Is There a New Physics Between Electroweak and Planck Scale ?

Is there a new physics between electroweak and Planck scale ?

Mikhail Shaposhnikov

Colloquium in the University of Nottingham

Nottingham, 14 November 2012 – p. 1 Electroweak scale ≡ Fermi scale GF : energies E ∼ 100 GeV distances l ∼ 10−16cm time intervals δt ∼ 10−26s Domain of particle physics

Planck scale is associated with Newton constant of gravitation GN : 19 energies E ∼ MP ∼ 10 GeV distances l ∼ 10−33cm time intervals δt ∼ 10−43s Domain of quantum gravity

17 orders of magnitude to go!

Nottingham, 14 November 2012 – p. 2 If yes

proton decay yes (?) Λ4 τ ∼ new p 5 mp

32 Current limit τp > 10 years; new physics at LHC yes (?) Electroweak scale solution to the hierarchy problem - stability of the weak scale against quantum radiative corrections. Supersymmetry, composite Higgs boson, large extra dimensions, etc. Scale of new physics hundreds of GeV.

Nottingham, 14 November 2012 – p. 3 If yes

searches for Dark Matter Weakly Interacting Massive Particles (WIMPS) yes (?) SUSY relic - neutralino searches for Dark Matter annihilation yes (?) SUSY relic - neutralino searches for axions yes (?) Axion is a hypothetic particle used for solution of the strong CP problem

Nottingham, 14 November 2012 – p. 4 If no

proton decay no 45 τp ≃ 10 years for Λnew ≃ MP Higgs and nothing else at LHC searches for Dark Matter Weakly Interacting Massive Particles (WIMPS) no searches for Dark Matter annihilation no searches for axions no

Interacts too weakly if Λnew ≃ MP

Nottingham, 14 November 2012 – p. 5 The answer to the question:

Is there a new physics between electroweak and Planck scale ?

Nottingham, 14 November 2012 – p. 6 The answer to the question:

Is there a new physics between electroweak and Planck scale ?

Is not known,

Nottingham, 14 November 2012 – p. 6 The answer to the question:

Is there a new physics between electroweak and Planck scale ?

Is not known, and is not up to a theorist to deside!

Nottingham, 14 November 2012 – p. 6 Outline

Is there a new physics beyond Standard Model?

Do we need an intermediate energy scale between MW and

MP lanck? Higgs mass and new physics Cosmological inﬂation Neutrino masses, dark matter and baryogenesis

Crucial tests and experiments

Conclusions

Nottingham, 14 November 2012 – p. 7 The Standard Model of particle interactions is in great shape: no convincing deviations from it were seen in any of accelerator experiments

The evidence for the Higgs boson with the mass 125 − 126 GeV has been reported recently by Atlas and CMS collaborations at LHC.

Nottingham, 14 November 2012 – p. 8 Is there a new physics beyond SM?

Nottingham, 14 November 2012 – p. 9 Is there a new physics beyond SM?

Yes: SM contradicts to experiments in neutrino physics and to a number of cosmological observations!

Nottingham, 14 November 2012 – p. 9 Neutrino masses and oscillations

Nottingham, 14 November 2012 – p. 10 CDHSW

CHORUS NOMAD NOMAD NOMAD

0 KARMEN2 CHORUS Problem with solar neutrinos 10 LSND Bugey BNL E776 since late 60, R. Davis K2K SuperK Masses: CHOOZ –3 PaloVerde 10 Super-K+SNO ∆m2 Cl +KamLAND

21 ]

= 7.65 ± 0.23 2 10−5 eV2 KamLAND

2 [eV 2 SNO ∆m32 –6 m 10 − = 2.40 ± 0.12 Super-K 10 3 eV2 ∆ Mixing matrix: Ga

0.79 − 0.88 0.47 − 0.61 < 0.20 –9   10 νe↔νX ν ↔ν 0.19 − 0.52 0.42 − 0.73 0.58 − 0.82 µ τ   νe↔ντ  0 20 − 0 53 0 44 − 0 74 0 56 − 0 81  ν ↔ν  ......  e µ SM: neutrinos are massless 10–12 10–4 10–2 100 102 tan2Nottingham,θ 14 November 2012 – p. 11 http://hitoshi.berkeley.edu/neutrino Dark matter in the universe

Nottingham, 14 November 2012 – p. 12 Problem since 1933, F. Zwicky. Most of the matter in the universe is dark Evidence:

Rotation curves of galaxies

Big Bang nucleosynthesis

Structure formation

CMB anisotropies

Supernovae observations

Non-baryonic dark matter:

ΩDM ≃ 0.22 SM: no particle physics candidate

Nottingham, 14 November 2012 – p. 13 Baryon asymmetry of the universe

Nottingham, 14 November 2012 – p. 14 Problem since 1930, P. Dirac. Observational evidence: no antimatter in the Universe. Required (Sakharov): T

Baryon number non-conservation symmetric phase (OK) critical point

CP-violation (OK) Higgs phase Substantial deviations from ther- MH mal equilibrium. Present for Higgs Electroweak theory masses larger than ≃ 73 GeV † 2 (ﬁrst order electroweak phase hφ φi ≪ (250GeV ) T = 109.2 ± 0.8GeV , transition).

MH = 72.3 ± 0.7GeV

† 2 hφ φiT =0 ∼ (250GeV ) SM: Higgs mass > 114 GeV CP violation present but too small to accommodate observed BAU.

