Proton form factors: Interesting at all scales

Proton form factors: Interesting at all scales

Jan C. Bernauer

SPhN Seminar Saclay, October 2013

OL MPUS

1

Overview

MotivationHigh Q2: Two-Photon-ExchangeMiddle Q2: Pushing the precision boundaryLow Q2: The size of the protonNew data

2

What is a proton?

2rconfinement

π

π

π

3

Cross section and form factors for elastic e-pscattering

The cross section:(dσdΩ

)(

dσdΩ

)Mott

=1

ε (1 + τ)

[εG2

E

(Q2)

+ τG2M

(Q2)]

with:τ =

Q2

4m2p, ε =

(1 + 2 (1 + τ) tan2 θe

2

)−1

Fourier-transform of GE , GM −→spatial distribution(Breit frame)

⟨r2E

⟩= −6~2 dGE

dQ2

∣∣∣∣Q2=0

⟨r2M

⟩= −6~2 d (GM/µp)

dQ2

∣∣∣∣Q2=0

4

Unpolarized: Rosenbluth

0.001

0.01

0.1

1

10

100

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Q2/(G

eV/c)2

YearAndivahisBartelBergerBernauer

BorkowskiBostedChristyGoitein

JanssensLittPriceQattan

RockSillSimonStein

Walker

5

Polarized: Ratio

0.001

0.01

0.1

1

10

100

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Q2/(GeV

/c)

2

Yearunpolarized

CrawfordDieterich

GayouJones

MacLachlanMezianeMilbrath

PospischilPuckett

PunjabiRon

Zhan

6

Large Q2

Q2Q2

Q2

7

Ratio: Difference!

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6 7 8 9 10

µpG

E/G

M

Q2/(GeV/c)2

Rosenbluth Polarization

8

Most likely solution: Two Photon Exchange

2

=⇒ + +

2

Two-Photon-Exchange

Not in standardradiative correctionsOff-shell proton!How to handle highmomenta in loop?

MeasurementRosenbluth/polarizedreconciled?How to treat thehadron line?

9


2

=⇒ + +

2

Two-Photon-Exchange



10


2

=⇒ + +

2

Two-Photon-Exchange



11

Measure TPE

Interference termchanges sign withlepton sign!Measured in the 1960sNot much dataA lot of predictions!

e+/e

−-

ratio

ε

Yount+Pine 1962Browman 1965

Mar 1968Bouquet 1968

Yang phen.Guttmann phen.

AfanasevBlunden (g.s.)

Blunden (g.s. + ∆)Borisyuk (g.s.)

Gorchtein (inel.)

0.95

1

1.05

1.1

1.15

1.2

0 0.2 0.4 0.6 0.8 1

12

Three modern experiments

Novosibirsk/VEPP-3

Analysis inprogress1.6/1 GeV beamNo magneticfield

CLAS/Jlab

Analysis inprogresse− to γ to e+/−

-beam

OL MPUS

Doris/DESY2 GeV beamdata takingfinished 01/2013

13

The OLYMPUS collaboration

Arizona State University, USADESY, Hamburg, GermanyHampton University, USAINFN, Bari, ItalyINFN, Ferrara, ItalyINFN, Rome, ItalyMIT Laboratory for Nuclear Science, Cambridge, USASt. Petersburg Nuclear Physics Institute, St. Petersburg,RussiaUniversity of Bonn, Bonn, GermanyUniversity of Glasgow, United KingdomUniversity of Mainz, Mainz, GermanyUniversity of New Hampshire, USAYerevan Physics Institute, Armenia

14

At DESY: DORIS

15

Projected performance

e+/e

−-

ratio

ε

Yount+Pine 1962Browman 1965

Mar 1968Bouquet 1968

Olympus projected

Yang phen.Guttmann phen.

AfanasevBlunden (g.s.)

Blunden (g.s. + ∆)Borisyuk (g.s.)

Gorchtein (inel.)

