G.Fedotovich Budker Institute of Nuclear Physics

Novosibirsk, Russia

LNF, Frascati 7 - 10 April 2008

Prospect of accuracy improvements of the hadronic cross sections measurements to the level 10-3: experimental and theoretical problems

Outline

1. Current status of the accuracy of the hadronic cross sections measurements. Inspection of the last generation experiments - CMD-2, SND & KLOE

2. Main sources of systematic errors: • Accelerator • Detector • Theory 3. What can we expect in the nearest future

4. Usage of space-like data to calculate VP operator (-q2)

5. Conclusion

Some features of CMD-2, SND and KLOE

experiments • Large data sample due to high integrated luminosity and

large detectors acceptance (calorimeter covers about 0.94). Every detector collected several millions +- events

• Multiple scan (up and down) of the same energy range to avoid possible systematic in energy determination: step (2E) = 10 MeV in the continuum and about 1 MeV near and peaks (CMD-2 and SND)

• Absolute calibration of beam energy using the resonance depolarization method (better than 10-4) negligible systematic error comes due to energy uncertainty (CMD-2 and SND)

• Good space resolution resulting in perfect momentum resolution (p/p ~ 0.4%, KLOE) powerful instrument for charged PID

• Excellent energy resolution at a few percent level (E/E ~ 4%, SND & KLOE) leads to small background & helps to separate events

Some features of CMD-2, SND and KLOE experiments

• Detection efficiencies and calorimeter response were studied

using “pure” experimental data rather than MC events (~2106

and meson decays have been used, CMD-2 & SND)

• Charged and neutral triggers for the same data sample – possibility to measure and monitor triggers efficiencies (CMD-2 & SND)

• Changing events selection criteria to check cross section

stability. All detectors carefully studied this item

• Cross check possibility – unstable particles detected via different decay modes (º→2, e+e-; →2, +-0, 30)

• MC generators based on differential cross sections with precise RC

for the processes of e+e- annihilation were developed (CMD-2 & KLOE)

• Efficiency is calculated via Monte Carlo + corrections for detector imperfections

• Integrated luminosity L

is measured using LAB events

• RC accounts for ISR effects only

• VP effects are included in cross section properties

• Ratio N(2)/N(ee) is measured directly detection inefficien-cies are cancelled out in part

• RC account for ISR and FSR effects

• Events separation procedure & analysis don’t rely on simulation

• Form factor is measured to better precision than L

)1(

)1(||

..2

lp

eeeeee

eeN

NF

How cross sections are measured to understand the main factors giving dominant contributions to systematic uncertainty for hadronic cross sections

All modes except 2 mode

( )(1 )H bgN N

ee HL

Luminosity measurement

• Precision of luminosity measurement will be improved significantly due to better extraction of Bhabha events, increasing detection efficiency and more accurate calculation of the radiative corrections.

• Alternative method to measure luminosity based on the process e+e- γ γ. In that case Feynman graph does not contain VP effects. Powerful instrument to understand systematic. Source of error CMD-2 SND KLOE CMD-3

Event separation

0.5% 0.6% 0.1% < 0.2%

Fiducial volume 0.2% 0.8% 0.2% or <

Energy calibration

<0.1% 0.3% 0.3% < 0.1%

Efficiency correct.

1% 0.6% 0.1%

Radiative correct.

0.2% 0.5% 0.5%(0.1%)

< 0.1%

Total 1.2% 1.3% 0.5th0.3ex

p

0.3% or <

Source of error CMD-2 /98

SND KLOE

Event separation 0.2/0.4% 0.5% 0.1%

Fiducial volume 0.2% 0.8% 0.3%

Energy calibration 0.1/0.3% 0.3% 0.2%

Efficiency correction 0.2%/0.5% 0.6% 0.6% (rec.filter)

Pion losses (decay, NI)

0.2% 0.2% 0.2%

Other 0.2% 0.5% 0.5%

Radiative corrections

0.4% 0.2% 0.5%

Total 0.6/0.8% 1.2% 0.9%

R measurement at CMD-2, SND and KLOE (for √s<1GeV 2pi dominant channel)

R measurement at CMD-3(systematic errors review)

Source of error 2pi√s<1 GeV

2pi√s>1.0 GeV

4pi√s>1.1 GeV

Event separation 0.2% (0.4%) 0.2% 1% (cuts)

Fiducial volume 0.2% 0.2% 2% (model)

Energy calibration < 0.1% (0.3%)

<0.1% (1%) <0.1% (0.3%)

Efficiency correction

0.1% 0.1% 1% (tr.+ bg.)

