The Hierarchy Problem and other short-comings of the Standard Model (SM) Thorsten Feldmann [email protected] Seminar WiSe 20/21 – Extensions of the Standard Model 4. January 2021 TRR 257 particle physics phenomenology after the Higgs discovery Th. Feldmann Hierarchy Problem 1 / 25 Current Understanding of Fundamental Physics 4 classical forces: electromagnetic, weak and strong nuclear forces + gravity | {z } ! SM symmetry: SU(3)C × SU(2)L × U(1)Y ! General Relativity elementary matter particles (fermions): Quarks + Leptons (3 families + anti-particles) electric charges (2/3,-1/3) electric charges (0,-1) additional observations: - Baryon-antibaryon Asymmetry in the Universe (BAU) . - Neutrinos have tiny (but finite) mass . - A scalar Higgs boson with mass of ∼ 125 GeV . - Abundance of Dark Matter (DM) in the Universe . .[ 7! Ch. Papior] ... Th. Feldmann Hierarchy Problem 2 / 25 Current Understanding of Fundamental Physics 4 classical forces: electromagnetic, weak and strong nuclear forces + gravity | {z } ! SM symmetry: SU(3)C × SU(2)L × U(1)Y ! General Relativity elementary matter particles (fermions): Quarks + Leptons (3 families + anti-particles) electric charges (2/3,-1/3) electric charges (0,-1) additional observations: - Baryon-antibaryon Asymmetry in the Universe (BAU)... - Neutrinos have tiny (but finite) mass . - A scalar Higgs boson with mass of ∼ 125 GeV . - Abundance of Dark Matter (DM) in the Universe . .[ 7! Ch. Papior] ... Th. Feldmann Hierarchy Problem 2 / 25 Table of Contents 1 The Standard Model (recap. of subtle issues) 2 The Hierarchy Problem 3 (some) Popular NP Ideas 4 Conclusion/Outlook ! SMEFT Th. Feldmann Hierarchy Problem 3 / 25 The Standard Model Th. Feldmann Hierarchy Problem 4 / 25 Theoretical features of the SM Formulated as a Quantum Field Theory: (special relativity + QM) ! restricted to renormalizable operators of dim≤ 4 in Lagrange density Interactions from Gauge Principle: ! fundamental forces mediated by massless Vector Bosons Quarks and leptons distinguished by Chirality: ! different quantum numbers for left- and right-handed fermions ! gauge symmetry forbids explicit fermion masses ! right-handed neutrinos decouple (all SM quantum numbers vanish) 3 1 X X X L = − X X µν + F¯ (i) (iD=) F (i) gauge 4 µν X=G;W ;Y i=1 F=QL;UR ;DR ;LL;ER µν ~ theoretically possible additional term / G Gµν that violates CP experimentally constrained to ' 0 −! strong CP problem [7! J. Steinberg] Th. Feldmann Hierarchy Problem 5 / 25 ! the running couplings in the SM 3 independent gauge couplings g1;2;3 depend on energy resolution µ 2 gi (αi = 4π ) @α i = β (µ) = −β(0) α2 + ::: @ ln µ2 i i i 2 1 1 (0) µ ) ' + βi ln 2 αi (µ) αi (µ0) µ0 coefficients in the ”β-functions” depend on particle content WARNING: U(1)Y coupling in the SM has arbitrary normalization ! 15 α3 and α2 tend to meet above 10 GeV Unification of EW and strong forces? modified particle content between EW scale and 1015 GeV ? embed SU(3) × SU(2) × U(1) in larger (non-abelian) group ? [7! A. Boushmelev] Th. Feldmann Hierarchy Problem 6 / 25 The Higgs and EWSB Add a Complex Scalar Higgs Doublet ! φ+(x) φ(x) = φ0(x) Postulate a non-trivial scalar potential 2 2 y y Lpot = −V (φ)= µ φ φ − λ φ φ q 2 ! non-vanishing VEV hφ0i = pv = µ ' 246 GeV 2 2λ ! spontaneous symmetry breaking: SU(2)L × U(1)Y ! U(1)Q ! 