0.95

1

1.05

1.1

1.15

1.2

0 0.2 0.4 0.6 0.8 1

2 GeV beam, Q2-range: 0.6 to 2.2 GeV2

16

Target / Vacuum

Beam direction

17

Open cell designCryogenicTarget density: 3 · 1015 cm−2

Multi-stage pump system

Toroid

18

From BLAST±5000 A = 75% of BLAST=⇒ Peak field: 2.8 kG8 coils

4 shown

Toroid

19

From BLAST±5000 A = 75% of BLAST=⇒ Peak field: 2.8 kG8 coils4 shown

Wire chamber

20

From BLASTHDC design, 3 signalwirescompletely rewired2 · 3 planes / chamber,3 chambers / side10 stereo angle

Time Of Flight

21

From BLASTRewrapped, testedTrigger

Top/bottom coinc.kinematicallyconstrained

+ 2nd level WC

Time Of Flight

22

From BLASTRewrapped, testedTrigger

Top/bottom coinc.kinematicallyconstrained+ 2nd level WC

Luminosity

23

Tight control crucial!Redundant systems:

12-detector(Hampton, PNPI)SymmetricMøller/Bhabha (Mainz)

12-detector

umin

24

3 GEM (Hampton) + 3MWPC (PNPI) eachhighly redundantSiPM triggerscintillators

Symmetric Møller/Bhabha

25

2×9 crystals (Mainz)1.3 symmetric anglehigh rate, no deadtime

Timeline

OLYMPUS full proposal September 2008Experiment funded by DOE January 2010BLAST moved to Germany Spring 2010Target test experiment February 2011Drift chambers installed Spring 2011Luminosity monitors installed Summer 2011Olympus roll-in July 2011First full Olympus test August 2011Sym. Møller/Bhabha installed Fall 2011First data run January 2012Second data run October-December 2012DORIS shut down January 2013

26

Luminosity

Inte

grat

edLu

min

osity

[fb−1]

Date

Electron, positive toroid: 1.93 fb−1

Positron, positive toroid: 1.96 fb−1

Electron, negative toroid: 0.24 fb−1

Positron, negative toroid: 0.32 fb−1

Total: 4.45 fb−1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Jan ’12 Mar ’12 May ’12 Jul ’12 Sep ’12 Nov ’12 Jan ’13

Exceeded goal for integrated luminosity: > 4 fb−1

27

Analysis

CAVEAT: The analysis has just started. All plots arepreliminary.

28

Analysis software stack: Cooker

Xerces-C, XQilla Root, CLHEP, Geant4

Chef Plugin

FrontendsCommandlineGUI...

Plugins

IndependentOne for each detectorCan be chained

29

Plugin System

Raw

data

SlowCtrl

Time Of Flight

Wire Chamber

LumiGEM

MWPC

Møller

LumiTrack

TrackFit

eP elastic

Pions

...

30

Symmetric Møller - Coincidence

Ener

gyrig

ht[a

.u.]

Energy left [a.u.]

0

50

100

150

200

250

0 50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

4000

4500

5000


31

Symmetric Møller - Coincidence

Ener

gyrig

ht[a

.u.]

Energy left [a.u.]

0

50

100

150

200

250

0 50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

4000

4500

5000


32

Symmetric Møller - Left MasterEn

ergy

right

[a.u

.]

Energy left [a.u.]

0

50

100

150

200

250

0 50 100 150 200 2501

10

100

1000

10000

100000

1e+06

Sym. M/B

Rndm. M/B + ep

Rndm. ep + M/B

Rndm. ep + ep

Single ep

Cross check!Can detect lepton from lepton-proton scatteringCross check for energy calibrationCross check for rate estimate

33


ergy

right

[a.u

.]

Energy left [a.u.]

0

50

100

150

200

250

0 50 100 150 200 2501

10

100

1000

10000

100000

1e+06

Sym. M/B

Rndm. M/B + ep

Rndm. ep + M/B

Rndm. ep + ep

Single ep


34


ergy

right

[a.u

.]

Energy left [a.u.]

0

50

100

150

200

250

0 50 100 150 200 2501

10

100

1000

10000

100000

1e+06

Sym. M/B

Rndm. M/B + ep

Rndm. ep + M/B

Rndm. ep + ep

Single ep


35

Wire chamber / Event-Display

36

Reconstructed proton momentum(p(θ)−pmeasured) p

roton

[MeV

]

Proton scattering angle

"ep.dat" u 1:2:3 index 146

0

500

1000

1500

2000

0 20 40 60 80 1000

100

200

300

400

500

600

700

800

PRELIMINARY!Will change!Small subset of data from first run.

37

Middle Q2

Q2Q2

Q2

38

Motivation: Structure

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

GE

P/G

dip

ole

Q / (GeV/c)

totalsmooth

Simon et al.Price et al.

Berger et al.Hanson et al.

polarisation data

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

GM

P/(

µpG

dip

ole

)

Q / (GeV/c)

totalsmooth

Hoehler et al.Janssens et al.

Berger et al.Bartel et al.

Walker et al.Litt et al.

Andivahis et al.Sill et al.

-0.1

-0.05

0

0.05

0.1

0.001 0.01 0.1 1 10

GE

P-G

EP

,sm

ooth

Q2 / (GeV/c)

2

total-smoothSimon et al.Price et al.

