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Search for a Dark Photon: proposal for the experiment at VEPP3. - - PowerPoint PPT Presentation

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Search for a Dark Photon: proposal for the experiment at VEPP3. I.Rachek, B.Wojtsekhowski, D.Nikolenko IEBWorkshop Cornell University June 18, 2015 I.Rachek dark photon at VEPP-3 June 18, 2015 1 Latest results of dark photon searches

slide-1
SLIDE 1

Search for a Dark Photon: proposal for the experiment at VEPP–3.

I.Rachek, B.Wojtsekhowski, D.Nikolenko

IEBWorkshop Cornell University June 18, 2015

I.Rachek dark photon at VEPP-3 June 18, 2015 1

slide-2
SLIDE 2

Latest results of dark photon searches

BABAR (2014): e+e− → γA′, A′ → e+e−, µ+µ− NA48/2: π0 → γe+e−

)

2

(MeV/c

A’

m 10

2

10

  • 7

10

  • 6

10

  • 5

10 NA48/2

) σ (3

e

2) − (g

µ

2) − (g APEX A1 HADES KLOE WASA E141 E774 BaBar 2

ε

KLOE 2015 e+e− → γ(e+e−)

10−7 10−6 10−5 10−4 1 10 100 1000 ε2 mU (MeV/c2) (g − 2)µ 5σ (g − 2)µ ± 2σ favored (g − 2)e E774 E141 BaBar prelim. APEX A1 HADES WASA KLOE (φ → ηe+e−) KLOE (µ+µ−γ) KLOE (e+e−γ) preliminary

results of 2013-2015

WASA 2013 π0 → γ(e+e−) PLB 726 (2013) 187 KLOE 2013 φ → η(e+e−) PLB 720 (2013) 111 KLOE 2014 e+e− → γ(µ+µ−) arXiv:1404.7772 MAMI-A1 2014 e−N → e−N(e+e−) PRL 112 (2014) 221802 PHENIX 2014 π0, η → γ(e+e−) arXiv:1409.0851 HADES 2014 pN → X(e+e−) PLB 731 (2014) 265 KLOE 2015 e+e− → γ(e+e−) arXiv:1501.05173 NA48/2 2015 π0 → γ(e+e−) arXiv:1504.00607

no A’ signal observed to date

I.Rachek dark photon at VEPP-3 June 18, 2015 2

slide-3
SLIDE 3

Latest results of dark photon searches

BABAR (2014): e+e− → γA′, A′ → e+e−, µ+µ− NA48/2: π0 → γe+e−

)

2

(MeV/c

A’

m 10

2

10

  • 7

10

  • 6

10

  • 5

10 NA48/2

) σ (3

e

2) − (g

µ

2) − (g APEX A1 HADES KLOE WASA E141 E774 BaBar 2

ε

KLOE 2015 e+e− → γ(e+e−)

10−7 10−6 10−5 10−4 1 10 100 1000 ε2 mU (MeV/c2) (g − 2)µ 5σ (g − 2)µ ± 2σ favored (g − 2)e E774 E141 BaBar prelim. APEX A1 HADES WASA KLOE (φ → ηe+e−) KLOE (µ+µ−γ) KLOE (e+e−γ) preliminary

results of 2013-2015

WASA 2013 π0 → γ(e+e−) PLB 726 (2013) 187 KLOE 2013 φ → η(e+e−) PLB 720 (2013) 111 KLOE 2014 e+e− → γ(µ+µ−) arXiv:1404.7772 MAMI-A1 2014 e−N → e−N(e+e−) PRL 112 (2014) 221802 PHENIX 2014 π0, η → γ(e+e−) arXiv:1409.0851 HADES 2014 pN → X(e+e−) PLB 731 (2014) 265 KLOE 2015 e+e− → γ(e+e−) arXiv:1501.05173 NA48/2 2015 π0 → γ(e+e−) arXiv:1504.00607

no A’ signal observed to date Decay of A’ to invisible particles

2 −

10

1 −

10 1

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10 BaBar A') π → BNL (K

A' is 'welcome'

µ

a A' is excluded

µ

a

e

a

(GeV)

