The Higgs boson and the cosmological constant puzzle

The Higgs boson and the cosmological constant puzzle Steven Bass Symmetry breaking Condensates produce a potential in the vacuum Light mass pions as Goldstone bosons within QCD, extensions to eta and eta Higgs boson and mass generation in Standard Model particle physics e.g. LHC Cosmological constant puzzle: Accelerating Universe: believed to be driven by energy of nothing (vacuum) Vacuum energy density (cosmological constant or dark energy) is 10 56 times less than what Standard Model particle physics expects, though curiously ~ (light neutrino mass) 4 Krakow, January 2017 1

Dark energy and its size Particle physics Nice thing (QED, QCD, Higgs,... LHC, LEP...) Standard Model works very well, no sign yet of BSM also in dark matter searches (Xenon100, LUX...), precision measurements: eedm..., CPT and Lorentz invariance... meets General relativity Nice thing (Binary pulsars, lensing, black holes, Lab tests of Inverse Square Law to 56 µm...) Curious result: discrepancy of 10 56 (!) + wrong sign (!) Also, within present errors, couplings and masses are time independent 2

Vacuum Energy and the cosmological constant puzzle Cosmological constant puzzle: SDB, Mod. Phys. Lett. A 30 (2015) 1540033 Accelerating Universe: believed to be driven by energy of nothing (vacuum) Positive vacuum energy = negative vacuum pressure Vacuum energy density (cosmological constant or dark energy) is 10 56 times less than what Standard Model particle physics expects, though curiously ~ (light neutrino mass) 4 Explore possible interface of dark energy and LHC results: Higgs vacuum (meta-)stability Coincidence puzzle: Very different time dependence of matter, radiation and vacuum energy densities since Big Bang. Today matter and vacuum energy densities are within order of magnitude of each other. 3

Quarks, leptons and gauge bosons 4

Do we see everything? 5

Dark Matter 6

Our evolving Universe 7

Gravity and particle physics Gravitation and the cosmological constant are fundamentally different from particle physics and other physics in that gravity couples to everything whereas other physics processes and experiments involve measuring the differences between quantities. Absolute values of the zero-point vacuum energy only enters when coupling to gravity. 8

General relativity Energy and mass connected» E = m c 2 Newton gravity couples to mass Einstein gravity couples to energy Matter tells space how to warp. And warped space tells matter how to move If nothing (the vacuum) has energy (e.g. Vacuum condensates), then the vacuum gravitates Nothing also tells space how to warp.» How big is the energy of nothing? 9

The Cosmological Constant Puzzle Cosmological constant behaves like a vacuum energy (plus counterterm) Quantum field theory (particle physics): zero point energies Normal ordering zero, but then Spontaneous Symmetry Breaking (Higgs) and condensates Accelerating Universe corresponds to 10

General Relativity Postulates SDB, J Phys G 38 (2011) 043201 11

General Relativity General Relativity as a gauge theory Tensor transormation rules under change of co-ordinate system 12

General Relativity Gravitational covariant derivative Is like the gauge covariant derivative in particle physics Can be expressed in terms of the metric and derivatives» Christoffel symbols 13

General Relativity En route to Einstein s equations Riemann curvature tensor Ricci tensor and scalar Satisfy Bianchi identity 14

Einstein s equations Einstein tensor (built from the metric) Satisfies (from Bianchi identity) In the presence of matter, can couple to conserved and symmetric tensor: the energy momentum tensor With cosmological term as constant of integration 15

Einstein s equations and gravity General relativity: dynamical theory of gravity linking gravity with spacetime geometry Matter tells space how to warp. And warped space tells matter to move Cosmological principle: homogeneous and isotropic Evaluate Einstein s equations for 16

The geometry of space 17

Solutions of possible (flat) Universes Matter dominated, p=0 Radiation dominated, Vacuum dominated 18

Einstein s original guess and blunder Einstein originally guessed at a closed and static Universe So solving With H=0 for K=+1 gives the equations With solution The cosmological constant here is balancing usual gravitational attraction Then Einstein retracted the CC with Hubble s discovery of expanding Universe... 19

Convergence of measurements 70% of the energy budget of the Universe is vacuum energy 20

Supernova 1a Redshift measures how much the space between the supernova and the observer has stretched Compare brightness to redshift for distant (type 1a) supernovae to see how the expansion rate has changed If just matter Universe, then the further away (back in time) a supernova is, the brighter (closer) it would appear relative to its redshift. The opposite is observed for z < 1. 21

Supernovae (type 1a) Star uses up its nuclear fuel, collapses under gravity and then recoils with explosion leaving black hole or neutron star remnant White dwarf star: size of earth, mass of the sun in binary star system Accretion onto carbon/oxygen white dwarf Standard candle, uniform brightness, 5 billion times sun Time lasts about 20 days to reach maximum brightness 10 43 watts, 3x in galaxy per millenium 22

