G. Eigen, HASCO 17-07-17 Göttingen

r In particle physics, we build so-called multi-purpose detectors

r These are dedicated instruments that measure particular observables:

vertex, track positions, particle IDs, momentum, energy, time, … r In colliding-beam experiments, subdetectors are placed in layers

around the interaction region in cylindrical geometry, like onion shells r In fixed-target experiments, they are stacked behind the target in

a fixed fiducial volume

r Though physics processes can be manifold and complex, we only encounter six particles in the final state: e^±, µ^±, p^±, K^±, p^±, g

r In matter, these particles interact electromagnetically

r Each LHC experiment has about 100 million sensors

r Think that your 6MP digital camera takes 40 million pictures/s

six-storey building ATLAS CMS

r Ionization, excitation & electron in gases r Gaseous tracking detectors

r Solid state detectors

r Momentum measurements

r Electrons and Photons in Matter r Electromagnetic Calorimeters r Hadronic Calorimeters

r Particle Flow Calorimeters

r Particle identification detectors r LHC detectors

Pelican nebula

Medium

• A: atomic weight

• Z: atomic number

• r: density

• I: ionization potential

• a=1/137

• m_e: electron mass

• C: shell correction

• d(bg): density effect

• K=0.307 MeV cm²/g Particle

• Tmax: maximum kkkkkkkinetic energy

• z: particle charge

• b=|p|/E

• g=E/m

(m>>m_e) r The average energy loss for a heavy particle is given by Bethe-Bloch

− dEdx = Kz²ρ ^Z A

1 β²

1

2ln 2m_ec²β²γ ^{2 Tmax} I²

⎛

⎝⎜⎜ ⎞

⎠⎟⎟ − β² − δ(βγ )

2 − C Z

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

r Since the measured energy loss allows us to determine the particle velocity, it can be used to identify particle types at low momenta r The instantaneous energy

loss in thin layers is given by a Landau distribution

Measured energy loss in the ALICE TPC

dE/dx in liquid Ar fitted with a Landau distribution

Bethe- Bloch

r For low bg values, dE/dx decreases as 1/b²

r Average energy loss at the minimum is at bg of 3-4

r Minimum energy loss can be parameterized by: 2.35- 0.28 ln(Z)

~1/b² Relativistic rise

Energy loss at minimum

Minimum

r A charged particle traversing a gas produces e^-i⁺ pairs

r A cloud of positive ions, i⁺, placed in an electric field of strength 𝐸𝐸, is accelerated by the 𝐸𝐸 field and decelerated by collisions in the gas è the motion can be described by a constant drift velocity v_D

r According to measurements, v_D is proportional to 𝐸𝐸/P

where µ⁺ is the ion mobility, units [cm²/(Vs)] P₀=760 Torr

r Examples: He⁺ in He: µ⁺= 10.2 cm²/(Vs) v_D^" = 0.01 cm/µs Ar⁺ in Ar: 1.7 “ 0.0017 “ CH₄⁺ in Ar: 1.87 “ 0.00187 “ (OCH₃)CH₂⁺ in (OCH₃)CH₂ 0.26 “ 0.00026 “ r Mobility is high (low) for small (big) atoms/molecules

v_D⁺⁺ == µµ⁺⁺

E ^P_P^{0 pressure}

For 𝐸𝐸=1kV/cm

r The drift velocity can be expressed in terms of the mean free path ^ll, thermal velocity u, electric field 𝑬𝑬, charge q and particle mass m

r If the mean free path is independent of the thermal velocity, the second term vanishes

r For some gases, v_D is independent of 𝑬𝑬 in some range (Ar-CH₄ 90:10) or is only slightly dependent on 𝑬𝑬 r Electron drift velocities of are

~1-10cm/µs and e^- mean free paths are considerably larger:

l_e=l_ion×5.66

v_D == q E m

2 3

λλ_e(u)

u ++ 1 3

dλλ_e(u) du

""

##$$

%%$$

&&

''$$

(($$

l: average distance between 2 collisions

r A charge in an electromagnetic field moving through a gas-filled volume is subject to the force

r Stochastic acceleration averaged over time compensates translational acceleration

where t is average time between 2 collisions

r In a constant 𝑬𝑬 field we have

r In the presence of 𝑬𝑬 & 𝑩𝑩 fields the drift velocity has 3 terms i) one parallel to 𝑬𝑬

ii) one parallel to 𝑩𝑩

iii) one perpendicular to plane spanned by 𝑬𝑬 & 𝑩𝑩

r If 𝑬𝑬 and 𝑩𝑩 are not parallel, there is angle between v_D and 𝑬𝑬 called Lorentz angle

