Conformal Electroweak Symmetry Breaking and Implications for Neutrinos and Dark matter Manfred Lindner Mass 2014, Odense, May 19-22, 2014 M. Lindner, MPIK Mass 2014 1
Introduction Physics Beyond the Standard Model must exist - observed neutrino masses & mixings - observed BAU (Baryon Asymmetry of the Universe) - evidence for Dark Matter - evidence for Dark Energy - strong CP problem - - hierarchy problem è there should be TeV-scale BSM physics But. so far nothing seen à only SM Higgs: ``nightmare scenario ß à a lot happened in the last 20 years: H, t, W, Z, m ν, SM as gauge theory Different ways to see (or guess) new physics: - direct effects of new particles and interactions (t, H, neutrino mass, DM, ) - indications from QFT effects: consistency, extrapolation, ç this talk M. Lindner, MPIK Mass 2014 2
wait for the upgrade this may already point into new directions M. Lindner, MPIK Mass 2014 3
Look very careful at the SM as QFT The SM itself (without embeding) is a QFT like QED - infinities, renormalization è only differences are calculable - SM itself is perfectly OK è many things unexplained Has (like QED) a triviality problem (Landau poles ß à infinite λ) - running U(1) Y coupling (pole well beyond Planck scale - like in QED) - running Higgs / top coupling à upper bounds on m H and m t è requires some scale Λ where the SM is embedded è the physics of this scale is unknown Another potential problem is vacuum instability (ß à negative λ) - does occur in SM for large top mass > 79 GeV è lower bounds on m H SM as QFT (without an embeding): - a hard cutoff Λ and the sensitivity towards Λ has no meaning - renormalizable, calculable - just like QED M. Lindner, MPIK Mass 2014 4
Triviality and Vacuum Stability Bounds Λ(GeV) 126 GeV < m H < 174 GeV SM does not exist w/o embeding - U(1) copling, Higgs self-coupling λ Landau pole ML 86 126 GeV is here! è λ(m pl ) ~ 0 - EW-SB radiative - just SM? Holthausen, ML, Lim (2011) triviality allowed vacuum stavility ln(µ) è RGE arguments seem to work è we need some embeding Λ M. Lindner, MPIK Mass 2014 5
The allowed Range ç è Experiment è interesting experimental cases (for Λ = M Planck ): 1) m H < ca. 126 GeV è instability è new physics (or disaster) 2) 126 GeV 135 GeV perfect: SM + MSSM range, 3) 135 GeV 157 GeV perfect: SM, non-minimal SUSY, 4) above 157 GeV BSM è Remarkable aspects: - SM parameters allow quantum corrections over large scales - we seem to be very precisely at the transition between 1) and 2) M. Lindner, MPIK Mass 2014 6
A special Value of λ at M planck? ML 86 Holthausen, ML Lim (2011) Different conceivable special conditions: downward flow of RG trajectories è IR QFP è random λ flows to m H > 150 GeV è m H ~ 126 GeV flows to tiny values at M Planck M. Lindner, MPIK Mass 2014 7
m H < 150 GeV è random λ = Ο(1) excluded Why do all these boundary conditions work? - suppression factors compared to random choice = O(1) - λ = F(λ, g i2, ) è loop factors 1/16π 2 - top loops à fermion loops è factors of (-1) è scenarios predicting sufficiently suppressed (small/tiny) λ at M planck are OK è more precision à selects options ; e.g. γ m = 0 now ruled out M. Lindner, MPIK Mass 2014 8
Is the Higgs Potential at M Planck flat? Holthausen, ML, Lim Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia 2-loop α s error difference 1à 2 loop Notes: - remarkable relation between weak scale, m t, couplings and M Planck ß à precision - strong cancellations between Higgs and top loops à very sensitive to exact value and error of m H, m t, α s = 0.1184(7) à currently 1.8σ in m t - higher orders, other physics, Planck scale thresholds Lalak, Lewicki, Olszewski, è important: watch central values & errors è important: new physics ß à DM, m ν M. Lindner, MPIK Mass 2014 9
What if the SM were metastable? è for large m t the Higgs potential has two minima. If m t > stability bound - EW (false, required, local, metastable) - true (deeper, global minimum) m t - 1 st bubble of true vacuum in U grows (surface vs. volume) - mechanisms producing a 1 st bubble in the Universe: r~1/m H è tunneling / random CR collision è metastability (slightly negative λ) is OK (yellow region) - do other (faster) mechanisms exist? è maybe some intelligent form of life did already collide somewhere particles to form a critical bubble? M. Lindner, MPIK Mass 2014 10
The dynamics of metastability: - the bubble discussion ignores thermal cool-down, i.e. how/why we ended up in the (metastable) EW vacuum - calculate thermal evolution of fluctuations and of field expectation value in cooling Universe è Langevin eqs. è does the fluctuating field fall into EW or global (wrong) vacuum? Bergerhoff, ML, Weiser <φ> The answer depends on exact parameters: - correct vacuum è bubble discussion - wrong vacuum è always instable! à metastability è SM metastability potentially dangerous è or avoid it: embeding into è importance of precise m H, m t determinations time M. Lindner, MPIK Mass 2014 11
