The Higgs Boson & Beyond

Joint Colloquium

National Taiwan University, Dec. 8, 2015

The Higgs Boson & Beyond

Tao Han

PITT PACC, Univ. of Pittsburgh

TsingHua U. / CFHEP, Beijing

François Englert and Peter W. Higgs

"for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the

predicted fundamental particle, by the ATLAS and CMS

experiments at CERN's Large Hadron Collider"

The discovery:

A neutral boson decay to two photons

Phys. Lett. B716, 30 (2012) Phys. Lett. B716, 1 (2012)

The combined signal significance:

ATLAS: 5.9σ CMS: 5.0σ

At λ ≈ 10

nm.

July 4

, 2012:

Particle mass [GeV]

10 1 1 10 10²

vV

m F or Vv

m _F

10 4

10 3

10 2

10 1

1 Z

W t

b µ

ATLAS and CMS

LHC Run 1 Preliminary

Observed

SM Higgs boson

κV

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Fκ

0.4 0.6 0.8 1 1.2 1.4

1.6 ATLAS and CMS LHC Run 1

Preliminary

ATLAS CMS

ATLAS+CMS

SM 68% CL

Best fit 95% CL

Summer 2015 update:

5σ for both fermion coupling h à ττ

& bosonic coupling WW à h

- it’s neutral, a boson

- it’s spin-0, parity-even

- it couples to mass, non-universally

50 years theoretical work …

25 years experimental work …

Congratulations to our CMS colleagues in Taiwan !

A milestone discovery:

It is a brand new class!

long range

~(^G_N m₁m₂)/

r

long range

~(α e₁e₂)/

r

The Nature of Forces:

short range ~

e

/r

•  At low energies à Maxwell’s theory; vector-like coupling by a U

(1) gauge symmetry

E&M: Most Successful in Theory & Practice!

↵(Q

) = ↵(Q

)

1

ln(Q

/Q

) L = 1

4 F

F

+ ¯ (i

D

m

)

F

= @

A

@

A

, D

= @

+ ieA

•  At high energies à Quantum-mechanical, renormalizable, most accurate (in science!): a part of trillion

a^theo_e = 0.001159652181643(763) a^exp_e = 0.00115965218073(28)

•  QED becomes strongly interacting asymptotically (screening effects)

At ultra-violet (UV) à theory is invalid.

•  At short distances/high energies à

asymptotically free (anti-screening effects)

The strong force: SU

(3) Quantum Chromo-Dynamics Successful Theory, Challenging in Practice!

L = 1

4F_µ⌫^a F^aµ⌫ +

n_f

X

f

¯q_f(i ^µ@_µ g_s ^µA_µ m_f)q_f F_µ⌫ = @µA_⌫ @µA_⌫ + ig_s[A_µ, A_⌫]

A^µ(x) =

X8 1

A(x)^µ_a T^a, [T^a, T^b] = if_abcT^c.

QCD α_s(M_z) = 0.1185 ± 0.0006

Z pole fit

0.1 0.2 0.3

α_s (Q)

1 10 100

Q [GeV]

Heavy Quarkonia (NLO)

e⁺e jets & shapes (res. NNLO)

DIS jets (NLO)

Sept. 2013

Lattice QCD (NNLO)

(N³LO)

τ decays (N³LO)

1000 pp > jets ^{( )} (NLO)

Highly predictable at high energies:

Crucial for HEP, early Universe …

•  At long distances/low energies >

à  Strongly interacting: quarks condensate (π

, π

…) & (colorless) hadrons (p

, n) formed.

↵_s(Q²) = 12⇡

(33 2n_f) ln(Q²/⇤²)

The local gauge symmetry prevents gauge bosons masses!

The Weak force: Quark & Lepton Flavor Transitions

Beta decay n à p

e

ν ➔ Charged current interaction: W

L^weak = G_F

p2 J^µ(p⁺n)J_µ(e ⌫) force range ⇠ p

G_F ⇠ M_W¹ ⇠ 10 ¹⁸m

However,

Pauli’s rejection to the Yang-Mills theory.

Inspired by EM current-current interactions, Fermi proposed (1934)

Weak interaction based on SU(2) x U(1):

− g 2√

2

!

i

Ψ_i γ^µ (1 − γ⁵)(T⁺ W_µ⁺ + T⁻ W_µ⁻) Ψ_i

− e!

i

q_i ψ_i γ^µψ_i A_µ

− g

2 cos θ_W

!

i

ψ_i γ^µ(g_Vⁱ − g_Aⁱ γ⁵) ψ_i Z_µ .