Nottingham, 14 November 2012 – p. 15 Cosmological inﬂation

Nottingham, 14 November 2012 – p. 16 Important cosmological problems: Horizon problem: Why the universe is so uniform and isotropic?

t present horizon

recombination

horizon at recombination r

Expected ﬂuctuations at θ ∼ 1o: δT/T ∼ 1. Observed ﬂuctuations: δT/T ∼ 1O−5

Nottingham, 14 November 2012 – p. 17 Flatness problem: Why ΩM +ΩΛ +Ωrad is so close to 1 now and was immensely close to 1 in the past?

All this requires enormous ﬁne-tuning of initial conditions (at the Planck scale?) if the Universe was dominated by matter or radiation all the time!

Nottingham, 14 November 2012 – p. 18 Accelerated expansion of the Universe

Nottingham, 14 November 2012 – p. 19 Nottingham, 14 November 2012 – p. 20 Theoretical problems

Nottingham, 14 November 2012 – p. 21 Uniﬁcation with gravity?

4 Cosmological constant problem: Why ǫvac/MPl ≪ 1? Dynamical Dark Energy or cosmological constant?

Hierarchy problem: Why the Fermi scale is so much smaller than the Planck scale?

Stability of the Higgs mass against radiative corrections.

Strong CP-problem: Why θQCD ≪ 1? No CP-violation in strong interactions is seen.

Fermion masses: Why me ≪ mt? ...

Nottingham, 14 November 2012 – p. 22 Overwhelming point of view: these problems should ﬁnd their solution by physics beyond the SM which contains some intermediate energy scale

MW < Mnew < MPlanck

Nottingham, 14 November 2012 – p. 23 Do we need an intermediate energy

scale between MW and MP lanck?

Nottingham, 14 November 2012 – p. 24 Do we need an intermediate energy

scale between MW and MP lanck?

No: the SM problems can be solved by new physics below the Fermi scale !

Nottingham, 14 November 2012 – p. 24 Our strategy

Select the most important problems to solve (may be subjective). Most important for us: those where Standard Model is in conﬂict with observations: neutrino masses, dark matter, baryon asymmetry of the universe, inﬂation, accelerated expansion of the universe

Use Ockham’s razor principle: “Frustra ﬁt per plura quod potest ﬁeri per pauciora” or ”entities must not be multiplied beyond necessity”. For particle physics: entities = new hypothetical particles and new scales different from Fermi and Planck scales.

Nottingham, 14 November 2012 – p. 25 William of Ockham (Occam, Hockham,... ) 1288 - 1348

Nottingham, 14 November 2012 – p. 26 Higgs mass and new physics

Nottingham, 14 November 2012 – p. 27 July 4, 2012, Higgs at ATLAS and CMS

3500 ATLAS Data Sig+Bkg Fit (m =126.5 GeV) 3000 H Bkg (4th order polynomial) CMS 2500 Events / 2 GeV 2000

1500 s=7 TeV, ∫Ldt=4.8fb-1 1000 s=8 TeV, ∫Ldt=5.9fb-1 γγ→ 500 H (a) 200100 110 120 130 140 150 160 100 0 -100

Events - Bkg (b) -200 100 110 120 130 140 150 160 Data S/B Weighted 100 Sig+Bkg Fit (m =126.5 GeV) H Bkg (4th order polynomial) 80 weights / 2 GeV

Σ 60

20 (c) 8100 110 120 130 140 150 160 4 0 -4 (d) -8 Σ weights - Bkg 100 110 120 130 140 150 160 m γγ [GeV]

Nottingham, 14 November 2012 – p. 28 July 4, 2012, Higgs at ATLAS and CMS

According to CMS,

MH = 125.3 ± 0.4(stat) ± 0.5(syst) GeV,

According to ATLAS,

MH = 126 ± 0.4(stat) ± 0.4(syst) GeV.

Nottingham, 14 November 2012 – p. 29 July 4, 2012, Higgs at ATLAS and CMS

According to CMS,

MH = 125.3 ± 0.4(stat) ± 0.5(syst) GeV,

According to ATLAS,

MH = 126 ± 0.4(stat) ± 0.4(syst) GeV.

What does it mean for high energy physics?

Nottingham, 14 November 2012 – p. 29 Self-consistency of the SM

Within the SM the mass of the Higgs boson is an arbitrary parameter which can have any value (if all other parameters are ﬁxed) from

mmeta ≃ 111 GeV (metastability bound)

mLandau ≃ 1 TeV (triviality bound)

Nottingham, 14 November 2012 – p. 30 Triviality bound

L. Maiani, G. Parisi and R. Petronzio ’77; Lindner ’85; T. Hambye and K. Riesselmann ’96;... The Higgs boson self-coupling has a Landau pole at some energy determined by the Higgs mass. For MH ≃ mLandau ≃ 1 TeV the position of this pole is close to the electroweak scale.

ΛHΜL

strong coupling

Higgs mass 1 TeV ≃ M1 > M2 > M3 ≃ 175 GeV

Fermi Planck Nottingham, 14 November 2012 – p. 31 Triviality bound

If mH < mmax ≃ 175 GeV the Landau pole appears at energies higher than the Planck scale E>MP .

LHC: The Standard Model is weakly coupled all the way up to the Planck scale

Nottingham, 14 November 2012 – p. 32 Metastability bound

Krasnikov ’78, Hung ’79; Politzer and Wolfram ’79; Altarelli and Isidori ’94; Casas, Espinosa and Quiros ’94,’96;...

