Title: Hadrons @
1Hadrons _at_ . Structure, Spectroscopy and
More
- Klaus Peters
- GSI Darmstadt/JWGU Frankfurt
- IWHSS08, Torino
- 2.4.2008
2Nov. 7, FAIR Start-Even
Offical Start Signed By 12 Partners Volume in
Phase A 940 M (already more now) 16 Countries
3Five Areas of Research at FAIR
Nuclear Structure Astrophysics with radioactive
beams
Nuclear Matter Physics with 35-45 GeV/u HI beams
Hadron Physics with antiprotons
Plasma Physics with compressed ion beams
high-intensity petawatt-laser
100 m
High EM Field (HI) Fundamental Studies (HI
p) Applications (HI)
4p _at_
PANDA
FLAIR
HESR
NESR
5HESR Storage Ring for Antiprotons
- Parameters of HESR
- Injection of p at 3.7 GeV
- Slow synchrotron (1.5-14.5 GeV/c)
- Storage ring for internal target operation
- Luminosity up to L 2x1032 cm-2s-1
- Beam cooling (stochastic electron)
- Resonance scan
- Energy resolution 50 keV
- Tune ECM to probe resonance
- Get precise mass and width
ECM
6PANDA
p
p
- High luminosity mode
- Luminosity 2 x 1032 cm-2s-1
- dp/p 10-4 (stochastic cooling)
- High resolution mode
- dp/p few 10-5 (electron cooling)
- Luminosity gt 1031 cm-2s-1
- Gas-Jet/Pellet/Wire Target
7PANDA Collaboration
U Gießen KVI Groningen U Helsinki IKP Jülich I
II U Katowice IMP Lanzhou U Mainz U INFN
Milano Politecnico di Milano U Minsk TU München U
Münster BINP Novosibirsk LAL Orsay U INFN
Pavia
IHEP Protvino PNPI Gatchina U of Silesia,
Katowice U Stockholm KTH Stockholm U INFN
Torino Politechnico di Torino U Oriente, Torino U
INFN Trieste U Tübingen U TSL Uppsala U
Valencia SMI Vienna SINS Warsaw U Warsaw
U Basel IHEP Beijing U Bochum U Bonn U INFN
Brescia IFIN Budapest U INFN Catania U
Cracow GSI Darmstadt TU Dresden
JINR Dubna (LIT,LPP,VBLHE) U Edinburgh U
Erlangen NWU Evanston U INFN Ferrara U
Frankfurt LNF-INFN Frascati U INFN Genoa U
Glasgow
more than 400 scientistsfrom 57 Institutions
8PANDA Physics
Structure Dynamics of Hadrons ...
... in the transition regime of QCD
- Low(est) order quark-binding?
- Charmonium spectroscopy
- ? Quark confinement
- High(er) order strong-binding?
- How are color neutral states formed?
- Hadrons (qqq or qq)
- Gluonic excitations
- Multi-quark systems
- ? QCD predictions
- What is the structure of the nucleon?
- Electromagnetic Formfactors
- Hard scattering processes
- ? From partons to hadrons
- How do hadrons obtain mass?
- p-A interactions
- Meson properties in nuclear medium
- ? Restoration of chiral symmetry
Strong coupling constant vs R
perturbative
strong
QCD
9The Potential A Guide
G. Bali et al.,hep-lat/0003012
G. Bali, hep-ph/0412158
10 The Fluxtube in a Meson
qq bound state
strong interaction strength
Rotation
0.7 fm
1.0 fm
1.35 fm
Vibration
Lattice QCD calculationsG. Bali, hep-lat/9409005
11Exotic Quantum Numbers with Simple Hybrids
- S-Wave Gluon (qq)8g with ()8colored
- 1S0 3S1 combined with 1 or 1- gluon
SS1S2 JLS P(-1)L1 C(-1)LS
L
S2
Gluon 1 (TM) 1(TE)
1S0, 0 1 1
3S1, 1 0- 0
1- 1
2- 2
S1
JPC exoticimpossible for qq
12Spin-exotic Summary (Light Quarks)
13X(3872) and Confirmation
9.4s
11.6 s
Phys. Rev. Lett. 91(2003)262001152 Mill. BB
BABAR
hep-ex/0406022
14Mass Differences in ?pp and DDp
- X(3872) in (?pp) K
- Belle m38720.60.5
- Babar m3871.30.60.1
- X(3872) in (?pp) KS
- Belle m3871.81.10.6
- Babar m3868.61.21.2
- Glt2.3
- X(3872) in DDp K
- Belle m3875.40.70.9-1.6
- Babar m3875.10.7-0.50.5
- G3.01.9-1.40.9
- mD0D0 3871.80.3
- mDD- 3879.90.3
about 3 MeV between final states
E. Braaten, only D0D0 threshold considered
15Y(4260), one of the many XYZ states
- Y(4260)
- in rad. Returnee- ? ?ISRJ/?pp
- M4259(8)(4) MeV/c2G88(23)(5) MeV/c2
- definitely a vector state
- ? cc(33D1) ? 4460 MeV!