Pion losses (decay,NI)

0.1%(opt.ass.)

0.1%(opt.ass.)

0.1%(opt.ass.)

Other 0.1% (0.1 – 0.3)% 1%

Radiative corrections

0.1% 0.1% < 0.5%

TotalTotal (no depolariz.)

0.35%0.6%

(0.35 – 0.5)%1.1%

2.7%2.7%

Derivative d|F(E)|²/dE/|F(E)|²x E/E

Energy determination

Derivative jumps up and down inside corridor 1%. Near and mesons reach values 6%.Conservative upper estimation is 1% - energy region gives the main hadronic contribution to aµ = (g –2)/2Very important task for machine physicists to determine beam energy with relative accuracy E/E 10-4 or even better

(E/E = 10-3)

π/μ/e separation based on charged

particle momentum

Vertical axis – the number of standard deviations between average momentum of pions and muons

CMD-2 260 MeV

CMD-3320 MeV

• DC resolution will be 2.5 times better (already achieved)

• Magnetic field will be increased 1.5 times (already achieved)

• As a result π/μ/e separation based on momentum will be possible up to 2*320 MeV - practically to the peak

π/μ/e separation based on energy deposition

CМD-3

CMD-2

• Energy resolution of barrel part will be improved (8X0 15X0)

•π/e separation will be considerably better

•Part pions “looks” like muons will be suppress to the level 10% (was 25% at CMD-2) . We can try π/μ separation based on energy deposition

•Information of energy deposition in depth of calorimeter provides additional factor for π/µ separation

Fiducial volume

1. Z-chamber: In first approach we will have the same z-coordinate resolution the accuracy of the fiducial volume measurement will not change. At polar angles ~ 60° z ≈ 0.7 mm & system. shift is smaller 0.1 mm. For LAB events it leads to acceptance uncertainty about 0.2%

2. LXe calorimeter: For normal incident particles ~ 90° z ≈ 0.9 mm. The acceptance will be determined with the same accuracy. The capability for cross check will be in hand. Very possible we improve the measurement accuracy of the detector acceptance by factor of 1.5

We assume that fiducial volume will be determined at least with the same accuracy (or better) as we had at CMD-2

3. Huge statistics: Help to study systematic of z-coordinate determination in DC & to improve the accuracy of DC calibration procedure. Study in detail angular distributions of multi hadrons events to choose model for simulation

What we have currently and what we can expect in

the nearest future - theoretical aspects.• For all three detectors MC generators with precise RC were developed.

• Channel e+e- e+e-: BHWIDE (LEP, 0.5%), MCGPJ (CMD-2, 0.2%) photon jet radiation in collinear region, BabaYaga (KLOE, 0.5 0.1%) used parton shower approach. We plan to include NLO corrections and increase the accuracy of our MCGPJ to 0.1% level (for all other channels too). This work is in progress with Dubna, E.Kuraev et.al.

• Channel e+e- +-, +-: KKMC used in LEP experiments adopted for low energies, 0.1%, BUT for VP effects smooth approximation was applied. Resulting systematic accuracy is not better than 1% (out of & energy region). MCGPJ (CMD-2, 0.2%). Quite possible that in our case systematic uncertainty is better than 0.1%. B.Smith, M.Voloshin: PL B 324 – all enhanced second order corrections contribute not more than 0.02% and quickly decrease with energy increase

Radiative corrections

Radiative corrections

• Channel e+e- MCGPJ (CMD-2, 0.2%). This process has a big cross section. Very important channel for luminosity measurement – cross check possible. ISR only. Feynman graph does not contain VP effects.