3 massless Goldstone modes g±; g0 0 2 2 ! 1 massive scalar mode h with mh = 2λ v Th. Feldmann Hierarchy Problem 7 / 25 Higgs Mechanism and Gauge-Boson Masses Masses for gauge bosons from kinetic Higgs terms y µ LHiggs−kin: =( Dµφ )(D φ) ! Goldstone modes become longitudinal modes for W ± and Z 0 ! gauge-boson masses proportional to VEV p g g2 + (g0)2 M = v ; M2 = v ; W 2 Z 2 ! Higgs VEV sets the interaction range of weak force: g2 GF = p 2 4 2 MW ! weak mixing angle between photon and Z 0 e = g sin θW ; MW = MZ cos θW (at tree level) dimensionful parameter µ2 ! v 2 introduced ”by hand” sets the energy scale for EW dynamics (range of weak force) Th. Feldmann Hierarchy Problem 8 / 25 ! the Custodial Symmetry of the Higgs Potential The Higgs potential has a larger symmetry than SU(2)L × U(1)Y This can be seen by introducing the notation ! ! φ0∗ φ+ Φ = ≡ φ~ ; φ −φ− φ0 such that the potential can also be written as 2 2 h y i h y i V = −Lpot = −µ tr Φ Φ + λ tr Φ Φ This is obviously symmetric under SU(2)L × SU(2)R transformations, y Φ ! UL Φ UR protects SM relations against quantum corrections ! ”Custodial Symmetry” ! confirmed by ElectroWeak Precision Tests (LEP etc.) the custodial symmetry is broken by (a) the gauge couplings, which only respect SU(2)L × U(1)Y (b) the Yukawa couplings to fermions (see below) Th. Feldmann Hierarchy Problem 9 / 25 Higgs Yukawa Couplings and Fermion Masses Higgs doublet interacts with chiral fermions via Yukawa Couplings: ij ¯ i ~ j ij ¯ i j ij ¯i j Lyuk = −YU QL φ UR − YD QL φ DR − YE LL φ ER + h.c. ! fermion mass matrices from Higgs Yukawa couplings v v Mij = p Y ij ; Mij = p Y ij U 2 U D 2 D diagonalized with different trafos for left-handed up- and down-quarks: ! CKM matrix for quark transitions: 3 mixing angles + 1 weak CP-violating phase ! hierarchical pattern for fermion masses: v mu ∼ md ms mc < mb n mt ∼ p 2 me mµ mτ ! massless (left-handed) neutrinos, no lepton-flavour violation ! accidental symmetries: baryon number B and lepton number L Th. Feldmann Hierarchy Problem 10 / 25 ! Cancellation of chiral gauge anomalies gauge symmetries in QFT can be broken by quantum corrections (”triangle anomalies”) proportional to trace of the representation matrices for the involved gauge bosons, with opposite sign for left- and right-handed fermions Example ”U(1)3” (for one family): 8 1 2 right-handed : tr[Y 3] = 3 · y 3 + 3 · y 3 + y 3 = 3 · − 3 · − 1 = − UR DR ER 27 27 9 1 1 2 left-handed : −tr[Y 3] = −3 · 2 · y 3 − 2 · y 3 = −6 · + 2 · = + QL LL 216 8 9 ! fermions must come in complete families! ! can/must not be accidental! ! more symmetry? Th. Feldmann Hierarchy Problem 11 / 25 Standard Model: Goods and Bads + predictive power and efficiency (more experimental observables than free parameters) + unification of electromagnetic and weak forces (tested to high accuracy with EWPTs) + CKM mechanism confirmed as dominant source of flavour decays (BaBar, Belle I+II, LHCb, . ) + Higgs boson observed with ”reasonable” mass value (LHC) - SM does not include gravity (not to mention dark energy) - Electroweak scale enters as ad-hoc parameter in Higgs potential - SM does not explain fermion charges and origin of families - SM does not explain hierarchies in Yukawa couplings - CP violation in CKM matrix not sufficient to explain BAU - Strong CP parameter fine-tuned to zero ? - SM does not