day1- determining particle properties

Peter WittichCornell University

One view of experiment

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looks like ATLAS!CMS is clearly

different. :)

xkcd, http://xkcd.com/

my goal for these lectures• give you a glimpse of experiment

⇨difference between what we think about and what you think about

• give you tools to read an experimental paper• give you tools to listen to an experimental

seminar• maybe help you learn how to talk to your

experimental colleagues• what do they do all day, if not giving helicopters

cancer?• all this with the specific case of the LHC energy

frontier program3

ask me questions!

• I can’t promise to be able to answer them all but I’ll try

• it is more fun for me when there is give-and-take.

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goals of measurement• reconstruct the four-vectors of individual events

⇨pT, η, Φ, ET -- the language of exp. HEP

⇨particle identification• e,γ, μ, “jets” (b), τ -- all you have• missing energy & other event information

• understand the composition of events

⇨sources? known and unknown?• extract physics parameter

⇨cross section, coupling constant …

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but first we need to collide the beams -- accelerators.

accelerators

• two types: linear vs circular• Linear: cathode ray TV’s to SLC (SLAC)

⇨ILC (future)• RF accelerators

⇨radio-frequency cavities “kick” beams

⇨superconducting• one-shot acceleration, no synchrotron radiation

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superconducting RF

• wall power losses due to heating in normal RF cavities• superconducting cavities, high Q ~ 1011.• exotic materials, often niobium tin compounds

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circular accelerators• synchrotrons:• many passes at acceleration• vary B to accelerate particles on fixed path • time structure corresponding to RF frequency• synchrotron radiation limits for light particles,

but not for e.g. protons

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P !!

E

m

"4

Colliding beams• modern accelerators are synchrotrons• energy frontier machines are colliding beam

machines:

• important parameters in colliders are the energy of the beams and the rate of collisions

⇨“luminosity”

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R =dN

dt= L!

fixed target: Ecm =!

2Ebeanmtarget

colliding beams: Ecm = 2Ebeam

units of luminosity• [L]=1/cm2 1/s → 1/(cross section x time)• [integrated luminosity] = unit of 1/cross section• easy conversion from data size to number of

events for a given process• in 100/pb of data, LHC will produce this many

top quark pairs (σ = 800 pb)• some numbers: LHC lumi goal 100/fb

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N = !

!L dt = 800pb! 100/pb = 80k

what we observe in the experiment is a different story…

Making luminosity

• important factors are• frequency f• number of particles in a bunch (n1,n2)• size of the beam in the transverse plane (σx, σy)• β*, ε - accelerator language re size• β* - beam optics: “beta star”• ε - bunch preparation: “emittance”

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Thus, to achieve high luminosity, all one has to do is make high population bunches of low emittance to collide at high frequency at locations where the beam optics provides as low values of the amplitude function as possible. -- Particle Data Group

L = fn1n2

4!"x"y= f

n1n2

4!

#x$!x#y$!

y

LHC machine parameters• f = 11.25 kHz• Nbunch = 2808• protons/bunch: 1.7 x 1011

• bunch spacing 25 ns (75 ns)• normalized εn = 3.75 μm, β*=0.55 m• bunch length 7.5cm

⇨all together lead to L = 1.0 x 1034 cm-2 s-1

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hep units and measures• GeV, cm, ns, barns• ET, PT, MT

⇨transverse plane• η = -ln tan θ/2

⇨ “pseudo-rapidity”• ΔR• missing ET -- MET

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! = ! ln tan"

2

!ET

ET = E sin !

!R !!

!!2 + !"2

transverse plane• we focus on the transverse plane

⇨opposite of “forward”• high q2 interactions• B field: measure (transverse) momentum

⇨curvature of charged particle• transverse energy, mass analogs

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ET = E sin !m2

T = E2T ! p2

T

η - pseudo-rapidity

• dN/dy is constant under boost • but η = - ln tan(θ/2) ~ y for p≫m

• and better yet we can calculate η w/o knowing the mass of the particle

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y ! 12

ln!

E + pz

E " pz

"(“rapidity”)

= tanh!1#pz

E

$

! = ! ln tan"

2

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η = 0

η = 1

η = 2η = 3

η = large

x

y

z

interaction point

ranges for η • Typical η values for general-purpose detectors are

⇨|η|<2 (“central”)

⇨2<|η|<5 (“forward”)

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D0

η = 1

η = 3

delta R

• used to measure distance in HEP events• used to group particles for jet reconstruction• used to determine proximity between particles

⇨isolation in calorimeter or tracking chambers• typical values: 0.5, 0.7 (jet algorithms)

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!R !!