• Channel e+e- +-, K+K-: MCGPJ (CMD-2, 0.2%). ISR & FSR are taken into account. Unfortunately there are no other MC generator with similar accuracy for comparison. Experimental and theoretical evidences are required to prove validity of sQED application for pions & kaons

• Channels with neutral particles in FS: e+e- KLKS, 0, ,

0. ISR are taken into account. MCGPJ (CMD-2, 0.2% or better). Very possible that accuracy is better than 0.1%

• VP effects currently are calculated with accuracy better than 0.05% (on with 0.5% & on - 0.15%) and do not contribute to final systematic error

Trigger & reconstruction efficiencies

Trigger efficiency close to 100%. Charged & neutral triggers for the same data sample – powerful instrument to monitor trigger stability and it’s real efficiency (CMD-2, KLOE & CMD-3)

Efficiency of track reconstruction in DC will be better than 98% with uncertainty <0.1% (CMD-3 & new SND)

Bremsstrahlung of electrons (positrons) on the wall of the machine vacuum chamber. At CMD-2 and SND we had correction about (0.5 0.05)% (s<1GeV). We (& SND) hope to have the same accuracy in experiments at VEPP-2000.

Optimization of selection criteria for collinear events: Polar angle – compromise for every detector, Threshold on transverse momentum of charged particles in DC, Choice of optimal acollinearity angle between tracks in DC Choice threshold on energy deposition in calorimeters and so on…

reconstruction – main source of systematic error for

processes with in FS. LXe calorimeter will significantly push down this error

Another way for aµ calculation

Special experiment is necessary to measure cross sections of ONLY THREE PURE QED PROCESSES : e+e- , for luminosity measurement (no VP effects, accuracy < 0.1%). BUT special calorim. is required to detect photon conversion point (LXe in CMD-3)

e+e- +- direct cross section measurement to extract |1 + (s)|² (accuracy < 0.1%). VP effects must be removed from RC. Effects of FSR and CI must be included into RC

SCAN EXPERIMENT: Luminosity ~ 1032 cm-2 s-1 ,~ 100 energy points with number of muon events 108 /per year (statistical accuracy about 0.1% in every point). Cross section has practically isotropic distribution vs polar angle

e+e- e+e- process to extract (-q²) from t-channel in space-like region (accuracy <0.1%)

2|)(1|

exp

sBorn

dxmx

xxahad )

1()1( 2

21

0

.

Contribution to aµ Time-like region Space-like region

Red lines – resonance contributionsx < 0.7 analytical approximation

Cross section of all three QED processes can be measured in one direct scan experimentAccuracy of RC calculation will not contribute to final systematic error (-q²)We hope to achieve experimental systematic error for LAB better than 0.3% with CMD-3 at VEPP-2000.

t = -s(1-cos)/2t -0.04 GeV²x 0.75

Analytical behavior of (q²) in space-like region

This interval of q² variations corresponds to x changing from 0.01 to 0.99 Very ghostly chance to measure (q²) in this region with pro mille accuracy

22

1 mx

xt

ConclusionsConclusions Despite decades of experiments, precise studies of e+e annihilation into hadrons at low energies are still interesting and can provide a lot of important information

● In a few years new precision data from CMD-3 and SND working at VEPP-2000 as well as with ISR at DAFNE and B–factories and BELLE are expected

● Progress is particularly expected for the channel e+e-→+-, where systematic uncertainty 0.3% or even better will be achieved

● MC generators were done : ee ee, BHWIDE (0.5%), MCGPJ (0.2%?!) and BabaYaga (0.1%) ee ,-, KKMC (0.1% adopted for low ener.), MCGPJ (0.2%) ee and K+K-, MCGPJ (0.2%?!) Only ISR is taken into account for processes with neutral particles in final state: ee , KlKs, 0,,’, 0, MCGPJ(0.2%) We can expect progress in theoretical improvement of the accuracy of RC calculation with pro mille accuracy

● Measurement of beam energy with relative accuracy better than 10-4 are extremely needed (resonance depolarization techniques only)

● To have enough statistic ~106 at every energy point (~100) machine with luminosity greater than 1032 cm-2s-1 in meson energy region is required

● To illuminate possible systematic error in hadronic cross sections more accurate and independent measurements (CMD-3 & SND) are necessitated

● Efforts of theorists are required to build models to describe in detail energy dependence of cross sections with 4 & more pions in FS

● CMD-3 and SND will measure hadronic cross sections with accuracy close to pro mille. DAFNE HEPr can provide independent measurement of the hadronic cross sections - valuable information for cross check accuracy with CMD-3 & SND

● Luminosity and trigger efficiency must be measured in different channels at the same data sample to arrange cross check for better study of systematic

● Usage of space-like data can help in understanding of systematic in hadronic contribution to aµ (in far future, JLAB)