December 24, 2008 11:29 WSPC - Proceedings Trim Size: 9in x 6in tasi08˙pgl

3

or large distances it becomes strongly coupled (infrared slavery),⁸ presum- ably leading to the confinement of quarks and gluons. QCD incorporates the observed global symmetries of the strong interactions, especially the spontaneously broken global SU(3) ⇥ SU(3) (see, e.g., 9).

0.1 0.12 0.14

Average Hadronic Jets

Polarized DIS

Deep Inelastic Scattering (DIS) τ decays Z width

Fragmentation

Spectroscopy (Lattice) ep event shapes

Photo-production

Υ decay

e⁺e^- rates

α_s(M_Z)

0 0.1 0.2 0.3

1 10 10²

µ GeV α s(µ)

Fig. 2. Running of the QCD coupling ↵_s(µ) = g_s(µ)²/4⇡. Left: various experimental determinations extrapolated to µ = M_Z using QCD. Right: experimental values plotted at the µ at which they are measured. The band is the best fit QCD prediction. Plot courtesy of the Particle Data Group,⁵ http://pdg.lbl.gov/.

1.2. The Electroweak Theory

The electroweak theory^10–12 is based on the SU(2) ⇥ U(1) Lagrangian^b L^{SU (2)}_⇥U(1) = L^gauge + L + L^f + L^{Y uk}. (5) The gauge part is

L^gauge = 1

4W_µ⌫ⁱ W^µ⌫i 1

4B_µ⌫B^µ⌫, (6)

where W_µⁱ, i = 1, 2, 3 and B_µ are respectively the SU(2) and U(1) gauge fields, with field strength tensors

B_µ⌫ = @_µB_⌫ @_⌫B_µ

W_µ⌫ⁱ = @_µW_⌫ⁱ @_⌫W_µⁱ g✏_ijkW_µ^jW_⌫^k, (7)

bFor a recent discussion, see the electroweak review in 5.

(Glashow, ‘63)

Fermion masses also forbidden by gauge symmetry!

Even worse:

``The Left- and right-chiral electrons carry different Weak charges’’ (Lee & Yang)

The Weak force: Quark & Lepton Flavor Transitions

Electroweak gauge theory à massless!

“ The Lagrangian of the system may display an symmetry, but the ground state does not respect the same symmetry.”

Known Example: Ferromagnetism

Above a critical temperature, the system is

symmetric, magnetic dipoles randomly oriented.

Below a critical temperature, the ground state is a completely ordered configuration in which

all dipoles are ordered in some arbitrary direction SO(3) à SO(2)

The Spontaneous Symmetry Breaking

Low temperature super-conductivity is another example!

The concept of SSB: profound, common.

Except the photon, no massless boson

(a long-range force carrier) has been seen in Nature!

(Recall Pauli’s criticism)

The Spontaneous Symmetry Breaking:

Brilliant idea & common phenomena, confronts the Nambu-Goldstone theorem!

-- A show stopper ?

The Nambu-Goldstone Theorem

“If a continuous symmetry of the system is spontaneously broken, then there will appear a massless degree of freedom,

called the Nambu-Goldstone boson.”

“If a LOCAL gauge symmetry is spontaneously broken, then the gauge boson acquires a mass by absorbing the Goldstone mode.”

PRL

PLB

PRL

PRL

The Higgs Mechanism:

The Magic in 1964

An illustrative (original) Model:

An illustrative (original) Model:

After the EWSB,

The gauge field acquires a mass, mixes with the Goldstone boson.

Upon diagonalization:

the resultant Lagrangian is then:

•  By virtue of a gauge choice - the unitary gauge, the ζ-field disappears in the spectrum: a massless photon “swallowed” the massless NG boson!

Degrees of freedom count:

Before EWSB: After:

2 (scalar)+2 (gauge pol.); 1 (scalar)+3 (gauge pol.)

•  Two problems provide cure for each other!

massless gauge boson + massless NG boson

➞ massive gauge boson + no NG boson

the Higgs boson!

A. The Higgs mechanism ≠ a Higgs boson !

From theoretical point of view,

3 Nambu-Goldstone bosons were all we need!

A non-linear realization of the gauge symmetry:

U = exp{i!ⁱ⌧ ⁱ/v}, D^µU = @_µU + igW_µⁱ ⌧ ⁱ

2 U ig⁰U B_µ ⌧³ 2

L = v

2 [D

U

D

U ] ! v

4 ( X

i

g

W

+ g

B

)

The theory is valid to a unitarity bound ~ 2 TeV

The existence of a light, weakly coupled Higgs boson carries important message for our

understanding & theoretical formulation

in & beyond the SM –

A Few Observations

The Higgs potential: V = -µ

/ ϕ /

+ λ|ϕ|

•  In the SM, λ is a free parameter, now measured:

λ = m

/ 2v

≈ 0.13

•  In composite/strong dynamics, harder to make λ big enough.

