Generalized Parton Distributionstheor.jinr.ru/~spin/Spin-Dubna07/1 03MoB/1...
Transcript of Generalized Parton Distributionstheor.jinr.ru/~spin/Spin-Dubna07/1 03MoB/1...
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Generalized Parton Distributions @
Physics MotivationsNow with 6LiD or NH3 polarized target
and without recoil detectorAfter 2010 with H2 or D2 target and a recoil detector
and a supplemented calorimetry
« Expression of Interest » SPSC-EOI-005 and presentation to SPSC
writing of the proposal, preparation of the future GPD program ~2010
Nicole d’Hose, Saclay, CEA/DAPNIAOn behalf of the COMPASS collaboration
DSPIN-07 Dubna, September 3-7, 2007
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GPDs ≡ a 3-dimensional picture of the nucleon partonic structure
Px
ep→ eXDeep Inelastic Scattering
Q²xBj
x
p
γ*
Parton Density q ( x )
x boost
x P
z
x1
0
y
Form Factor F( t )
Elastic Scattering
ep→ ep
p
ee
p
γ*
t = -Q²
x boost y
z
r⊥
r⊥
ry,z
Hard Exclusive ScatteringDeeply Virtual Compton Scattering
Burkard,Belitsky,Müller,Ralston,Pire
Generalized Parton Distribution H( x,ξ,t )
ep→ epγ
pGPDs
γ* Q²
x+ξ x-ξp
γ
t
x P
y
z
r⊥
x boost
( Px, ry,z )
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The complete nucleon mapRobust and exhaustive studies
Deep inelastic scatteringat DESY, SLAC, CERN, JLab
Elastic scatteringstill at JLab
-0.3 < Δg < 0.3(COMPASS)Large orbitalmomentum ?
Semi-inclusive reactions
Exclusive reactionsNucleon tomography
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x+ξ x-ξ
t
γ, π, ρ, ω…
The observables are some integrals of GPDs over x
H, ,E, (x,ξ,t)
Dynamics of partons
in the Nucleon Models:
Parametrization
Fit of Parameters to the data
Elastic Form Factors
∫ H(x,ξ,t)dx = F(t)
“ordinary” partondensity
H(x,0,0) = q(x)(x,0,0) = ∆q(x)
Ji’s sum rule
gq L∆GLΣ ∆1/21/2 +++=
2Jq = ∫ x(H+E)(x,ξ,0)dx
xx
factorization
GPDs and relations to the physical observables
H~ E~
H~
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Reveal a 3-dim picture of the nucleon partonic structure
or probability densities of quarks and gluonsin impact parameter space
H(x, ξ, t) ou H( Px, ry,z )
measurement of Re(H) viaVCS and BCA or Beam Charge Difference
x P
1rst goal of the « Holy-Grail »
y
z
r⊥
x boost
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From Schierholz, JLab May 2007GPDs in Latticeprobability densities of quarks and gluons
in impact parameter space
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Sensitivity to the 3-D nucleon pictureLattice calculation (unquenched QCD):
Negele et al., NP B128 (2004) 170Göckeler et al., NP B140 (2005) 399• fast parton close to the N center
≡ small valence quark core• slow parton far from the N center
≡ widely spread sea q and gluons
mπ=0.87 GeV
x
0.5 fm at small x
0.15fm at large x
Last result on 29 May 2007First comprehensive full lattice QCDIn the chiral regime with mπ =0.35 GeV
Hägler et al., hep-lat 07054295MIT, JLab-THY-07-651,DESY-07-077, TUM-T39-07-09
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Promising COMPASS domain
Chiral dynamics: Strikman et al., PRD69 (2004) 054012Frankfurt et al., Ann. Rev. Nucl. Part. Sci. 55 (2005) 403
at large distance : gluon density generated by the pion cloudincrease of the N transverse size for xBj < mπ/mp=0.14
>< ⊥2r 0.6fm 0.4fm
Sensitivity to the 3-D nucleon picture
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More correct behavior at small and large x:<b2⊥> = α’ (1-x) ln1/x + B(1-x)2
to reproduce perfectly the proton form factor
Chiral quark-soliton model: Goeke et al., NP47 (2001)This ansatz reproduces the
2 Parametrizations of GPDs
Factorization: H(x,ξ,t) ~ q(x) F(t)orRegge-motivated t-dependence: more realistic with x-t correlation
it considers that fast partons in the small valence coreand slow partons at larger distance (wider meson cloud)
<b2⊥> = α’ln 1/x transverse extension of partons in hadronic collisions
H(x,0,t) = q(x) e t <b⊥2> = q(x) / xα’t (α’slope of Regge traject.)
