Determina)on of the Polariza)on Observables C x, C z, and P y for the Quasi- Free Mechanism in. Tongtong Cao. ! d! K. +! n. Advisor: Yordanka Ilieva

Transcription

1 Determina)on of the Polariza)on Observables, C z, and P y for the Quasi- Free Mechanism in! d! K +! n Tongtong Cao Advisor: Yordanka Ilieva

2 Main Mechanisms of! d! K +! n Quasi&free*(QF)* K + Pion*mediated*sca5ering* N p n n N N K + n ******resca5ering* K + Kn ******resca5ering* p n n p n K + K + n 2

3 Experimental Observables Helicity- dependent polarized differen)al cross sec)on for hyperon photoproduc)on off the nucleon. d ± d = d ( ± P circ cos x ± P circ C z cos z + P y cos y ) d unpol Λ self- analyzing power: α =.642 ±.3 CMS$ ŷ ˆx K +!! Λ$Rest$Frame$ ẑ ˆx/ŷ/ẑ! K p 8 < : ẑ =ˆp ŷ = ˆp ˆp K ˆp ˆp K ˆx =ŷ ẑ 3

4 The g3a Experiment Circularly polarized photon beam E e = 2 GeV; 2.65 GeV Electron beam polariza)on: up to 85% Photon beam polariza)on: [27%, 8%] Target: LD 2, unpolarized, 4 cm long, upstream of CLAS center! d! K +! n Detected in CLAS pπ 4

5 Selec)on of Quasi- Free Events Counts P X (! d! K +! X) Quasi- free mechanism # of events: Final- state interac)ons # of events: (GeV/c) p X 5

6 Background Subtrac)on MM = q (ep + ep d ep K + ep p ep ) 2 counts M n =.9396 GeV/c MM (GeV/c ) Physical Background (K + Σ, K + Σ* ) Accidental Background MM (GeV/c ) 6

7 Observable- Extrac)on Methods One- dimensional fit: Asym = Y + Y Y + + Y = RR d + d d(cos RR y)d(cos z/x ) d d d(cos y)d(cos z/x ) RR d + d d(cos y)d(cos z/x )+ RR d d d(cos y)d(cos z/x ) = P circ/z cos x/z Two- dimensional fit: Asym = Y + Y Y + + Y = R d + d d(cos R d y)) d d(cos y) R d + d d(cos y)) + R d d d(cos y) = P circ cos x + P circ C z cos z Maximum likelihood Method: PDF = d d unpol( ± P circ cos x ± P circ C z cos z + P y cos y ) 7

8 Results for and C z from Different Methods.4.2 d fit 2d fit Maximum likelihood cosθ K : [.35,.55] E γ (GeV) d fit 2d fit Maximum likelihood cosθ K : [.35,.55] C z E γ (GeV) 8

9 Comparison With gc Results.4.2 d fit 2d fit Maximum likelihood Bradford's results.2 C z E γ (GeV) Maximum likelihood.8.6 d fit 2d fit Maximum likelihood Bradford's results E γ (GeV) Mcnabb's results -.2 cosθ K : [.35,.55] Py E γ (GeV) and C z from Robert K. Bradford P y from John W.C. McNabb Dataset: gc Reac)on:! p! K +! 9

10 Simula)on Study to Understand Different Methods A study was used to evaluate poten)al bias of the maximum likelihood method and the binned methods. 6 different experiments, with 6 events in each experiment, were generated according to the differen)al polarized cross sec)on with realis)c values of, C z, and P y for! p! K +!. Generated data were processed through GSIM and gpp. Aqer raw data were skimmed, the observables were extracted using the maximum likelihood method and the binned methods d; mean=.48±.53 2d; mean=.3±.5 ML; mean=.48± d; mean=-.±.5 2d; mean=-.64±.5 ML; mean=-.26± est true C zest C ztrue

11 Simula)on Study to Compare Different Methods Mean of Obs ext -Obs true.2 C z C z P y P y for Constant acceptance for GSIM for Constant acceptance for GSIM for Constant acceptance for GSIM -.2 Maximum Likelihood d binned method 2d binned method 2 3 Fitting method