(due to the loop suppression by design)

It represents a weakly coupled new force (a fifth force):

Is it fundamental or induced?

•  In SUSY, it is related to the gauge couplings tree-level: λ = (g

+ g

)/8 ≈ 0.3/4 ß a bit too small

B. λ: a “New Force’’

For m

= 126 GeV, rather light:

At higher energies, λ is NOT asymptotically free.

It blows up at a high-energy scale (the Landau pole), unless it starts from small (or zero à triviality).

M H [GeV/c2 ]

600

400 500

100 200 300

0 3 5 7 9 11 13 15 17 19

log₁₀ ! [GeV]

Triviality

EW vacuum is absolute minimum

EW Precision

Top-Yukawa drags the vacuum meta-stable,

New physics below 10

GeV?

126

The SM can be a consistent

perturbative theory up to M

! allowing M

, M

, …

The new coupling λ very important!

C. Electroweak Super-Conductivity

The Higgs potential is of the Landau-Ginsburgh form,

Michelson–Morley experiments (1887):

“the moving-off point for the theoretical aspects of the second scientific revolution”

Will History repeat itself (soon)?

“... most of the grand underlying principles have been firmly established. An eminent

physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals. ”

--- Albert Michelson (1894)

Nima Arkani-Hamed

(Director of CFHEP, Beijing)

New Era:

Under the Higgs lamp post

The “Observation” papers:

Now 3600 cites each!

Vast scope of topics, from

interpretations, explorations in & beyond the SM;

applications in astronomy, cosmology, CC; strings/branes,

to “Philosophical Perspectives ….”

m

≈ 126 GeV

Question 1: The Nature of EWSB ?

V ( | |) = µ

+ (

)

) µ

H

+ vH

+

4 H

Fully determined at the weak scale:

v = (p

2G_F ) ^1/2 ⇡ 246 GeV

m²_H = 2µ² = 2 v² ) µ ⇡ 89 GeV, ⇡ 1 8.

In the SM:

It is a weakly coupled new force,

underwent a 2

order phase transition.

Is there anything else?

Question 1: The Nature of EWSB ?

These possibilities are associated with totally di↵erent underlying dynam- ics for electroweak symmetry breaking than the SM, requiring new physics beyond the Higgs around the weak scale. They also have radically di↵er- ent theoretical implications for naturalness, the hierarchy problem and the structure of quantum field theory.

The leading di↵erence between these possibilities shows up in the cubic Higgs self-coupling. In the SM, minimizing the potential gives v² = 2|m|²/ . Expanding around this minimum h = (v + H)/p

2 gives V (H) = ¹₂m²_HH² +

1

6µH³ + · · · , with m²H = v² and µ_SM = 3(m²_H/v). Consider the example with the quartic balancing against a sextic and, for the sake of simplicity to illustrate the point, let’s take the limit where the m² term in the potential can be neglected. The potential is now minimized for v² = 2| |⇤², and we find m²_H = v², µ = 7m²_H/v = (7/3)µ_SM, giving an O(1) deviation in the cubic Higgs coupling relative to the SM. In the case with the non-analytic (h^†h)² log(h^†h) potential, the cubic self-coupling is µ = (5/3)µ_SM.

Even larger departures from the standard picture are possible — we don’t even know whether the dynamics of symmetry breaking is well-approximated by a single light, weakly coupled scalar, as there may be a number of light scalars, and not all of them need be weakly coupled!

Nature of EW phase transition

-

Simplest, but also hardest to discover.

Good testing case.

h

Wednesday, August 13, 14

?

See also Jing Shu and Tao Liu’s talk

Tuesday, January 20, 15

Figure 8: Question of the nature of the electroweak phase transition.

Understanding this physics is also directly relevant to one of the most fun- damental questions we can ask about any symmetry breaking phenomenon, which is what is the order of the associated phase transition. Is the elec- troweak transition a cross-over, or might it have been strongly first-order instead? And how do we attack this question experimentally? This question is another obvious next step following the Higgs discovery: having understood

17

25

All we know:

λ(h

h)

term could be made “-”:

leading to EW phase transition strong 1

order!