Berger et al.Hanson et al.

polarisation data

-0.1

-0.05

0

0.05

0.1

0.001 0.01 0.1 1 10

GM

P-G

MP

,sm

ooth

Q2 / (GeV/c)

2

total - smoothHoehler et al.

Janssens et al.Berger et al.Bartel et al.

Walker et al.Litt et al.

Andivahis et al.Sill et al.

(see J. Friedrich and Th. Walcher, Eur. Phys. J. A 17 (2003) 607)39

High-precision p(e,e’)p measurement at MAMI

Three spectrometer facility of the A1 collaboration:

40

Design goal: High precision

Statistical precision: 20 min beam time for <0.1%

Control of luminosity and systematic errors:

Redundancy!

Redundant beam current measurementFoerster probe⇐⇒ pA-meter

Redundant luminosity:current × density × target length⇐⇒ spectrometer asmonitor

Overlapping acceptanceWhere possible: Measure at the same scatteringangle with two spectrometers

41

Design goal: High precision through redundancy

Statistical precision: 20 min beam time for <0.1%Control of luminosity and systematic errors:

Redundancy!




42



Redundancy!




43



Redundancy!




44

Measured settings

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

0.04

0.16

0.36

0.64

1

1.44

Q [G

eV

/c]

Q2

[(G

eV

/c)2

]

ε

Spectrometer A limitSpectrometer B limitMAMI min. E= 180 MeVMAMI-C max. E=1.53 GeV

MAMI-B max. E= 855 MeVSpectrometer ASpectrometer BSpectrometer C

1400 settings

45

How to extract the form factors?

Two methods:1 Classical Rosenbluth separation

0 0.2 0.4 0.6 0.8 1

σred.

ε

τG2M

G2E

2 ”Super-Rosenbluth separation”: Fit of form factormodels directly to the measured cross sections

Feasible due to fast computers.All data at all Q2 and ε values contribute to the fit, i.e.full kinematical region used, no projection (to specificQ2) needed.Easy fixing of normalization.

Model dependence?

For radii extraction: Needs a fit anyway!Classical Rosenbluth: Extracted GE and GM highlycorrelated! =⇒Error propagation very involved.

46


Two methods:1 Classical Rosenbluth separation2 ”Super-Rosenbluth separation”: Fit of form factor

models directly to the measured cross sections

Feasible due to fast computers.All data at all Q2 and ε values contribute to the fit, i.e.full kinematical region used, no projection (to specificQ2) needed.Easy fixing of normalization.

Model dependence?


47




Feasible due to fast computers.All data at all Q2 and ε values contribute to the fit, i.e.full kinematical region used, no projection (to specificQ2) needed.Easy fixing of normalization.Model dependence?


48




Feasible due to fast computers.All data at all Q2 and ε values contribute to the fit, i.e.full kinematical region used, no projection (to specificQ2) needed.Easy fixing of normalization.Model dependence?


49

Models

Dipole, double DipoleFriedrich / Walcher phenomenological ansatzextended Gari-Krümpelmann (VMD), Lomon et al.Polynomials (+/× dipole)Splines

50

Cross sections: 180 MeV

0.96

0.97

0.98

0.99

1

1.01

1.02

0 0.02 0.04 0.06 0.08 0.1

σe

xp/σ

std

. d

ipo

le

Q2 [(GeV/c)

2]

PolynomialPoly. + dipPoly. × dip

Inv. poly.Spline

Spline × dipFriedrich-Walcher

Double dipoleExtended G.K.

51


0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

0 0.05 0.1 0.15 0.2 0.25

σe

xp/σ

std

. d

ipo

le

Q2 [(GeV/c)

2]


Inv. poly.Spline



52


0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

σe

xp/σ

std

. d

ipo

le

Q2 [(GeV/c)

2]


Inv. poly.Spline



53


0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

0 0.1 0.2 0.3 0.4 0.5 0.6

σe

xp/σ

std

. d

ipo

le

Q2 [(GeV/c)

2]


Inv. poly.Spline



54


0.95

1

1.05

1.1

1.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

σe

xp/σ

std

. d

ipo

le

Q2 [(GeV/c)

2]


Inv. poly.Spline



55


0.95

1

1.05

1.1

1.15

1.2

0 0.2 0.4 0.6 0.8 1

σexp/σ

std

. dip

ole

Q2 [(GeV/c)

2]


Inv. poly.Spline



56

GE

0.8

0.85

0.9

0.95

1

1.05

1.1

0 0.2 0.4 0.6 0.8 1

GE/G

std

. dip

ole

Q2 [(GeV/c)

2]

Spline + stat. error + exp. syst. error + theo. syst. errorF.-W. fit

Arrington et al.F.-W. 2003Christy et al.Simon et al.Price et al.