A'

m

2 −

10

1 −

10 1

2

ε

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10

I.Rachek dark photon at VEPP-3 June 18, 2015 2

slide-4
SLIDE 4

A′ from annihilation of beam’s positrons and target electrons

instead of standard two-photon annihilation e+e− → γ + γ

θγ

cm

θγ

lab electron positron photon photon

e e+ γ γ

  • photon

photon positron

CM LAB

. . . annihilation with the production of dark photon e+e− → A′ + γ:

θγ

lab

A' boson

e e+ γ

electron positron photon

θγ

cm

  • CM

photon positron

LAB

A' differential cross section (in Lab System):

dσ dy ≈ ε2 · πr 2 yγ+

  • (1+µ)2

1−(y+µ) − 2y

  • where

y = E lab

γ /E+ , µ = M2 A/s , MeV

A'

m

5 10 15 20

A'), nbarn γ →

−

e

+

(e σ

1 10

  • 3

=10 ε =500 MeV,

+

e

E

I.Rachek dark photon at VEPP-3 June 18, 2015 3

slide-5
SLIDE 5

Kinematic correlations in annihilation

Photon energy depends on its emission angle and the mass of the 2nd particle: Eγ ≈ E+ · 1 − M2

A/s

1 + γ+(1 − cos θγ), s = 2me(E+ + me) for E+ = 500 MeV → √s = 22.6 MeV :

[deg]

Lab

γ Θ

1 1.5 2 2.5 3 3.5 4 4.5 5

[MeV]

Lab

γ E

50 100 150 200 250 300 350 400 450 500

=10 MeV

A'

M =15 MeV

A '

M =20 MeV

A '

M

γ γ

I.Rachek dark photon at VEPP-3 June 18, 2015 4

slide-6
SLIDE 6

The concept of search in annihilation

measure energy and emission angle of γ-quantum search for a “bump” on top of QED background A’-boson should appear in a missing mass spectrum as a peak above QED background: peak width is defined by energy and angular resolutions of the γ-detector

[MeV] γ E

50 60 70 80 90100 200 300 400

[deg] γ Θ

1 2 3 4 5 6 7 8 1 10

2

10

3

10

4

10

5

10 gamma background

[MeV] γ E

50 60 70 80 90100 200 300 400

[deg] γ Θ

1 2 3 4 5 6 7 8

=15 MeV

A'

A' for M γ →

  • +e

+

e γ γ →

  • +e

+

e

γ H

+

e → +H

+

e γ H

+

e → +H

+

e , MeV

missing

M

2 4 6 8 10 12 14 16 18 20 22

events

2

10

3

10

4

10

5

10

=15 MeV, veto on 2nd cluster

A

M all events background only

I.Rachek dark photon at VEPP-3 June 18, 2015 5

slide-7
SLIDE 7

VEPP–3 approach

positron beam repeatedly crosses the internal hydrogen gas target working with the new injector complex, which provides 2 · 109 e+ per second; staying at injector energy Ee+ = 500 MeV – no energy ramping in VEPP–3 6 bunches in VEPP–3; every 10 seconds the oldest bunch is replaced by a new

  • ne with up to 2 · 1010 positrons, stored in the injector’s cooler ring;

designed luminosity of the experiment: 1033cm−2s−1 special magnetic system providing free flight for γ–quanta from target to detector is needed using a segmented EM-calorimeter placed at a distance of ∼ 8 m from the target searching for a peak in a missing mass distribution. VEPP-3 beam microstructure: 6-bunches mode

T

1ns

revolution period = 249 ns

41.5 ns 1 2 3 4 6 1 5

bunch #

I.Rachek dark photon at VEPP-3 June 18, 2015 6

slide-8
SLIDE 8

1st configuration for the experiment at VEPP–3

2.6 Θ

γ =

  • Θγ

4.5 =

  • Pump 2,3

Sextupole Valve Pump 4 Pump 1 Valve Photon Detector Q3 Q2 D3 D2 Q1 D1 Sandwich Cold Head