12 Examples of D Fit E γ : [.5875,.6875] GeV and cosθ K : [.35,.55] Asym χ 2 / ndf / 8 Prob 7.434e-9 p.535 ±.85 p ±.464 = slope P circ Real Data χ 2 / ndf 7.49 / 8 Prob.2542 p.474 ±.86 p.837 ±.4696 C z = slope P circ χ 2 / ndf 32.8 / 8 χ 2 / ndf 8.47 / 8. Prob 7.532e-25 p.779 ± Prob.798 p.579 ±.4822 p -.87 ±.334 p -.69 ± Simulated Data cosθ x cosθ z 2

13 Why is the Bias Small for C z from D Fit? In the spherical coordinate system: 8 < : cos x =sin cos cos y =sin sin cos z = cos cos 2 x + cos 2 y + cos 2 z = θ x, θ y, and θ z are not independent. Event yield: A( ) = A x ( ) = Z 2 Z 2 Y ± (, )=N ± N T ± (, )A(, ) Integral over ϕ: Y ± ( ) =c(a( ) ± P circ sin A x ( ) ± P circ C z cos A( )+ P y sin A y ( )) Z 2 A(, )d ; A x ( ) = A(, ) cos d ; A y ( ) = A(, ) cos d < Z 2 Asymmetry: Asym = Y + Y Y + + Y Generally, << C z, P y < C z Z 2 Z 2 A(, ) cos d < cos max A(, )d = Z 2 = P circ sin A x ( )+ P circ C z cos A( ) A( )+ P y sin A y ( ) A(, )sin d A(, )d = A( ) Therefore, Asym P circ C z cos z 3

14 Why is the Bias Large for from D Fit? Spherical coordinate system for the convenience of analysis: 8 < cos x = cos cos y =sin cos : cos z =sin sin Asymmetry: Asym = Y + Y Y + + Y d fit 2d fit Maximum likelihood Bradford's results E γ (GeV) = P circ cos A( )+ P circ C z sin A z ( ) A( )+ P y sin A y ( ) In general, is small rela)ve to C z and P y, so C z and P y terms do not cancel. Therefore, the asymmetry for is not a linear func)on of cosθ x. The effect of acceptance cannot be ignored in D fit, especially for. The situa)on with P y is somewhat in- between and C z if it s extracted by D fit. 2D fitng can reduce the effect of the acceptance to some extent. 4

15 Effect of Missing Momentum Cut C z E γ (GeV) cut at.2 GeV/c cut at. GeV/c cut at.5 GeV/c E γ (GeV).7.8 Py cosθ K : [.5,.35] The missing momentum was cut at points.2,. and.5 GeV/c E γ (GeV) 5

16 (g3 Results).4 E γ : [.9,.2434] GeV.4 E γ : [.2434,.3284] GeV.4 E γ : [.3284,.3896] GeV.4 E γ : [.3896,.4474] GeV E γ : [.4474,.4984] GeV.4 E γ : [.4984,.546] GeV.4 E γ : [.546,.5936] GeV.4 E γ : [.5936,.6446] GeV E γ : [.6446,.699] GeV E γ : [.699,.7534] GeV E γ : [.7534,.878] GeV E γ : [.878,.8656] GeV E γ : [.8656,.968] GeV.4 E γ : [.968, 2.7] GeV.4 E γ : [2.7, ] GeV.4 E γ : [2.2974, 2.6] GeV cosθ K 6

17 C z (g3 Results) E γ : [.9,.2434] GeV E γ : [.2434,.3284] GeV E γ : [.3284,.3896] GeV E γ : [.3896,.4474] GeV E γ : [.4474,.4984] GeV E γ : [.4984,.546] GeV E γ : [.546,.5936] GeV E γ : [.5936,.6446] GeV C z E γ : [.6446,.699] GeV E γ : [.699,.7534] GeV E γ : [.7534,.878] GeV E γ : [.878,.8656] GeV E γ : [.8656,.968] GeV E γ : [.968, 2.7] GeV E γ : [2.7, ] GeV E γ : [2.2974, 2.6] GeV cosθ K 7

18 P y (g3 Results) E γ : [.9,.2434] GeV E γ : [.2434,.3284] GeV E γ : [.3284,.3896] GeV E γ : [.3896,.4474] GeV E γ : [.4474,.4984] GeV E γ : [.4984,.546] GeV E γ : [.546,.5936] GeV E γ : [.5936,.6446] GeV P y E γ : [.6446,.699] GeV E γ : [.699,.7534] GeV E γ : [.7534,.878] GeV E γ : [.878,.8656] GeV E γ : [.8656,.968] GeV E γ : [.968, 2.7] GeV E γ : [2.7, ] GeV E γ : [2.2974, 2.6] GeV cosθ K 8