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3 frameworks or models for GPD )2Qt,ξ,(x,
Gluon domain : Freund, Frankfurt, Strikman (FFS) + Schoeffel
GPDS,V,g(x,ξ) ≡ QS,V,g(x)ξDependence generated via the QCD evolution
Gluon + quark domain (x<0.2): GuzeyPRD74 (2006) 054027 hep-ph/0607099v1
Dual parametrization with Mellin moments decompositionQCD evolution + separation x, ξ and ξ, t
Quark domain: Vanderhaeghen, Guichon, Guidal (VGG)PRD60 (1999) 094017, Prog.Part.Nucl.Phys.47(2001)401-515
Double distribution x,ξ a la Radyushkinx,t correlation no Q2 evolution
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E=19
0,10
0GeV
HERA
Gluons valence quarks valence quarksand sea quarksand gluons
Competition in the world and COMPASS role
COMPASS JLab 12 GeV, FAIR,…2010 2014
Ix2
COMPASS at CERN-SPS
High energy muon beam100/190 GeV
μ+ or μ-change once per daypolar(μ+)=-0.80polar(μ+)=+0.80
2.108 μ per SPS cycle
in 2010 ?new Linac4 (high intensity H- source)as injector for the PSB + improvements
on the muon line
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t)ξ,ξ,H(xξx
t)ξ,H(x,dx
iξx
t)ξ,H(x,dx
11
11 =
−ε+−∫∫+−
+− == i -PH π
q(x)
ERBL
DGLAP
DGLAP
DGLAP
hard
soft
For example at LO in αS: p p’
γ
GPDs
γ*
x + ξ x - ξ
t =Δ2
Q2
In DVCS and meson productionwe measure integrals over the GPDs
t, ξ~xBj/2 fixed By Beam Charge difference
By Beam Spin difference
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dσ(μp→μpγ) = dσBH + dσDVCSunpol + Pμ dσDVCSpol
+ eμ aBH Re ADVCS + eμ Pμ aBH Im ADVCS
Twist-3 M01
)coscos()()(
),,(ϕϕ
ϕϕσ 2
21021
2BHBHBHBBH cCc
PPtQx
d ++Γ
=
DVCS + BH with polarized and charged leptons and unpolarized target
← Known expression
Twist-2 M11 Twist-2 gluon M-11
=ℑ DVCSBH Aa m
=ℜ DVCSBH Aa e
eμ Pμ ×
eμ ×
Pμ ×
>>
)sinsin()()(
ϕϕϕϕ
221
213
6IntInt ss
PtPxye
+
φ
θμ’μ γ* γ
p
)coscos( ϕϕσ 221022
6DVCSDVCSDVCSDVCS
unpolcCc
Qyed ++=
)sin( ϕσ DVCSDVCSpol
sQye
d122
6
=
μp
μp
BH calculableDVCS+
Belitsky,Müller,Kirchner
)coscoscos()()(
ϕϕϕϕϕ
323210
213
6IntIntIntInt cccc
PtPxye
+++
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)~)(( EHH22211 4
FmtFFF −++ ξ
m e
ℑ∝ℜ∝
IntInt
sc
1
1
∫+− −
=ℜ 11 e
ξx
t)ξ,H(x,dxP H
t)ξ,ξ,H(x==ℑ H mq
q qe HH ∑= 2
F1H dominance with a proton target
F2E dominance with a neutron target (F1<<)very attractive for Ji’s sum rule study
with
Both c1Int and s1
Int accessible at COMPASS with μ+ and μ-
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E=19
0,10
0GeV
HERA
Competition in the world and COMPASS role
Gluons valence quarks valence quarksand sea quarks
and gluons
COMPASS 2010 JLab 12 GeV 2014, FAIR, …
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Q2
xBj
7
6
5
4
3
2
0.05 0.1 0.2
6 month data taking in 201025 % global efficiency
Beam Charge Asymmetry at Eμ = 100 GeVCOMPASS predictionWith a 2.5m H2 target
φ
μ’μ
γ* γ
p
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φ
μ’μ
γ* γ
pBeam Charge Asymmetry at Eμ = 100 GeVCOMPASS prediction
model 1: H(x,ξ,t) ~ q(x) F(t)
VGG: double-distribution in x,ξ
<b2⊥> = α’ ln 1/x
H(x,0,t) = q(x) e t <b⊥2>= q(x) / xα’t
α’ slope of Regge traject.α’=0.8α’=1.1
model 2 and 2*: correl x and t
Guzey: Dual parametrization model 3: also Regge-motivated
t-dependence with α’=1.1
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C1cosφ
⊃
model 2
model 1
VGG prediction
model 2
model 1
2
α’ determined within an accuracy of ~10% at xBj =0.05 and 0.1
)DVCSBH(atormindeno
intintintint cosccosccosccBCA+
Φ+Φ+Φ+=
32 3210
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Contribution to the nucleon spin knowledge½ = ½ ∆Σ + ∆G + < Lz