à O(1) deviation on λ

With new physics near the EW scale:

2. The Electroweak Phase Transition 2.1. General Remarks

For decades, particle physics has been driven by the question of what breaks the electroweak symmetry. With the discovery of the Higgs, we have discovered the broad outlines of the answer to this question: the symmetry breaking is associated with at least one weakly coupled scalar field. However, this gives us only a rough picture of the physics, leaving a number of zeroth order questions wide open that must be addressed experimentally, but can- not be definitively settled at the LHC. These questions include what is the shape of the symmetry breaking potential, and how is electroweak symmetry restored at high scales.

The SM picture for electroweak symmetry breaking follows the Landau- Ginzburg parametrization of second-order phase transitions,

V (h) = m²_hh^†h + 1

2 (h^†h)², (5)

with m²_h < 0 and > 0. This is the simplest picture theoretically, and the one we would expect on the grounds of e↵ective field theory, in which we include the leading relevant and marginal operators to describe low energy physics. On the other hand, as we will review in more detail in our discussion of naturalness, this picture is far from innocuous or “obviously correct” — for instance it is precisely this starting point that leads to the all vexing mysteries of the hierarchy problem!

The central scientific program directly continuing from the discovery of the Higgs must thus explore whether this simplest parametrization of elec- troweak symmetry breaking is actually the one realized in Nature. And while we have discovered the Higgs, we are very far from having confirmed this pic- ture experimentally. As illustrated in Fig. 8, the LHC will only probe the small, quadratic oscillations around the symmetry breaking vacuum, without giving us any idea of the global structure of the potential. For example, the potential could trigger symmetry breaking by balancing a negative quartic against a positive sextic [14, 15, 16], i.e.

V (h) ! m²h(h^†h) + 1

2 (h^†h)² + 1

3!⇤²(h^†h)³, (6) with < 0. The potential might not even be well-approximated by a poly- nomial function, and may instead be fundamentally non-analytic, as in the

17

early Coleman-Weinberg proposal for symmetry breaking [17]:

V (h) ! 1

2 (h^†h)²log

(h^†h)

m² . (7)

These possibilities are associated with totally di↵erent underlying dynam- ics for electroweak symmetry breaking than the SM, requiring new physics beyond the Higgs around the weak scale. They also have radically di↵er- ent theoretical implications for naturalness, the hierarchy problem and the structure of quantum field theory.

Nature of EW phase transition

-

Simplest, but also hardest to discover.

Good testing case.

h

Wednesday, August 13, 14

?

See also Jing Shu and Tao Liu’s talk

Tuesday, January 20, 15

Figure 8: Question of the nature of the electroweak phase transition.

The leading di↵erence between these possibilities shows up in the cubic Higgs self-coupling. In the SM, minimizing the potential gives v² = 2|m|²/ . Expanding around this minimum h = (v + H)/p

2 gives V (H) = 1

2m²_HH²+1

6µH³+· · · , with m²H = v² and µ_SM = 3(m²_H/v). (8) Consider the example with the quartic balancing against a sextic and, for the sake of simplicity to illustrate the point, let us take the limit where the m²_h term in the potential can be neglected. The potential is now minimized for v² = 2| |⇤², and we find

m²_H = v², µ = 7m²_H/v = (7/3)µ_SM, (9) giving an O(1) deviation in the cubic Higgs coupling relative to the SM. In the case with the non-analytic (h^†h)² log(h^†h) potential, the cubic self-coupling is µ = (5/3)µ_SM.

àλ

= ^(7/3)λ

àλ

= ^(5/3)λ

Question 2: The “Naturalness”

Natural: O(1 TeV) new physics, associated with ttH.

Unknown: Deep UV-IR correlations?

Agnostic: Multiverse/anthropic?

“… scalar particles are the only kind of free particles whose mass term

does not break either an internal or a gauge symmetry.” Ken Wilson, 1970

The Higgs mass fine-tune:

δm

/m

~ 1% (1 TeV/Λ)

Unbelievable!

4 mm

/ 20 cm

~ 10

fine-tune.

“Naturalness” à TeV scale new physics.

“Naturalness” in perspective:

Z,h funnel

H,A

Question 3: The Dark Sector

k_sH^†H S S, k

H^†H ¯ .

The un-protected operator may reveal secret

Higgs portal:

•  Particle mass hierarchy

Question 4: The “Flavor Puzzle”

Higgs Yukawa couplings as the pivot!

•  Patterns of quark, neutrino mixings

•  New CP-violation

sources?