If mH < mmin, there is a deeper vacuum with the Higgs vacuum expectation value larger than the EW vev.

VHΦL VHΦL VHΦL

mH > mmin mH = mmin mH < mmin

Φ Φ Φ

The life-time of our vacuum is smaller than the age of the Universe if mH < mmeta, with mmeta ≃ 111 GeV Espinosa, Giudice, Riotto ’07

Nottingham, 14 November 2012 – p. 33 Metastability bound

If the Higgs mass happened to be smaller than mmeta ≃ 111 GeV, we would be forced to conclude that there must be some new physics beyond the SM, which stabilizes the SM vacuum.

However, already since LEP we know that mH > mmeta so that new physics is not needed from this point of view. LHC: SM is a consistent effective theory all the way up to the Planck scale!

Nottingham, 14 November 2012 – p. 34 Stability bound

The value of mmin does not represent any “singular" point in the parameter space of the pure SM, if time scales smaller than the age of the universe are considered . If MH = mmin, effective potential for the Higgs ﬁeld has two degenerate minima, one corresponding to the EW vev and another one much larger VHΦL

Still, let us discuss the value of mmin. Nottingham, 14 November 2012 – p. 35 Most recent computation of MH (Bezrukov, Kalmykov, Kniel, M.S.,

May 13, 2012), incorporating O(ααs) two-loop matching and 3-loop running of coupling constants (Chetyrkin, Zoller, May 13, 2012)

mt − 172.9 αs − 0.1184 mcrit = [129.0+ × 2.2 − × 0.56] GeV , 1.1 0.0007

Theoretical uncertainties: ±1.2 GeV (different sources are summed quadratically) or ±2.3 GeV (different sources are summed linearly).

4 2 2 4 Effect of contributions ∝ yt ,yt λ ,λ (Degrassi et al., May 29, 2012): shift of the Higgs mass by 100 − 200 MeV. Quadratic theoretical uncertainty is reduced to ∼ 0.8 GeV.

Nottingham, 14 November 2012 – p. 36 Nottingham, 14 November 2012 – p. 37 Prediction MH = mmin has been made a number of years before the Higgs boson was discovered:

Froggatt, Nielsen ’95: “...Imposing the constraint that the Standard Model effective Higgs potential should have two degenerate minima ( vacua), one of which should be - order of magnitudewise - at the Planck scale, leads to the top mass being 173 ± 5 GeV and the Higgs mass 135 ± 9 GeV...”

M.S., Wetterich ’09: Asymptotic safety of gravity and the Higgs boson mass

“... This results in MH = mmin = 126 GeV, with only a few GeV uncertainty...”

Also, MH = mmin is a critical point for Higgs inﬂation Bezrukov, M.S., ’09

Nottingham, 14 November 2012 – p. 38 Higgs mass and inﬂation

Nottingham, 14 November 2012 – p. 39 “Standard” chaotic inﬂationH self-reproducing inßationary universe. This theory is rather SPACE-TIME FOAM especially promising and leads to the most text of the chaotic inßation scenario. PLANCK DENSITY

LARGE alize quantum ßuctuations of the scalar QUANTUM Þeld in an inßationary universe as FLUCTUATIONS waves. They Þrst moved in all possible directions and then froze on top of one another. Each frozen wave slightly in creased the scalar Þeld in some parts of the universe and decreased it in others.

INFLATION SMALL QUANTUM verse where these newly frozen waves

POTENTIAL ENERGY FLUCTUATIONS persistently increased the scalar Þeld. Such regions are extremely rare, but still they do exist. And they can be ex tremely important. Those rare domains HEATING OF UNIVERSE of the universe where the Þeld jumps high enough begin exponentially ex SCALAR FIELD panding with ever higher the scalar Þeld jumps, the faster Courtesy: Linde

Nottingham, 14 November 2012 – p. 40 orey Linde Courtesy: SIZE OF UNIVERSE

10 SPACE-TIME FOAM –43 INFLATION CLOSED 10

–35 HEATING AGE OF UNIVERSE (SECONDS) 10 10 UNIVERSE SCENARIO 12 INFLATIONARY PLANCK LENGTH 10 17 10 BIG BANGMODEL STANDARD 30 AT PRESENTTIME UNIVERSE otnhm 4Nvme 02–p 41 p. – 2012 November 14 Nottingham, CLOSED FLAT OPEN FLAT OPEN Challenge for particle physics

Almost flat potential for large scalar fields is needed! Required for inflation: (to get δT/T ∼ 10−5)

quartic coupling constant λ ∼ 10−13:

mass m ∼ 1013 GeV,

Present in the Standard Model: Higgs boson

λ ∼ 1, mH ∼ 100 GeV δT/T ∼ 1

Nottingham, 14 November 2012 – p. 42 Challenge for particle physics

Almost flat potential for large scalar fields is needed! Required for inflation: (to get δT/T ∼ 10−5)

quartic coupling constant λ ∼ 10−13:

mass m ∼ 1013 GeV,

Present in the Standard Model: Higgs boson

λ ∼ 1, mH ∼ 100 GeV δT/T ∼ 1

New particle is required?

Nottingham, 14 November 2012 – p. 42 non-minimal coupling of Higgs ﬁeld to gravity

ξh2 ∆S = d4x −g − R ( 2 ) Z p

Feynman, Brans, Dicke,... Consider large Higgs ﬁelds h.

eﬀ 2 2 Gravity strength: MP = MP + ξh ∝ h All particle masses are ∝ ph

MP eff For h > ξ (classical) physics is the same (MW /MP does not depend on h)! Existence of effective flat direction, necessary for successful inflation.

