Atlas for High Schoolers - University of Pennsylvania High ...

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Transcript of Atlas for High Schoolers - University of Pennsylvania High ...

What do Particle Physicists do ?

Protons

AtomsMoleculesEverything

? uQuarks

No Body Knows

What’s in the Lunch Box ?

Look inside.

What’s in the Lunch Box ?

No Fun!

Bang!

What’s in the Lunch Box ?SMASH THEM!!!

Bang!

What’s in the Lunch Box ?

What’s in the Proton ?Protons are Too small to look inside.

Bang!

What’s in the Proton ?Protons are Too small to look inside.

SMASH THEM!!!

Philadelphia

CERNSwitzerland/France

The Worlds Biggest Cannon

The Worlds Biggest Cannon

The Worlds Biggest Cannon

Philadelphia

The Worlds Biggest Cannon

Really Big Camera!!!

Really Big Camera!!!

Really Big Camera!!!

Really Big Camera!!!

Building Atlas Video

e

What do Particle Physicists really do ?

Everything* that we know:Particles + Interactions

e - electron ν - neutrino

u - up-quarkd - down-quark

The Particles

γ / graviton / W / Z / gluon

e - electron ν - neutrino

u - up-quarkd - down-quark

The Particles

Essentially all of everything that matters to you. - periodic table (chemistry/biology) - light - gravity. - electricity - mechanics

γ / graviton / W / Z / gluon

The Interactions

The Higgs

where s, t are the Mandelstam variables [the c.m. energy s is the square of the sum of

the momenta of the initial or final states, while t is the square of the difference between

the momenta of one initial and one final state]. In fact, this contribution is coming from

longitudinal W bosons which, at high energy, are equivalent to the would–be Goldstone

bosons as discussed in §1.1.3. One can then use the potential of eq. (1.58) which gives the

interactions of the Goldstone bosons and write in a very simple way the three individual

amplitudes for the scattering of longitudinal W bosons

A(w+w− → w+w−) = −

[

2M2

H

v2+

(M2

H

v

)2 1

s − M2H

+

(M2

H

v

)2 1

t − M2H

]

(1.150)

which after some manipulations, can be cast into the result of eq. (1.149) given previously.

W−

W+ W−

W+

• •H

•H

Figure 1.15: Some Feynman diagrams for the scattering of W bosons at high energy.

These amplitudes will lead to cross sections σ(W+W− → W+W−) # σ(w+w− → w+w−)

which could violate their unitarity bounds. To see this explicitly, we first decompose the

scattering amplitude A into partial waves a! of orbital angular momentum "

A = 16π∞∑

!=0

(2" + 1)P!(cos θ) a! (1.151)

where P! are the Legendre polynomials and θ the scattering angle. Since for a 2 → 2 process,

the cross section is given by dσ/dΩ = |A|2/(64π2s) with dΩ = 2πdcos θ, one obtains

σ =8π

s

∞∑

!=0

∞∑

!′=0

(2" + 1)(2"′ + 1)a!a!′

∫ 1

−1

d cos θP!(cos θ)P!′(cos θ)

=16π

s

∞∑

!=0

(2" + 1)|a!|2 (1.152)

where the orthogonality property of the Legendre polynomials,∫

d cos θP!P!′ = δ!!′ , has

been used. The optical theorem tells us also that the cross section is proportional to the

imaginary part of the amplitude in the forward direction, and one has the identity

σ =1

sIm [ A(θ = 0) ] =

16π

s

∞∑

!=0

(2" + 1)|a!|2 (1.153)

60

W

W

W

W

W

W

W

W

H

at the TeV scale, the Higgs boson mass is allowed to be in the range

50 GeV <∼ MH <∼ 800 GeV (1.181)

while, requiring the SM to be valid up to the Grand Unification scale, ΛGUT ∼ 1016 GeV,

the Higgs boson mass should lie in the range

130 GeV <∼ MH <∼ 180 GeV (1.182)

Figure 1.19: The triviality (upper) bound and the vacuum stability (lower) bound on theHiggs boson mass as a function of the New Physics or cut–off scale Λ for a top quark massmt = 175 ± 6 GeV and αs(MZ) = 0.118 ± 0.002; the allowed region lies between the bandsand the colored/shaded bands illustrate the impact of various uncertainties. From Ref. [136].