Berger et al.Hanson et al.Borkowski et al.Janssens et al.Murphy et al.

57

GE - low Q2

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

0 0.05 0.1 0.15 0.2 0.25 0.3

GE/G

std

. dip

ole

Q2 [(GeV/c)

2]


Arrington et al.F.-W. 2003Christy et al.Simon et al.Price et al.

Berger et al.Hanson et al.Borkowski et al.Janssens et al.Murphy et al.

58

GM

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

0 0.2 0.4 0.6 0.8 1

GM

/(µ

pG

std

. dip

ole

)

Q2 [(GeV/c)

2]


Arrington et al.F.-W. 2003Christy et al.Price et al.Berger et al.

Hanson et al.Borkowski et al.Janssens et al.Bosted et al.Bartel et al.

59

GE/GM

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0 0.2 0.4 0.6 0.8 1

µpG

E/G

M

Q2 [(GeV/c)

2]


Arr. et al. w/o TPEArr. et al. w/ TPEF.-W. 2003Crawford et al.Gayou et al.Milbrath et al.Punjabi et al.

Jones et al.Pospischil et al.Dieterich et al.Ron et al.(updated)Zhan et al.

60

Inclusion of world data

Extend data base with world data=⇒ Cross check, extend Q2 reach

Take cross sections from Rosenbluthexp’sSidestep unknown error correlation

Update / standardize radiativecorrectionsOne normalization parameter persource (Andivahis: 2)

Two models:

Splines with variable knot spacing=⇒ Adapt knot density to datadensityPadé-Expansion=⇒ Low(er) flexibility, for comparison

L. Andivahis et al.,Phys. Rev. D50, 5491 (1994).

F. Borkowski et al.,Nucl. Phys. B93, 461 (1975).

F. Borkowski et al.,Nucl.Phys. A222, 269 (1974).

P. E. Bosted et al.,Phys. Rev. C 42, 38 (1990).

M. E. Christy et al.,Phys. Rev. C70, 015206 (2004)

M. Goitein et al.,Phys. Rev. D 1, 2449 (1970).

T. Janssens et al.,Phys. Rev. 142, 922 (1966).

J. Litt et al.,Phys. Lett. B31, 40 (1970).

L. E. Price et al.,Phys. Rev. D4, 45 (1971).

I. A. Qattan et al.,Phys. Rev. Lett. 94, 142301 (2005).

S. Rock et al.,Phys. Rev. D 46, 24 (1992).

A. F. Sill et al.,Phys. Rev. D 48, 29 (1993).

G. G. Simon et al.,Nucl. Phys. A 333, 381 (1980).

S. Stein et al.,Phys. Rev. D 12, 1884 (1975).

R. C. Walker et al.,Phys. Rev. D 49, 5671 (1994).

61


Extend data base with world data=⇒ Cross check, extend Q2 reachTake cross sections from Rosenbluthexp’sSidestep unknown error correlation


Two models:

















62


Extend data base with world data=⇒ Cross check, extend Q2 reachTake cross sections from Rosenbluthexp’sSidestep unknown error correlation


Two models:

















63

It works!

-8%

-6%

-4%

-2%

0%

+2%

+4%

+6%

+8%

0.01 0.1 1 10

∆σ

Q2[(GeV/c)2]

64

Model dependence

Vary spline model knots

Select the 68% best tries.

Construct envelope ofmodels.

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

2050 2100 2150 2200 2250 2300

Den

sity

M2

nominal knots Padé fit

68%

Band will cover at least 68% of all model variations!

65

Form factor ratio GE/GM

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

µpG

E/G

M

Q2[(GeV/c)2]

Difference between polarization data andRosenbluth dataAdd polarization data as a constraint to the fit:=⇒ ∆χ2 = 216 for 67 new data points!

66


-0.5

0

0.5

1

1.5

0 2 4 6 8 10

µpG

E/G

M

Q2[(GeV/c)2]

Polarization data


67


-0.5

0

0.5

1

1.5

0 2 4 6 8 10

µpG

E/G

M

Q2[(GeV/c)2]

Polarization data


68

Two Photon Exchange - A parametrisation

Available data is sparseMostly Q2 dependenceFew data on ε dependence

Only possible to fit simple modelIn addition to Feshbach Coulomb-correction!

