2.2 W Pair Production in e
2.2.5 Motivation for the M
W
Measurement
The gauge bosons W and Z couple directly to all particles which have weak
interactions. Even those particles which are too heavy to be pair-produced at
the Z will aect the properties of these resonances through their virtual eects
in loop diagrams. The loop eects are typically of order 0.1% in size. To see
these eects, the parameters of the SM have to be determined to an accuracy
of 0.1% or better. The three parameters in the SM are directly sensitive to the
propertiesoftheZ:thenestructureconstant ,the FermiconstantG
fromthe
muon decayandthe Zmass. G
andarethebestknown electroweakconstants
of nature. LEP has measured M
Z
to a similar accuracy as G
, which is more
than we hoped for, with its value [22]:
M
Z
=91:18820:0022 GeV ; (2.62)
where the valuesof G
=(7:2973525330:000000027)10 3
(2.64)
Nowthe currentmeasurements aresuÆciently precisethatthey are sensitive
to the loopeects like in Figure 2.6. The mass for the W and Z are related in
the SM by the formula
M
loopdiagrams due to virtual boson and fermion exchanges as in Figure 2.6 are
Abbildung 2.6: Loopquantum corrections toM
W
inthe Standard Model
included. The predicted mass of the W boson from precision electroweak data
(LEP1, SLD, N)[23] is
M
W
=80:3860:025GeV: (2.66)
130 140 150 160 170 180 190 200
79.8 80.0 80.2 80.4 80.6
80.8 SM
MSSM
M W (GeV)
M t (GeV)
Abbildung 2.7: Predictions for M
W
asa function of M
t
in the SM (solid
lines) and inthe MSSM (dashed lines).
The principleuncertainty in theprediction of theW mass isprovided by the
top and Higgs masses. Conversely, a precise directmeasurementof the W mass
together with an accurate top mass will indirectly constrain the Higgs mass.
The comparison of the direct measurement of the W boson with the indirect
prediction is particularly important to test the standard theory of electroweak
unicationatthelooplevel. Further,adirectmeasurementof theWmass helps
to constrain a possible extension of the Standard Model such as the Minimal
Supersymmetric Standard Model (MSSM), Figure 2.7[18]. MSSM predicts new
particles and these particles could contribute to the W boson mass via loop
corrections,whichwouldbevisibleinthecomparison ofthe directmeasurement
with the indirect prediction of the W boson mass. Thus, the comparison can
constrain the allowed parameter space ofthese kinds of models.
Description of the Experiment
An understanding of experimental tools is an important part of the study of
elementaryparticlephysics. Howareelementaryparticlesproducedandhoware
they detected ?
Nowadays accelerators are used to produce particles in controlled collisions
between subatomic particles. The advantage of accelerators is that beams of
particlescanbeprepared accordingtothepurposeofthe study. Fortheanalysis
presented in this thesis, the Large Electron Positron Collider (LEP) at CERN,
theEuropeanLaboratoryforParticlePhysicsisused. Whenthebeamsof
partic-lescompressed intobunches of up tosome 10 11
particlescollidewith each other,
many particles can be produced. To obtain as much information as possible
about these particles, their interactions with the material of the detectors must
beobserved. Theexperimentshouldconsistofmanydierentsub-detectorswith
specic characteristics. To avoid a loss of particles, the complex detector has a
4 coverage. For this thesis, the L3 detector isused.
Inthe following the LEP colliderand the L3experimentare described.
Em-phasis is placed onthe parts of the detector which are important for the direct
reconstruction of the W boson ine +
e !W +
W !qqq q events.
3.1 The LEP Collider
The LEP machine is an e +
e colliderbuilt at CERN inthe vicinity of Geneva,
Switzerland. Thiscircularmachinewithcircumferenceof 26.67kmisthelargest
particlecollider inthe world.
The basic components of this accelerator are the radio frequency (RF)
cavi-ties,the dipolemagnets, thequadrupoleandsextupolemagnetsand thevacuum
chamber. The cavitiesrepresent the acceleratingcomponentandact likeashort
section of a linear accelerator. The radio frequency oscillations in the cavities
are used to establish a moving electromagnetic wave in the structure, with the
longitudinal component of the electric eld moving in phase with the particles.