1.4.3 The fine–tuning constraint

Finally, a last theoretical constraint comes from the fine–tuning problem originating from

the radiative corrections to the Higgs boson mass. The Feynman diagrams contributing to

the one–loop radiative corrections are depicted in Fig. 1.20 and involve Higgs boson, massive

gauge boson and fermion loops.

69

not allowed

not allowed

allowed

The Particles

γ / graviton / W / Z / gluon / Higgs

e - electron ν - neutrino

u - up-quarkd - down-quark

e - electron ν - neutrino

u - up-quarkd - down-quark

The Particles

µ - muon ν - neutrino

c - charm-quarks - strange-quark

τ - tauon ν - neutrino

t - top-quarkb - bottom-quark

γ / graviton / W / Z / gluon / Higgs

(masses, coupling strengths and so on). Because the number of different experimental measurements that can be made is much larger than the number of free parameters in the standard model, we are dealing with an ‘over-constrained’ system. That is, our experimental measurements not only determine the values of the free parameters of the standard model, they also provide stringent tests of the consistency of the model’s predictions.

Electrons versus protons For more than a quarter of a century, the high-energy frontier of particle physics has been dominated by experiments performed at particle–anti-particle colliders. In these accelerators, beams of electrons and posi-trons, or protons (p) and antiprotons (p‒), travel with equal and opposite momenta and collide head-on in the centre of the particle detectors.

Experiments at electron colliders have several advantages over those at proton colliders, which stem from the fact that electrons are elementary particles. When an e+e− pair annihilates, the initial state is well defined and, if the pair collide at equal and opposite momentum, the centre-of-mass energy of the system (Ecm) is equal to the sum of the beam energies. Ecm is the energy available to produce the final-state particles.

Electrons participate only in the electroweak interaction. This means that the total e+e− annihilation cross-section is small, so event rates in experiments are low, but essentially every annihilation event is ‘interest-ing’, and the observed events are relatively simple to analyse. Initial-state bremsstrahlung (radiation from the beam particles) can reduce the avail-able centre-of-mass energy, but because this is a purely electromagnetic process it can be calculated with great precision, and it introduces no significant systematic uncertainties into the analysis of annihilation events.

The disadvantage of using electrons as beam particles is their small rest mass. When high-energy electrons are accelerated, they lose energy (producing synchrotron radiation), and that energy loss must be com-pensated by the machine’s accelerating cavities. The energy radiated by a charged particle in performing a circular orbit of radius, R, is pro-portional to γ4/R, where γ is the ratio of the particle’s total energy to its rest mass, m0c2. Even though the world’s largest particle accelerator, the Large Electron–Positron Collider (LEP), at CERN, had a circumference of 27 km, its maximum beam energy of around 104 GeV was limited by the fact that each particle radiated about 2 GeV per turn. By contrast, the large rest mass of the proton means that synchrotron energy loss is not a significant limiting factor for proton–antiproton colliders. For example, the world’s highest energy collider at present is the Tevatron proton–antiproton collider, at Fermilab (Batavia, Illinois), which, with

a circumference of only 6 km, achieves a beam energy of 1,000 GeV (or 1 TeV); the Large Hadron Collider (LHC), using two proton beams in the 27-km LEP tunnel, will achieve beam energies of 7 TeV.