Coulomb mv = q( Lorentz E + v × B) + mA

(t) Langevin

A

(t) = − v

D

τ

v_D == µµ 1 ++ ωω²ττ²

E ++

E ×× 

 B

B ωωττ ++ ( E ⋅⋅ 

B) ⋅⋅  B B ²

ω ω²ττ²

%%

&&

'''' ''

((

))

****

**

ω

ω == −− q m

B

ω

ω 17.6MHz / G Cyclotron frequency

tan

αα

ω ωττ

r A charge distribution Q(t) localized at (0,0,0) at t=0 is diffused by multiple scattering

r At time t, Q(t) is Gaussian with center at origin

r The rms spread is proportional to the diffusion coefficient

where F(e) is the Maxwell-Boltzmann distribution

r For energy-independent ll we obtain r For a classical ideal gas we have

where s(e) is the collision cross section and N is number of molecules per unit volume

D == ¹₃

∫∫

D == ¹₃ uλλ

λλ(εε) == 1 Nσσ (εε)

N == 2.69 ×× 10^{19 P 273 molecule}

ee : kinetic energy x

r Diffusion parallel (L) and perpendicular (T) to the drift direction depends on the nature of the gas

r Typically faster gases yield smaller diffusion than slower gases

r The spatial resolution is depends on time and the diffusion coefficient

r Since t=L/|v_D| & D=ull/3, we get in absence of a magnetic field

r In the presence of a magnetic field spatial resolution improves by

1 ++ ωω²ττ²

(( ))

σσ = 2L

3v!_D ^uλλ

σσ

ALICE TPC

r Consider a tube with a wire placed at its center filled with a gas r If we apply a high electric field

between anode wire and cathode cage (10⁴-10⁵ V/cm), electrons from the primary ionization

gain enough energy between 2 collisions to cause further ionizations

r For certain 𝑬𝑬 fields & gas pressures, A is independent of the amount of primary ionization ^èè observed signal is proportional to primary

ionization

r This domain of field strengths is called proportional region è

è here A»10⁴-10⁶

r Achieve high field strengths with thin wires (20 µm-100 µm) as anode r Amplification will start in close vicinity to anode

r The number of e^--i⁺ pairs formed by an electron along a 1cm path is called the first Townsend coefficient

where s_i is ionization cross section and N=2.69x10¹⁹ atoms/cm³

r If N₀ is number of primary e^- at x=0 and N(x) is number of e^- at path x

è

r So

and gas amplification is since a(x)=1/l(x)

r For fast gases, Townsend coefficients are considerably smaller than those for slow gases

α

α == σσ_iN

dN(x) == N(x)ααdx

N(x) == N₀ exp αα (x')dx'

∫∫

A(x) ∝∝ exp αα(x') dx'

∫∫

λλ(x')

∫∫

r In addition to the secondary electrons, ionization processes due to UV photons contribute

r These UV photons originate from de-excitations of atoms excited in collisions & produce e^- via photo-effect in gas atoms or cathode ð

ð Assume that in avalanche formation N₀×A electrons are produced from N₀ primary electrons

ð

ð From UV photons additional N₀×A×g photoelectrons are formed (g « 1) ð

ð By gas amplification these photoelectrons produce N₀×A²×g electrons ð

ð From them another N₀×A²×g² photoelectrons are formed which in turn produce N₀×A³×g² electrons, and so on

r Summing up all terms we get the total gas amplification factor Ag

r For A×g®1, Ag diverges & signal no longer depends on primary ionization è This is called Geiger-Müller region (A ~10⁸-10¹⁰)

N₀A_{n≥≥ 0}

^{∑ ∑} (( ))

r In a multi-wire proportional chamber (MWPC) a plane of anode wires is sandwiched between cathode planes r Cathode planes are segmented

into strips; strips in one (other) plane run parallel (perpendicular) to the anode wires

r A traversing charged particle liberates e^- i⁺ pair along its path

r e^- are accelerated towards the anode wire & i⁺ towards cathode plane r The 𝑬𝑬 field is chosen sufficiently high so that secondary ionization

sets in and an avalanche is formed near the anode wire and signals are induced on the cathode strips

r Anode wires: 20 µm thick Au-plated W, Al; 2 mm spacing

Counting gas: Ar, Kr, or Xe with admixture of CO₂, CH₄, isobutane, … Amplification: 10⁵; efficiency: ~100%

with cathode readout measure x and y positions

r Position is usually obtained by center-of-gravity method

y ==

Q_i −− b

(( ))