Pump 5 Storage Cell

217 cm 10.7 o

arXiv:1207.5089 Three dipole magnets in the 2nd straight section of VEPP-3

I.Rachek dark photon at VEPP-3 June 18, 2015 7

slide-9
SLIDE 9

1st configuration for the experiment at VEPP–3

2.6 Θ

γ =

  • Θγ

4.5 =

  • Pump 2,3

Sextupole Valve Pump 4 Pump 1 Valve Photon Detector Q3 Q2 D3 D2 Q1 D1 Sandwich Cold Head

Pump 5 Storage Cell

217 cm 10.7 o

arXiv:1207.5089 Three dipole magnets in the 2nd straight section of VEPP-3

  • bvious drawbacks

very busy space – difficult to clean-up the path from the target to the calorimeter VEPP–3 becomes completely unavailable for other programs (SR,KEDR,VEPP-4) when the dipoles are installed

I.Rachek dark photon at VEPP-3 June 18, 2015 7

slide-10
SLIDE 10

2nd configuration: The ByPass at VEPP–3

+

e

SR

1B1B 3B8A

BYPASS along the 4th straight section of VEPP–3 – where the FEL was previously situated

  • vacuum chamber with pumping system
  • 3 dipole magnets
  • 6 quadrupoles
  • elements of beam diagnostics

I.Rachek dark photon at VEPP-3 June 18, 2015 8

slide-11
SLIDE 11

2nd configuration: The ByPass at VEPP–3

length of bypassed segment of VEPP−3 = 1830 cm

V

D2

4.5

e+

CsI calorimeter

D3 Q3 Q4 Q5 Q6 D1 Q2 Q1

distance = 8 m

Target

kG/cm Q2: 0.45 Q3: −0.57 Q4: 0.54 Q5: −0.19 Q6: 0.28 Q1: −0.86

∆

D1: 12.0 L/L = 0.5% D2: 13.4 D3: 19.6 1B1B 3B8A

BYPASS along the 4th straight section of VEPP–3 – where the FEL was previously situated

  • vacuum chamber with pumping system
  • 3 dipole magnets
  • 6 quadrupoles
  • elements of beam diagnostics

I.Rachek dark photon at VEPP-3 June 18, 2015 8

slide-12
SLIDE 12

Photon detector

The desired specifications: energy resolution σE/E ≤ 5% in the range Eγ = 50 ÷ 500 MeV angular resolution ∆θ ∼ 0.1◦ angular acceptance in θlab: 1.5◦ ÷ 4.5◦ – corresponds to θCM = 90◦ ± 30◦ angular acceptance in φ: 360◦

I.Rachek dark photon at VEPP-3 June 18, 2015 9

slide-13
SLIDE 13

Photon detector

The desired specifications: energy resolution σE/E ≤ 5% in the range Eγ = 50 ÷ 500 MeV angular resolution ∆θ ∼ 0.1◦ angular acceptance in θlab: 1.5◦ ÷ 4.5◦ – corresponds to θCM = 90◦ ± 30◦ angular acceptance in φ: 360◦ Considering an option of using the crystals from the CLEO EM–calorimeter CsI(Tl) crystals 1650 rectangular crystals in endcaps crystal size: 5 × 5 × 30cm3 (16.2X0) 4 Hamamatsu S1790 photodiodes per crystal

I.Rachek dark photon at VEPP-3 June 18, 2015 9

slide-14
SLIDE 14

Calorimeter based on CsI(Tl) crystals from CLEO

608 crystals are assembled in a “ring” calorimeter is placed at a distance of 8 m from the target based on CLEO measurements with 180 MeV positrons: energy resolution σE = 3.8% spatial resolution σx = 12 mm ⇒ angular resolution: σθ = 0.09◦ event rate at threshold 25 MeV and luminosity 1033: total background rate: 850 kHz maximum per a crystal < 20 kHz

I.Rachek dark photon at VEPP-3 June 18, 2015 10

slide-15
SLIDE 15

Main background processes

background QED processes

1

positron bremmstrahlung on hydrogen e+ + H → e+ + X + γ

2

Bhabha scattering with bremsstrahlung e+ + e− → e+ + e− + γ

3

2-photon annihilation e+ + e− → γ + γ

4

3-photon annihilation e+ + e− → γ + γ + γ – Part of background events can be identified and rejected. – The rest form a smooth “substrate”; their fluctuations define a search sensitivity. – For realistic background estimation a Monte Carlo simulation is required. – Such simulation was performed using GEANT4 toolkit and a set of dedicated event generators.