Although the beam energies of proton colliders may be much higher, for experiments at these colliders there are a number of challenges that stem from the fact that protons and antiprotons are strongly interacting, composite particles. A high-energy proton–antiproton collision is shown schematically in Fig. 1b. The highest energy collisions take place between a valence quark from the proton and an antiquark from the antiproton. These colliding partons carry fractions x1 and x2 of the momentum of the incoming proton and antiproton, respectively. The energy, Q, in the parton–parton centre-of-mass frame is given by Q2 = x1x2E2

cm. The prob-ability of a proton containing a parton of type i at the appropriate values of x1 and Q2 is given by a ‘parton distribution function’ (PDF), fi(x1, Q2). The cross-section for the parton–parton collision to produce a given

Electromagneticcalorimeters Muon

detectors

Jetchamber

Vertexchamber

Microvertexdetector

Z chambers

Solenoid andpressure vessel

Time of flightdetector

Presamplers

Silicon–tungstenluminometer

Forwarddetector

y

z x

Hadroncalorimeters

and return yoke

θ ϕ

Figure 2 | The OPAL experiment at LEP. The typical, hermetic design of this detector comprises central track detectors inside a solenoid, calorimeters and — the outermost layers — muon detectors.

Cro

ss-s

ectio

n (p

b)

Centre-of-mass energy (GeV)

105

104

CESRDORIS

PEP

PETRAKEKBPEP-II

TRISTAN SLC

Z

LEP1 LEP2

W+W–

103

102

10

0 20 40 60 80 100 120 140 160 180 200 220

Figure 3 | The cross-section for e+e– annihilation to hadrons as a function of Ecm. The solid line is the prediction of the standard model, and the points are the experimental measurements. Also indicated are the energy ranges of various e+e− accelerators. (A cross-section of 1 pb = 10−40 m2.) Figure reproduced, with permission, from ref. 12.

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NATURE|Vol 448|19 July 2007 INSIGHT REVIEW

Measurement Fit |Omeas Ofit|/ meas

0 1 2 3

0 1 2 3

had(mZ)(5) 0.02750 ! 0.00033 0.02759mZ "GeV#mZ "GeV# 91.1875 ! 0.0021 91.1874

Z "GeV#Z "GeV# 2.4952 ! 0.0023 2.4959

had "nb#0 41.540 ! 0.037 41.478RlRl 20.767 ! 0.025 20.742AfbA0,l 0.01714 ! 0.00095 0.01645Al(P )Al(P ) 0.1465 ! 0.0032 0.1481RbRb 0.21629 ! 0.00066 0.21579RcRc 0.1721 ! 0.0030 0.1723AfbA0,b 0.0992 ! 0.0016 0.1038AfbA0,c 0.0707 ! 0.0035 0.0742AbAb 0.923 ! 0.020 0.935AcAc 0.670 ! 0.027 0.668Al(SLD)Al(SLD) 0.1513 ! 0.0021 0.1481sin2

effsin2 lept(Qfb) 0.2324 ! 0.0012 0.2314mW "GeV#mW "GeV# 80.385 ! 0.015 80.377

W "GeV#W "GeV# 2.085 ! 0.042 2.092mt "GeV#mt "GeV# 173.20 ! 0.90 173.26

March 2012

Predicted 1845

John Couch Adams Urbain Jean-JosephLe Verrier

Neptune

Observed 1846

Top-Quark Mass !GeV"

mt !GeV"160 170 180 190

2/DoF: 6.1 / 10

CDF 172.5 # 1.0

D 174.9 # 1.4

Average 173.2 # 0.9

LEP1/SLD 172.6 $ 13.5172.6 10.4

LEP1/SLD/mW/ W 179.7 $ 11.7179.7 8.7

March 2012

MH !GeV"