∑

∑

Q_i −− b

(( ))

∑

∑

y-position of wire i Charge of wire i

Small bias voltage to correct for noise

r Achieve resolutions of 110-170 µm, 35 µm in small chamber

r Position along the wire is obtained via charge division

è Need to read out both wire ends

r For charge measurements Q_A & Q_B obtain position along the wire

r Accuracies are ~0.4% of wire length

x == L Q_A −− b Q_A ++ Q_B −− 2b

y_i

r We can obtain spatial information by measuring the drift time of electrons produced in ionization processes

r The drift time Dt between primary ionization t₀ & the time t₁ when e^- enters the high 𝑬𝑬 field generating an avalanche is correlated with the rising edge of the anode pulse

ð

ð For constant drift velocity v_D^"(t) drift distance for this Dt interval is

r Constant v_D^" results from constant 𝑬𝑬, which is not achieved in MWPCs

è Need to introduce a field wire at potential -HV1 between anode wires r Choice of gas Ar-C₄H₁₀ (purity)

Use slower v_D^" to optimize spatial

resolution ^ðð large DC: 55-200 µm, small DC: 30-70 µm z == v_D⁻⁻

((

))

r 𝑬𝑬 field lines lie in the r-j plane, perpendicular to axial 𝑩𝑩 field

r The 𝑬𝑬 field is generated by a suitable arrangement of potential wires, which are parallel to each other surrounding a single signal wire

r A large fraction of layers (typically ³ 50%) have wires running parallel to 𝑩𝑩 field (axial layers) & rest have wires

running skew under stereo angle g=±few ⁰ wrt 𝑩𝑩 field axis (stereo layer) r Axial wires only give r-j position, stereo wires allow to get z position r One determines r-j position from all axial wires,

then the stereo wires are added by moving along z-position till the r-j fits with that of axial layers r For each signal wire t₀ and the time-to-distance

relation need to be measured

r BABAR drift chamber: 40 layers, s_rj≈125 µm

Max: 1cm drift distance

r The Time Projection Chamber combines principles of a drift chamber &

proportional chambers to measure 3-dimensional space points r A high 𝑬𝑬 field is placed parallel to a high 𝑩𝑩 field (1.5 T)

è no Lorentz force on drifting e^-

• 845 < r < 2466 mm

• drift length 2 x 2.5 m

• drift gas Ne:CO₂:N₂ (85.7:9.5:4.8)

• gas volume 95 m³

• 557568 readout pads

ALICE TPC

E E

400 V / cm High Voltage electrode

(100 kV)

field cage

readout chambers

Endplates housing 2 x 2 x 18 MWPC

r e^- produced by ionization of a charged track passing the TPC drift towards the endcaps, which are instrumented with MWPCs

r The image is broadened by diffusion during the drift process è broadening can be considerably reduced by strong 𝑩𝑩 field r e^- are forced to perform helical

movement around 𝑩𝑩 field lines r Transverse diffusion coefficient

is reduced by 1/(1+w²t²), with w=(e/m)| 𝑩𝑩 | & t is mean free time between 2 collisions

r TPC measures 3-dimensional space points, r-f in MWPC

and z from drift time r Spatial resolution:

s_rf=180 µm, s_z=200 µm

r Position-sensitive gas detectors based on wire structure are limited by diffusion processes and space charge effects to accuracies of 50-100 µm r A GEM detector consist of a thin Cu-Kapton-Cu

sandwich into which a high density of holes is

chemically processed: 25-150 µm ⍉, 50-200 µm pitch

r A high E field 50-70 kV/cm is applied across holes è broadening electron produces avalanche in hole r Coupled with a drift electrode above and a readout

electrode below it acts as a highly performing micro amplifying detector

r Amplification and detection are decoupled

è broadening operate readout at zero potential r With several layers gain of 10⁴ is achievable r GEMs have higher rate capability than MWPCs

70µm140µm

r The micro-mesh gaseous structure is a thin parallel-plate avalanche counter r It has a drift region & a narrow amplification gap (25-150 µm) between a thin

micro mesh & the readout electrode (conductive strips or pads printed on insulator board)

r Primary e^- drift through the mesh holes into the amplification gap where they are amplified

r Homogeneous E fields, 1 kV/cm in drift region & 50-70 kV/cm in amplification gap

r Excellent spatial resolution of 12 µm, good time resolution and good energy resolution for 6 keV X-rays of 12% at FWHM

r New developments of MicroMEGAs with pixel readout will integrate amplification grid

with the CMOS readout, use 1 µm Al grid above

50 µm è broadening expect excellent spatial and time resolutions

ATLAS SCT module

r Si has 4 valence e^-

è Each valence e^- is coupled to e^- of neighboring atom via covalent bound r At T=0, all e^- are bound & cannot conduct any current