δ = a · (1− ε) · log(

1 + b ·Q2)

69

Two Photon Exchange - A parametrisation

Available data is sparseMostly Q2 dependenceFew data on ε dependenceOnly possible to fit simple modelIn addition to Feshbach Coulomb-correction!

δ = a · (1− ε) · log(

1 + b ·Q2)

70

GE fit incl. polarized data

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

GE/G

std.dip.

Q2[(GeV/c)2]

71

GE fit incl. polarized data

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

GE/G

std.dip.

Q2[(GeV/c)2]

SplinePadé

Arrington 07

72

GM fit incl. polarized data

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 2 4 6 8 10

GM/(µpG

std.dip.)

Q2[(GeV/c)2]

73

GM fit incl. polarized data

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 2 4 6 8 10

GM/(µpG

std.dip.)

Q2[(GeV/c)2]

SplinePadé

Arrington 07

74

GE/GM fit incl. polarized data

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

µpG

E/G

M

Q2[(GeV/c)2]

75

GE/GM fit incl. polarized data

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

µpG

E/G

M

Q2[(GeV/c)2]

SplinePadé

Arrington 07Polarization data

76

Low Q2

Q2Q2

Q2

77

Radius

0.740.760.780.8

0.820.840.860.880.9

0.92

<r E

>[fm

]

CO

DAT

A’0

2

Mel

niko

v’0

0

Ude

m’9

7

Blu

nden

’05

Sick

’03

Ros

enfe

lder

’00

Mer

gell

’96

Won

g’9

4

Esch

rich

’01

McC

ord

’91

Sim

on’8

0

Bor

kow

ski’

75

Aki

mov

’72

Frer

ejac

que

’66

Han

d’6

3

78

Electric and magnetic radius

Final result from flexible models

⟨r2E

⟩ 12

=0.879± 0.005stat. ± 0.004syst. ± 0.002model ± 0.004group fm,⟨r2M

⟩ 12

=0.777± 0.013stat. ± 0.009syst. ± 0.005model ± 0.002group fm.

Results with world data ⟨r2E

⟩ 12

⟨r2M

⟩ 12

+ Rosenbluth data 0.878 0.772+Rosenbluth and Polarization data 0.878 0.769

(Eur.Phys.J. D33 (2005) 23-27: Zemach and magneticradius of the proton from the hyperfine splitting inhydrogen: 0.778(29) fm)

79

Electric and magnetic radius

Final result from flexible models

⟨r2E

⟩ 12

=0.879± 0.005stat. ± 0.004syst. ± 0.002model ± 0.004group fm,⟨r2M

⟩ 12

=0.777± 0.013stat. ± 0.009syst. ± 0.005model ± 0.002group fm.

Results with world data ⟨r2E

⟩ 12

⟨r2M

⟩ 12

+ Rosenbluth data 0.878 0.772+Rosenbluth and Polarization data 0.878 0.769

(Eur.Phys.J. D33 (2005) 23-27: Zemach and magneticradius of the proton from the hyperfine splitting inhydrogen: 0.778(29) fm)

80

Lamb Shift: muonic Hydrogen

81

Timeline of proton radius results (current)

0.740.760.780.8

0.820.840.860.880.9

0.92

<r E

>[fm

]

CO

DAT

A’0

6

CO

DAT

A’0

2

Mel

niko

v’0

0U

dem

’97

Blu

nden

’05

Sick

’03

Ros

enfe

lder

’00

Mer

gell

’96

Won

g’9

4

Esch

rich

’01

McC

ord

’91

Sim

on’8

0B

orko

wsk

i’75

Aki

mov

’72

Frer

ejac

que

’66

Han

d’6

3

Bel

ushk

in’0

6

Ber

naue

r’1

0Poh

l’10

Ant

ogni

ni’1

3

Paz

’10

Lore

nz’1

2Zh

an’1

1

82

Puzzle!

[fm]ch

Proton charge radius R0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

H spectroscopy

scatt. Mainz

scatt. JLab

p 2010µ

p 2013µ electron avg.

σ7.9

Many ideasSome disprovedNone acceptedNeed more data

83

New Data!

Hyperfine measurements:

Heavier Nucleielectronic Hydrogen

Radius from scattering

Deuterium (Mainz)Proton: ISR (Mainz), Smallangle scattering (JLab)

Form factors

Low Q2 polarized (JLab)MAMI-C (1.6 GeV)High precision crosssection at high Q2 (JLab)

Two photon exchange

VEPP-3JLabOlympus

Interesting at all scales

Precision measurements drive precise understanding(through puzzles!)

RadiusTwo photon exchange

More data will come84

Proton form factors: Interesting at all scales

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