)1()(

L

NNHee bgH

22

1 mx

xt

VEPP-2000

CMD-3

SND

• circumference – 24.4 m• revolution time – 82 nsec• beam current – 0.2 A• beam length – 3.3 cm• energy spread – 0.7 MeV• x= z =6.3 cm• L = 1032 cm-2s-1 at 2E=2.0 GeV• L = 1031 cm-2s-1 2E=1.0 GeV

-1 per dete50 ctor per ye a0 r Ldt pb

Total integrated luminosity with all detectors on VEPP-2M ~ 70 pb-1

Luminosity measurementBhabha scattering events are preferable for normalize purpose to calculate cross sections with collinear events in FS

Main sources of systematic errors in previous experiments wereQuality of events separation Nee , Nxx typical value 0.4 %- 5% Accuracy of beam energy measurement typical value 0.3% - 1%Events detection reconstruction efficiencies typical value 0.2% - 2%Systematic error of RC calculation typical value 0.3% - 1%

Very soon accuracy of RC calculation with systematic error less than 0.1% will be required for future forthcoming experiments (for example CMD-3 experiments at VEPP-2000)

L=Nee

vis(ee ee)

L=Nxx

vis(ee xx)

vis(ee ee) vis(ee xx) = -----

Dominant channelDominant channel ee++ee-- → → ++--

energy interval energy interval energy interval energy interval

390 – 520 MeV390 – 520 MeV 600 – 960 MeV 600 – 960 MeV

Group aGroup aµµ((), 10), 10-10 -10 aaµµ((), 10), 10-10-10

Old 48.72 ± 1.45 ± 1.12 (1.83) 374.8 ± 4.1 ± 8.5 Old 48.72 ± 1.45 ± 1.12 (1.83) 374.8 ± 4.1 ± 8.5 (9.4)(9.4)

CMD-2 46.17 ± 0.98 ± 0.32 (1.03) 377.1 ± 1.9 ± 2.7 CMD-2 46.17 ± 0.98 ± 0.32 (1.03) 377.1 ± 1.9 ± 2.7 (3.3)(3.3)

SND 47.80 ± 1.73 ± 0.69 (1.86) 376.8 ± 1.3 ± 4.7 SND 47.80 ± 1.73 ± 0.69 (1.86) 376.8 ± 1.3 ± 4.7 (4.8)(4.8)

CMD-2/SND 46.55 ± 0.85 ± 0.29 (0.90) KLOE: 375.6 ± 0.8 ± 4.9 (5.0)CMD-2/SND 46.55 ± 0.85 ± 0.29 (0.90) KLOE: 375.6 ± 0.8 ± 4.9 (5.0)

Average 46.97 ± 0.73 ± 0.45 (0.86) 376.5 ± 0.6 ± 1.5 Average 46.97 ± 0.73 ± 0.45 (0.86) 376.5 ± 0.6 ± 1.5 (1.7)(1.7)

energy interval 1040 – 1380 MeVenergy interval 1040 – 1380 MeV

Group aGroup aµµ((), 10), 10-10-10

OLYA 7.49 ± 0.18 ± 0.83 (0.83)OLYA 7.49 ± 0.18 ± 0.83 (0.83)

CMD-2 7.01 ± 0.10 ± 0.16 (0.19)CMD-2 7.01 ± 0.10 ± 0.16 (0.19)

Average 7.03 ± 0.09 ± 0.16 (0.18)Average 7.03 ± 0.09 ± 0.16 (0.18)

π/μ separation

Vertical axis - radius (in cm) where pions and muons penetrate

320 MeV

230 MeV

130 MeV

440 MeV

480 MeV360 MeV

280 MeV

170 MeV

LXE

CSI

Iron yoke

LXE

CSI

Iron yoke

• At any energies π and μ escape LXE – it is bad

• At energies above φ meson – muon range system will serve to suppress cosmic events, below to mark muon events

• At energies below 2*400 MeV π /μ does not escape CsI calorimeter – it is fine

Pion formfactor (CMD-2)

0.7% 0.6% (95)/ 0.8% (98) 1.2-4.2%Systematic error

~ 9105 +- events

Event separation (CMD2)

• e// separation using particles momentum• can measure N()/N(ee) and compare to QED

0.6 GeV

ee,

> 0.6GeV

• e// separation is based on energy deposition in calorimeter • N()/N(ee) is fixed according to QED

ee