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Kenematic Calibration of Hypernuclear Missing Mass by using Geant4 simulationOutline:• 1, Data Generating• 2, Kenematics Calibration a) E0&P Calibration b) Angle Calibration• 3, Summerize and to do

Zhihong Ye May 8th 2009 HKS/HES Collaboration Meeting

Zhihong Ye

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1, Data Generating using Geant4 a) Optics events for intrinsic matrice fitting No other physics effects, and with perfect optics setting. Matrice fitted by optics events are used to fit the initial missing mass spectra of hypernuclei before calibration. b) Physics events With all phyiscs effects above, and change magnet fields values to get a defected optics: HKS D+0.02%, Q1+0.5%, Q2-0.5%HES D-0.02%, Q1-0.5 %, Q2+0.5% c) Sieve Slit events Carbon target, with physics effects and defected optics. For optics calibration.

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Targets :

Polyethylene (Λ & Σ), 7Li (7ΛHe), 12C (12

ΛB), 28Si (28 ΛAl),

52Cr(52 ΛV)

States: -- (G.S – Ground State, F# - Fake state, S# - Spin Flip sub state)

Λ, Σ(+76.965Mev), Quasi-free (from Carbon), Accidental

12 ΛB : G.S., F1 (+3Mev), F2 (+6Mev), F3(+10Mev) S1(+140Kev), S2(+10Mev+70Kev), Accidental

28 ΛAl : G.S, F1 (+6Mev), F2 (+12Mev), F3(+18Mev) S1(+110Kev), S2(+6Mev+220Kev), Accidental

52 ΛV: G.S., F1 (+6Mev), F2 (+12Mev), F3(+18Mev) S1(+80Kev), S2(+12Mev+320Mev), Accidental

Hypernuclei:

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Statistic

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Missing Mass reconstruction:Using EFP3 and KFP2 as focal planes. Smear the info with detectors' resolution:

Reconstruct two missing mass data sets:1, With optics effect Using intrisic matrices to fit physics events, which includes optics defect.2, Without optics effect Using matrices fitted by physics events itself, so optics defect is cancelled.

HES: x = 0.007 cm, y =0.015 cm, x' = 0.5 mrad, y' = 0.9 mradHKS: x = 0.015 cm, y =0.015 cm, x' = 0.3 mrad, y' = 0.3 mrad

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Λ

Σ

Missing Mass Spectra

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2, Kenematic Calibration

PePeMMPk

PkMME

EMM

MMMM

PePkEfMM

ee

ke

ek

00

0,

coscos

coscos

),,,cos(cos

Deviation of bounding energy of missing mass spectra depences on the offsets of beam energy, angle and momentum for both arm, given by:

where ΔcosΘk, ΔcosΘe are the offsets from central angle of HES and HKS.ΔE0 ΔPe, ΔPk are the offsets from beam energy, and central momemtum of two arms. The partial coefficients in front of those parameters represent the sensitivity to missing mass. Optics and kinematics calibrations are two separately

procedure and can be treated independently. E0&P: Angle: )',',','()cos,cos( KyKxEyExggMM ek

),,( 0 ek PPEhMM

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B.E. offset: Central momentum and beam energy offsets contribute the major part of B.E offset. The heaver mass, the bigger effect. Central angle offset only affects on low mass.

Resolution;

Effect from central angle offset is must lower than one from defected optics, specially for heavier masses. No effect from central momentum offset.

Contribution of MM offset and resolution:

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Scanning:

)'','','',''(')',',','( dKyKydKxKxdEyEydExExgdKydKxdEydExfangle

),,('),,( 0 dPePedPkPkdEEhdPedPkdEfep

Assuming there are unknown kenematic offsets from setting values ofbeam energy, central angles, central momenta of HKS and HES, correction parameters are added to ΔEx', ΔEy', ΔKx', ΔKy' and ΔE0 ΔPe, ΔPk. When values of parameters changing separately within certain range,for each combination, or said, each scanning point. A program recalculates the missing mass of each hypernuclear, and fits the B.E and width of its spectra. E&P scanning and Angle scanning are running respectively. The missing mass offset has new functions depending on correction parameters:E0&P:

Angle:

Ideally, if the correction values are equal to their corresponding offsets, missing mass deviation should be minimum. Mathematically,

0),,(

...