19 q R = C 2 x + C 2 z + P 2 y.5 E γ : [.9,.2434] GeV.5 E γ : [.2434,.3284] GeV.5 E γ : [.3284,.3896] GeV.5 E γ : [.3896,.4474] GeV E γ : [.4474,.4984] GeV E γ : [.4984,.546] GeV E γ : [.546,.5936] GeV E γ : [.5936,.6446] GeV R E γ : [.6446,.699] GeV E γ : [.699,.7534] GeV E γ : [.7534,.878] GeV E γ : [.878,.8656] GeV E γ : [.8656,.968] GeV E γ : [.968, 2.7] GeV E γ : [2.7, ] GeV E γ : [2.2974, 2.6] GeV cosθ K 9

20 Summary and Outlook Comprehensive results for, C z, and P y in the kinema)c bins of E γ ( GeV) and cosθ K (-, ) have been obtained for K+ Λ photoproduc)on off the bound proton. Fermi- mo)on does not seem to significantly influence the polariza)on observables, C z, and P y. Systema)c uncertain)es to be es)mated. Currently the discrepancy gc vs g3 is not understood. To analyze free proton data from g3. To publish results eventually. 2

21 Backup Slides 2

22 Why Study KΛ Channel? The study of nucleon resonance excita)on plays an important role in building a comprehensive picture of the strong interac)on. The theore)cal work on quark models in the intermediate energy range predicts a rich resonance spectrum. Besides have been observed in N! N scaxering experiments, those missing resonances may couple strongly to other channels, such as KΛ and KΣ channels. 22

23 ! Interests of QF Study in d! K +! n Many experimental results for! p! K +! have been published, from total cross sec)on to polariza)on observables. This study is to extract polariza)on observables for the quasi- free mechanism in! d! K +! n, where the target proton is not free, but bounded in deuterium. The comparison of results between reac)ons with free and bounded proton target can be used to test how great influence of the fermi- mo)on in the deuterium system. 23

24 Wien Angle The electron moves in a straight line but the spin precesses around the magne)c field. The rotated angle is called Wien angle which determines the degree of beam polariza)on 24

25 Photon Polariza)on The electron polariza)on for some special runs were measured by the M ller polarimeter. The polariza)on of the photon beam was calculated using the Maximon and Olson rela)on Electron Beam Polarization P e hwp=in E e : 2 GeV 2.65 GeV Wien- angle: hwp=out Run number P /P e P cir = E (E + 3 E )P e E 2 + E EE E /E e

26 Reac)on Yields Par)cle Iden)fica)on meas calc = meas β.2 Photon Selec)on p2 m2 + p 2 t = t x+.65x2-.8x (tt AGR + z + 2 (cm) ) c x-.2x2+.344x p (GeV/c) Z- Vertex Cut 3 Invariant- Mass Cut q Mp = 3 Count Counts dsc ) c calc t = (tsc 3 Counts = s 4 35 (e pp + pe )2 χ2 / ndf 4 Prob 3432 / 38 Constant.388e+5 ± 9.669e+ 2 Mean 3 6 t (ns) Sigma.6 ±..75 ± M =.57 GeV/c Z-component of vertex (cm) IM (GeV/c2)

27 Method 2 of Observable- Extrac)on: Weight for Each Event Weight = (All Backgrounds) / All counts 6 5 All Backgrounds MM (GeV/c ) 27

28 Method 2 of Observable- Extrac)on: The Maximum Likelihood Method Non- normalized Probability Density Func)on (PDF) defined from the polarized differen)al cross sec)on: PDF = d d unpol( ± P circ cos x ± P circ C z cos z + P y cos y ) Total likelihood is the product of the likelihoods for all individual events: logl = b + n + X i= log[( + P i circ cos i x + P i circc z cos i z + P y cos i y)w i ] nx log[( P j circ cos x j P j circ C z cos z j + P y cos y)w j j ] j= Next side will introduce how to set weight w i and w j for each event. 28

