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Home , Coupling (physics), Higgs mechanism, Quark, Scalar boson, Top quark

11. The Top and the and Nuclear

Dr. Tina Potter

Dr. Tina Potter 11. The and the Higgs Mechanism 1 In this section...

Focus on the most recent discoveries of fundamental The top quark – prediction & discovery The Higgs mechanism The Higgs discovery

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 2 Third Generation Quark Weak CC Decays 173 GeV t Cabibbo Allowed |Vtb|~1, log() |Vcs|~|Vud|~0.975 Top are special. Cabibbo Suppressed m(t)  m(b)(> m(W )) |Vcd|~|Vus|~0.22 |V |~|V |~0.05 −25 cb ts τt ∼ 10 s ⇒ decays b 4.8GeV before hadronisation Vtb ∼ 1 ⇒ 1.3GeV c BR(t → W + b)=100% s 95 MeV 2.3MeV u d 4.8 MeV Bottom quarks are also special. b quarks can only decay via the Cabbibo suppressed Wcb

vertex. Vcb is very small – weak ! Interaction b- point ⇒ τ(b)  τ(u, c, d, s) b Jet initiated by b quarks look different to other jets. b quarks travel further from interaction point before decaying. b-jet traces back to a secondary vertex –“ b-tagging”. Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 3 The Top Quark The predicted the existence of the top quark 2     +3e u c t 1 −3e d s b which is required to explain a number of observations. d µ− Example: Non-observation of the decay W − 0 + − 0 + − −9 K → µ µ B(K → µ µ ) < 10 u/c/t νµ The top quark cancels the contributions W + from the u and c quarks. s¯ µ+ Example: Electromagnetic anomalies γ This diagram leads to infinities in the theory unless f¯ P Q = 0 f γ f where the sum is over all (and colours) f  2  1  Q = [3 × (−1)] + 3 × 3 × + 3 × 3 × (− ) = 0 γ f 3 3 Requires t quark f Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 4 The Top Quark The top quark is too heavy for Z → tt¯ or W + → tb¯ so not directly produced at LEP. However, precise measurements of mZ , mW ,ΓZ and ΓW are sensitive to the existence of virtual top quarks: b t t t¯ Z W W + W + ZZ t

¯b t¯ ¯b

Example Standard Model prediction Also depends on the Higgs mass

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 5 The Top Quark

The top quark was discovered in 1994 by√ the CDF experiment at the worlds (then) highest pp collider ( s = 1.8 TeV), the at , US. q b Final state W +W −bb¯ g t W + Mass reconstructed in a similar manner to mW

t¯ W − at LEP, i.e. measure jet/ /momenta. q¯ ¯b + Vtb ∼ 1, so decay of top quark is ∼100% t → bW + mt  mW , so the W is real. The weak decay is just as fast as a strong decay (∼ 10−25s), so the quark has no time to hadronise ⇒ there are no t-

Possible top quark decays are t → bqq¯ or t → b`ν` In collisions, multijet final states are the norm – for rare processes it’s much easier to look for leptonic decays, accompanied by b-quark jets.

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 6 First observation of top (1995)

Current status CDF collaboration published first PRL 74 2626 (1995) Results from LHC as well as Tevatron. All

t ¯t →bW + b¯W − consistent, and in agreement with indirect

Final state expectation from LEP data. l ν + qq + bb

data

signal

background

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 7 Higgs mechanism and the Higgs

Recall – the Klein-Gordon equation for massive is: ∂2ψ = ∇∇∇2 − m2 ψ ∂t2 2 1 2 2 However, the term m ψ (or 2m ψ in the Lagrangian formulation), is not gauge invariant. So in gauge field theories, the gauge bosons should be massless. OK for QED and QCD, but plainly not for W ± and Z. The Higgs mechanism tries to fix this. Imagine introducing a scalar Higgs field φ, which has interactions with the W ± and Z fields, with coupling strength y, giving a term in Lagrangian yφψψ. Looks like a mass term( ∝ ψ2). Mass of the bosons becomes effectively related to their coupling to the Higgs field. Requires the vacuum (lowest energy state of space) to have a non-zero expectation value for the Higgs field. How can this come about?

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 8 Higgs potential

Suppose the Higgs field φ (actually a complex doublet) has self interactions yielding V (φ) = aφ4 − bφ2 The equilibrium point, φ = 0, respects the , but is unstable. 2 The stable equilibrium point is at |φGS| = b/2a. The symmetry is “spontaneously broken”. A weak boson propagating in the Higgs field will appear to have a mass ∼ yφGS. 2 Expanding about the ground state V (φGS + x) = Vmin + 2bx So can get excitations of the Higgs field about the minimum. These form the physical Higgs , H – the observable physical manifestation of the operation of the Higgs mechanism. Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 9 Classical analogue of the Higgs mechanism

Maxwell’s equations lead to waves travelling at velocity c, hence to massless . Consider waves propagating in a charged , with density n per unit volume. ~ 2 ~ ~ ∂~v ~ ∂J ne E Plasma: J = ne~v; me = eE ⇒ = ∂t ∂t me Maxwell: ! ! ∂B~ ∂∇∇∇~ ∧ B~ ∂ 1 ∂E~ ∇∇∇~ ∧∇∇∇~ ∧E~ = −∇∇∇2E~ = ∇∇∇~ ∧ − = − = − µ J~+ ∂t ∂t ∂t 0 c2 ∂t

µ ne2E~ 1 ∂2E~ 1 ∂2E~ µ ne2E~ 0 ∇2 ~ 0 = − − 2 2 ⇒ ∇∇ E − 2 2 = me c ∂t c ∂t me Compare with Klein-Gordon. propagates with effective mass µ ne2 m2 = ~ 0 eff 2 Note meff ∝ e, the coupling. mec Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 10 Higgs theory summary

Gauge bosons (and also fermions) are intrinsically massless, and need to be so to satisfy Gauge Invariance. Nevertheless, interactions with the Higgs field make particles look like they have mass. Apparent are controlled by free parameters called Yukawa Couplings (the strength of the coupling to the Higgs field) A arises as an excitation of the Higgs field. It must be a scalar particle to make everything work. The Higgs Boson has a mass, but the mass is not predicted by the theory – we have to find it experimentally. The Higgs Boson has couplings to all the particles to which it gives mass (and so has many ways it could decay), all fully calculable and determined by the theory as a function of its (a priori unknown) mass.