March 2012

ZZ

had0

RlR0

AfbA0,l

Al(P )Al(P )RbR0

RcR0

AfbA0,b

AfbA0,c

AbAbAcAc

Al(SLD)Al(SLD)sin2

effsin2 lept(Qfb)mWmW

WW

QW(Cs)QW(Cs)sin2 (e e )sin2

MS

sin2W( N)sin2W( N)

gL( N)g2

gR( N)g2

10 102

103

80.3

80.4

80.5

155 175 195

LHC excluded

mH !GeV"114 300 600 1000

mt !GeV"

mW

!G

eV" 68# CL

LEP1 and SLDLEP2 and Tevatron

March 2012

0

1

2

3

4

5

6

10030 500mH [GeV]

!"2

Excluded

!#had =!#(5)

0.02758±0.000350.02749±0.00012incl. low Q2 data

Theory uncertainty

0

1

2

3

4

5

6

10030 300mH !GeV"

2

Excluded

had =(5)

0.02750#0.000330.02749#0.00010incl. low Q2 data

Theory uncertaintyJuly 2011 mLimit = 161 GeV

0

1

2

3

4

5

6

10040 200mH !GeV"

2

LEPexcluded

LHCexcluded

had =(5)

0.02750#0.000330.02749#0.00010incl. low Q2 data

Theory uncertaintyMarch 2012 mLimit = 152 GeV

14

129.2 GeV to 541 GeV at 95% CL under the SM (µ = 1)876

hypothesis. The mass range 122.1 GeV to 129.2 GeV877

is not excluded due to the observation of an excess of878

events above the expected background. This excess and879

its significance are discussed in detail in Section. VII880

A small mass region near mH ∼ 245 GeV was not ex-881

cluded at the 95% CL in the combined search of Ref. [14],882

mainly due to a slight excess in the H → ZZ(∗) →883

!+!−!+!− channel. This mass region is now excluded884

in the SM. The CLs values for µ = 1 as a function of the885

Higgs boson is shown in Fig. 5, where it can also be seen886

that the regions between 130.7 GeV and 506 GeV are ex-887

cluded at the 99% CL. The observed exclusion covers a888

large part of the expected exclusion range.889

[GeV]Hm100 200 300 400 500 600

SM

σ/σ95%

CL L

imit

on

-110

1

10

Obs. Exp.

σ1 ±σ2 ± = 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

CLs Limits

(a)

[GeV]Hm110 115 120 125 130 135 140 145 150

SM

σ/σ95%

CL L

imit

on

-110

1

10 Obs. Exp.

σ1 ±σ2 ± = 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

CLs Limits

(b)

FIG. 4. The observed (full line) and expected (dashed line)95% CL combined upper limits on the SM Higgs boson pro-duction cross section divided by the SM expectation as a func-tion of mH (a) in the full mass range considered in this anal-ysis and (b) in the low mass range. The dotted curves showthe median expected limit in the absence of a signal and thegreen and yellow bands indicate the corresponding 68% and95% intervals.

[GeV]Hm100 200 300 400 500 600

CLs

-610

-510

-410

-310

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Exp. 95%

99% = 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

(a)

[GeV]Hm110 115 120 125 130 135 140 145 150

CLs

-510

-410

-310

-210

-110

1

Obs.

Exp.

95%

99%

= 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

(b)

FIG. 5. The value of the combined CLs for µ = 1 (testingthe SM Higgs boson hypothesis) as a function of mH (a) inthe full mass range of this analysis and (b) in the low massrange. The regions with CLs < α are excluded at the (1−α)CL or stronger.