I.Rachek dark photon at VEPP-3 June 18, 2015 11

slide-16
SLIDE 16

Event generators

1

e+ + H → e+ + X + γ root class TFoam, dif. cross section

dσγ dEγdΩγ

from “classic” paper Y-S. Tsai, Rev. Mod. Phys 46 815 (1974), Rev. Mod. Phys 49 421 (1977).

2

e+ + e− → e+ + e− + γ adapted event generator from CMD–3

A.B.Arbuzov, G.V.Fedotovich, F.V.Ignatov, E.A.Kuraev, A.L.Sibidanov, BINP preprint 2004-70

3

e+ + e− → γ + γ e+ + e− → γ + γ + γ event generator based on an aproach from:

  • F. A. Berends and R. Kleiss, “Distributions for electron-positron annihilation into

two and three photons”, Nucl. Phys. B186 (1981) 22

4

e+ + e− → γ + A′ root class TFoam, dif. cross section

dσ dy ≈ ε2 · πr 2 yγ+

  • (1+µ)2

1−(y+µ) − 2y

  • derived from P. Fayet, Phys.Rev. D 75 (2007) 115017, Eq.55

I.Rachek dark photon at VEPP-3 June 18, 2015 12

slide-17
SLIDE 17

Identification of background events

more than one γ-quantum in calorimeter

a symmetrical (around θCM = 90◦) calorimeter acceptance is required then events of 2-photon annihilation (and partially of 3-photon one) can be identified

veto-counter for positrons

bremsstrahlung is partially rejected rejection efficiency depends on configuration of veto-counter γ sandwich beam e +

Entries 987767 , MeV

γ

E 50 100 150 200 250 300 350 400 450 500 10000 20000 30000 40000 50000 60000 70000 80000 Entries 987767

Veto efficiency=43.2%

all >0.5 MeV

sand

E

w10

ǫ = 43% f = 2.4 MHz γ beam scintillator e+

Entries 49998 , MeV

γ

E 50 100 150 200 250 300 350 400 450 500 500 1000 1500 2000 2500 3000 3500 4000 Entries 49998

Veto efficiency=79.5%

all >0.5 MeV

sand

E

p02

ǫ = 80% f = 17 MHz

I.Rachek dark photon at VEPP-3 June 18, 2015 13

slide-18
SLIDE 18

Secondary sources of background events

large flux of bremsstrahlung photons, emitted at small angle:

miss the calorimeter, but are able to produce a shower, passing 8m of air (0.026X0) can be dumped by a blocker: 20cm-long tungsten rod at the exit of the dipole

charged veto scintillator W b l

  • c

k e r to calorimeter

Target

p

  • s

i t r

  • n

v e t

  • c
  • u

n t e r

M a g n e t

Entries 212087

, deg

γ

Θ

0.5 1 1.5 2 2.5

events

2000 4000 6000 8000 10000

Entries 212087

Air W blocker

h1_0

positrons that lost a small fraction of energy in the target are bent in the dipole magent and hit the vacuum chamber wall, producing showers. ⇒ Install:

Pb shields wherever it is possilble; vacuum pocket close to magnet exit (where there is no room for Pb-shield) guiding positrons to shielded area

γ e+ vacuum pocket

calorimeter acceptance

Pb

I.Rachek dark photon at VEPP-3 June 18, 2015 14

slide-19
SLIDE 19

The configuration accepted for Monte Carlo simulation

I.Rachek dark photon at VEPP-3 June 18, 2015 15

slide-20
SLIDE 20

Monte Carlo: energy and angular resolution

cluster 3 × 3 crystals is analyzed; threshold = 10 MeV

Signal = energy depositon + noise; noise = coherent + individual

noise parameters from CLEO paper [NIM A265(1988)258]: σcoh = 0.3 MeV, σind = 0.6 MeV

Energy resolution Angular resolution

measured simulated simulated

he

Entries 30582 Mean 0.988 RMS 0.04718

1.06 ×

γ

/E

cluster

E 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 Events 500 1000 1500 2000 2500 3000 he