Nottingham, 14 November 2012 – p. 43 Inﬂaton potential and observations

If inﬂaton potential is known one can make predictions and compare them with observations.

δT/T at the WMAP normalization scale ∼ 500 Mpc

The value of spectral index ns of scalar density perturbations

3 δT (x) δT (y) d k − − ∝ eik(x y)kns 1 T T k3 Z

The amplitude of tensor perturbations r = δρs δρt These numbers can be extracted from WMAP observations of cosmic microwave background. Higgs inﬂation: one new parameter, ξ =⇒ two

predictions. Nottingham, 14 November 2012 – p. 44 CMB parameters—spectrum and tensor modes

0.4 WMAP5 50 60

0.3

SM+ ξ h2 R 0.2

0.1

0.0 0.94 0.96 0.98 1.00 1.02

Nottingham, 14 November 2012 – p. 45 Inﬂation and the Higgs mass

Radiative corrections to inﬂationary potential: Higgs inﬂation works only for λ(MP / (ξ)) > 0 (Bezrukov, MS). Numerically,

MH > mmin −p200 MeV. The equality leads to the minimal value of non-minimal coupling, ξ ≃ 700, what extends the region of weak coupling of the theory.

V V

MH > mmin MH < mmin

φ φ

Fermi Planck Fermi PlanckNottingham, 14 November 2012 – p. 46 Neutrino masses, dark matter and baryogenesis

Nottingham, 14 November 2012 – p. 47 Neutrinos in the SM

SM fermions Neutrino is massless in the SM quarks since he does not have a right- left u d c s t b handed partner. Why? Because right u d c s t b at the time the SM was created ν ν µ ν τ left e e µ τ neutrinos were believed to be right e µ τ massless and lepton numbers leptons were believed to be conserved.

Now we know that neutrinos are massive and lepton numbers are not conserved.

Nottingham, 14 November 2012 – p. 48 The νMSM

Role of Ne with mass in keV region: dark matter

Role of Nµ,Nτ with mass in 100 MeV – GeV region: “give” masses to neutrinos and produce baryon asymmetry of the Universe Role of the Higgs: give masses to quarks, leptons, Z and W and inﬂate the Universe.

Nottingham, 14 November 2012 – p. 49 Constraints on DM sterile neutrino N1

Stability. N1 must have a lifetime larger than that of the Universe

Production. N1 are created in the early Universe in reactions l¯l → νN1, qq¯ → νN1 etc. We should get correct DM abundance

Structure formation. If N1 is too light it may have considerable free streaming length and erase ﬂuctuations on small scales. This can be checked by the study of Lyman-α forest spectra of distant quasars and structure of dwarf galaxies

X-rays. N1 decays radiatively, N1 → γν, producing a narrow line which can be detected by X-ray telescopes (such as Chandra or XMM-Newton). This line has not been seen yet

Nottingham, 14 November 2012 – p. 50 motn:D trl etiopouto eurstepre the large, requires production neutrino sterile DM Important: T 2 θ sin (2 1) ∼ 10 10 10 10 10 10 10 10 10 10 -15 -14 -13 -12 -11 -10 -7 -6 -9 -8 ∆ 100 / > L/L

e.I a nyb rdcdi the in produced be only can It MeV. Phase-space density constraints

BBN limit: L limit: BBN NRP Ω Ω 2 N N 1 1 > < × Ω Ω 10

DM DM

− BBN

3 2500 =

L L L

6 6

max

=25 =70 etnaymtya temperature at asymmetry lepton

M =700 1 [keV] 5 10 X-ray constraints ν MSM. 50 otnhm 4Nvme 02–p 51 p. – 2012 November 14 Nottingham, ec of sence Constraints on BAU sterile neutrinos N2,3

Baryon asymmetry generation: CP-violation in neutrino sector+singlet fermion oscillations+sphalerons

BAU generation requires out of equilibrium: mixing angle of N2,3 to active neutrinos cannot be too large

Neutrino masses. Mixing angle of N2,3 to active neutrinos cannot be too small

BBN. Decays of N2,3 must not spoil Big Bang Nucleosynthesis

Experiment. N2,3 have not been seen yet

Nottingham, 14 November 2012 – p. 52 NuTeV CHARM

10-6 NuTeV 10-6 CHARM PS191 PS191 BAU BBN BAU

2 -8 2 -8 BBN

U 10 U 10 BAU BAU

10-10 10-10 Seesaw Seesaw

10-12 10-12 0.2 0.5 1.0 2.0 5.0 10.0 0.2 0.5 1.0 2.0 5.0 10.0 M @GeVD M @GeVD

Constraints on U 2 coming from the baryon asymmetry of the Universe, from the see-saw formula, from the big bang nucleosynthesis and experimental searches. Left panel - normal hierarchy, right panel - inverted hierarchy. Canetti, Drewes, Frossard, MS

Nottingham, 14 November 2012 – p. 53 Crucial tests and experiments

Nottingham, 14 November 2012 – p. 54 Experiments, which will be done anyway

Unitarity of PMNS neutrino mixing matrix:

θ13, θ23 − π/4, type of neutrino mass hierarchy, Dirac CP-violating phase < −5 Absolute neutrino mass. The νMSM prediction: m1 ∼10 eV −2 −3 (from DM). Then m2 ≃ 5 · 10 eV, m3 ≃ 9 · 10 eV or −2 m2,3 ≃ 5 · 10 eV. (Double β decay, Bezrukov)

Normal hierarchy: 1.3 meV < mββ < 3.4 meV

Inverted hierarchy: 13 meV < mββ < 50 meV Crucial experimental test - the LHC, precise determination of the

Higgs mass, ∆MH ≃ 200 MeV Crucial cosmological test - precise measurements of cosmological parameters ns, r, ∆ns ≃ 0.004, the dark energy equation of state Nottingham, 14 November 2012 – p. 55 New dedicated experiments

Nottingham, 14 November 2012 – p. 56 High energy frontier

Construction of t-quark factory – e+e− or µ+µ− linear collider with energy ≃ 200 × 200 GeV.