Observations like dry skies 23

Our evolving Universe 24

Coincidence puzzle Very different evolution of matter, radiation and vacuum energy densities with evolution of the Universe Today: 69 % Dark energy, 26% Dark matter and 5% made of atoms (plus neutron stars) Is there something special about today? Weinberg: Large scale galactic structures stop to form when Dark Energy takes over Dark energy dominating since 5B years First single cell life on Earth ~ 3.5B years 25

Planck results Probing the dark energy equation of state, w = p/rho Assume Constant EoS Time dependent EoS Euclid target: Measure the DE equation of state parameters w 0 and w 1 to a precision of 2% and 10% respectively, using both expansion history and structure growth (2019+) 26

Expansion History of the Universe 27

Particles and space 28

Scales Dark energy scale ~ 0.002 ev Electroweak Higgs scale 250 GeV QCD Scale 1 GeV Planck mass (gravitation) 10 19 GeV Light neutrino mass ~ 0.005 ev (normal hierachy) Inflation (fourth root of r, Bicep2+...) ~ 10 16 GeV Jegerlehner (EWSB) 1.4 x 10 16 GeV (sign change of c-term) GUTs 10 15 GeV 30

Zero point energies Zero Point Energies done naively and with MSbar (Lorentz invariantly) Note here massless photon gives zero, biggest contribution from the top Question: Does vacuum zero-point energy gravitate? 31

Phases of gauge theories Particle physics is built from QED in the Coulomb Phase QCD in the Confining Phase» QCD condensates ~ - (200 MeV) 4 from DChSB Electroweak Interactions in the Higgs Phase» Higgs condensate ~ - (250 GeV) 4 32

Phenomenological observation Dark energy scale μ vac ~ 0.002 ev If taken literally, this formula connects Dark Energy, neutrino physics and EWSB to a new high mass scale M ~ 3 x 10 16 GeV which needs to be understood. Suggests perhaps the cosmological constant puzzle and electroweak hierarchy problems might have a common origin at very high mass scale, close to the Planck mass (?) 33

Dark energy: Challenges for theory Why is it finite? Why so very small << very large particle physics prediction? Why the positive sign? Do condensates gravitate? E.g. Freedom to define zero of energy in QFT, but time dependence Connection with inflation? Sum of many big numbers (quantum fields and particle physics) add up to very small number Usual trick: Assume solved by (gravity) counterterms or anthropic arguments Introduce new (time dependent) scalar field (quintesence) or modified gravity, resum quantum gravity with asymptotic safety... Can we understand the physics without elementary scalar fields? 35

Cosmological Constant ideas Connections to LHC physics (?) Time dependent couplings and scalar fields (?) Extra dimensions (?) Emergence arguments (?) Anthropic arguments (?) Connections with quantum gravity (?) 36

Results from LHC LHC: So far just Standard Model Higgs and no BSM, SUSY... Remarkable: the Higgs and top mass sit in window of possible parameter space where the Standard Model is a consistent theory up to the Planck mass close to the border of a stable and meta-stable vacuum. 38

Vacuum stability 39

Vacuum stability - Jegerlehner 41

Vacuum stability Buttazzo et al 42

Bednyakov, Kniehl et al 43

Vacuum stability - Masina 44

Veltman condition 45

Jegerlehner scenario Counter-terms for Higgs mass and vacuum energy density change sign together 46

Stability of Higgs mass 47

Standard Model consistent theory all the way up to the Planck scale Standard Model works all the way up to the Planck scale Are the Higgs sector and electroweak scale connected to physics at the Planck scale? Possible relationship between Standard Model parameters and Planck scale Implicit reduction of fundamental couplings 48

Electroweak Vacuum Stability Possible critical phenomena close to Planck mass with Standard Model as the long range tail of a critical Planck system Higgs mass and couplings linked to stable ground state Inflation associated with Higgs in very early Universe (?) Cosmological constant size here (perhaps) fixed by flatness, which is induced by inflation 49

Electroweak Vacuum Stability Possible critical phenomena close to Planck mass with Standard Model as the long range tail of a critical Planck system Is the Standard Model emergent? (cf. Low energy part of GUT spontaneously broken by multiple Higgs fields and condensates) If yes, possible violations of Lorentz invariance, gauge invariance &tc at very high scales close to the Planck mass - perhaps vanishing with vanishing dark energy and suppressed in laboratory experiments by powers of μ/m 50

Scales of dark energy Dark energy scale close to what we expect for light neutrino mass Relation to Hubble scale Geometric mean of Hubble scale and Planck mass Alternative curvature scale 51

Dark energy: driven by new scalar field Possible connection with inflation - first period of (rapid) acceleration Here equation of state different to w = p/rho = -1 Same fine tuning puzzle for quantum fields. Scalar field should decay from large potential» Very small mass So far, Cosmological constant describes all data with no evidence for more Time dependent couplings? Stability of scalar to quantum corrections? 52