è full valence band, empty conduction band, separation: 1.1 eV r At room temperature thermal energy is sufficient to

liberate e^- into conduction band (10¹¹/cm³)

r However, usually we add controlled level of impurities i) Elements with 3 valence e^- (p-type)

B, Ga, In Þ hole carriers, acceptor impurity ii) Elements with 5 valence e^- (n-type)

Sb, P, As Þ e^- carriers, donor impurity

r Concentration of electrons (n) and holes (p) satisfies

n ⋅⋅ p == N_cN_v exp E_g kT

""

##

$$$$

%%

&&

'''' == const N_c: # of allowed levels in conduction band N_v: # of allowed levels in valence band E : energy gap

e^- h⁺

No bias voltage

e^-

h⁺

e^- h⁺

Contact potential V₀

- +

n p

r Depletion layer

r When ionization liberates charge in depletion layer, e^- & h⁺ drift apart due to strong internal field & produce a current

With reverse bias voltage V_b

d ≅≅ 2εεεε

((

))

pitch

DC-coupling

r A typical n-type Si microstrip detector has

Ø p⁺n junction: N_p≈10¹⁵ cm^-3, N_n≈1-5×10¹⁵ cm^-3 Ø N-type bulk: r>2 kWcm, thickness 300 µm Ø Operating voltage < 200 V

Ø n⁺ layer at the backplane to improve ohmic contact

Ø Aluminum metalization r About 30000 e^-h⁺ pairs are

liberated by a traversing charged particle via dE/dx by ionization r Charges drift towards electrodes

where they produce a signal on that strip

r Each strip is coupled to a preamplifier

r Use AC-coupling block leakage currents from amplifier

ENC

= 8kTC

f

ττ

r The main source of noise is due to statistical fluctuations in the number of carriers, leading to changes in conductivity

r The most important noise contributions are (Equivalent Noise Charge) Ø leakage current (ENC_I)

Ø detector capacity (ENC_C)

Ø detector parallel resistor (ENC_Rp) Ø detector serial resistor (ENC_Rs)

r The overall noise is the quadratic sum of all contributions

r The detector capacity is typically the dominant noise source

r For typical values of f_T=1GHz and τ_f=100 ns we estimate ENC_C=1.13×10² C_d^1/2 [rms e^-] with C_d in pF

Ø for C =1pF è ENC ≈113 e^-, for C =100pF è ENC ≈1130 e^-

kT=25.85 T/300K [meV] frequency for unity gain of amplifier

time constant of filter

Signal: 30,000e^-

r The dE/dx energy loss produces a Landau-like distribution that is different for pions and

protons of the same momentum

r For a single strip the position resolution is

r For two or more strip hits we use the center- of-gravity method

r Here, a large signal-to-noise (S/N) ratio improves the spatial resolution

r Diffusion broadens the spatial resolution è broadening depends on the drift length

x = p

s

_x ∝ p

s

p: pitch

r 4 layers with 2 planes each, r-j strips and r- j strips slightly tilted by 40 mrad

r In f, modules are tilted wrt to surface of support structure by ^{(110, 110, 11.250 & 11.50)} r ~ 61 m² of Si, ~6.3´10⁶ readout channels r Sensor thickness: 285 µm, 80 µm pitch r Position resolution in barrel from Z→µ⁺µ^-:

s =24.0 µm

SCT module Due to radiation issues ATLAS uses p-in-n Si

r The power of Si vertex detector measurements (ALEPH)

r Pixel detectors are made of an array of small Si

pixels, i.e. physically isolated pads, providing both r-j & z measurements r Pixels are bump-bonded to

a pixelated readout chip

r Advantage: excellent 2-track

resolution, take high occupancies

è important for high rates close to beam pipe r They are used in colliding beam experiments:

e.g. DELPHI, ATLAS, CMS, ILD, SiD r Typical pixel dimensions:

ATLAS: 50´300 µm² Þ 8.´10⁷ pixels CMS: 150´150 µm² Þ 3.9´10⁷ pixels

r ATLAS Pixel detector

Barrel: r=5.05 cm, 8.85 cm, 12.25 cm Endcap: z=±49.5 cm, ±56 cm, ±65 cm r Position resolution from Z→µ⁺µ^-:

s_x=9.0 µm, s_y=87.0 µm

r Cosmic muon traversing through the pixel detector and SCT

ATLAS solonoid

t

projected (transverse) length

r Particles with transverse momenta p_t placed in a magnetic field 𝑩𝑩 =(0,0,B) are deflected along a circular orbit with radius R = p_t/(e|𝑩𝑩 |)

r If the magnetic field is active on length L_t, the change in transverse momentum for small deflection angles is

r The error in position measurement s(x) leads to an error in the momentum measurement via

h: lever arm for angle measurement before & after magnet

r Example: |𝑩𝑩|=0.5 Tm, s(x)=300 µm p= 100 GeV/c & h=3cm è s_pt/p_t~1.3%

r If the position is measured at 3 equidistant points along L_t, sagitta S of circular orbit is given by with precision

r For N measurements precision becomes σσ_p

t

p_t = 2p_t Δp_t

σσ_x h

σσ_s = 3 2σσ_x

σσ = 720 σσ

s = 0.038 ⋅B_zL²_t p_t

Δp

= p

⋅sin ! θθ ! −eBL

r The momentum resolution typically has a contribution from the position measurement and one from multiple scattering

r If s_rj=s_x is measurement error in (r-j) plane, p_t is measured with uncertainty:

r Multiple scattering yields mean p_t change r This leads to an multiple scattering error of

r Obtain total momentum from where q is the track angle wrt z-direction ^{p =}

p_t sinθθ

Δp_t^MS = 21 MeV L_t X₀

⎛

⎝⎜

⎜

⎞

⎠⎟

⎟

σσ_p

t

p_t

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

MS

= 0.05 BL_t

1.43L_t X₀

⎛

⎝⎜

⎜

⎞

⎠⎟

⎟

σσ_p

t

p_t

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

M

= σσ_rϕϕp_t 0.3BL²_t

720 N + 4

Simulated electromagnetic shower

r Electrons & positrons suffer energy losses by radiation in addition to the energy losses by collisions (ionization)

r Thus

r The basic mechanism of energy loss via collisions is also valid for e^±, but Bethe-Bloch must be modified for 3 reasons:

i) their small mass

è Incident particle may be deflected ii) For e^- we have collisions

between identical particles è Account for indistinguishable

particles

è Obtain some modifications, e.g. T_max=T_e/2

iii) e⁺ and e^- are fermions while

heavy particle are typically bosons dEdx

""

## $$ %%

&&

'' tot == dE dx

""

## $$ %%

&&

'' rad ++ dE dx

""

## $$ %%

&&

'' coll

<dE/dx> [MeV/cm]

e^-

e⁺ Bethe-Bloch

Si

dE/dx|_ionization

r A photon traversing a medium can experience different processes i) Photoelectric absorption

ii) Rayleigh scattering iii) Compton scattering

iv) Pair creation in nucleon/electron field v) Photonuclear interaction

r All processes reduce initial intensity

where µ is linear absorption coefficient

that is related to photon absorption cross section s by µ=sN₀r/A r Photoelectric absorption decreases as ~1/Eg3.5 & increases as Z⁵

(e.g. for energies between K&L)

r Compton scattering decreases as 1/Eg & increases as Z r Pair creation requires minimum energy of E≥2m c²

I z

( )

( )

E_c == 610

Z ++ 1.24 for solids

E.g. Pb: E_c=7.3 MeV Air: E_c=102 MeV

E_c == 710

Z ++ 0.92 for gases

1

X₀ ≅≅ 4αα r_e²ρρ ^N_A⁰ Z² ⎡⎡ln(184.15 i Z⁻⁻¹³) −− f(Z)

⎣⎣⎢⎢ ⎤⎤

⎦⎦⎥⎥ ++ Zln(1194 i Z⁻⁻²³)

⎧⎧⎨⎨

⎩⎩

⎫⎫⎬⎬

⎭⎭

N : Avogadro’s # 6.022´10²³ mole^-1

r The critical energy, E_c, is the energy where (dE/dx)_rad=(dE/dx)_ion r Approximate formulae

r Calculated E_c values agree well with

with approximate formulae (solids: <2%) r The radiation length is the distance

over which the e^- energy is reduced by 1/e=37% due to radiation loss only

r The radiation length depends only on the parameters of the material

H2: X0=63 [g/cm²] Al: 24 “ Pb: 6.3 “

r At high energy a photon is likely to convert into e⁺e^-

r e^± particles loose energy via bremsstrahlung producing new g’s that are likely to convert into e⁺e^-

r Result is a cascade or shower of e⁺, e^-, & g’s r Process stops once energies of e⁺,

e^-, & g’s become so small that energy loss of g’s occurs

preferentially via photoelectric absorption & that energy loss of e⁺ & e^- occurs preferentially

via ionization (E_e≈E_c, Eg≈E_c) r A similar shower is obtained if

we start with a high-energy e^- or e⁺

L3 BGO calorimeter

r The most exact calculations of detailed shower development is obtained with MC simulations (EGS)

r We obtain the following properties of the e^--g shower

i) Number of particles at shower maximum, N_p, is proportional to E₀ ii) Total track length s of e^- & e⁺, is proportional to E₀

iii) Depth at which shower maximum occurs, X_max, increases as log where t=-0.5 for e^-