Precise measurement of top and Higgs masses, to elucidate the relation between the electroweak and Planck scales.

Nottingham, 14 November 2012 – p. 57 Search for N1

X-ray telescopes similar to Chandra or XMM-Newton but with better energy resolution: narrow X-ray line from decay Ne → νγ One needs:

Improvement of spectral resolution up to the natural line width (∆E/E ∼ 10−3).

FoV ∼ 1◦ (size of a dwarf galaxies).

Wide energy scan, from O(100) eV to O(50) keV.

Nottingham, 14 November 2012 – p. 58 Search for N2,N3

2 −7 GeV Challenge - from baryon asymmetry: θ . 5 × 10 M CERN SPS is the best existing machine to uncover new physics below the electroweak scale. For l ∼ 100 m detector.

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▼ ❅●✝✞❉ ▼ ❅●✝✞❉ Gorbunov, MS

Nottingham, 14 November 2012 – p. 59 Conclusions

None of the arguments in favour of existence of the intermediate energy scale really requires it:

Inﬂation can happen due to non-minimal coupling of the Higgs to gravity

neutrino masses, dark matter and baryogenesis can all be explained by the particles with the masses below the electroweak scale

The minimal model dealing with many drawbacks of the SM requires only 3 new particles - Majorana neutrinos

There are plenty of experiments which can conﬁrm or reject the minimal model

Nottingham, 14 November 2012 – p. 60 Collaborators

Takehiko Asaka, Niigata U. Mikko Laine, Bern U. Fedor Bezrukov, Connecticut U. Amaury Magnin, EPFL Steve Blanchet, EPFL Andrii Neronov, Versoix Diego Blas, CERN Javie Rubio, EPFL Alexey Boyarsky, Leiden Oleg Ruchayskiy, CERN Laurent Canetti, EPFL Sergei Sibiryakov, INR Moscow Marco Drewes, Aachen U. Igor Tkachev, INR Moscow Juan Garcia-Bellido, Madrid U. Christof Wetterich, Heidelberg U. Dmitry Gorbunov, INR Moscow Daniel Zenhausern, EPFL

Nottingham, 14 November 2012 – p. 61 Back up slides

Nottingham, 14 November 2012 – p. 62 Solution of horizon and ﬂatness problems: Inﬂation = accelerated Universe expansion in the past

t present horizon

recombination

inflation

horizon at recombination r

t present horizon

recombination

horizon at recombination r Nottingham, 14 November 2012 – p. 63 To decrease uncertainty: (the LHC accuracy can be as small as 200 MeV!)

Compute remaining two-loop O(α2) corrections to pole - MS matching for the Higgs mass and top masses. Theoretical uncertainty can reduced to ∼ 0.5 GeV, due to irremovable

non-perturbative contribution ∼ ΛQCD to top quark mass.

Measure better t-quark mass (present error in mH due to this uncertainty is ≃ 4 GeV at 2σ level): construct t-quark factory – e+e− or µ+µ− linear collider with energy ≃ 200 × 200 GeV. The same conclusion - Alekhin et al, ’12

Measure better αs (present error in mH due to this uncertainty is ≃ 1 GeV at 2σ level)

Nottingham, 14 November 2012 – p. 64 Formalism: go from Jordan frame to Einstein frame with the use of conformal transformation:

2 2 2 ξh gˆµν = Ω gµν , Ω =1+ 2 MP Potential in Einstein frame

U(χ)

λM4/ξ2/4

Standard Model

λ v4/4 λM4/ξ2/16 Reheating 0 0 v 0 χ χ 0 end COBE χ Nottingham, 14 November 2012 – p. 65 How to ﬁnd DM sterile neutrino?

Boyarsky et al: Flux from DM decay N1 → νγ:

fov ΓradMdm ΓradΩfov Fdm = ≈ I, I = ρdm(r)dr 8πD2 8π L Z line of sight

(Valid for small redshifts z ≪ 1, and small ﬁelds of view Ωfov ≪ 1) Strategy: Use X-ray telescopes (such as Chandra and XMM Newton) to look for a narrow γ line against astrophysical background. Choose astrophysical objects for which:

The value of line of sight DM density integral I is maximal

The X-ray background is minimal

=⇒ Look at Milky Way and dwarf satellite galaxies ! Nottingham, 14 November 2012 – p. 66 Experimental signature

Two charged tracks from a common vertex, decay processes N → µ+µ−ν, etc. (sensitivity U 4 = U 2 × U 2) First step: proton beam dump, creation of N in decays of K,D or B mesons: U 2 Second step: search for decays of N in a near detector, to collect all Ns: U 2

MN < MK : Any intense source of K-mesons (e.g. from proton targets of PS.)