- Many speculations e.g.
- ?c?c-Baryonium or cscs-Tetraquark
- Other interesting states are X,Y,Z(3930-3940)
BaBar
CLEOc
16Z(4433)
arXiv0708.1790
17Why Antiprotons for Heavy Flavor Spectroscopy
- high resolution spectroscopy with p-beams in
formation experiments - ?E ?Ebeam
- ee- interactions
- Only 1-- states are formed
- Other states only bysecondary decays moderate
mass resolution
100
CBall ev./2 MeV
- pp reactions
- All states directly formed
- very good mass resolution
ECM
3500
3520 MeV
3510
CBall, Edwards et al. PRL 48 (1982) 70 E835,
Ambrogiani et al., PRD 62 (2000) 052002
18Heavy Glueballs
- Light gg/ggg-systems are complicated to identify
(mixing!) - Exotic heavy glueballs
- m(0-) 4140(50)(200) MeV
- m(2-) 4740(70)(230) MeV
- Width unknown, but!
- nature invests more likely in mass than in
momentum - newest proof double cc yield in ee-
- Flavour-blindness
- predicts decays into charmed final states too
- Same run period as hybrids
- In addition scan mgt2 GeV/c2
0- 2-
Morningstar,Peardon, PRD60 (1999)
34509 Morningstar,Peardon, PRD56 (1997) 4043
19Accessible Charmed Hadrons at PANDA
exotic charmonium
conventional charmonium
- Other exotics with identical decay channels
same region
20Final State Dspp-
- Precise Mass determination
- syst. error dom. by uncertainty of Ds mass
m GeV/c2
Ds1
DK
Ds2
DsJ (2458)
D0K
DsJ (2317)
Ds
Belle cc
Ds
Babar cc preliminary
JP
CLEO cc
Belle B-decay
Belle cc
no Signal
Babar cc preliminary
MeV/c2
21Mass and Width Determination DsJ()(2xxx)
possible experimental result for G 1 MeV, S/B1,
1 nb, few days/mom req. e--cooling to HESR
limit !
threshold Ds0Ds0
threshold DsDs0
- Deduce mass and width from excitation function
- Many channels, but all require e-cooling at large
energies
22Time-like Proton Form Factors
Crossed channel
- PANDA
- Wide kinematical range
- Large solid angle coverage
- Large statistics
- Goals
- To measure time-like FF from threshold up to
high s q2 in one experiment(reduced systematic
error) - To compare with space-like FFs (pQCD at large s?)
- High-quality measurement of both GE and GM
23Physics Counting Rates and GE/GM separation
T1 GeV T5 GeV T10 GeV q25.4(GeV2/c) q212.9
(GeV2/c) q222.3(GeV2/c) 100 days, L2 1032
cm-2s-1, 2 fb-1 Ntot 106 Ntot
2750 Ntot 82
Fermilab 14 evts at 13 (GeV/c)2
24Hard Exclusive Reactions
- The prototype of all hard exclusive reactions is
Deeply Virtual Compton Scattering - DVCS is one of the modern tools to explore the
structure of the nucleon - Simplest process to measure Generalized Parton
Distributions - Allows to access the orbital angular momentum of
quarks - Current and future experiments at HERMES,
COMPASS and JLAB
25DVCS at PANDA
- PANDA can measure the cross channel or
time-like version of the same process, that
depends on the same GPDs - More precisely on Generalized Distribution
Amplitudes, introduced by M.Diehl et.al. to
describe the inverse process - PRL.811782 (1998)
?
26Hard Exclusive Reactions at PANDA
p, ?, f, ...