& t=0.5 for g

r Example: photon in NaI crystal: E₀ =1 GeV, X₀=2.59 cm, E_c=12.5 MeV è

è N_p=80, n=6.3, & X_max=11.8 cm

r Basically 2 types of em calorimeters 1) homogeneous shower counters:

(inorganic crystals [NaI, CsI(Tl), BGO, BaF₂, PbWO_4, LSO, LYSO]

Pb glass

liquid noble gases [Ar, Kr, Xe]) 2) sampling shower calorimeters

X_max = X₀ ln E₀ E_c

⎛

⎝⎜

⎜

⎞

⎠⎟

⎟ + t

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

r The energy resolution of a crystal calorimeter is given by:

σ σ_E

E

""

##

$$$$

%%

&&

''''

2

== σσ_noise²

E² ++ a E

""

##$$

%%

&&

''

2

++ b² ++ σσ_FL² ++ σσ_SL² ++ σσ_RL² f(E) ++ σσ_NC²

stochastic term

term for intercalibration, inhomogeneity

noise term leakage terms

front,side,rear nuclear counter term

particles passing through detector

b²

r F(E) =1+c₁E+c₂E²

r For a sufficiently large calorimeter F(E)≅1

r All energy-independent terms are typically combined into one constant b²

r For a CsI(Tl) calorimeter, stochastic term is expressed

r Energy & angular resolution of BABAR CsI(Tl) crystal calorimeter

Ø Use photons & electrons from physics processes

Ø Low-energy point is obtained from radioactive source

r Sampling calorimeters are devices in which the fluctuations of energy degradation & energy measurement are separated in alternating layers of different substances

r The choices for passive absorber are plates of Fe, Cu, W, Pb, U

r For energy measurement a gas mixture, liquid noble gases, or plastic scintillators are used r This allows to build rather compact devices &

permits optimization for specific experimental requirements Þ e^- - p discrimination

è

è longitudinal shower profile è

è good angular measurements è

è good position measurements

r Plate thickness p ranges from fraction of X₀ (EM) to few X₀(hadronic) r Disadvantage is that only a fraction of total energy of em shower

is detected (sampling) in active planes resulting in additional sampling fluctuations of the energy discrimination

ground ground

HV

p

d=g+p

r Longitudinal energy distribution is parameterized by with b=0.5, a=bt_max, c=b^a+1/G(a+1),& t=X/X₀

r Transverse shower dimensions results from MS of low-energy e⁺ & e^- r Useful unit for transverse shower is Molière radius

r Transverse energy distribution in units of R_M independent of material

è inside 1R_M 90% of shower is contained è inside 3R_M, 99% of shower

dE

dt ⁼⁼ E₀Ct^ααe^−−ββt

R^M == 21 MeV X₀ / E_c

r The total energy resolution of a sampling calorimeter is

where

r The sampling fluctuations include multiple scattering and effects of an energy cut-off

r The path length fluctuations depend on the density of the medium

σ_E E

"

#

$$

%

&

''

tot

= σ_E E

"

#

$$

%

&

''

sampling 2

+ σ_E E

"

#

$$

%

&

''

Landau 2

+ σ_E E

"

#

$$

%

&

''

path length

( 2

)

**

*

+

, -- -

1/2

σ_E

E

"

#

$$

%

&

''

sampling

≥3.2% ΔE [MeV]

F(ξ)cos ^{21 MeV}_E

cπ

( )

,

- .. .