The Higgs as pivot for “seesaw”:

Type I seesaw: M = M

right-handed (sterile) N

H à NN, N à Hν, …

m

⇠  hH

i

M

Type II seesaw: M = M

, a Higgs triplet Φ

Type III seesaw: M = M

, a fermionic triplet T

:

H

à l

l

T

à H l

, T

à W

l

Watch out: H

à µτ (l

l

) for BSM flavor physics!

Nature News, July ’14

LHC Leads the Way

T a b l e 1 - 1 . P r o p o s e d r u n n i n g p e r i o d s a n d i n t e g r a t e d l u m i n o s i t i e s a t e a c h o f t h e c e n t e r - o f - m a s s e n e r g i e s f o r e a c h f a c i l i t y .

F a c i l i t y H L - L H C I L C I L C ( L u m i U p ) C L I C T L E P ( 4 I P s ) H E - L H C V L H C

s ( G e V ) 1 4 , 0 0 0 2 5 0 / 5 0 0 / 1 0 0 0 2 5 0 / 5 0 0 / 1 0 0 0 3 5 0 / 1 4 0 0 / 3 0 0 0 2 4 0 / 3 5 0 3 3 , 0 0 0 1 0 0 , 0 0 0 L d t ( f b ^{− 1} ) 3 0 0 0 / e x p t 2 5 0 + 5 0 0 + 1 0 0 0 1 1 5 0 + 1 6 0 0 + 2 5 0 0 5 0 0 + 1 5 0 0 + 2 0 0 0 1 0 , 0 0 0 + 2 6 0 0 3 0 0 0 3 0 0 0

ILC as Higgs Factory & beyond

FCC?

CEPC/SppC?

Snowmass 1310.8361

e+e-&Z,240-350GeV

ILC: E

= 250 (500) GeV, 250 (500) fb

•  Model-independent measurement:

Γ

~ 6%, Δm

~ 30 MeV

(HL-LHC: assume SM, Γ

~ 5-8%, Δm

~ 50 MeV)

•  TLEP 10

Higgs : Γ

~ 1%, Δm

~ 5 MeV.

Higgs-Factory: Mega (10

) Higgs Physics

JHEP01(2014)164

Figure 7. The Higgs boson production cross section as a function of the centre-of-mass energy in unpolarized e⁺e⁻ collisions, as predicted by the HZHA program [39]. The thick red curve shows the cross section expected from the Higgs-strahlung process e⁺e⁻ → HZ, and the thin red curve shows the fraction corresponding to the Z → ν ¯ν decays. The blue and pink curves stand for the WW and ZZ fusion processes (hence leading to the Hν_eν¯_e and He⁺e⁻ final states), including their interference with the Higgs-strahlung process. The green curve displays the total production cross section. The dashed vertical lines indicate the centre-of-mass energies at which TLEP is expected to run for five years each, √

s = 240 GeV and √

s ∼ 2m^top.

rapidly decreasing with the new physics scale Λ, typically like 1/Λ². For Λ = 1 TeV, departures up to 5% are expected [7, 8]. To discover new physics through its effects on the Higgs boson couplings with a significance of 5σ, it is therefore necessary to measure these couplings to fermions and gauge bosons with a precision of at least 1%, and at the per-mil level to reach sensitivity to Λ larger than 1 TeV, as suggested at by the negative results of the searches at the LHC.

The number of Higgs bosons expected to be produced, hence the integrated luminosity delivered by the collider, are therefore key elements in the choice of the right Higgs factory for the future of high-energy physics: a per-mil accuracy cannot be reached with less than a million Higgs bosons. The Higgs production cross section (obtained with the HZHA generator [39]), through the Higgs-strahlung process e⁺e⁻ → HZ and the WW or ZZ fusion processes, is displayed in figure 7. A possible operational centre-of-mass energy is around 255 GeV, where the total production cross section is maximal and amounts to 210 fb.

The luminosity profile of TLEP as a function of the centre-of-mass energy (figure 3) leads to choose a slightly smaller value, around 240 GeV, where the total number of Higgs bosons produced is maximal, as displayed in figure 8. The number of WW fusion events has a broad maximum for centre-of-mass energies between 280 and 360 GeV. It is therefore convenient to couple the analysis of the WW fusion with the scan of the t¯t threshold, at

√s around 350 GeV, where the background from the Higgs-strahlung process is smallest and most separated from the WW fusion signal.