27Experimental Requirements
- Estimates for pbeam 15 GeV/c
- Photon kinematics
- E? 15.5 .... 0.5 GeV _at_ 0º...180º
- Photon angle in CMS and transverse momentum are
large for wide angle Compton - pT few 100 MeV ... 2.7 GeV
- Interesting range in Lab around
- E? 8 GeV and ? 20º
- ? 4p calorimeter needed !
- Background suppression by
- Large acceptance charged particle detector veto
- Good resolution calorimeter for check of
exclusivity - (momentum balance)
- Large acceptance neutral particle veto
- (neutrons)
pbeam15 GeV/c, s30 GeV²
pT
?
E?
28First Simulation Results
Experiment appears feasible
29Parton Distribution Functions
Leading twist
Chirally odd
PAX
Directly accessible in Drell-Yan
T-odd
PANDA
30Boer-Mulders Function
- Boer-Mulders distribution function h1- can be
measured in unpolarised Drell-Yan at PANDA - Boer-Mulders function expected to be larger than
Sivers function (measured at HERMES) - M.Burkhardt, hep-ph/0611256
31pp cross sections exclusive final states
100 mb
10 mb
1 mb
- Cross sections expectations for
- glueballs and light hybrids
- rates comparable to light hadrons
- charmed hybrids and molecules
- rates comparable to charmed hadrons
- Anyhow
- high luminosity and
- effective triggers and
- excellent background rejection
- are mandatory
100 µb
10 µb
Glueballs
1 µb
?c
?c2
100 nb
X(3872)
?cp0
10 nb
?c0
Hybrids
1 nb
32Electron Identification
- Energy/Momentum Measurement (E/p)
- Shower-Shapes (Zernicke-Momenta) spatial
distribution - Neural Nets trained with MC/real data
MC Studies
33PANDA Spectrometer Target and Vertexing
Pellet or cluster jet target
Dipole magnet for forward tracks
Solenoid magnet for high p t tracks Superconducti
ng coil iron return yoke
34PANDA Spectrometer - Tracking
Silicon Microvertex
Forward Drift Chambers
Central Tracker
35PANDA Spectrometer - PID
Muon Detectors
Forward RICH
Barrel DIRC
Barrel TOF
Endcap DIRC
Forward TOF
36PANDA Spectrometer - Overview
PWO Calorimeters
Forward Shashlyk EMC
Hadron Calorimeter
37Prototype 60
Dry N2
NI ?
38PWO Calorimeter w/ LAAPD Readout
Fixing screws into the support beam (stainless
steel)
LAAPD (10 x 10) mm2 (PANDA)
Back plate of the module
Group of 4 preamplifiers / alveole
Cooling plates and thermal shields
APD plastic cover with optical fiber insert
Fixing points between plate and insert with
thermally expanded freedom
Insert alveoles glued on alveoles Carbon
interface between alveoles and module plate
Group of 4 crystals wrapped and tight together /
1 alveole. An internal carbon cross is added to
keep the homogeneity in the gap
APDs (5 x 5) mm2 (CMS)
Alveoles pack of 16 crystals
Single Channel Preamp Prototype
First Chip Prototyp
VPT (Forward Endcap)
39Silicon Micro Vertex Detector
- Layout of MVD
- General structure
- 4 Barrels 6 Disks
- Inner layers pixels
- Outer layers strips
- (forward mixed)
- Pixel part
- Hybrid pixels 100 x100 µm2
- 140 modules
- 13M channels ? 0.15 m2
- Strip part
- Double sided silicon
- 400 modules
- 70k channels ? 0.5 m2
Disks
Target pipe
Beam pipe
Barrels
- Full size model (11)
- More realistic model concerning
- Sensor arrangement
- Support structure
- Volumes for electronics and cooling
- Pixel layers integrated schematically
40DIRC Principle PANDA Barrel DIRC
- Detector for internally reflected Cherenkov light
PANDA will use a mirror system for a flat focal
plane
41PANDA Endcap DIRC
Two different readout designs
Time-of-Propagation
Focussing Lightguide
(11)D design
2D t design
Endcap Disc DIRC
1-dimensional imaging type
42PAX Detector
Designed for (asymmetric) collider but compatible
with fixed target
Polarized Antiproton Experiments
43PAX Physics
Proton EFFs