/

0 11 1

1/2

σ_E E

"

#

$$

%

&

''

Landau

= 3

N_x ×ln 1.3 × 10

(

)

*

+ ,, ,

-

. // /

N_x = E₀X₀ E_cd ⁼

E₀ ΔE

N_x: number of crossings in sampling calorimeter=total track length divided by distance between active plates

r Simulation of em shower using EGS IV

3 GeV g

r Use accordion geometry

r Full f coverage w/o cracks

r 3 layers with

|h|<3.2

r 173312 readout

r channels (98.5% work)

r ATLAS Pb-LiAr sampling calorimeter

r The ATLAS LiAr calorimeter works well

r Energy response is linear r Energy resolution is

r Z⁰ s_m=1.73±.08 GeV is slightly worse than MC

r J/y s =132±2 MeV agrees with MC

(GeV) Ebeam

0 50 100 150 200 250

>mc/Edata<E

0.98 0.99 1 1.01 1.02

0 mm = 1.6 X0

25 mm = 1.9 X0

50 mm = 2.2 X0

75 mm = 2.5 X0

(GeV) Ebeam

0 50 100 150 200 250

/EEσ

0 0.01 0.02 0.03 0.04

0.05 Data: σ_E/E = (10.2 ± 0.4)%/ E⊕ (0.2 ± 0.1)%

0.2%

E⊕ 0.1)%/

/E = (9.5 ± σE

Simulation:

Energy Linearity from test beam Energy Resolution from test beam

J/y reconstruction

σ_E

E = 0.1

E ⊕ 0.007

Z⁰ reconstruction

ATLAS tile calorimeter

r Conceptually, the energy measurement of hadronic showers is analogous to that of electromagnetic showers, but due to complexity & variety of

hadronic processes, a detailed understanding is complicated

r Though elementary processes are well understood, no simple analytical description of hadronic showers exist

r Half the energy is used for multiple particle production ^(<pt> @ 0.35 GeV), the remaining energy is carried off by fast, leading particles

r 2 specific effects limit the energy resolution of hadronic showers i) A considerable part of secondary particles are p⁰’s, which will

propagate electromagnetically without further nuclear interactions Average fraction of hadronic energy converted into p⁰’s is

Ø fp⁰ » 0.1 ln(E) [GeV] for few GeV £ E £ several 100 GeV

Ø Size of p⁰ component is largely determined by production in first

interaction & by event-by-event fluctuations about the average value ii) A sizable amount of available energy is converted into excitation

or breakup of nuclei ® only a fraction of this energy will be see

σ_E E

"

#

$$

%

&

''

intrinsic

≅ 0.45

E [GeV]

e/h ratio in different hadron calorimeters

holding for materials from Al to Pb (exception ²³⁸U)

r The intrinsic hadron energy resolution is

r The level of nuclear effects and level of invisible energy is sensitively measured by comparing the calorimeter

response to e and h at the same available energy

Ø Ideally, we want e/h≅1

Ø Typical values are e/h≅1.4

Ø e/h drops to ~0.7 below 1 GeV r Unless event-by-event fluctuations

in the EM component are not corrected for, 𝜎𝜎_,/E ≅0.45/ E

r This applies likewise to homogeneous and to sampling calorimeters

r To cure these fluctuations we need to equalize response for e^- & h Þ either decrease e^- response or boost h response

r The latter can be achieved in U-scintillator calorimeters Ø Due to nuclear break-up one gets neutron-induced fission

liberating about 10 GeV of fission energy

Ø Just need to detect 300-400 MeV to compensate for nuclear deficit measure either the few MeV g component or the fission neutrons r Intrinsic resolution for ²³⁸U is

r This was achieved in the ZEUS calorimeter (U-scintillator) r In addition sampling fluctuations

contribute to the total energy resolution

where DE is energy loss per unit sampling for MIPs

r Hadronic sampling fluctuations are approximately twice as large as EM sampling fluctuations

σ σ_E

E (U)

""

##$$

%%

&&''_{int rinsic} ≅≅ 0.22 E [GeV]

σ_E

E

"

#$

%

&'hadronic sampling

≅ 0.09 ΔE[MeV ] E[GeV ]

r In analogy to X₀ define a hadronic interaction length l as the length in which a hadron has interacted with probability of 63%

r Longitudinal shower distributions parametrized in l are similar for different materials

r Shower maximum

r 95% longitudinal shower containment

where l_att @ l×(E[GeV])^0.13 è

è L_0.95(l) describes data in few GeV£ E £few 100 GeV within 10%

r 95% radial shower containment is R_0.95 £ 1l

r Useful parameterization of longitudinal shower development l_max(λ) ~ 0.2 ln E[GeV] +0.7

L_0.95(λ) = l_max + 2.5λ_att

dE / ds = K w^#_$ ⋅t^ae^−bt + (1−w)l^ce^{−dl %}_& a,b,c,d: fit parameters

r Steel-scintillator sampling calorimeter (total thickness ~11l) Ø 14 mm thick steel plates