Solong asthis phaserelationship can bemaintained,the particleswillbe
conti-nually accelerated. The dipolemagnetsare used tobend the particles and keep
themmovinginacircle. Themagneticeldhastobegraduallyincreasedtokeep
in step with the accelerating particles. The quadrupole and sextupole magnets
areusedtofocustheparticlesandtokeepthemtightlypacked. Theparticlescan
belosttravellinginsidethe beampipe,sincecollisionsmayoccur withmolecules
of air. To prevent this, the beam pipe consists of avacuum chamber.
LEP has 3368 magnets to bend the particle beams and keep them in orbit.
In the dipole magnets an electron bends one way and a positively charged
po-sitron bends the other way. Thus LEPcan circulatethe beams of electrons and
positrons in opposite directions using the same magnets. Each bunch contains
more than 10 11
particles, but on average only one in about 40 000 1
collisions
between the bunches producesanelectron-positroncollision. Forthis reasonthe
LEPdesign isbasedon the principleof astorage ring. Thebunches of electrons
and positrons are accelerated to a desired nal energy and then kept at their
nalenergy forseveral hours, allowingeachbunch totravelround thering more
than 10 000 times a second. The acceleration scheme used at LEP2 is a 2 4
bunch-mode 2
. Four equally spacedbunches perbeam collideevery 22 s at the
1
ThisnumberistakenfromtheoperationofLEPattheZpeak.
2
Forthe operationof LEP at theZ peak, the bunch trainschemewasused. Hereby, the
bunchesare replacedby trainsofupto 4smallerbunchlets,whichhaveadistanceof 250ns
intime. Therefore, collisionsmay occur morefrequently than in bunch-modeleading to an
interaction points around the LEP ring, where the bunches are about 1500 m
long, 250 m wide in the horizontal direction and 10 m wide in the vertical
direction intheplanetransverse tothebeam direction. Tworeasonsaccount for
the large scale of the machine. First, a charged particlemoving along a curved
path radiates photons and loses energy, which is proportional to E
4
m 4
per turn.
Here E is the energy, m is the mass of the particleand isthe bending radius.
For a xed energy of the particles in the accelerator, the loss of energy can be
reduced, if the bending radiusis large. Secondly, if the bending radius is small,
themagneticeldrequiredforthebendingmustbestrongerforthesamedesired
beam energy. ThesereasonsmakethingsdiÆcult,ifthe particlesare accelerated
to very high energies. For electrons the losses are very severe. At LEP, a 100
GeV electron loses on average approximately 3 GeV of energy per turn, which
must be replenished by the acceleration system.
The stages through which electrons and positronsare injected into LEP are
shown in Figure 3.1. The injection system consists of several steps: First the
LEP Injector Linearaccelerator (LIL)ramps electronsto200 MeV and smashes
themontoatungstentargettoproducepositrons,or,alternatively,simplypasses
them through toa second LIL whichalternately pushes electrons and positrons
up to 600 MeV. The following Electron Positron Accumulator (EPA) collects
the two particle species into geometrically smallpackages called bunchlets, and
groups up to four bunchlets into bunches. When accumulated to a suÆciently
largeintensity,theparticlesarepassedtotheProtonSynchrotron(PS)operating
as a 3.5 GeV e +
e synchrotron. Lastly the Super Proton Synchrotron (SPS) is
used to bring particle bunches up to an energy of 20{22 GeV. And nally the
bunches are injected into LEP and accelerated to the nal energy of e.g. 189 3
GeV.
