q5 are anomalous, (QFD) and strong (QCD) inter- ∆(B + L) = −2 n ∆N [W ] actions extremely successful g CS ∆Q5 = 2 nf ∆NCS[G] ⇐ Ordinary perturbation theory • Topological fluctuations of the • There are processes inaccessible to gauge fields W/G, i.e. fluctuations ordinary perturbation theory with integer 4NCS 6= 0, induce [Adler ‘69; Bell,Jackiw ‘69; Bardeen ‘69] anomalous processes • Instanton: lowest Euclidean action B+L/Chirality-violating processes in configuration with ∆NCS = 1 ⇒ QFD/QCD tunneling • Induced by topological fluctuations • Sphaleron: lowest static energy of non-Abelian gauge fields, in configuration with NCS = 1/2 ⇒ barrier particular instantons [Belavin et al. ‘75; ‘t Hooft ‘76] A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 4 1. Introduction • Standard Model of electroweak (QFD) and strong (QCD) inter- actions extremely successful E ⇐ Ordinary perturbation theory sphaleron • There are processes inaccessible to ordinary perturbation theory [Adler ‘69; Bell,Jackiw ‘69; Bardeen ‘69] B+L/Chirality-violating processes in instanton QFD/QCD 0 1 N cs • Induced by topological fluctuations of non-Abelian gauge fields, in particular instantons [Belavin et al. ‘75; ‘t Hooft ‘76] A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 5 • Theory: Topological gauge field fluctuations and associated anomalous processes are predicted to play very important role in – QCD in various long-distance aspects: [...; Shuryak; ...] ∗ U(1)A problem (mη0 mη) [‘t Hooft ‘76; ...] – QFD at high temperatures: [Kuzmin,Rubakov,Shaposhnikov ‘85; ...] ∗ Crucial impact on baryon and lepton asymmetries of the universe • Experiment: Are they directly observable in high energy reactions? – QFD: Intense studies in early 1990s; inconclusive [AR ‘90; Espinosa ‘90; ...] – QCD: Hard instanton induced processes in deep-inelastic lepton-hadron scattering or in virtual γ/W /Z production at hadron colliders ∗ reliably calculable and sizeable rate [...; Moch,AR,F.Schrempp ‘97; F.Schrempp ‘05; Brandenburg,AR,Utermann ‘06; F.Schrempp,M.Petermann ‘08] ∗ characteristic final state “fireball” signature [AR,F.Schrempp ‘94–‘01] ∗ first encouraging search results from HERA I data [H1 ‘02; ZEUS ‘04] ∗ looking forward to search in HERA II data and at LHC A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 6 Outline: 2. Evidence for QCD-Instantons in the Vacuum 3. Searches for QCD-Instantons at HERA 4. Conclusions and Outlook A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 7 2. Evidence for QCD-Instantons in the Vacuum • Euclidean functional integral formulation of QCD, 1 Z hOi = [dA][dψ][dψ] O[A, ψ, ψ] e−S[A,ψ,ψ] , Z Z Z = [dA][dψ][dψ] e−S[A,ψ,ψ] . • Perturbation theory: ◦ perturbative QCD: expansion about trivial vacuum solution, i.e. vanishing gluon field and vanishing quark fields and thus vanishing Euclidean action, S = 0. ◦ instanton perturbation theory: generalized saddle-point expansion of the Euclidean functional integral about non-trivial minima of the Euclidean action, S 6= 0. A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 8 • Non-trivial minima (⇔ solutions) have integer Pontryagin index (topological charge) α Z 1 Q ≡ s d4x tr(G G˜ ) ≡ 4N = ±1, ±2,..., 2π 2 µν µν CS and their action is a multiple of 2π/αs, Z 4 1 2 π 2 π S ≡ d x tr(GµνGµν) = |Q| = · (1, 2,...). 