Ø 460 000 3 mm thick scintillator tiles

Ø Calorimeter is built in 3 sections: barrel & 2 extended barrels

G. Eigen, HASCO 17-07-17 Göttingen

r Energy response in a cell of the ATLAS tile calorimeter showing noise plus showers

r Tile calorimeter energy resolution stochastic: a=52%; constant: b=3%

r e/h ratio is larger than 1

σσ_E

E = a

E ⊕ b ⊕ c E

1

1.1 1.2 1.3

10² e/h=1.35±0.04 (94) e/h=1.37±0.01 (96)

e/h=1.31±0.01 (G-CALOR)

E_beam (GeV) e// e/h ratio

energy resolution

Analog Hadron Calorimeter Prototype (scintillator plane)

r New idea: Perform particle tracking inside a jet, since individual particle species have characteristic signatures

r Need high granularity in ECal & HCal to isolate single particles

r jet composition: 65% charged tracks, 25% photons, 10% neutral hadrons

r Ignoring the (typically) negligible tracking term:

σ_E²_jet = σ_E²_charged +σ_E²_photons +σ_E²_neut.had. +σ_confusion²

σ

≈ ( 0.17 )

( E

⋅ GeV ) ^{+ σ}

^{≈ ( ) 0.3}

( ^E

^{⋅ GeV} )

σ

σ

σ_E²_charged ≈

(

)

_∑

⁽

⁾

_∑

r is the largest term of all >25%

r With anticipated resolutions

σ_E²_photons ≈

(

)

∑

⁽

⁾

∑

σ_Eneutral hadrons

2 ≈

(

)

∑

⁽

⁾

∑

r Implementing particle flow we have get jet energy resolution r Jet energy:

E

= E

+ E

+ E

65% 25% 10%

VII.6.5 EM Calorimeter

Detector slab

W plates 4.2mm

2.8mm 1.4mm

62 mm Silicon wafers With 6×6 pads (10×10 mm² )

Metal inserts (interface)

active area (18´18 cm²)

r Si-W ECAL prototype, 3 W structures r 15 active layers (Si)

r 1 cm × 1 cm Si pixels

r Good linearity

linearity resolution

σσ_E

E = 16.5 ± 0.14%

E ⊕1.1 ± 0.1

Analog Hadron Calorimeter

SiPM 3M reflector

r 38-layer Fe-scintillator sampling calorimeter (4.5 l)

r Layer: 2 cm steel absorber plates + 1/2 cm scintillator tiles

Ø core tiles: 3×3 cm² (10×10 matrix) increasing towards outside

r Total of 7608 tiles, each is read out with wavelength-shifting (WLS) fiber + SiPM (216 tiles/layer)

pedestal

1pe

3pe 4pe

5pe 6pe

7pe8pe

SiPM

Photoelectrum spectrum

2pe

layer

3´3 cm² 6´6 cm² 12´12 cm²

Performance of Analog Hadron Calorimeter

σ_E

E = 48.8 ± 0.2

E[GeV] ⊕0.0 ± 0.23

#

$% &

'(%

r Response of the hadron tile calorimeter is linear

r Resolution with appropriate energy weighting yields

G. Eigen, HASCO 17-07-17 Göttingen

Test of Particle Flow

r In a test beam concept of particle flow cannot be studied directly since the beam typically consists of a single particle and not of jets è do a trick to

simulate this dependence: select hadron shower of a given energy and then overlay another hadron shower at a selected distance

r Consider 2 examples: 10 GeV neutral hadron separated from 10 GeV p &

10 GeV neutral hadron separated from 30 GeV p separated by Dz=5-30 cm r For a 10 GeV p with Dz=5cm, a fair amount of energy is assigned wrong r Mean value of the difference between recovered and measured energy

approaches zero with Dz faster for 10 GeV p than for 30 GeV p r For sufficient separation particle flow

works

Distance between shower axes [mm]

0 50 100 150 200 250 300

Mean of recovered-measured [GeV]

-5 -4 -3 -2 -1 0 1 2

10-GeV track CALICE data LHEPQGSP_BERT

CALICE CALICE

30-GeV track CALICE data LHEPQGSP_BERT

CALICE CALICE

Recovered energy - Measured energy [GeV]

-15 -10 -5 0 5 10 15

# of events / Total # of events

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

CALICE data LHEP QGSP_BERT

CALICE

10 GeV track at 5 cm

Recovered energy - Measured energy [GeV]

-15 -10 -5 0 5 10 15

# of events / Total # of events

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

CALICE data LHEP QGSP_BERT

CALICE

10 GeV track at 30 cm

10 GeV p, Dz=5 cm 10 GeV p, Dz=30 cm

BABAR DIRC photomultipliers