LEP has four interaction points, where the four LEP experiments L3 [24],
ALEPH[25], DELPHI[26]and OPAL[27]are installed. Untilthenalenergy is
reached the electron and positron beams are separated in the interaction points
using electrostatic separators. In the case of colliding beams, a system of
qua-muchhighercurrent
3
Theenergyof189GeVwasreachedintheyear1998. AttheendofLEP2,thenalenergy
*
electrons *
positrons protons antiprotons Pb ions
LEP: Large Electron Positron collider SPS: Super Proton Synchrotron AAC: Antiproton Accumulator Complex ISOLDE: Isotope Separator OnLine DEvice PSB: Proton Synchrotron Booster PS: Proton Synchrotron
LPI: Lep Pre-Injector
EPA: Electron Positron Accumulator LIL: Lep Injector Linac
LINAC: LINear ACcelerator LEAR: Low Energy Antiproton Ring
CERN Accelerators
ALEPH OPAL
L3 DELPHI
SPS LEP
West Area
TT10
AAC
TT70
East Area
LPI
e-e + EPA
PS
LEAR LINAC2
LINAC3 p Pb ions
E2
South Area North Area
LIL
TTL2 TT2 E0
PSB ISOLDE
E1 pbar
Abbildung3.1: CERNacceleratorsincludingLEPstorageringwith
inter-actionpointsand injection system.
drupolemagnetsallowsfocusingand transversal adjustmentof the beamswhich
is important because this controls the luminosity.
The instantaneous rate of events fromcolliding beams is given by
dN
dt
= L; (3.1)
where is the cross section of the process of interest and L is the
luminosi-ty, which is the rate of the electron-positron interaction per unit surface. The
luminosityat LEPfor one interaction point can be calculatedvia
L =
is the numberof electrons and positrons inthe collidingbunches, n
b
isthe numberofbunches perbeam andf istherevolution frequencyofabunch.
The surfaceisintroducedinthedenominatorbythe productof
x and
y
which
are thetransversedimensionsofthe beamattheinteractionpoint(IP).The
ma-ximum luminosityof 10 32
cm 2
s 1
[28, 29]wasreached in1998 and 1999. Inthe
following analysis only the integrated luminosity isused which can be obtained
by integrating the above equation 3.2 over the time interval of the data taking
period. See section 3.2.6 fora more preciseprocedure.
Energy Calibration
One of the main goals atLEP2 isthe precisemeasurement of the Wmass. But
the beam energy sets the absolute energy scale for this measurement, leading
to an uncertainty. The experiments reconstruct the decay of the W +
W pair
using a kinematic t, and the kinematic t takes the beam energy, E
beam as a
constraint. Therefore theerror onE
beam
enters directlyasanerror onM
W . The
expected statistical error on the W mass at the end of LEP2 is 25 MeV. To
avoidasignicant inuenceof the beam energyuncertainty onthe totalerror, a
precisionof 10 - 15MeV onE
beam
is desired.
DuringtheLEP1 period,aprecise measurementof the beam energy was
ob-tainedusingthemethodofresonantdepolarization(RDP),whichallowed ahigh
Flux Loop NMR probe
Beampipe
Dipole Flux Loop
Abbildung 3.2: The NMR probes and ux-loops used for monitoring the
LEPmagnetic eld.
be used, since polarisationhas only been observed in LEP up to beam energies
of 60 GeV. For the data analysed in this thesis, an alternative NMR (nuclear
magnetic resonance) -extrapolation method is used. Here, the local magnetic
elds, as measured by 16 NMR probes installed inside some selected bending
dipolesaround the LEPring (seeFigure3.2), are calibrated againstRDP inthe
energy interval 40 - 60 GeV. This calibration is applied to give the energy in
the physics regime of around 100 GeV. It is assumed that the relation between
NMRand the beam energyis linearand validup tophysicsenergies. The NMR
sample corresponds to a small fraction of the eld, while the ux-loops 4
also
installed inside the dipoles (see Figure 3.2) provide a measurement of 97 % of
thetotalbendingeld. Thusthe ux-loopmeasurementsare usedtocross-check
the beam energy determined by the NMR probes [31].
AtLEP2, the beam energy isdeterminedwith aprecisionof 25MeV[32]for
the datataken during1997 at p
s=183 GeV.The analysis ofthe 1998 data led
toa beam energy uncertainty of20 MeV [33] at p
s=189 GeV.Forthe runs at
4
The Flux Loop consists of a closed electrical loop threading through the dipoles; the
integratedinducedvoltagewhenalteringthedipolecurrentsisadirectmeasureofthemagnetic
higher center-of-mass energies, LEP plans to use the LEP spectrometer[34] for
further improvementinthe measurementof the beamenergy. Thespectrometer
determinesthebeamenergybymeasuringthebendangleofthebeaminalattice
dipoleof known integrated eld.