account for non-vanishing neutrino masses - SM does not provide a viable DM candidate Th. Feldmann Hierarchy Problem 12 / 25 Hierarchy Problem Th. Feldmann Hierarchy Problem 13 / 25 Quantum corrections to mass parameter in potential 2-point function: 2 2 assume that SM is valid for momenta p < ΛUV 1-loop contribution to dimensionful parameter µ2 in Higgs potential: 2 2 02 2 ΛUV 9 g + 3 g 2 δµ = 3 λ + − 3 yt 1−loop 16π2 8 15 for ΛUV & 10 GeV one has δµ2 µ2 + δµ2 = µ2 ∼ m2; v 2 quantum UV quantum physical h ) THE ”Hierarchy Problem in the SM” Th. Feldmann Hierarchy Problem 14 / 25 How could the scale ΛUV come into play? The Landau pole, associated with the scale µLandau where the U(1)Y charge α1 diverges 19 the Planck scale MPlanck ∼ 10 GeV, where quantum gravitational effects become relevant 15 the Grand Unification Scale MGUT ∼ 10 GeV, where strong and electroweak forces unify any mass parameters of New (super-)heavy Particles which have not yet been seen in particle experiment (e.g. dark matter) ... Th. Feldmann Hierarchy Problem 15 / 25 Possible Explanations / Solutions 2 2 1 the values of µ jUV and the coupling constants entering δµ jquantum are fine-tuned to yield the observed physical value of µ2 at the electroweak scale: 2 2 ) one out of many possible universes where, by accident, µ ΛUV 2 the SM is only valid up to energies of the order of ΛNP ∼ a few TeV: ) new particles/interactions, possibly to be found at the LHC ) still, the ”new physics model” has to explain why ΛNP ΛUV Conclusions for Research Directions: exp.: search for ”Physics beyond the SM” theo.: investigate ”NP Models” that can address the hierarchy problem (and possibly some of the other problems/puzzles in the SM) pheno.: precise predictions for observables in the SM or with NP Th. Feldmann Hierarchy Problem 16 / 25 Popular NP Ideas Th. Feldmann Hierarchy Problem 17 / 25 Example 1: (low-scale) Supersymmetry (SUSY) Idea: bosons and fermions contribute with different sign to δµ2 implement ”Supersymmetry" on the level of the Lagrangian ) bosonic and fermionic contributions cancel to arbitrary loop-order ! new partners for SM particles with opposite spin/statistics ! in particular, any elementary scalar comes with a fermionic partner complex Higgs boson fields φ $ chiral fermions: ”higgsinos” φ~ ! masses of higgsinos are ”protected” by chiral symmetry, i.e. δmφ~ / mφ~ ΛUV ! masses of Higgs and higgsinos related by SUSY, i.e. δmφ = δmφ~ ΛUV # Th. Feldmann Hierarchy Problem 18 / 25 Goods and Bads of (low-energy) SUSY + theoretically appealing as only non-trivial extension of Poincare symmetry + SUSY can account for a spin-2 graviton −! Supergravity (SUGRA) + allows unification of strong and electroweak couplings in SU(5) GUT + naturally favours a light Higgs boson as observed at the LHC + SUSY can be supplemented with discrete R-parity ) candidates for stable weakly-interacting dark matter + SUSY provides additional mechanisms for neutrino-mass generation + /- new sources of CP violation (! BAU / electric dipole moments) - SUSY must be broken at low energies: ) need to postulate different options for ”soft” SUSY breaking )O (100) new parameters to be fitted to experimental data - new sources for flavour transitions ) ”NP flavour problem” - SUSY still does not explain origin of fermion families - strong CP problem remains Th.