TLEP Report: 1308.6176

ILC Report: 1308.6176

~ 200 fb

-

Snowmass QCD Working Group: 1310.5189

λt : 1%

λ: 8%

The Next Energy Frontier:

100 TeV Hadron Collider

Higgs Self-couplings:

L = − 12 m 2H H 2 − g H H H

3 ! H 3 − g H H H H

4 ! H 4 ,

g H H H = 6 v = 3 m ²_H

v , g H H H H = 6 = 3 m ²_H

v 2 .

Triple coupling sensitivity:

Test the shape of the Higgs potential, and

the fate of the EW-phase transition!

HHH coupling

Coupling precision (%)

-80 -60 -40 -20 0 20 40 60

80 e⁺e^- : ILC or TLEP-500, ILC-1TeV, CLIC-3TeV

pp : HL-LHC, HE-LHC, VHE-LHC

0.5 ab^-1 1 ab^-1 3 ab^-1 1 ab^-1 3 ab^-1 2 ab^-1 3 ab^-1

±20%

TLEP Report: 1308.6176

Snowmass 1310.8361

H H

H ?

H H H

LHC 100 TeV pp

mass reach of new physics

30 Higgs working group report

Table 1-24. Expected per-experiment precision on the triple-Higgs boson coupling. ILC numbers include bbbb and bbW W^⇤ final states and assume (e , e⁺) polarizations of ( 0.8, 0.3) at 500 GeV and ( 0.8, 0.2) at 1000 GeV. ILC500-up is the luminosity upgrade at 500 GeV, not including any 1000 GeV running. ILC1000- up is the luminosity upgrade with a total of 1600 fb ¹ at 500 GeV and 2500 fb ¹ at 1000 GeV. CLIC numbers include only the bbbb final state and assume 80% electron beam polarization. HE-LHC and VLHC numbers are from fast simulation [102] and include only the bb final state. ^‡ILC luminosity upgrade assumes an extended running period on top of the low luminosity program and cannot be directly compared to CLIC numbers without accounting for the additional running period.

HL-LHC ILC500 ILC500-up ILC1000 ILC1000-up CLIC1400 CLIC3000 HE-LHC VLHC

ps (GeV) 14000 500 500 500/1000 500/1000 1400 3000 33,000 100,000

R Ldt (fb ¹) 3000/expt 500 1600^‡ 500+1000 1600+2500^‡ 1500 +2000 3000 3000

50% 83% 46% 21% 13% 21% 10% 20% 8%

Table 1-25. Expected precision on the triple-Higgs boson coupling for combined facilties, assuming the final states, polarizations, and integrated luminosities assumed above in Table 1-24. Here “ILC-up” refers to ILC1000-up, and “CLIC” refers to CLIC3000 with the two numbers shown assuming unpolarized beams or 80% electron beam polarization, respectively. TLEP is in parantheses since it would not contribute to the measurement of the self-coupling, but could be a step along the way to the higher-energy hadron colliders.

LHC HL-LHC

+ILC +ILC-up +(TLEP) +ILC-up +CLIC

+CLIC +HE-LHC +VLHC +HE-LHC +VLHC +HE-LHC +VLHC

21% 12.6% 15.2/9.8% 18.6% 7.9% 10.9% 6.8% 12.5/8.9% 7.2/6.2%

Pushing the “Naturalness” limit

The Higgs mass fine-tune: δm

/m

~ 1% (1 TeV/Λ)

Thus, m

> 8 TeV à 10

fine-tune!

Stop like T’ search at hadron collider

-

-

[GeV]

mT

600 800 1000 1200 1400

Production cross-section [pb]

10-3

10-2

10-1

1 10 102

103 ^MadGraph5

14 TeV

Fermion Scalar QCD top ttZ

[GeV]

mT

2000 4000 6000 8000

Production cross-section [pb]

10-4

10-3

10-2

10-1

1 10 102

103

104

105 ^MadGraph5

100 TeV

Fermion Scalar QCD top ttZ

Figure 2: Cross-sections at 14 TeV (left) and 100 TeV (right).

MT

MAH

10

5

1

0.1 FERMIONIC TOP PARTNER

400 600 800 1000 1200 1400

400

200 600 800 1000 1200

MT

MAH

10

5

1

0.1

1400 400 600 800 1000 1200

400

200 600 800 1000

1200 SCALAR TOP PARTNER

Figure 3: Search significance as computed in [1] for fermions (left) and scalar (right).