q > + < Lzg >
the GPDs correlation between the 2 pieces of information:-distribution of longitudinal momentum carried by the partons-distribution in the transverse plane
the GPD E allows nucleon helicity flipso it is related to the angular momentum
2Jq = ∫ x (Hq (x,ξ,0) +Eq (x,ξ,0) ) dx
with a transversely polarized target DVCS et MVwith a deuterium or neutron target DVCS
tp p
q q
2nd goal of the « Holy-Grail »
rp
E
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modelisation of the GPD E (in a modified VGG code)
Factorization: H(x,ξ,t) ~ q(x) F(t)(and Regge-motivated t-dependence)
the GPD E is related to angular momentum
tp p
q q
E
known: Hq (x,0,0) = q(x) unknown: Eq (x,0,0) = eq(x)=Aqqval (x) +Bqδ(x) (based on chiral soliton)
2Jq = ∫ x (q (x) +eq (x) ) dx
+ 2 sum rules:
κq = ∫ eq (x) dx
Aq and Bq are functions of Ju and Jd
Eu ~ - Ed
Eg ~ 0
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Model-Dependent Constraint on Ju and Jd
In DVCS :
but… no recoil detection around the polarized target
φφ−φ⋅ℑ∝π+φφσ−φφσ cos)sin()EF - Hm(F),(d),( d S12SS
In Meson production :
with COMPASS Li6D deuteron Data 2002-3-4 (J.Kiefer, G.Jegou)NH3 proton Data 2007
1-Transversaly polarised target
2-Neutron (or deuterium) target + DVCS
Through the modeling of GPD E
φφ−φ⋅ℑ+ sin)(osc)E~ξF - H~m(F S12
for the complete program after 2010
)sin()E m(H),( d),( d SSS φ−φ⋅ℑ∝π+φφσ−φφσ
φ⋅−++ℜ∝φσ−φσ −+ cosE)F4m
t H~)2F1(F i He(F),( d),( d 221
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1m
Two 60 cm long target cells with opposite polarisation
Superconducting solenoid (2.5 T)
The polarized 6LiD-Target COMPASS 2002-3-4-6
4 possible spin combinations:
3He – 4He dilutionrefrigerator (T~50mK)
μ
longitudinal transverse
Reversed once a weekReversed every 8 hours
SuperconductingSolenoid (2.5T) + Dipole(0.5T)
Target Polarization ~ 50%
Dilution factor f ~ 0.36
Two 60cm long target cells with opposite polarization
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Different flavor contents:Hρ0 = 1/√2 (2/3 Hu + 1/3 Hd + 3/8 Hg)Hω = 1/√2 (2/3 Hu – 1/3 Hd + 1/8 Hg)Hφ = -1/3 Hs - 1/8 Hg
Hard exclusive meson production
Collins et al. (PRD56 1997): -factorization applies only for γ*
L-probably at high Q2
1/Q4
1/Q6
vector mesons pseudo-scalar mesons
H,E ~H,E~
Scaling predictions:meson
p p’GPDs
γ*
x + ξ x - ξ
t =Δ2
Lhard
soft
ρ production studied with present COMPASS data
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Selection of Incoherent exclusive ρ0 production
Incoherent production0.15 < pt²< 0.5 GeV²scattering off a quasi-free nucleon
Assuming both hadrons are π0.5 < Mππ< 1 GeV
Mππ
Emiss
pt²
Exclusivity of the reaction
Emiss=(M²X-M²N) /2MN-2.5 < Emiss < 2.5 GeV
W
t
Q 2*
N N’
Kinematics: ν > 30 GeVEμ’ > 20 GeV
quasi-free nucleons in6LiD polarized target
Background ~12%
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2002
2003-4-6
Determination of Rρ° =σL/σT
- High statitics from γ-production to hard regime
- Better coverage at high Q2
with 2003-4-6 data
With COMPASS + μComplete angular distribution ⇒ Full control of SCHC
Impact on GPD study:easy determination of σLfactorisation only valid for σLσL is dominant at Q2>2 GeV2
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Preliminary Transverse Target Spin asymmetry AUTin rho production
off deuteron
COMPASS<Q2>=1.9 GeV2
<x> = 0.03
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1- Factorization for longitudinal photons onlySuppression of transverse component σT/σL ~ 1/Q2