Interpretating special Conditions: E.g. λ(m Planck ) = 0 λφ 4 è 0 at the Planck scale è no Higgs self-interaction (V is flat) è m H at low E radiativly generated - value related to m t and g i è SM emdeded directly into gravity!? - What about the hierarchy problem? à GR is different: Non-renormalizable! à requires new concepts beyond QFT/gauge theories:? à BAD: We have no facts which concepts are realized by nature à Two GOOD aspects: 1) QFTs cannot explain absolute masses and couplings - QFT embedings = shifting the problem only to the next level à new concepts beyond QFT might explain absolute values M. Lindner, MPIK Mass 2014 12
2) Asymmetry SMß à Planck scale may allow new solutions of the HP à new non-qft Planck-scale concepts could have mechanism which explain hierarchies à lost in effective theory = SM Anaology: Type II superconductor Ginzburg-Landau effective QFT ß à BCS theory ß à α, β, dynamical details lost è The hierarchy problem may be an artefact from a bottom-up QFT perspective. New physics beyond QFT at the Planck-scale could explain things from the top. M. Lindner, MPIK Mass 2014 13
Embeding the SM Remember: The SM does not exist without some embeding triviality/vacuum stab. è scale Λ required è cannot be ignored! What kind of embeding? è two options: 1) some new concept beyond d=4 QFT ß à λ(m Planck )=0 above 2) some d=4 QFT 2 nd route ß à work over many years - add representations - extended gauge groups with and without GUTs - include SUSY: MSSM, NMSSM,, SUSY GUTs - hidden (gauge) sectors, mirror symmetry, è Must face the gauge hierarchy problem M. Lindner, MPIK Mass 2014 14
The Hierarchy Problem: Specify Λ Renormalizable QFTs with two scalars ϕ, Φ with masses m, M and a mass hierarchy m << M These scalars must interact since ϕ + ϕ and Φ + Φ are singlets è λ mix (ϕ + ϕ)(φ + Φ) must exist in addition to ϕ 4 and Φ 4 Quantum corrections ~M 2 drive both masses to the (heavy) scale è two vastly different scalar scales are generically unstable Therefore: If (=since) the SM Higgs field exists è problem: embeding with a 2 nd scalar with much larger mass è solutions: a) new scale @TeV b) protective symmetry @TeV à LHC! This is usually SUSY, but SUSY & gauge unification = SUSY GUT à à doublet-triplet splitting problem à hierarchy problem back M. Lindner, MPIK Mass 2014 15
Conformal Symmetry as Protective Symmetry - Exact (unbroken) CS è absence of Λ 2 and ln(λ) divergences è no preferred scale and therefore no scale problems - Conformal Anomaly (CA): Quantum effects explicitly break CS existence of CA à CS preserving regularization does not exist - dimensional regularization is close to CS and gives only ln(λ) - cutoff reg. è Λ 2 terms; violates CS badly à Ward Identity Bardeen: maybe CS still forbids Λ 2 divergences è CS breaking ß à β-functions ß à ln(λ) divergences è anomaly induced spontaneous EWSB IMPORTANT: The conformal limit of the SM (or extensions) may have no hierarchy problem! M. Lindner, MPIK Mass 2014 16
Implications Gauge invariance è only log sensitivity Relics of conformal symmetry è only log sensitivity With CS there no hierarchy problem, even though it has anomaly Dimensional transmutation due to log running like in QCD è scalars can condense and set scales like fermions è use this in Coleman Weinberg effective potential calculations ß à most attractive channels (MAC) ß à β-functions M. Lindner, MPIK Mass 2014 17
Why the minimalistic SM does not work Minimalistic: SM + choose µ= 0 ß à CS Coleman Weinberg: effective potential è CS breaking (dimensional transmutation) è induces for m t < 79 GeV a Higgs mass m H = 8.9 GeV This would conceptually realize the idea, but: Higgs too light and the idea does not work for m t > 79 GeV Reason for m H << v: V eff flat around minimum ß à m H ~ loop factor ~ 1/16π 2 AND: We need neutrino masses, dark matter, M. Lindner, MPIK Mass 2014 18
Realizing the Idea via Higgs Portals SM scalar Φ plus some new scalar ϕ (or more scalars) CS à no scalar mass terms the scalars interact è λ mix (ϕ + ϕ)(φ + Φ) must exist è a condensate of <ϕ + ϕ> produces λ mix <ϕ + ϕ>(φ + Φ) = µ 2 (Φ + Φ) è effective mass term for Φ CS anomalous à breaking à only ln(λ) è implies a TeV-ish condensate for ϕ to obtain <Φ> = 246 GeV Note that this opens many other possibilities: - ϕ could be an effective field of some hidden sector DSB - further particles could exist in hidden sector; e.g. confining - extra U(1) potentially problematic ß à U(1) mixing - avoid Yukawas which couple visible and hidden sector à phenomenology safe since NP comes only via portal M. Lindner, MPIK Mass 2014 19