MN < MD: Best option: SPS beam + near detector

MN < MB: Project X (?) + near detector

MN > MB: extremely difﬁcult

Nottingham, 14 November 2012 – p. 67 Dark energy

Gravity =⇒ Unimodular Gravity + spontaneously broken scale invariance. Consequences:

Consistency with all tests of GR

Dynamical origin of all mass scales

Hierarchy problem gets a different meaning - an alternative (to SUSY, techicolor, little Higgs or large extra dimensions) solution of it may be possible.

Cosmological constant problem acquires another formulation.

Natural chaotic cosmological inﬂation

Low energy sector contains a massless dilaton

There is dynamical Dark Energy even without cosmological

constant Nottingham, 14 November 2012 – p. 68 July 4, 2012, Higgs at ATLAS and CMS

m = 126.0 GeV ATLAS 2011 - 2012 H W,Z H → bb s = 7 TeV: ∫Ldt = 4.7 fb-1 H → ττ s = 7 TeV: ∫Ldt = 4.6-4.7 fb-1 (*) H → WW → lνlν s = 7 TeV: ∫Ldt = 4.7 fb-1 s = 8 TeV: ∫Ldt = 5.8 fb-1 H → γγ s = 7 TeV: ∫Ldt = 4.8 fb-1 s = 8 TeV: ∫Ldt = 5.9 fb-1 (*) H → ZZ → 4l s = 7 TeV: ∫Ldt = 4.8 fb-1 s = 8 TeV: ∫Ldt = 5.8 fb-1

Combined s = 7 TeV: ∫Ldt = 4.6 - 4.8 fb-1 µ = 1.4 ± 0.3 s = 8 TeV: ∫Ldt = 5.8 - 5.9 fb-1

-1 0 1 Signal strength (µ)

Nottingham, 14 November 2012 – p. 69 Gauge coupling uniﬁcation: the three couplings of the SM intersect with each other at three points scattered between 1013 and 1017 GeV 16 – indication for Grand Uniﬁcation at MGUT ∼ 10 GeV (?) The constants of the SM do not meet at the same point: there must exist one more intermediate threshold for new physics between the GUT scale and the electroweak scale, chosen in such a way that all the three constants do intersect at the same point – indication for low energy supersymmetry (?)

i i α α 60 60 1/α 1/ 1/ 1 MSSM 50 50

40 40 α 1/ 2 30 30

20 20

10 10 α 1/ 3 0 0 0 5 10 15 0 5 10 15 10log Q 10log Q

Nottingham, 14 November 2012 – p. 70 Ways out

Possibility No 1:

Nottingham, 14 November 2012 – p. 71 Ways out

Possibility No 1: The standard model gauge couplings evolve and do not meet at the same point.

Nottingham, 14 November 2012 – p. 71 Ways out

Possibility No 1: The standard model gauge couplings evolve and do not meet at the same point. This is an indication that there is no Grand uniﬁcation. Possibility No 2

Nottingham, 14 November 2012 – p. 71 Ways out

Possibility No 1: The standard model gauge couplings evolve and do not meet at the same point. This is an indication that there is no Grand uniﬁcation. Possibility No 2

Gauge coupling uniﬁcation at MPl! (Hill, 1984; Shaﬁ and Wetterich, 1984..., Calmet et al, 2009)

Nottingham, 14 November 2012 – p. 71 Ways out

Possibility No 1: The standard model gauge couplings evolve and do not meet at the same point. This is an indication that there is no Grand uniﬁcation. Possibility No 2

Gauge coupling uniﬁcation at MPl! (Hill, 1984; Shaﬁ and Wetterich, 1984..., Calmet et al, 2009) Take any GUT and add 4+ n, n ≥ 1 dimensional operators like

2 n n Tr F Φ /MPl If hΦi ∼ MPl higher dimensional operators can shift the crossing point to MPl– uniﬁcation of gravity with other forces!

Nottingham, 14 November 2012 – p. 71 Higgs mass hierarchy problem

Actually, two different problems:

1. Why MW ≪ MP lanck?

2. Quantum corrections to the Higgs mass MH are (from power counting) quadratically divergent. What is the mechanism of their cancellation? Naturalness problem.

Only the second problem will be discussed.

Nottingham, 14 November 2012 – p. 72 Quadratic divergences

One can hear often: since the quantum corrections MH diverge as Λ2, one must introduce new physics which cancels these divergences, and that new physics should appear close to the EW scale.

Nottingham, 14 November 2012 – p. 73 Quadratic divergences

One can hear often: since the quantum corrections MH diverge as Λ2, one must introduce new physics which cancels these divergences, and that new physics should appear close to the EW scale.

Apply this argument to the vacuum energy ǫvac(quartically divergent): 1/4 −3 necessity of new physics at energies larger than ǫvac ≃ 10 eV?

Nottingham, 14 November 2012 – p. 73 Quadratic divergences

One can hear often: since the quantum corrections MH diverge as Λ2, one must introduce new physics which cancels these divergences, and that new physics should appear close to the EW scale.

Apply this argument to the vacuum energy ǫvac(quartically divergent): 1/4 −3 necessity of new physics at energies larger than ǫvac ≃ 10 eV?

Since this is not observed, we should either conclude that the case of quartic divergences is very much different from the case of quadratic divergences, or accept that this type of logic can be wrong.

