Atlas for High Schoolers - University of Pennsylvania High ...
Transcript of Atlas for High Schoolers - University of Pennsylvania High ...
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 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)
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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.
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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
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
-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
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
-410
-310
-210
-110
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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
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(a)
[GeV]Hm
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Obs. Comb.
γγ →Exp. H
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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Obs. Asym w/o ESSExp. Asym w/o ESSObs. Toy w/ ESS
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
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40
60
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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
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σ1 ±σ2 ±
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ATLAS Private 2011 Data
(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
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canc
e,
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10=7 TeVs -110fb
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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.
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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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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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