Drell-Yan
p-p elastic
Fixed target experiment pol./unpol. p
internal H polarized target
Asymmetric collider polarized antiprotons in
HESR (p15 GeV/c) polarized protons in CSR
(p3.5 GeV/c)
Designed for (asymmetric) collider but compatible
with fixed target
Polarized Antiproton Experiments
44PAX
- Polarized antiprotons
- will open the way to a new spin-physics era
- Proton-spin structure
- Complete map of transversity
- Flavor separation
- Electromagnetic Form Factors
- Independent extraction of moduli of GE-GM in
Time-Like region - Test of the Rosenbluth separation in TL
- Measurement of the phase
- Hard pp scattering
- Additional measurement in one of the most
intriguing puzzles of HF - Low-t pp scattering
- Spin and isospin dependence of nucleon-antinucleon
interaction at low energy -
- (Wealth of single-spin asymmetries)
45Antiproton Polarizer Ring (APR)
Injection/Extraction
Target
Electron Cooler
Snake
Ring Parameter Ring Parameter
Beam energy 250 MeV
Number of antip. 1012
Ring acceptance 250 mm mrad
Betatron ampl. at IP lt 0.3m
Ring circumference 86,5 m
Snake strength 2.4 Tm
Atomic Beam Source (ABS) parameter Atomic Beam Source (ABS) parameter
ABS flow in feeding tube 1,51017 /s
Storage cell length 40 cm
Feeding tube diameter length 1 cm 15 cm
Long. holding field 300 mT
Electron polarization 0.9
Cell temperature 100 K
Ion-optics at IP
461992 Filter Test at TSR with protons
Experimental Setup
Results
T23 MeV
F. Rathmann. et al., PRL 71, 1379 (1993)
Expectation Expectation
Target Beam
? ?
? ?
Low energy pp scattering ?1lt0 ? ?totlt?tot-
47Present Status
- Spin Filtering works, but
- Controversial interpretations of FILTEX
experiment - Further experimental tests necessary
- Which role do electrons play?
- How does spin filtering work?
- Tests with protons at COSY
- No data to predict polarization from filtering
with antiprotons - ? Measurements with antiprotons at AD/CERN
48Outlook until 2012
- Fall 2008
- Technical proposal to COSY-PAC for spin filtering
- Technical proposal to SPSC for spin filtering at
AD - 2008-2009
- Design and construction phase
- 2009
- Spin-filtering studies at COSY
- Commissioning of AD experiment
- Then
- Installation at AD
- Spin-filtering studies at AD
49Summary
- PANDA at FAIR will be a versatile multi purpose
detector opento a wide physics program - Precision charmonium spectroscopy
- full mass range, all quantum numbers
- Search for exotic hadrons
- excited glue, unusual topologies, higher
Fock-components - Investigation of proton structure
- especially time-like form factors over large
kinematic range, hard exclusive processes and
Boer-Mulders function - PAX at FAIR is an interesting upgradeoption
using polarized antiprotons - Rich programme in single-spin and doubly
polarized physics - Reasonable p polarization has to be demonstrated
- In the coming decade FAIR will be one of the
leading facilities in hadron physics worldwide
addressing and answering many interesting
questions
50 51Hadrons are very complicated
- Quarkmodels usually account for qq states
- works well non-relativistically !
- Other color neutral configurations can (and
will) mix - same quantum numbers !
- Decoupling possible only if
- states are narrow !
- no qq term allowed !
Fock Decomposition
52Another one, X(3940)
- 350/fb
- no signal of X(3872)
- significant peak at
- M3.94000.011GeV/c2
- N14833 events (4.5s)
- surprisingly narrow
- background curve2nd order polynomialplus
D()D()J/?threshold term - so far only spin-0 particlesin recoil mass
- ?c ?inconsistent w/potential model m4060
MeV(should be accurate for S0, L0)
J/?
recoil
?c ?c0 ?c
2005
53LQCD ccg 1- vs. cc 1-- (J/?)