VII. SIGNIFICANCE OF THE EXCESS890

The observed local p-values, calculated using the891

asymptotic approximation, as a function of mH and the892

expected value in the presence of a SM Higgs boson signal893

at that mass are shown in Fig. 6 in the entire search mass894

range and in the low mass range. The asymptotic approx-895

imation has been verified using ensemble tests which yield896

numerically consistent results.897

The largest significance for the combination is observed898

formH=126 GeV, where it reaches 3.0σ with an expected899

value in the presence of a signal at that mass of 2.9σ. The900

observed (expected) local significances for mH=126 GeV901

are 2.8σ (1.4σ) in the H → γγ channel and 2.1σ (1.4σ)902

in the H → ZZ(∗) → !+!−!+!− channel. In the H →903

WW (∗) → !+ν!−ν channel, which has been updated and904

included additional data, the observed (expected) local905

significance formH=126 GeV is 0.8σ (1.6σ), the observed906

14

129.2 GeV to 541 GeV at 95% CL under the SM (µ = 1)876

hypothesis. The mass range 122.1 GeV to 129.2 GeV877

is not excluded due to the observation of an excess of878

events above the expected background. This excess and879

its significance are discussed in detail in Section. VII880

A small mass region near mH ∼ 245 GeV was not ex-881

cluded at the 95% CL in the combined search of Ref. [14],882

mainly due to a slight excess in the H → ZZ(∗) →883

!+!−!+!− channel. This mass region is now excluded884

in the SM. The CLs values for µ = 1 as a function of the885

Higgs boson is shown in Fig. 5, where it can also be seen886

that the regions between 130.7 GeV and 506 GeV are ex-887

cluded at the 99% CL. The observed exclusion covers a888

large part of the expected exclusion range.889

[GeV]Hm100 200 300 400 500 600

SM

σ/σ

95%

CL L

imit

on

-110

1

10

Obs. Exp.

σ1 ±σ2 ± = 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

CLs Limits

(a)

[GeV]Hm110 115 120 125 130 135 140 145 150

SM

σ/σ

95%

CL L

imit

on

-110

1

10 Obs. Exp.

σ1 ±σ2 ± = 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

CLs Limits

(b)

FIG. 4. The observed (full line) and expected (dashed line)95% CL combined upper limits on the SM Higgs boson pro-duction cross section divided by the SM expectation as a func-tion of mH (a) in the full mass range considered in this anal-ysis and (b) in the low mass range. The dotted curves showthe median expected limit in the absence of a signal and thegreen and yellow bands indicate the corresponding 68% and95% intervals.

[GeV]Hm100 200 300 400 500 600

CLs

-610

-510

-410

-310

-210

-110

1Obs.

Exp. 95%

99% = 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

(a)

[GeV]Hm110 115 120 125 130 135 140 145 150

CLs

-510

-410

-310

-210

-110

1

Obs.

Exp.

95%

99%

= 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

(b)

FIG. 5. The value of the combined CLs for µ = 1 (testingthe SM Higgs boson hypothesis) as a function of mH (a) inthe full mass range of this analysis and (b) in the low massrange. The regions with CLs < α are excluded at the (1−α)CL or stronger.

VII. SIGNIFICANCE OF THE EXCESS890

The observed local p-values, calculated using the891

asymptotic approximation, as a function of mH and the892

expected value in the presence of a SM Higgs boson signal893

at that mass are shown in Fig. 6 in the entire search mass894

range and in the low mass range. The asymptotic approx-895

imation has been verified using ensemble tests which yield896

numerically consistent results.897

The largest significance for the combination is observed898

formH=126 GeV, where it reaches 3.0σ with an expected899

value in the presence of a signal at that mass of 2.9σ. The900

observed (expected) local significances for mH=126 GeV901

are 2.8σ (1.4σ) in the H → γγ channel and 2.1σ (1.4σ)902

in the H → ZZ(∗) → !+!−!+!− channel. In the H →903

WW (∗) → !+ν!−ν channel, which has been updated and904

included additional data, the observed (expected) local905

significance formH=126 GeV is 0.8σ (1.6σ), the observed906

17

[GeV]Hm

100 200 300 400 500 600

0L

oca

l p

-510

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Exp. Comb.