Time dependent fundamental constants (?) Time dependent couplings (?) Lagrangian with coupling to time dependent scalar Constraints from experiments on time dependence of fine structure constant from CMB (13 B years), Quantum Optical Clocks (today)... M p /m e ratio (transitions in methanol in early Universe, 7B years and Quantum optical clocks today) 53

Time dependent fundamental constants (?) Constraints from quantum optics (today) Molecular clouds in space (7.5B years ago) on ratio of electron to proton mass CMB contraints Newton s constant (variety of measurements) [Refs and discussions in SDB, Mod Phys Lett A30 (2015) 1540033] 54

Extra dimensions and modified gravity Living on a membrane in a bigger dimensional space, e,g, 5 dimensional Minkowski bulk space Membrane breaks the rotational symmetry of the 5D space yielding small effective mass for the graviton Gravitational action is Where L determines change over for the gravitational potential So far, general relativity consistent with all astronomical observations 55

Theoretical speculations Dynamical Symmetry Breaking (Quantum) and GR (Classical) Do vacuum condensates gravitate (Brodsky)? Quintessence: add a scalar field... Time dependence (Sola) Stability to radiative corrections and matter coupling... Screening mechanisms... Chameleons &tc Resummation of gravity (Ward) + Asymptotic Safety (Weinberg) Modification of general relativity (extra dimensions) Emergent gauge bosons, cf Volovik and bubble of He3 Anthropic arguments 56

Attempts to understand Analogy based on Ising model (spin magnet) In the ground state all the spins line up and the energy per spin and free energy density go to zero, corrections are suppressed by powers of e -βj With no external field, pressure is equal to minus the free energy density Looks like neutrino vacuum Neutrinos so far observed are left handed Free energy density in Statistical Mechanics (same equation of state as cosmological constant) vacuum energy density in Quantum Field Theory Resultant picture: Standard Model like an impurity in a spin system which exists near the Planck scale, at about 3x10 16 GeV. Phase transition involving the neutrino generates parity violation and Higgs phase for gauge bosons which couple to the neutrino. The vacuum energy of the Higgs system diluted by same physics which generates parity violation SDB, Acta Phys Pol B 45 (2014) 1269; arxiv:1210.3297 [hep-ph] 57

Neutrinos Confining SU(2) with vector interactions: Mesons made of electrons and neutrinos Decouble RH neutrino: What happens to Confinement? No RH neutrino no scalar condensate usual confining solution disappears! (in the Bag model, a LH quark would bounce off the confining wall as a RH quark) Change in non-perturbative propagator, DSB to Higgs (or Coulomb) phase, or confinement radically reorganised? Small QCD correction ~ 30 MeV 58

Look for analogous system: Spin model Consider Ising model for spin system with no external field Pressure is equal to minus the free energy density Ground state: spins line up and energy per spin and free energy density go to zero. Corrections suppressed by powers of 59

Spin model neutrinos Suppose we identify the chirality of the neutrino with the spins in an Ising model» phenomenological guess (toy model), see what happens Scale must be very large (so J does not appear in the ground state) Turn on Ising interaction generates parity violation (no RH neutrino) Anomaly cancelation wanted in UV, so DSB should be active there DSB scale should not appear smaller than any power of running coupling 60

DSB in spin model + gauge theory With mass scale in particle physics Lagrangian Higgs sector with finite mass gap gives non-zero ground state vacuum energy (behaves like an impurity in the Ising system) Ground state energy in spin basis Diagonalising The energy density of the combined spin -gauge system (e.g. whole thing that couples to gravity) is suppressed by the same physics which gives parity violation 61

Where are we going? 62

Open questions The Standard Model of particle physics and general relativity work very everywhere they have been tested in experiments What energy scale does the new physics enter, which we need to describe the baryon asymmetry, dark matter...? Why are there 3 families of fermions? Simplicity = less parameters or more symmetry (bigger symmetry groups but coming with extra parameters to explain why not seen in present experiments) Unification versus emergence How can we reconcile particle physics and gravity? Is there a theory of quantum gravity waiting to be discovered? 63

Open questions Can we find a rigorous theory of quark and gluon confinement?» QCD inspired model phenomenology works very well» Lattice QCD calculations» Detailed confinement mechanism for light quarks to be understood Dense matter the structure of neutron stars with challenge to test QCD with astronomy observations Black holes mass ranges What will we learn from neutrino and gravitational wave astronomy? What are dark energy and dark matter? Are fundamental constants time dependent? 64

Zero point energies RQM: Klein Gordon equation allows positive and negative energies Negative energy solutions resolved with using quantum fields Generalise commutation relations to canonical field momenta 65

Zero point energies - bosons Evaluating Hamiltonian gives Where N is particle number operator Process of normal ordering (creation operators to left of annihilation operators) sets energy of vacuum to zero decouples from processes where we always measure differences between quantities 66

Zero point energies - fermions Repeating for fermions satisfying the Dirac equation Fields now satisfy anticommutation relations Pauli principle 67

Zero point energies - fermions Evaluate Hamiltonian Gives negative zero point energy 68