1- m(ccg) m(ccg) m(ccg) Model Group Reference
4390 80 200 isotropic MILC97 PRD56(1997)7039
4317 150 isotropic MILC99 NPB93Supp(1999)264
4287 isotropic JKM99 PRL82(1999)4400
4369 37 99 anisotropic ZSU02 hep-lat/0206012
D(1-,1--) m(ccg)- m(cc) m(ccg)- m(cc) m(ccg)- m(cc)
1340 80 200 isotropic MILC97 PRD56(1997)7039
1220 150 isotropic MILC99 NPB93Supp(1999)264
1323 130 anisotropic CP-PACS99 PRL82(1999)4396
1190 isotropic JKM99 PRL82(1999)4400
1302 37 99 anisotropic ZSU02 hep-lat/0206012
54Experimental Questions
- Do Charmonium hybrids exist?
- Like 1- (expected to be the lightest spin-exotic
state) - Are there JPC exotics in Charmonium?
-
- Some observed states are extremely narrow
- Like X(3872), DsJ(2317), DsJ(2459),
- What is the real width?
- Some are observed near thresholds
- Like X(3872) (DD), Y(4260) (DsDsJ),
- What is the line shape, dispersive/coupled
channel effects? - There is one charged candidate multiquark
candidate - Z(4433)
- Are there neutral partners? Are there more?
What is the line shape? Is it a real resonance?
55Experimental techniques
- Do Charmonium hybrids exist?
- Like 1- (expected to be the lightest spin-exotic
state) - Are there JPC exotics in Charmonium?
-
- Some observed states are extremely narrow
- Like X(3872), DsJ(2317), DsJ(2459),
- What is the real width?
- Some are observed near thresholds
- Like X(3872) (DD), Y(4260) (DsDsJ),
- What is the line shape, dispersive/coupled
channel effects? - There is one charged candidate multiquark
candidate - Z(4433)
- Are there neutral partners? Are there more?
What is the line shape? Is it a real resonance?
Charmonium production w/ light recoil particles
large pp (15 GeV/c)
Charmonium formation?p 30-100 keV
Charmonium formation w/ anisotropic momentum steps
Charmonium production w/ light recoil particles _at_
threshold (e.g. Zp-)pp gt10 GeV/c, ?p 100-200
keV
56Exotic Charmonium Production
- Expected cross sections are O(1nb)
- typical channels involve DD or J/? ? leptons
- BR lead to small yields O(1-few )
- Reconstruction e10-40
- L21032, duty e0.5?(Le) 8.6 pb-1/d
- Example
- ?1? 1 nb ? ?c1pp? ? ll-7? 10 pb incl. e,
multichannel ll-/? - Goal minimum 10k for PWA ? 116 d or 1 fb-1
- Ideal 50k ? 600 d or 5 fb-1
- Strategy
- 1 p-year running (200 d) at pp15 GeV/c for a
survey - additional running at optimized (slightly lower)
momentum - to improve PWA sensitivity (final goal total
600 d, 3 p-year ?)
) depending on findings
57Electromagnetic Form Factor
- vector current of quarks Qf q?µq
- element of renormalisation group
- vector current two form factors
- internal structure of hadron ground state
Dirac
Pauli
lt N(p) q?µq N(p)gt F1(q2) ?µ i(?p/2Mp)
F2(q2) sµ?qµ
58Definitions
q2 lt 0 space like
q2 gt 0 time like
F1(q2)
4Mp2
q2 GeV2c2
meltltmp
annihilation
electron scattering
59Definitions
q2 lt 0 space like
q2 gt 0 time like
F1(q2)
4Mp2
q2 GeV2c2
Form Factor real
Form Factor complex
connected by Dispersion relations no interference
in cross section F1, F2
imaginary part Polarisation
60Definitions
q2 lt 0 space like
q2 gt 0 time like
F1(q2)
4Mp2
q2 GeV2c2
unphysical region accesible via ee-p
61Sachs Form Factor
GE F1 t F2 GM F1 F2
- space-like
- Fourier transform of charge and magnetization
- time-like (q2gt0)
- at threshold, t 1
- GE(4 Mp2) GM (4 Mp2)
- GE,GM analytical continuation of
- non-spin-flip and spin-flip space-like FF
- lim q2 ? 8
- F1(q2) ? as q-4 F2(q2) ? as q-6
- F1,2(q2)time like F1,2(q2)space like
- Form Factors in space like and time like
intimately connected
at threshold GEGM
62EM form factor (q2 gt 0)
Adone ee- 25, 69 ev.ELPAR pp 34 ev. DM1,2
ee- 63, 172 ev. GE/GM 0.34 PS170 pp
3667 ev. GE/GM 1 E760 pp 29 ev. E835 pp
206 ev. CLEO ee- 14 ev. BES ee- higher
stat BaBar ee- high stat
all data Measure absolute cross section GE GM
63Production of (double) hypernuclei
KK
Trigger
Protons
3 GeV/c
?-
Secondary Target
Neutrons
?-(dss)p(uud) ? ?(uds)?(uds)
64pp cross sections
CITATION W.-M. Yao et al., J. Phys. G 33,1 (2006)
Crystal Barrel
E760/E835
PS185
http//pdg.lbl.gov/2007/hadronic-xsections/hadroni
crpp_page11.pdf
PANDA
Obelix
Jetset
65Electromagnetic Calorimeters
Backward Endcap 800 Crystals Worse resolution
due to service lines of trackers Needed for
hermeticity
Barrel Calorimeter 11000 PWO Crystals LA APD
readout s(E)/E1.5/vE const.