!!2 + !"2

missing ET

• one of the most interesting and most difficult quantities in experimental HEP

⇨calorimeter towers

⇨junk collector

⇨hadronic energy scale

⇨muons are missing (MIP)

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!ET " #!

i

EiTni

why transverse?

• hadron collisions: you don’t know the initial state

⇨proton is not what scatters • pz of partons that are in hard scatter?• to good approximation: ∑pT

i = 0

⇨momentum conservation in transverse plane• final state: only get estimate of vector sum ∑pT

f

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example: mT in W→ μν

• for pTW=0 edge at mW/2 (“jacobian peak”)

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) (GeV)!µ(Tm60 70 80 90 100

even

ts /

0.5

GeV

0

500

1000

) MeVstat 54± = (80349 WM

/dof = 59 / 482"

-1 200 pb# L dt $CDF II preliminary

mT !!

E2T " p2

T =!

2pµT#ET (1" cos !!)

MET = junk

• anything going wrong produces MET• need careful work to understand samples

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now our protons collide• initial state radiation (ISR)• hard scattering of partons (parton density func)• final state radiation (FSR)• underlying event

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p

p

PDF’s

• Parton model allows factorization of QCD into two parts, long and short distance

⇨long: dynamics of hadrons in quark

⇨short: describes the hard event - calculable• PDF’s determined with input experiment

⇨neutrino DIS, ep, ppbar, pp• scale PDF’s from one energy scale to next,

allowing us to apply these results to LHC (Q2)• MRST, CTEQ collaborations

⇨uncertainties24

!(pp! CX) =!

ij

"fp

i (xi, Q2)fp

j (xj , Q2)!̂(ij ! C)dxidxj

hadronization

• consider final state above• hadronization: “dressing” of the colored particles• jets! (later: jet algorithms)

⇨collimated spray of particles

⇨electrons, γ’s, and hadrons

⇨neutral and charged particles

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pp ! tt̄

t ! Wb! !"b

t̄ ! Wb̄! qq̄b̄

Consider:

underlying event

• everything except the hard scatter is called the “underlying event”

• includes initial state, final state radiation• remnants of the beam particles

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!"#$#%& '%$(!"#$#%&

)*+",-&./+$$0"(%1&

!234+",5&

67$1#(%1&!+"$#%&

67$1#(%1&!+"$#%&

8%,0"9:(%1&;<0%$& 8%,0"9:(%1&;<0%$&

=%($(+9>.$+$0&?+,(+$(#%&

@(%+9>.$+$0&?+,(+$(#%&

R. Field

now on to the detector• end view• layers

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PDG

passage of particles

• same segmentation, but now unrolled• need to understand physics underlying these

design choices28

PDG

bethe-bloch

• describes average ionization loss of relativistic particles

⇨main source of loss for most particles besides electrons

• does not include radiative corrections

⇨will start to become important at the LHC

⇨(π energies above ~10 GeV e.g.)

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!dE

dx= kz2 Z

A

1!2

!12

ln2mec2!2"2Tmax

I2! !2 ! #

2

"

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PDG

• min at beta γ ~3• example:

⇨MIP in silicon • dE/dx: 1.6 MeV/(g/

cm2) x 2.33 g/cm3 = 3.7 MeV/cm

⇨(not much!)

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electron/photon

• radiative losses cannot be ignored (not π and μ)

⇨e: mostly bremsstrahlung, γ mostly pair prod.

⇨electromagnetic shower, radiation length X0

• (bethe-bloch different too… )

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T. Dorigo

electrons & γs

• characteristic length that describes the energy decay of a beam of electrons

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Bremsstrahlung

Lead (Z = 82)Positrons

Electrons

Ionization

Møller (e!)

Bhabha (e+)

Positronannihilation

1.0

0.5

0.20

0.15

0.10

0.05

(cm

2g!

1 )

E (MeV)10 10 100 1000

1 E!

dE dx

(X0!

1 )

PDG

X0 =716.4 g cm!2A

Z(Z + 1) ln(287/!

Z); " dE

dx=

E

X0

Material X0[cm] Ec[MeV]

Pb 0.56 7.4

Fe 1.76 20.7

muons• for HEP purposes muon is

stable particle

⇨cτ ~ 700 m• no strong interaction -

only MIP

⇨Ec scales like m2

⇨Fe: Ec=890 GeV!• μ’s are very penetrating

⇨TeV μs after 5000 mwe• muon id

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SNO/Chris Kyba

multiple scattering

• multiple Coulomb scattering off nuclei• well approximated by Gaussian with above width

⇨depends on 1/beta, x/X0• important for tracking accuracy (large scatters too)

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!0 =13.6MeV

"cpz!

x/X0 [1 + 0.0038 ln(x/X0)]

x

splaneyplane

!plane

"plane

x /2