2 αs αs ⇒ Dominant saddle-point for αs 1: | Q |= 1 A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 9 ⇒ Instanton (Q = 1): [Belavin et al. ‘75; ‘t Hooft ‘76; Callan,Dashen,Gross ‘76; Jackiw,Rebbi ‘76] 2 (I) i ρ σµ (x − x0) − (xµ − x0µ) † Aµ (x; ρ, U, x0) = − 2 U 2 2 U g (x − x0) (x − x0) + ρ ◦ size ρ, color orientation U, position x0 ◦ localized in Euclidean space and time (“instantaneous”) (I) L Aµ (x; ρ, U, 0) 4 6 12 ρ 5 = · 2 2 4 4 παs (x + ρ ) L(z,t)3 2 h (I)i 2 π 1 -0.4 ⇒ S Aµ = 0 -0.2 α -0.4 0z s -0.2 0 0.2 t 0.2 0.4 0.4 ◦ tunneling between topologically inequivalent (4NCS = 1) vacua A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY Page 1 – Instantons/Sphalerons: Searching for New Physics within the SM – 10 • Instanton-contribution to vacuum-to-vacuum amplitude, Z(I) = h0|0i(I): ∞ 1 dZ(I) Z Z = dρ D (ρ) dU Z(0) d4x m 0 • Size distribution Dm(ρ) known in instanton perturbation theory [‘t Hooft ‘76; Bernard ‘79] αs(µr) ln(ρ µr) 1, ρ mi(µr) 1, in 2-loop renormalization-group invariant form, [Morris et al. ‘85] nf dnI Y αs(µr) = D (ρ) = D(ρ) (ρ m (µ )) (ρ µ )nf γ0 4π d4x dρ m i r r i=1 A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 11 • Suppression of instanton contribution to the vacuum-to-vacuum amplitude for small quark masses ρmi 1: ⇐ Axial anomaly: [Adler ‘69; Bell, Jackiw ‘69] Any gauge field fluctuation with topological charge Q must be accompanied by a corresponding change in axial charge, 4Q5 = 2 nf Q ⇒ pure vacuum-to-vacuum transitions vanish in massless limit ⇒ Green’s functions corresponding to anomalous Q5 violation: [‘t Hooft ‘76] uL uR dL Is dR ∗ main contribution due to instantons (fermionic zero modes) ∗ do not suffer from any mass suppression sL sR A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 12 • Reduced size distribution D(ρ): 2 Nc d 2π − 2π αs(µr) αs(µr) β0+(β1−4 Ncβ0) 4π D(ρ) = 5 e (ρ µr) ρ αs(µr) − 2π • Clearly non-perturbative: ∝ e αs(µr) • Power-law behaviour of (reduced) size distribution, 11 2 D(ρ) ∼ ρβ0−5+O(αs); β = N − n 0 3 c 3 f ◦ dominant contribution to ρ integral generically originates from large ρ ◦ spoils the applicability of instanton perturbation theory, αs(1/ρ) 1 A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 13 • Size distribution basic building block of instanton perturbation theory: ◦ appears in generic instanton contributions to Green’s functions ⇒ important to know the region of validity of the perturbative result • Crucial information from lattice investigations on the topological structure of the QCD vacuum – Evidence for topological charge fluctuations: e.g. [Chu et. al ‘94] Lagrange density (raw data) 4 3 15 2 10 5 z 10 5 t 15 20 A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 14 • Size distribution basic building block of instanton perturbation theory: ◦ appears in generic instanton contributions to Green’s functions ⇒ important to know the region of validity of the perturbative result • Crucial information from lattice investigations on the topological structure of the QCD vacuum – Evidence for topological charge fluctuations: e.g. [Chu et. al ‘94] Lagrange density (smoothed) 0.03 0.02 15 0.01 0 10 5 10 5 z 15 t 20 A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 15 • Size distribution basic building block of instanton perturbation theory: ◦ appears in generic instanton contributions to Green’s functions ⇒ important to know the region of validity of the perturbative result • Crucial information from lattice investigations on the topological structure of the QCD vacuum – Evidence for topological charge fluctuations: e.g. [Chu et. al ‘94] Topological charge density (smoothed) 0.002 0.001 15 0 -0.001 10 5 10 5 z 15 t 20 A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 16 – Small size topological charge fluctuations ≡ QCD-instantons: [AR,F. Schrempp ‘99] < ⇒ Instanton perturbation theory reliable for ρ ΛMS ∼ 0.4 A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 17 – Small size topological charge fluctuations ≡ QCD-instantons: [AR,F. Schrempp ‘99] A. Ringwald (DESY) Festkolloquium Fridger Schrempp, DESY – Instantons/Sphalerons: Searching for New Physics within the SM – 18 • First principle calculations of instanton contributions only possible for quantities to which large size instantons do not contribute: – Short-distance coefficient functions in the operator product expansion of two-point functions [Andrei,Gross ‘78;...;Novikov et al.