Nottingham, 14 November 2012 – p. 73 Quadratic divergences

One can hear often: since the quantum corrections MH diverge as Λ2, one must introduce new physics which cancels these divergences, and that new physics should appear close to the EW scale.

Apply this argument to the vacuum energy ǫvac(quartically divergent): 1/4 −3 necessity of new physics at energies larger than ǫvac ≃ 10 eV?

In fact, besides the problem of Landau pole, the EW theory itself is known to be a perfectly valid theory without any new physics!

Nottingham, 14 November 2012 – p. 73 Naturalness and GUTs

Suppose that there is an intermediate high energy GUT scale,

MGUT ≪ MP lanck. Then one has to choose carefully counter-terms 2 2 up to N ≃ log(MGUT /MW )/ log(π/αW ) ≃ 13 loop level to get

MH ≪ MGUT ! This is enormous ﬁne-tuning and is an argument for existing of new physics right above the EW scale. Possible solution:

Compensation of divergent diagrams by new particles at TeV scale (supersymmetry, composite Higgs boson). Consequence: new physics at LHC

Nottingham, 14 November 2012 – p. 74 Naturalness without GUTs

Suppose that there are no GUTs or uniﬁcation happens at the Planck scale.

Easy “solution” to the problem of quadratic divergences: since we do not know what happens at the Planck scale, Planck mass cannot be considered as a ﬁeld-theoretical cut-off (or as a mass of some particle in dimensional regularisation). Consequence: Nothing but the Higgs at the LHC in the mass interval

mmin < mH < mmax.

Nottingham, 14 November 2012 – p. 75 Naturalness without GUTs

New symmetry – exact, but spontaneously broken scale invariance. Higgs mass is kept small in the similar way as photon mass is kept zero by gauge invariance. Consequences: validity of the SM all the way up to the Planck scale, nothing but the Higgs at the LHC. Existence of new massless particle – dilaton, which can play the role of dynamical Dark Energy. Dilaton – Goldstone boson of the broken scale invariance. It has only derivative couplings to matter, “gives” mass to the Higgs boson and determines the Planck mass via non-minimal coupling to gravity.

Scale-invariant renormalization procedure: Zenhäusern, M.S; Englert, Trufﬁn, Gastmans, 1976

Nottingham, 14 November 2012 – p. 76 Strong CP-problem

Invisible axion solution to strong CP-problem: Peccei-Quinn scale is bounded from above and below by cosmology and astrophysics to be 8 < < 12 in the region 10 GeV ∼MP Q ∼10 GeV.

Intermediate scale appears again?

Nottingham, 14 November 2012 – p. 77 Strong CP-problem

Invisible axion solution to strong CP-problem: Peccei-Quinn scale is bounded from above and below by cosmology and astrophysics to be 8 < < 12 in the region 10 GeV ∼MP Q ∼10 GeV.

Intermediate scale appears again? Not necessarily:

Strong CP-problem is essentially related to the topology of space. It appears only if the space is continuous and has non-trivial topological mapping onto 3-sphere.

Nottingham, 14 November 2012 – p. 77 Strong CP-problem

Invisible axion solution to strong CP-problem: Peccei-Quinn scale is bounded from above and below by cosmology and astrophysics to be 8 < < 12 in the region 10 GeV ∼MP Q ∼10 GeV.

Intermediate scale appears again? Not necessarily:

Strong CP-problem is essentially related to the topology of space. It appears only if the space is continuous and has non-trivial topological mapping onto 3-sphere.

Is there space at all at short distances if gravity is included?

Nottingham, 14 November 2012 – p. 77 Strong CP-problem

Invisible axion solution to strong CP-problem: Peccei-Quinn scale is bounded from above and below by cosmology and astrophysics to be 8 < < 12 in the region 10 GeV ∼MP Q ∼10 GeV.

Intermediate scale appears again? Not necessarily:

Strong CP-problem is essentially related to the topology of space. It appears only if the space is continuous and has non-trivial topological mapping onto 3-sphere.

Is there space at all at short distances if gravity is included?

Is the topology of space always non-trivial?

Nottingham, 14 November 2012 – p. 77 Topology

If extra dimensions have topology such that the mapping

D − dim Space → S3

is trivial no θ angle exists! Planck scale compactiﬁcation is sufﬁcient - the solution to the strong CP-problem may occur at MPl (Khlebnikov, M.S., 1988, 2004)

Nottingham, 14 November 2012 – p. 78 2 + 1 U(1) example, brane-world

2 π jump Brane-world compactiﬁcation, S2 → U(1) = S1 - trivial mapping → no N-vacua → no θ φ < 0 vacua.

BRANE Extra dimensions are not seen if φ > 0 we live on a brane. Major ingredients: Maxwell equations do not admit (i) compactness of the space existence of source-less static (ii) non-factorizable geometry electric ﬁeld.

Nottingham, 14 November 2012 – p. 79 Constraints on DM sterile neutrino

Production. Ne are created in the early Universe in reactions l¯l → νNe, qq¯ → νNe etc. We should get correct DM abundance.

X-rays. Ne decays radiatively, Ne → γν, producing a narrow line which can be detected. This line has not been seen (yet).

Structure formation. If Ne is too light it may have considerable free streaming length and erase ﬂuctuations on small scales. This can be checked by the study of Lyman-α forest spectra of distant quasars.