For COMPASS kinematics <Q2>=2GeV2 R= σL/σT ~1
separation using the angular distribution of the ρ° decay + SCHCand the last works of Diehl and Sapeta
2- Coherent contribution Pire,Cano, Strikmann?
Incoherent contribution Kroll, Goloskokov (quark and gluon contribution) Guzey (quark and gluon contribution)VGG (mainly quark contribution)
cut on PT2
3- 6LiD or Deuterium target in 2002-3-4 proton + neutron contribution NH3 or Proton target in 2007 proton contribution
The way to get GPDs from the Transverse Target Spin asymmetry
with ρ0 production
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With VGG Code
Present status ofthe MODEL-DEPENDENT Ju-Jd extraction
Lattice hep-lat 07054295
expected results with AUT measuredin the rho production at COMPASS
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μ’
p’μ
DVCS μp → μ’p’γ
Additional equipment to the COMPASS setup
γ ECal1 + ECal2θγ ≤ 10°
Nμ=2.108/SPS cycle(duration 5.2s, each 16.8s)
2.5m liquid H2 targetto be designed and builtL = 1.3 1032 cm-2 s-1
Recoil detector to insure exclusivityto be designed and built
+ additional calorimeter ECal0 at larger angle
all COMPASS tra
ckers:
SciFi, Si, μΩ
, Gem, DC, Straw, MWPC
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Recoil detector + extra calorimetry
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Calorimeter coverage foreseen for DVCS γ
DVCS γ impact point at ECAL 0 location
ECAL 0
ECAL 1ECAL 2(existing)(existing)
To be builtStudied with the Dubna Group
DVCS γ kinematics
ϑ Eγ threshold detection
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xbj
Q2 Existing Calorimeters
Xbj-bins
Calorimeter acceptance
+ 3m x 3m ECAL0
+ 4m x 4m ECAL0
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Light brought by light shifting fibers to Avalanche Micro-Pixel PhotodiodeVery Challenging development for new and cheap AMPDs
- magnetic fielf- low threshold detection- high rate environment
New ASIC for preamplifier-shaper followed by a sampling ADC
Studies for a new ECAL0 (Dubna,…)
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Recoil Detector Prototype Tests (2006)
i
CHTarget
Inner Layer
OuterLayer
A0
A1
A2
B0
B1
25cm
110cm
All scintillators are BC 408A: 284cm x 6.5cm x 0.4cmEquiped with XP20H0 (screening grid)
B: 400cm x 29cm x 5cmEquiped with XP4512
To reject the pile up Use 1GHz sampler (300ns window)MATACQ board Designed by CEA-Saclay/LAL-Orsay
15°
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Requirements for the recoil detector1) Time of Flight measurement
t is the Fourier conjugate of the impact parameter r⊥t is the key of the measurement
σ(ToF) < 300 ps Δ P/P ~ 3 à 15 %
t = (p-p’)²= 2m(m-Ep’)
Δ t/t ~2 Δ P/P ⇒ 10 bins in t from tmin to 1 GeV2
2) Hermiticity + huge background + high counting rates
Detection of extra pi0 at a reasonable cost in a large volume
315 ± 12 ps have been achieved during the 2006 testintrinsic limit due to the thin layer A
Further studies with the thick B layer + fast muon detectorGood solution for both proton and neutron measurement
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Conclusion & prospects• Possible physics ouput
– Sensitivity to total spin of partons : Ju & Jd– Sensitivity to spatial distribution of partons– Working on a variety of models (VGG, Müller, Guzey and FFS-Sch)
to quantify the Physics potential of DVCS and HEMP at COMPASS
• Experimental realisation– Recoil Detection for proton and neutron (and extra π0)– High performance and extension of the calorimetry
• Roadmap– Now with the transversely polarized targets:
Li6D ( 2006) and NH3 (2007)– 2008-9: A small RPD and a liquid H2 target will be available
for the hadron program (ask for 2 shifts μ+ and μ-)– > 2010: A complete GPD program at COMPASS
with a long RPD + liquid H2 target
before the availability of JLab 12 GeV, FAIR, EIC…
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Physical Background to DVCS
detector requirements:24° coverage for neutral50 MeV calorimeter threshold40° for charged particles
Competing reactions: Deep pi0, Dissociative DVCS, DIS…
Study of DIS with Pythia 6.1 event generatorApply DVCS-like cuts: one μ’,γ,p in DVCS range
no other charged & neutral in active volumes
in this caseDVCS is dominant
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Geant Simulation of recoil detector
With simulation of δ-rays
2 concentric barrels of 24 scintillators counters read at both sidesaround a 2.5m long H2 target
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Red is DVCS proton
Blue is background
upstreamPMT
downstreamPMT
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
INNER
OUTER
PMT signals : only 1μ in the set-up
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PMT signals : 2 108 μ/spill (5s)
recording thewaveform of all
signals and segmentation are
mandatory
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Criteria for proton candidates
βΔEA
ΔEB ΔEB
• Crude Waveform analysis
• Have points in corresponding A and B counters
• For each pair of “points” • Energy loss correlation • Energy loss vs βmeas correlation
( no backgroundin this plot –just for pedagogy )
i
Target
Inner Layer
OuterLayer
Ai+1
Ai
Ai-1
Bi+1
Bi-1
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Proton detection efficiency
trigger = one event with at least one good combination of A and B with hitsidentified proton = proton of good A and B combination, good energy correlation,
and good timing with the muon
number of events with proton identifiednumber of “triggers”Efficiency =
0100200300400500600700800900
0 1.e8 2.e8 4.e800,10,20,30,40,50,60,70,80,91
S effectiveEfficiency
Sef
ffor
100
0 ev
ents
μ/5s spill
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Coincidence with the scattered muon
Use reconstructed muon vertex time to constraint proton candidates
S/BSSeff +
=1
Use vertex position to evaluate the effective signal
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Timing resolution
150
200
250
300
350
400
450
25 75 125 175 235
TOF resolution (+)
A only (-)
B only (-)
Tim
ing
Res
olut
ion
(ps)
position (cm)Reach 315 ps at the middle and 380 ps in the worst case at the edge
~50 γe
Performed with 160 GeV muon (0.8*MIP in A)Expect better resolution for slow protons
μ
B
A
Beam halo
( 150ps obtainedwith cosmics )
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Time of Flight measurement
tupB tdoB
tupA
zB tB
tdoAzA tA11
0cm
25cm
zB= (tupB - tdownB) VB/2 + LB/2 + Corup
tw – Cordowntw + Offup-Offdown
tB= (tupB + tdown
B)/2 + LB/2VB + Coruptw + Cordown
tw + Offup+Offdown
beam target
To be precisely determined (tw= time walk correction)
ToF = (tupB + tdownB)/2 - (tup
A + tdownA)/2 + …
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Obtained results with the prototype in 2006 with the MATACQ
at CERN (muon halo) at Saclay (cosmics)with external time references
σ(tupB - tdown
B) = 200 ± 6 ps σ(tupB + tdown
B) = 145 ps ± 10 ps σ(tup
A - tdownA) = 270 ± 6 ps
σToF= σ [ (tupB + tdownB) - (tup
A + tdownA)]
= 315 ± 12 ps to be still improved but intrinsic limit due to the thin layer A