Realizing this Idea: Left-Right Extension M. Holthausen, ML, M. Schmidt Radiative SB in conformal LR-extension of SM (use isomorphism SU(2) SU(2) ~ Spin(4) à representations) è the usual fermions, one bi-doublet, two doublets è a Z 4 symmetry è no scalar mass terms ß à CS M. Lindner, MPIK Mass 2014 20
è Most general gauge and scale invariant potential respecting Z4 è calculate V eff è Gildner-Weinberg formalism (RG improvement of flat directions) - anomaly breaks CS - spontaneous breaking of parity, Z 4, LR and EW symmetry - m H << v ; typically suppressed by 1-2 orders of magnitude Reason: V eff flat around minimum ß à m H ~ loop factor ~ 1/16π 2 à generic feature à predictions - everything works nicely v è requires moderate parameter adjustment for the separation of the LR and EW scale PGB? M. Lindner, MPIK Mass 2014 21
Rather minimalistic: SM + QCD Scalar S J. Kubo, K.S. Lim, ML New scalar representation S à QCD gap equation: C 2 (Λ) increases with larger representations ß à condensation for smaller values of running α è q=3 S=15 Λ QCD Λ S M. Lindner, MPIK Mass 2014 22
Phenomenology M. Lindner, MPIK Mass 2014 23
Realizing the Idea: Other Directions SM + extra singlet: Φ, ϕ Nicolai, Meissner Farzinnia, He, Ren Foot, Kobakhidze, Volkas SM + extra SU(N) with new N-plet in a hidden sector Ko Carone, Ramos Holthausen, Kubo, Lim, ML Since the SM-only version does not work è observable effects: - Higgs coupling to other scalars (singlet, hidden sector, ) - dark matter candidates ß à hidden sectors & Higgs portals - consequences for neutrino masses M. Lindner, MPIK Mass 2014 24
Neutrino Mass Terms _ SM quarks, charged leptons: ~mlφr = (2 L x2 L x1 L ) è 1) Simplest possibility: add 3 or N right handed neutrino fields ν L g N ν R x <φ> = v ν R x ν R Majorana L / è c 0 m ν c D L ( ν ) L ν R md MR ν R like quarks and charged leptons è Dirac mass terms (including NMS mixing) New ingredients: 1) Majorana mass (explicit) 2) lepton number violation 6x6 block mass matrix block diagonalization M R heavy è 3 light ν s NEW ingredients, 9 parameters è SM+ and sea-saw M. Lindner, MPIK Mass 2014 25
2) new: scalar tripelts (3 L ) ν L ν 3" L or fermionic 1 L ro 3 L x x è left-handed Majorana mass term: ν L 1,3" ν L x x _ è M L LL c 3) Both ν R + new scalars: à SS type II, III 4) Higher dimensional operators: d=5 m ν =M L - m D M -1 R m T _ D è M L LL c 5-N) radiative mass generation, SUSY, extra dimensions, è inspiring options, many questions, connections to LFV, LHC,... è SM+ è can/may solve two of the SM problems: - Leptogenesis as explanation of BAU - kev sterile neutrinos as excellent warm dark matter candidate M. Lindner, MPIK Mass 2014 26
Conformal Symmetry & Neutrino Masses No explicit scale è no explicit (Dirac or Majorana) mass term à only Yukawa couplings generic scales Enlarge the Standard Model field spectrum like in 0706.1829 - R. Foot, A. Kobakhidze, K.L. McDonald, R. Volkas Consider direct product groups: SM HS arxiv:1405.xxxx à next days Two scales: CS breaking scale at O(TeV) + EW scale è spectrum of Yukawa couplings TeV or EW scale è many possibilities M. Lindner, MPIK Mass 2014 27
Examples Yukawa seesaw: SM + ν R + singlet è generically expect a TeV seesaw BUT: y M might be tiny è includes pseudo-dirac case Radiative masses or è pseudo-dirac case M. Lindner, MPIK Mass 2014 28
Seesaw & LNV More Examples: Inverse Seesaw µ is suppressed (LNV) natural scale kev M. Lindner, MPIK Mass 2014 29
Further Comments Having a new (hidden) sector è not surprisingly DM or kev-ish sterile neutrios as warm DM Question: Isn t the Planck-Scale spoiling things? è conformal gravity = non-linear realization see e.g. 1403.4226 by A. Salvio and A. Strumia è `Agravity or K. Hamada, 1109.6109, 0811.1647, 0907.3969 Question: What about inflation see e.g. 1405.3987 by K. Kannike, A. Racioppi, M. Raidal M. Lindner, MPIK Mass 2014 30
Summary Ø SM works perfectly no signs of new physics" " Ø The standard hierarchy problem suggests TeV scale physics which did (so far ) not show up " Ø Revisit how the hierarchy problem may be solved" Embeding into new concepts beyond QFT at M planck ß à might be connected to λ(m Planck ) = 0? è precise value of top mass " Embedings into QFTs with classical conformal symmetry à SM: Coleman Weinberg effective potential excluded à extended versions: singlets, SM=subgroup, hidden sectors à implications for Higgs couplings, dark matter, neutrinos è testable consequences @ LHC, DM search, neutrinos" M. Lindner, MPIK Mass 2014 31