EdEke

ep

dPdPdEf

0)',',','( '...'

ExdEx

angle

dKydKxdEydExf

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222 /)( xxii

Chi-Squares definition:

The mathematic definition of Chi-Square is:

How to define fep and fangle? They must be:

For E&P and angle scanning, and are the mean and RMS of distributions of B.E and widthes of hypernuclei states fitting from whole scanning points.

x

mathematically correct (convergent), mass-independent, parameter-free, and so on.

12 i

i, andwhere i is event ID.

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22

22222

/)(

/)]()[(/)(

fitm

fitmm

mfit

theorytheoryfitmmfit

m

fitmmoffset

xx

xxxxxx

222 / mm

Chi-Squares definition (cont.):

Missing Mass Offset Chi-Square is mass independent, for each event:

Where ω is statistic weight. So other than Lambda and Sigma, other hypernuclei also can be involved in the calibration, even their masses are not well-known.A function can be solved with enough constrains (boundary conditions): ),,( dPedPkdEfep)',',','( dKydKxdEydExfangle

E0&P:

Angle:

Λ, Σ, 12 ΛB

Λ, Σ, 7ΛHe, 12 ΛB

Other constrains? Compensability effect in between defected Optics, central angle offset, central momentum offset and beam energy offset requires one more constratin -- I use:

m = Λ, Σ, 7ΛHe, 12 ΛB ...

m = Λ, Σ, 7ΛHe, 12 ΛB ...

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a) E0&P Calibration

)(

)(2

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12&

24

22

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2&

12

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BPE

BPE

MeVPMeVPMeVEmradKymradKxmradEymradEx

ek 8.0,0.1,2.18.2',1.3',2.1',7.2'

0

Add offsets:

Scan correction parameters dE0, dPe, dPk within range (-3MeV, +3MeV), using physics data with and without defected optics effect, respectively.

Three parameters, need three hypernucei:

Determine scanning points: Good: |dE-ΔE|<|ΔE| & |dPk-ΔPk|<|ΔPk| & |dPe-ΔPe|<|ΔPe|

Bad: |dE-ΔE|>|ΔE| or |dPk-ΔPk|>|ΔPk| or |dPe-ΔPe|>|ΔPe|

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][2 cutoffset

Cut and results:Due to compensability, Offset Chi-Square lose its uniqueness, so it can not be minimized but with a range:

To get about one hundred scan points.

With defected opticsWithout defected optics

If I plot the graphic with: ).(. 02

ekoffset PPEvs

We can see that the cut can give us one band on zero position.1i

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)(

)(2

22

12

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Angle

BHeAngle

MeVPMeVPMeVEmradKymradKxmradEymradEx

ek 8.0,0.1,2.18.2',1.3',2.1',7.2'

0 Same offsets:

Like E&P calibration, I scan correction parameters dEx', dEy', dKx', dKy' within range (-6 mrad, +6 mrad).

Four hypernuclei events data are probablly require:

With the same determination: Good: |dEx'-ΔE|x'<|ΔEx'| & ...

Bad: |dEx'-ΔEx'|>|ΔEx'| or ...

b) Angle Calibration

No working with four hypernuclei

I set all weights equal to one.

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The result by scanning data without optics effect. Work Good!The result by scanning data with optics effect. Work Bad!

Question? 1, Central angle offsets directly depends on ΔcosΘk, ΔcosΘe, or directly on ΔEx', ΔEy', ΔKx', ΔKy' ? (A function of two variables or four?)2, Need a more suitable Ω to form constrain?3, Adjust weights?4, Need to optimize optics first?5, Or ...?

Results: apply the same rule of cut as E&P

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3, Summarize and to do1, Use HKS&HES geant4 codes to generate simulation data close to real experiment data. 2, Concept of new Chi-Square definition can be explained clearly mathematically.3, New calibration method works very good on E&P part, but not for Angle calibration part.To do:1, Update Geant4 code from Kawama. Need to modify Splitter fields to continous create optics defect.2, Keep working on Angle cabliration.5, Optics calibration.