Forward Endcap 4000 PWO crystals High occupancy
in center Readout LA APD or vacuum triodes
Forward Shashlyk (after dipole magnet) 350
channels Readout via PMTs s(E)/E4/vE
const. Alternative Designs Spiral Shashlyk
Segmented composite Shashlyk-Sandwich for
(e/h/µ)
66Slice, barrel and mounting
Technical proposal principle
Mounting principle of the barrel
Inner vessel of the magnet Fixing points
Mounting principle of one slice
Support ring
One slice
Support beam
67Cooling at -25C Power summary, simulation and
results on prototypes
Cooling power summary
First temperature test with proto 60 stability
/-0.05C Uniformity 0.8C
68Central Tracker - Straw Tube Tracker Option
- Number of double layers 11
- Skew angle 23
- skewed double layers 5
- tube diameters 4, 6 and 10 mm.
- inner radius 15 cm.
- outer radius 42 cm.
- tube length 150 cm.
- tube wall thickness 20 µm.
- Anode wire diameter - 20 µm.
69Straw-Kammer à la PANDA für den TOF-Detektor in
Jülich
70Central Tracker TPC Option
- General layout GEM-TPC
- Multi-GEM stack for amplification
- and ion backflow suppression
- Gas Ne/CO2 (CH4/CF4)
- 100 k pads of 2 x 2 mm2
- 50-70 µs drift, 500 events overlap
- Simulations
- dp/p 1
- dE/dx resolution 6
- Challenges
- space charge build-up
- continuous sampling
- Requirements
- Field homogeneity better 2
- ?Br /Bz dz lt 2mm
71PANDA TPC-Testchamber in FOPI und CBELSA
Outer- Inner- Field cage
- Media distribution (HV gas) integrated in the
vessel - Core support structures
- Foam (Rohazell )
- Honeycomb (Nomex)
- Scenarios for field defining system
- Evaporated staggered strip line
- Al on Kapton ? OK
- Status
- Material parts purchasing ongoing
- Tooling in construction
- Tests on flat specimen in 04/05.2008
- Coupled simulations pending
- Planned completion 11.2008
- HV-Mainframe Modules in request ...
HV-Distribution strips
72Phase I Fixed target experiments in CSR
Physics EMFF pp elastic
direction of antiprotons
(antiprotons)
Independent from HESR running
73Phase II Asymmetric Proton-Antiproton Collider
Physics Transversity pp elastic
E-cool modification necessary
polarized protons in HESR (p15 GeV/c) polarized
antiprotons in CSR (p3.5 GeV/c)
direction of protons
direction of anti-protons
(anti-protons)
(protons)
Lgt1031s-1cm-2
74Interpretations of FILTEX result
Observed polarization build-up dP/dt (1.24
0.06) x 10-2 h-1 P(t)tanh(t/t1), 1/t1s1Qdtf
s1 72.5 5.8 mb
1994 Meyer and Horowitz three distinct
effects Selective removal through scattering
beyond ?acc4.4 mrad (sR?83 mb) Small angle
scattering of target prot. into ring acceptance
(sS?52 mb) Spin-transfer from pol. el. of target
atoms to stored prot. (sE?-70 mb) s1 sR? sS?
sE? 65 mb
- 2005 Milstein Strakhovenko Nikolaev Pavlov
only one effect - Only pp elastic scattering contributes
- No contribution from other two effects s1 85.6
mb