Nottingham, 14 November 2012 – p. 80 DM: production+ X-ray constraints + Lyman-α bounds

10-6

10-8

Ω > ΩDM

10-10 ) 1 θ (2 2

Sin 10-12

10-14

Ω < ΩDM

10-16 0.3 1 10 50 100 M1 [keV] Nottingham, 14 November 2012 – p. 81 DM: production + X-ray constraints+ Lyman-α bounds

10-6

10-8

Ω > ΩDM

10-10 ) 1 θ (2 2 N → νγ

Sin e 10-12

10-14

Ω < ΩDM

10-16 0.3 1 10 50 100 M1 [keV] Nottingham, 14 November 2012 – p. 82 DM: production + X-ray constraints + Lyman-α bounds

10-6

10-8

Ω > ΩDM

10-10 ) 1 θ (2 2 N → νγ

Sin e 10-12 Lyman-α

10-14

Ω < ΩDM

10-16 0.3 1 10 50 100 M1 [keV] Nottingham, 14 November 2012 – p. 83 Direct experimental test: astrophysics

Over the last years restrictions on sterile neutrino parameters were improved by several orders of magnitude. The new data from Chandra and XMM-Newton can hardly improve constraints by more than a factor 10. One needs:

Improvement of spectral resolution up to the natural line width (∆E/E ∼ 10−3).

FoV ∼ 1◦ (size of a dSph).

Wide energy scan, from O(100) eV to O(10) MeV.

Nottingham, 14 November 2012 – p. 84 Constraints on BAU Majorana fermions

BAU generation requires out of equilibrium: mixing angle of Nµ,τ to active neutrinos cannot be too large

Neutrino masses. Mixing angle of Nµ,τ to active neutrinos cannot be too small

Dark matter and BAU. Concentration of DM sterile neutrinos must be much larger than concentration of baryons

BBN. Decays of Nµ,τ must not spoil Big Bang Nucleosynthesis

Experiment. Nµ,τ have not been seen (yet).

Nottingham, 14 November 2012 – p. 85 Nµ,τ : BAU+ DM + BBN + Experiment

10-5

10-6

10-7 BAU

10-8 2 2 N ν θ 10-9

10-10

-11 See-saw 10

10-12 0.1 1 10 M [GeV] 2 Nottingham, 14 November 2012 – p. 86 Nµ,τ : BAU + DM+ BBN + Experiment

10-5

10-6

10-7 BAU

10-8 2 2 N ν θ 10-9

-10 10 DM preferred

-11 See-saw 10

10-12 0.1 1 10 M [GeV] 2 Nottingham, 14 November 2012 – p. 87 Nµ,τ : BAU + DM + BBN+ Experiment

10-5

10-6

10-7 BAU

10-8 2 2 N ν θ 10-9

-10 10 BBN DM preferred

-11 See-saw 10

10-12 0.1 1 10 M [GeV] 2 Nottingham, 14 November 2012 – p. 88 Nµ,τ : BAU + DM + BBN + Experiment

10-5 CHARM BEBC NuTeV 10-6

ExperimentsPS191 10-7 BAU SPS -8 10 NA62

2 20

2 2.5x10 PoT N

ν PS θ 10-9

-10 10 BBN DM preferred

-11 See-saw 10

10-12 0.1 1 10 M [GeV] 2 Nottingham, 14 November 2012 – p. 89 Search for Nµ,Nτ

2 −7 GeV Challenge - from baryon asymmetry: θ . 5 × 10 M Peak from 2-body decay and missing energy signal from 3-body decays of K,D and B mesons (sensitivity θ2) Example:

+ + 2 2 K → µ N,MN = (pK − pµ) =6 0

Similar for charm and beauty.

MN < MK : KLOE, NA62, E787

MK < MN < MD: charm and τ factories, CLEO

MN < MB: (super) B-factories

Nottingham, 14 November 2012 – p. 90 Search for Nµ,Nτ

Two charged tracks from a common vertex, decay processes N → µ+µ−ν, etc. (sensitivity θ4 = θ2 × θ2) First step: proton beam dump, creation of N in decays of K,D or B mesons: θ2 Second step: search for decays of N in a near detector, to collect all Ns: θ2

MN < MK : Any intense source of K-mesons

MN < MD: CERN SPS beam + near detector

MN < MB: Project X (?) + near detector

MN > MB: extremely difﬁcult

Nottingham, 14 November 2012 – p. 91 Previous searches at CERN

A. M. Cooper-Sarkar et al. [WA66 Collaboration] “Search For Heavy Neutrino Decays In The Bebc Beam Dump Experiment”, 1985

J. Dorenbosch et al. [CHARM Collaboration] “A search for decays of heavy neutrinos in the mass range 0.5-GeV to 2.8-GeV”, 1985

G. Bernardi et al., “Search For Neutrino Decay”, 1986; “Further Limits On Heavy Neutrino Couplings”, 1988

P. Astier et al. [NOMAD Collaboration], “Search for heavy neutrinos mixing with tau neutrinos”, 2001

P. Achard et al. [L3 Collaboration], “Search for heavy neutral and charged leptons in e+e− annihilation at LEP”, 2001

Nottingham, 14 November 2012 – p. 92 N2,3 production and decays

2 | | 2 Uτ4 |Uτ4|

+_ τ Ds - e + Proton beam, 450 GeV/c e ν 4 Z ν Target τ

Steel, earth NOMAD detector shielding

Type on neutrino mass hierarchy - from branching ratios of N2,3 decays to e, µ,τ .

CP asymmetry can be as large as 1% - from BAU and DM

Nottingham, 14 November 2012 – p. 93 Nottingham, 14 November 2012 – p. 94