[GeV]

mT

1000 1500 2000 2500

Cross-section ratio

0 2 4 6 8 10 12 14 16 18

20 ^MadGraph5

14 TeV Fermion/Scalar

[GeV]

mT

5000 10000 15000

Cross-section ratio

0 2 4 6 8 10 12 14 16 18

20 ^MadGraph5

100 TeV Fermion/Scalar

Figure 4: Ratio of scalar cross-section to fermion cross-section.

Meade and Reece,

Han, Mabhubani, Walker and LTW, etc

Wednesday, April 23, 14

11

contours of the two di↵erent search strategies.

The searches proposed here also have good discriminating power away from the massless neutralino limit. A 1.5 TeV stop could be discovered in the compressed region of parameter space. It is possible to exclude neutralino masses up to 2 TeV in most of the parameter space.

All of the results presented here have been obtained with very minimal cut-flows that do not rely on b-tagging or jet substructure techniques. Additional refinements should increase the search sensitivity, at the price of making assumptions on the future detector design.

(GeV)

~t

2000 4000m 6000 8000

(GeV) 10 ⇥⇤m

0 2000 4000 6000 8000

Significance

1 s 10

Boosted Top Compressed

Discovery CL

-1

= 100 TeV s

dt = 3000 fb L

= 20%

sys,bkg

⌅

= 20%

sys,sig

⌅

FIG. 5: Projected discovery potential [left] and exclusion limits [right] for 3000 fb ¹ of total integrated luminosity. At each signal point, the significance is obtained by taking the smaller CL_s between the heavy stop and compressed spectra search strategies, and converting CL_s to number of ’s. The blue and black contours (dotted) are the expected (±1 ) exclusions/discovery contours using the heavy stop and compressed spectra searches.

D. Di↵erent Luminosities

An open question in the design for the 100 TeV proton-proton collider is the luminosity that is necessary to take full advantage of the high center of mass energy. As cross sections fall with increased center of mass energy, one should expect that higher energy colliders require more integrated luminosity to fulfill their potential. The necessary luminosity typically scales quadratically with the center of mass energy, meaning that one should expect that the 100 TeV proton-proton collider would need roughly 50 times the luminosity of the LHC at 14 TeV.

This section shows the scaling of our search strategy as a function of the number of collected events. As the luminosity changes, we re-optimize the /E_T cut. For integrated

[TeV]

MT

0 1 2 3 4 5 6 7 8 9 10

[TeV]χM

0 1 2 3 4 5 6 7

8 ^{5σ discovery}

= 100 TeV s

L = 3000 fb-1

Fermion Partner

Boosted Top Compressed

A few 100 events

-

LUX collaboration, 2013"

DM Searches

GeV low mass:

DD difficult; 100 GeV or higher mass:

500 1000 1500 2000 2500 3000 3500 40000 500

1000 1500 2000 2500

m_NLSP@GeVD m LSP@GeVD

Wino-Higgsino L=3000êfb

1.96s

3L OSDL

SSDL

[TeV]

mχ∼

0 1 2 3 4 5 6

wino disappearing tracks

higgsino ) H~ / B~ mixed (

) W~ / B~ mixed (

gluino coan.

stop coan.

squark coan.

Collider Limits

100 TeV 14 TeV

WIMP DM:

with / g_e↵⁴ /M_DM² . This leads us to a limit on the dark matter mass of M_DM < 1.8 TeV

✓g_e↵² 0.3

◆

. (18)

As has been long appreciated, it is quite remarkable that the TeV scale emerges so naturally in this way, assuming dark matter couplings comparable in strength to the electroweak gauge interactions. This gives a strong, direct argument for new physics at the TeV scale, independent of any theoretical notions of naturalness.

Compellingly, dark matter often falls out of theories of physics beyond the SM without being put in by hand. Indeed, if the SM is augmented by new physics, not even necessarily close to the weak scale, but far beneath the GUT scale, the interactions with new states should respect baryon and lepton number to a very high degree. Since all SM particles are neutral under the discrete symmetry ( 1)^B+L+2S, any new particles that are odd under this symmetry will be exactly stable. This is the reason for the ubiquitous presence of dark matter candidates in BSM physics. It is thus quite plausible that the dark matter is just one part of a more complete sector of TeV- scale physics; this has long been a canonical expectation, with the dark matter identified as e.g. the lightest neutralino in a theory with TeV-scale supersymmetry. The dominant SUSY processes at hadron colliders are of course the production of colored particles—the squarks and gluinos—which then decay, often in a long cascade of processes, to SM particles and the lightest supersymmetric particle (LSP), resulting in the well known missing energy signals at hadron colliders. This indirect production of dark matter dominates, by far, the direct production of dark matter particles through electroweak processes.