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 11 Higgs boson decays

Higgs Boson interacts via couplings which are proportional to masses. Higgs boson therefore decays preferentially to the heaviest particles that are kinematically accessible, depending on its mass.

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 12 Higgs decay mechanisms

Directly to two fundamental fermions or bosons, coupling to mass, e.g.

b Z

H H

¯b Z

Indirectly to massless particles (photons or ) via massive loops

γ γ g t¯ W t¯ H t H W H t t W t γ γ g

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 13 Higgs at LEP

Higgs Production at LEP (Large Electron Collider – 1990s): √ If mH < s − mZ e+ Z

“Higgsstrahlung” mechanism Z∗

e− H √ In 2000, LEP operated with s ∼ 207 GeV, therefore had the potential to discover Higgs boson if mH < 116 GeV. Searches were conducted in many possible final states (different decays for Z and H). All negative. Ultimately, LEP excluded a Higgs Boson with a mass below 114 GeV.

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 14 Higgs at Large Higgs Production at the LHC The dominant Higgs production mechanism at the LHC is g t t H “ fusion” t¯ g Higgs Decay at the LHC γ b Z t¯ H t H H t γ ¯b Z Low mass Medium mass High mass One Z may be virtual

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 15 The The LHC is a new -proton collider now running in the old LEP tunnel at CERN. In 2012 4 + 4 TeV; in 2015 6.5 + 6.5 TeV; ultimately 7 + 7 TeV

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 16 ATLAS – a general purpose LHC detector

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 17 Higgs Observations (August 2014)

Indirect indications from LEP that Higgs mass should be not far above 115 GeV. Dominant decay modes are all difficult: bb¯, cc¯ (swamped by QCD jets) W +W −, τ +τ − (missing )

Best options are the rare decays: ZZ → `+`−`+`− γγ

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 18 H → ZZ → 4`

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 19 Higgs Boson Discovery

ATLAS σ(obs.) Total uncertainty Convincing signal consistent with m = 125.36 GeV ± σ µ H σ(exp.) 1 on m(H) = 126 GeV – seen in multiple decay H → γγ µ = 1.17+0.28 obs -0.26 µ = 1.00+0.25 exp -0.23 modes & in two experiments. H → ZZ* µ = 1.46+0.40 obs -0.34 µ = 1.00+0.31 exp -0.26 Is it the Higgs boson of the SM? H → WW* µ = 1.18+0.24 obs -0.21 µ = 1.00+0.21 exp -0.19 Need to check its quantum numbers H → bb µ = 0.63+0.39 obs -0.37 P + µ = 1.00+0.41 exp -0.38 (should be J = 0 ). H → ττ µ = 1.44+0.42 obs -0.37 µ +0.36 = 1.00-0.32

exp V

→ µµ +3.7 v H µ m = -0.7-3.7 obs V 1 ATLAS Preliminary κ − Z µ = 1.0+3.4 s = 13 TeV, 36.1 - 79.8 fb 1 exp -3.5 t H → Zγ µ +4.6 mH = 125.09 GeV, |y | < 2.5 = 2.7-4.5 H W

obs or

F − +4.2 1 SM Higgs boson µ = 1.0 v 10

exp -4.2 m F κ Combined µ = 1.18+0.15 obs -0.14 −2 µ = 1.00+0.13 10 τ b exp -0.12

-1 − s = 7 TeV, 4.5-4.7 fb 1 0 1 2 3 −3 10 µ s = 8 TeV, 20.3 fb-1 Signal strength (µ)

10−4 Check branching ratios and couplings. − 10 1 1 10 102 Look ok so far... Particle mass [GeV]

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 20 Higgs +?

ATLAS H → ZZ* → 4l -1 Observed s = 7 TeV, 4.5 fb Expected s = 8 TeV, 20.3 fb-1 + ± σ 0 SM 1 → → νµν 0+ SM ± 2 σ H WW* e -1 Studied using angular distributions of 0+ SM ± 3 σ s = 8 TeV, 20.3 fb J P ± 1 σ H → γγ P J ± 2 σ -1 decay products s = 7 TeV, 4.5 fb J P ± 3 σ s = 8 TeV, 20.3 fb-1 q ~ 40 So far it looks like the 0+ SM Higgs. 30 20 10 Alternative spin-parity possibilities are 0 -10 disfavoured. -20 -30 J P = 0+ J P = 0− J P = 2+ J P = 2+ J P = 2+ J P = 2+ J P = 2+ h κ =κ κ κ κ κ κ κ q g q=0 q=0 q=2 g q=2 g p <300 GeV p <125 GeV p <300 GeV p <125 GeV T T T T

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 21 Summary

Top quark – observed, and compatible with other precise electroweak measurements. Electroweak theory depends on the Higgs mechanism to endow particles with mass. This is a non-standard feature, which needs experimental verification. Higgs boson – detected in 2012 at 126 GeV. Work continues to determine the properties of the boson and check whether it is the Higgs boson of the Electroweak Standard Model.

Up next... Section 12: Beyond the Standard Model

Dr. Tina Potter 11. The Top Quark and the Higgs Mechanism 22