Entries 30582 Mean 0.988 RMS 0.04718

he

Entries 30582 Mean 0.988 RMS 0.04718

FWHM=9.0% =180 MeV

γ

E

γ

E ∆

hd Entries 152974 Mean -0.01009 RMS 0.09172 deg

,

γ

θ −

cluster

θ

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 0.5 Events 1000 2000 3000 4000 5000 6000 7000 hd Entries 152974 Mean -0.01009 RMS 0.09172

= 50 MeV

γ

E =0.091 θ

σ

γ

θ ∆

hd Entries 7995 Mean -0.005996 RMS 0.05948 deg

,

γ

θ −

cluster

θ

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 0.5 Events 100 200 300 400 500 hd Entries 7995 Mean -0.005996 RMS 0.05948

=400 MeV

γ

E =0.059 θ

σ

γ

θ ∆

Ee+ = 180 MeV Ee+ = 180 MeV Ee+ = 50 MeV Ee+ = 400 MeV , MeV

γ

E

50 100 150 200 250 300 350 400 450

/E, %

E

σ

1 2 3 4 5 6 7 measurement (CLEO) Monte Carlo E[GeV] 1.15%+1.11%/ energy resolution

, MeV

γ

E

50 100 150 200 250 300 350 400 450

, deg

θ

σ

0.02 0.04 0.06 0.08 0.1 0.12 measurement (CLEO) Monte Carlo angular resolution I.Rachek dark photon at VEPP-3 June 18, 2015 16

slide-21
SLIDE 21

Monte Carlo: missing mass reconstruction

Data analysis is aimed at selecting events with a single cluster in the calorimeter and searching for a peak in the missing mass distribution Results for 4 values of A′-boson mass: mmiss =5,10,15,20 MeV

Entries 199575 , MeV

missing

M 2 4 6 8 10 12 14 16 18 20 22 events 1 10

2

10

3

10

4

10

5

10 Entries 199575 =20 MeV

A

M =0.2 MeV

miss

σ Entries 48540 =15 MeV

A

M =0.5 MeV

miss

σ =10 MeV

A

M =1.0 MeV

miss

σ = 5 MeV

A

M =1.9 MeV

miss

σ

Missing Mass

, MeV

miss

M

2 4 6 8 10 12 14 16 18 20 22

, MeV

miss

σ

0.5 1 1.5 2 2.5

Constant 0.05354 ± 1.293 Slope 0.007235 ±

  • 0.1343

Constant 0.05354 ± 1.293 Slope 0.007235 ±

  • 0.1343

missing mass resolution

resolution is fitted by a function: σmiss(MA)= 3.6 · e−0.13·MA [MeV]

I.Rachek dark photon at VEPP-3 June 18, 2015 17

slide-22
SLIDE 22

Monte Carlo: missing mass distributions Event selection:

Ecluster > 25 MeV; 1.5◦ < θcluster < 4.5◦; Ncluster == 1; veto on signal in positron sandwich; veot on charged particle in the calorimeter aperture;

, MeV

missing

M

2 4 6 8 10 12 14 16 18 20 22

events

2

10

3

10

4

10

5

10 = 5 MeV, veto on 2nd cluster

A

M all events background only , MeV

missing

M

2 4 6 8 10 12 14 16 18 20 22

events

2

10

3

10

4

10

5

10 =10 MeV, veto on 2nd cluster

A

M all events background only , MeV

missing

M

2 4 6 8 10 12 14 16 18 20 22

events

2

10

3

10

4

10

5

10 =15 MeV, veto on 2nd cluster

A

M all events background only , MeV

missing

M

2 4 6 8 10 12 14 16 18 20 22

events

2

10

3

10

4

10

5

10 =20 MeV, veto on 2nd cluster

A

M all events background only

set:

ε = 0.1

Cross sections, mBarn

e+pγ 21.0 e+e−γ 7.7 γγ 1.4 γγγ 0.27

reaction identifier

1 2 3 4 5 6

events

3

10

4

10

5

10

6

10

7

10

8

10

9

10

10

10

γ p

+

e γ

−

e

+

e γ γ γ γ γ A' γ

events: generated passed all cuts

I.Rachek dark photon at VEPP-3 June 18, 2015 18

slide-23
SLIDE 23

Monte Carlo: search sensitivity search conditions

Beam energy Ee+ = 500 MeV luminosity L = 1033 cm−2s−1 →

– beam current 30 mA + – target thickness 5 × 1015 at/cm2 Run time T = 107 seconds → half-year with 65% time utilization

width of search window: ±2σmis

MC results

M′

A

Mmisswindow ε2 MeV MeV (95% CL) 5 ±3.8 9.5 × 10−8 10 ±2.0 8.5 × 10−8 15 ±1.0 5.4 × 10−8 20 ±0.4 3.0 × 10−8

A′ decays to e+e−

VEPP-3

I.Rachek dark photon at VEPP-3 June 18, 2015 19

slide-24
SLIDE 24

Search sensitivity: decay mode-independent search of A’

Invisible decay of A′

2 −

10

1 −

10 1

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10 BaBar NE Φ DA DarkLight A') π → BNL (K

VEPP-3

CESR

A' is 'welcome'

µ

a A' is excluded

µ

a

e

a

(GeV)

A'

m

2 −

10

1 −

10 1

2

ε

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10

Existing constraints decay mode-independent: muon (gµ − 2) electron (ge − 2) invisible: BaBar Υ(1S) → γA′ BNL: K→ πA′ Proposed measurements L duration, s VEPP-3: 1033, 107 CESR: 1034, 107 DAΦNE: 1028, 2 · 107 DarkLight 6 · 1035 2 · 106

I.Rachek dark photon at VEPP-3 June 18, 2015 20

slide-25
SLIDE 25

Conclusion

A decay mode independent search for a dark photon is effective in a setup with an intense positron beam and an internal hydrogen gas target. Crystals from the CLEO endcap EM-calorimeter would be a good choice for the photon-detector. If the proposal is accepted the measurement at the ByPass at VEPP-3 can be prepared and performed in 3-4 years. Budker Institute has a good opportunity to contribute to the worldwide hunt for a dark photon.

length of bypassed segment of VEPP−3 = 1830 cm

V

D2

4.5

e+ CsI calorimeter D3 Q3 Q4 Q5 Q6 D1 Q2 Q1 distance = 8 m

T a r g e t

kG/cm Q2: 0.45 Q3: −0.57 Q4: 0.54 Q5: −0.19 Q6: 0.28 Q1: −0.86 ∆ D1: 12.0 L/L = 0.5% D2: 13.4 D3: 19.6 1B1B 3B8A

2 −

10

1 −

10 1

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10 BaBar NE Φ DA DarkLight A') π → BNL (K

VEPP-3

CESR

A' is 'welcome'

µ

a A ' i s e x c l u d e d

µ

a e

a

(GeV)

A'

m

2 −

10

1 −

10 1

2

ε

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10

I.Rachek dark photon at VEPP-3 June 18, 2015 21

slide-26
SLIDE 26

Conclusion

A decay mode independent search for a dark photon is effective in a setup with an intense positron beam and an internal hydrogen gas target. Crystals from the CLEO endcap EM-calorimeter would be a good choice for the photon-detector. If the proposal is accepted the measurement at the ByPass at VEPP-3 can be prepared and performed in 3-4 years. Budker Institute has a good opportunity to contribute to the worldwide hunt for a dark photon.

length of bypassed segment of VEPP−3 = 1830 cm

V

D2

4.5

e+ CsI calorimeter D3 Q3 Q4 Q5 Q6 D1 Q2 Q1 distance = 8 m

T a r g e t

kG/cm Q2: 0.45 Q3: −0.57 Q4: 0.54 Q5: −0.19 Q6: 0.28 Q1: −0.86 ∆ D1: 12.0 L/L = 0.5% D2: 13.4 D3: 19.6 1B1B 3B8A

2 −

10

1 −

10 1

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10 BaBar NE Φ DA DarkLight A') π → BNL (K

VEPP-3

CESR

A' is 'welcome'

µ

a A ' i s e x c l u d e d

µ

a e

a

(GeV)

A'

m

2 −

10

1 −

10 1

2

ε

8 −

10

7 −

10

6 −

10

5 −

10

4 −

10

THANK YOU!

I.Rachek dark photon at VEPP-3 June 18, 2015 21