29 Why the Maximum Likelihood Method Can Ignore Acceptance? Non- normalized PDF with considera)on of acceptance: Total likelihood: PDF = A(, ) ± (, ;,C z,p y )w 8 Equa)on array to obtain, C z, and P y : >< >: z,p y z,p y z z,p y y = logl(,c z,p y )= n + X i= n+ P n+ P n+ P i= log[ log[ log[ n + X i= loga( i, + ( i, i;,c z,p y )w i ]+ + ( i, i;,c z,p y )w i + + ( i, i;,c z,p y )w i z + + ( i, i;,c z,p y )w i y + Acceptance is cancelled because it s independent of polariza)on observables. 29 i)+ nx loga( j, j) j= nx log[ ( j, j;,c z,p y )w j ] n P n P n P j= log[ ( j, j;,c z,p y )w j = log[ ( j, j;,c z,p y )w j z = log[ ( j, j;,c z,p y )w j y =

30 for LogLike for LogLike2 counts 8 Acc Acc2 Acc3 counts 8 Acc Acc2 Acc3 counts Comparison of 2- Track and 3- Track Topology Track est -true 3- Track est -true for LogLike4 for d for d for 2d counts 8 counts 8 Acc Acc2 Acc3 Acc Acc2 Acc3 counts 8 counts 8 Acc Acc2 Acc3 Acc Acc2 Acc3 counts est -true est -true est -true est -true for 3da for 3db for 3db for 3dc counts 8 counts 8 Acc Acc2 Acc3 Acc Acc2 Acc3 counts 8 counts 8 Acc Acc2 Acc3 Acc Acc2 Acc3 counts

31 s Conven)ons! ŷ ˆx ẑ K + K! CMS$ p 8 < : s Conven)on : ẑ =ˆp ŷ = ˆp ˆp K ˆp ˆp K ˆx =ŷ ẑ Lab$Frame$ K +! p! s Conven)on 2: s Conven)on 3: s Conven)on 4: < ẑ =ˆp < ẑ =ˆp >< ẑ = ˆp +ˆp K ŷ = ˆp ˆp K ŷ = ˆp ˆp +ˆp K ˆp K : ˆp ˆp K : ˆp ˆp K ŷ = ˆp ˆp K ˆp ˆx =ŷ ẑ ˆx =ŷ ẑ >: ˆp K ˆx =ŷ ẑ 3

32 C x E γ : [.4474,.4984] GeV.8.6 E γ : [.4984,.546] GeV.8.6 E s Convention s Convention 2 s Convention 3 s Convention cosθ KCM s Convention s Convention 2 s Convention 3 s Convention cosθ KCM E γ : [.6446,.699] GeV.8.6 E γ : [.699,.7534] GeV.8.6 E s Convention s Convention 2 s Convention 3 s Convention cosθ KCM s Convention s Convention 2 s Convention 3 s Convention cosθ KCM E γ : [.8656,.968] GeV.8.6 E γ : [.968, 2.7] GeV E.4.4.4

33 C z.2 E γ : [.4474,.4984] GeV.2 E γ : [.4984,.546] GeV.2 E γ : [ C z.6 C z.6 C z s Convention s Convention 2 s Convention 3 s Convention cosθ KCM.2 s Convention s Convention 2 s Convention 3 s Convention cosθ KCM E γ : [.6446,.699] GeV.2 E γ : [.699,.7534] GeV.2 E γ : [ C z.6 C z.6 C z s Convention s Convention 2 s Convention 3 s Convention cosθ KCM.2 s Convention s Convention 2 s Convention 3 s Convention cosθ KCM E γ : [.8656,.968] GeV.2 E γ : [.968, 2.7] GeV 33.2 E γ : [ z z z

34 P y P y E γ : [.4474,.4984] GeV s Convention s Convention 2 s Convention 3 s Convention cosθ KCM P y E γ : [.4984,.546] GeV s Convention s Convention 2 s Convention 3 s Convention cosθ KCM P y E γ : [ P y E γ : [.6446,.699] GeV s Convention s Convention 2 s Convention 3 s Convention cosθ KCM P y E γ : [.699,.7534] GeV s Convention s Convention 2 s Convention 3 s Convention cosθ KCM P y E γ : [ E γ : [.8656,.968] GeV.8.6 E γ : [.968, 2.7] GeV E γ : [ y y y

35 C y E γ : [.5875,.6875] GeV and cosθ K : [.35,.55] Real data Simulated data A.2 χ 2 / ndf 24.4 / 8.2 χ 2 / ndf 62.4 / 8. Prob p ±.77. Prob p ±.279 p ±.454 p -.45 ± cosθ z