Obs. Comb.γγ →Exp. H γγ →Obs. H

bb→Exp. H

bb→Obs. H

llll→ ZZ →Exp. H

llll→ ZZ →Obs. H

νν ll→ ZZ →Exp. H

νν ll→ ZZ →Obs. H

llqq→ ZZ →Exp. H

llqq→ ZZ →Obs. H

νlν l→ WW →Exp. H

νlν l→ WW →Obs. H

qqν l→ WW →Exp. H

qqν l→ WW →Obs. H

ττ →Exp. H

ττ →Obs. H

ATLAS Private

σ1

σ2

σ3

-1 L dt ~ 4.6-4.9 fb∫ = 7 TeVs

(a)

[GeV]Hm

110 115 120 125 130 135 140 145 150

0L

oca

l p

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Obs. Comb.

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γγ →Obs. H

llll→ ZZ →Exp. H

llll→ ZZ →Obs. H

νlν l→ WW →Exp. H

νlν l→ WW →Obs. H

bb→Exp. H

bb→Obs. H

ττ →Exp. H

ττ →Obs. H

ATLAS Private

σ1

σ2

σ3

-1 L dt ~ 4.6-4.9 fb∫ = 7 TeVs

(b)

[GeV]Hm105 110 115 120 125 130 135 140 145 150 155

0Loca

l p

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ATLAS Private

σ1

σ2

σ3

Obs. Asym w/o ESSExp. Asym w/o ESSObs. Toy w/ ESS

=7TeVs

-1Ldt = 4.6-4.9 fb∫

(c)

FIG. 6. The local probability p0 for a background-only exper-iment to be more signal-like than the observation, for individ-ual channels and the combination. (a) In the full mass rangeof 110–600 GeV and (b) in the low mass range of 110–150 GeV.The full curves give the observed individual and combined p0.The dashed curves show the median expected value under thehypothesis of a SM Higgs boson signal at that mass. Thecombined observed local p0 estimated using ensemble testsand taking into account energy scale systematic uncertaintiesis illustrated in (c), the observed and expected combined re-sults using asymptotic formulae is also shown therein. Thehorizontal dashed lines indicate the p0 corresponding to sig-nificances of 1σ, 2σ, and 3σ for (a), (b) and (c); and 4σ for(a) and (b) only.

[GeV]Hm100 200 300 400 500 600

(0)

λ(1

) /

λ-2

ln

-40

-20

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20

40

60

80

100

120Obs.Exp. b-only

σ1 ±σ2 ±

Exp. s+b = 7 TeVs

-1 Ldt = 4.6-4.9 fb∫

ATLAS Private 2011 Data

(a)

[GeV]Hm110 115 120 125 130 135 140 145 150

(0)

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) /

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(b)

FIG. 7. The ratio of profiled likelihoods for µ = 0 and µ = 1as a function of the Higgs boson mass hypothesis. The fullline shows the observed ratio, the lower dashed line showsthe median value expected under the signal-plus-backgroundhypothesis, and the upper dashed line shows the median ex-pected under the background-only hypothesis (a) for the fullmass range and (b) the low mass range. The ±1σ and ±2σintervals around the median background-only expectation isgiven by the green and yellow bands, respectively.

[GeV]Hm100 200 300 400 500

!Si

gnifi

canc

e,

0123456789

10=7 TeVs -110fb

=8 TeVs -110fb

=7 TeVs -15fb

=8 TeVs -15fb

120 150

ATLAS Preliminary (Simulation)

Figure 2: The expected level of significance as a function of mH for 5 or 10 fb−1 of luminosity at√s = 7

or 8 TeV.

4

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Figure 2: The expected level of significance as a function of mH for 5 or 10 fb−1 of luminosity at√s = 7

or 8 TeV.

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[GeV]Hm100 200 300 400 500

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canc

e,

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10=7 TeVs -110fb

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120 150

ATLAS Preliminary (Simulation)

Figure 2: The expected level of significance as a function of mH for 5 or 10 fb−1 of luminosity at√s = 7

or 8 TeV.

4

Last Year

Now

4th of July