However, as emphasized in our discussion of naturalness, it is also worth preparing for the possibility of a much more sparse spectrum of new particles at the TeV scale. Indeed, if the idea of naturalness fails even slightly, the motivation for a very rich set of new states at the hundreds-of-GeV scale evaporates, while the motivation for WIMP dark matter at the TeV scale still remains. This is for instance part of the philosophy leading to models of split SUSY: in the minimal incarnation, the scalars and the second Higgs doublet of the MSSM are pushed to ⇠ 10² 10³ TeV, but the gauginos (and perhaps the higgsinos) are much lighter, protected by an R-symmetry. The scalars are not so heavy as to obviate the need for R-parity, so the LSP is

40

[GeV]

mχ∼

0 500 1000 1500 2000

BδS/

0 1 2 3 4 5 6

-1MadGraph5 + Pythia6 + Delphes3, L = 3000 fb

Wino

1-2% syst.

Monojet

95%

σ 5

100 TeV 14 TeV

[GeV]

mχ∼

0 1000 2000 3000 4000 5000

BδS/

0 1 2 3 4 5 6

-1MadGraph5 + Pythia6 + Delphes3, L = 3000 fb

Wino

20-500% bkgd.

Disappearing Tracks

95%

σ 5

100 TeV 14 TeV

Figure 20: Left: The mass reach for the pure wino in the monojet channel with L = 3000 fb ¹ for the 14 TeV LHC (blue) and at 100 TeV (red). The bands are generated by varying the background systematics between 1 2% and the signal systematic uncertainty is set to 10% [65]. Right: The mass reach in the pure wino scenario in the disappearing track channel with L = 3000 fb ¹ for the 14 TeV LHC (blue) and at 100 TeV (red). The bands are generated by varying the background normalization between 20 500% [65].

background, which is varied between 1 2%, generating the bands in the plot.

Naively scaling by total event rates the systematics from current ATLAS studies [66] (see Ref. [67] for the CMS study) would yield 0.5% for 3000 fb ¹, but this is clearly overly optimistic. Choosing the systematic error ⇠ 1 2%

as we have done may also be optimistic, but it sets a reasonable benchmark, and underscores that minimizing these systematics should be a crucial factor taken into account in the design of the 100 TeV detectors. Given the same integrated luminosity, the monojet search increases the reach relative to the LHC by nearly a factor of 5, as shown in the left panel of Fig. 20 .

Due to the tiny mass splitting m = 166 MeV between the chargino and the neutralino, the decay lifetime can be long. The resulting disappearing

Mass reach at 100 TeV:

~ 5x over LHC

Electroweak Resonances: Z’,W’ Colored Resonances:

New Particle Searches

Excited Quark Black 100 TeV

Red 14 TeV ugØu^* dgØd^*

10^-3 10^-2 10^-1 10⁰ 10¹ 10² 10³ 10⁴

sHqgØq* LHpbL

M ~ 40 – 50 TeV!

[TeV]

mH

2 4 6 8 10 12 14 16 18 20

[fb]

10-3

10-2

10-1

1 10 102

103

104 ₀

H t

t

H+/-

b t

100 TeV

14 TeV

0 5 10 15

[fb]2 V/

10-3

10-2

10-1

1 10 102

103

104

105

± NLO l

N pp

± NLO

0T T pp

- NLO

+T T pp

100 TeV 14 TeV

New (vector-like) leptons Heavy Higgs bosons: H

, H

Mass reach at 100 TeV:

~ 5x over LHC

A Grand Picture:

î

Electroweak phase transition,

Particle mass generation Today’s puzzles

New physics associated

ì

with Higgs ?

Summary:

-   The Higgs boson is a new class, at a pivotal point of energy,

intensity, cosmic frontiers.

An exciting journey ahead!

“Naturally speaking”:

It should not be a lonely solitary particle.

Higgs

-  Precision Higgs physics:

LHC lights the way:

Higgs factory/SppC:

-   CEPC/SppC New physics reach:

6x ^LHC reach: 10 – 30 TeV à fine-tune < ¹⁰

WIPM DM mass ~ 1 – 5 TeV

Cancelation in perspective:

m

=

= (125 GeV)

! ?

Question 2: The “Naturalness”

Natural: O(1 TeV) new physics, associated with ttH.

Unknown: Deep UV-IR correlations?

“… scalar particles are the only kind of free particles whose mass term

does not break either an internal or a gauge symmetry.” Ken Wilson, 1970