The GEp-2γ Experiment at Jefferson Lab Hall-C

Transcription

1 The -γ xeriment at Jefferson Lab Hall-C JLab Users rou eeting, June 9 th, 00 ehdi ZIAN, The College of William and ar On behalf of the Jlab -γ Collaboration

2 OUTLIN Introduction Beond the Born Aroximation The -γ xeriment at Jlab: Conclusion oal Analsis Form Factor Ratio, l reliminar results

3 olarization/rosenbltuth data crisis Over the ast decade both intensive theoretical and exerimental effort have been done aiming at exlaining the Rosenbluth/olarization discreanc. The difference between the two exerimental ratios increases sstematicall with Q for Q > ev Two methods, two different results Incomlete radiative corrections? Something beond the Born Aroximation? (one hoton exchange) Rosenbluth data olarization data ossible Two-hoton exchange effect? (TX) This exeriment is a search for a kinematical deendence in t / l vs ε Jones et al., hs. Rev. Lett. 84, 398 (000); aou et al., hs. Rev. Lett. 88, 0930 (00); unjabi et al., hs. Rev. C 7, 0550 (005); uckett et al.,arxiv: (00); 3

4 Beond the Born-Aroximation arit, Wigner time reversal invariance and leton helicit conservation give the following exansion of the hadronic vertex function (not unique): (.A. uichon,. Vanderhaeghen, hs. Rev. Lett. 9, 4303 (003)) (, ') = ~ - F ~ F ~ 3. K Beond the Born Aroximation a third comlex amlitude arises. q q q q N N 4

5 Beond the Born-Aroximation arit, Wigner time reversal invariance and leton helicit conservation give the following exansion of the hadronic vertex function (not unique): (.A. uichon,. Vanderhaeghen, hs. Rev. Lett. 9, 4303 (003)) (, ') = ~ - F ~ F ~ 3. K Beond the Born Aroximation a third comlex amlitude arises. q q q q N N 4

6 Beond the Born-Aroximation arit, Wigner time reversal invariance and leton helicit conservation give the following exansion of the hadronic vertex function (not unique): (.A. uichon,. Vanderhaeghen, hs. Rev. Lett. 9, 4303 (003)) (, ') = ~ - F ~ F ~ 3. K Beond the Born Aroximation a third comlex amlitude arises. Born Arox. (Q ), F F ~ (Q,ε) 3 (Q ) = 0 Beond Born Arox. ~ (Q,ε), F ~ (Q,ε) F ~ (Q,ε) 3 q q N q q N real comlex The kinematical arameter ε is: (s - u) t(4 ε = (s - u) - t(4 - - t) t) 4

7 Beond the Born-Aroximation arit, Wigner time reversal invariance and leton helicit conservation give the following exansion of the hadronic vertex function (not unique): (.A. uichon,. Vanderhaeghen, hs. Rev. Lett. 9, 4303 (003)) (, ') = ~ - F ~ F ~ 3. K Beond the Born Aroximation a third comlex amlitude arises. Born Arox. (Q ), F F ~ (Q,ε) 3 (Q ) = 0 real Beond Born Arox. ~ (Q,ε), F ~ (Q,ε) F ~ (Q,ε) 3 comlex q q N q q N ~ (Q,ε) = (Q ) δ ~ (Q,ε) ~ (Q,ε) = (Q ) δ ~ (Q,ε) The kinematical arameter ε is: (s - u) t(4 ε = (s - u) - t(4 - - t) t) 4

8 Beond the Born-Aroximation formalism Born Arox. Transverse olarization. Longitudinal olarization. Reduced cross section. 5 } { ζ ε) ε( = r t - } { ζ - ε = r l r ε = ζ

9 Beond the Born-Aroximation formalism t = - ε( ε) ζ r { Re(δ ~ ) Re(δ ~ F ~ )} 3 O(e 4 ) l = - ε ζ r { Re( δ ~ ε ε F ~ ) 3 } O(e 4 ) ζ r = ε ε Re(δ ~ Re(δ ~ ε F ~ ) 3 F ~ ) 3 O(e 4 ) = Q Born Arox. Beond Born Arox. 5

10 Beond the Born-Aroximation formalism t = - ε( ε) ζ r { Re(δ ~ ) Re(δ ~ F ~ )} 3 O(e 4 ) l = - ε ζ r { Re( δ ~ ε ε F ~ ) 3 } O(e 4 ) ζ r = ε ε Re(δ ~ Re(δ ~ ε F ~ ) 3 F ~ ) 3 O(e 4 ) = Q Normal olarization: directl roortional to or multi-) hoton exchange n = ε( ε) ζ r Im ( δ ~ { - ε ε Im(δ ~ F ~ ) 3 } O(e F ~ ) 3 4 ) Born Arox. Beond Born Arox. 5

11 Hadronic odel Kee all nucleon intermediate states Full loo calculation using 4-oints assarino-veltman functions Direct Box Crossed Box 6

12 Hadronic odel Kee all nucleon intermediate states Full loo calculation using 4-oints assarino-veltman functions Aroximate correction Δ b a linear function of ε (over a given range): Δ a bε Δ: finite art of γ contribution relative to the IR art of o-tsai. Direct Box Crossed Box ζ R = a [ (ε / )(R ( εb/a) μ b/a)] Corrected F.F ratio R ~ - μ b/a R = ε b/a easured F.F ratio contained TX Average ε fitted over a given range 6

13 Hadronic odel Kee all nucleon intermediate states Full loo calculation using 4-oints assarino-veltman functions Aroximate correction Δ b a linear function of ε (over a given range): Δ a bε Δ: finite art of γ contribution relative to the IR art of o-tsai. Direct Box Crossed Box ζ R = a [ (ε / )(R ( εb/a) μ b/a)] Corrected F.F ratio R ~ - μ b/a R = ε b/a easured F.F ratio contained TX Average ε fitted over a given range artial reconciliation for Q 3.5 ev Inclusion of higher resonances makes almost no difference Kondratuk et al., hs.rev.lett.95 (005).Blunden et al., hs.rev.c7: 0346 (005) 6

14 artonic odel Hard scattering (H on the figure), where the TX takes lace, of letons off massless quarks Both hotons are couled to the same quark Quarks are embedded in the nucleon through the Ds (blue blob on the figure) 7

15 artonic odel Hard scattering (H on the figure), where the TX takes lace, of letons off massless quarks Both hotons are couled to the same quark Quarks are embedded in the nucleon through the Ds (blue blob on the figure) Calculations carried out using two models of Ds: - aussian D (figure) - Regge D ive similar results Agreement between olarization transfer and corrected Rosenbluth data u to Q = 3.5 ev then artial reconciliation A.Afanasev et al., hs. Rev.D7:03008 (005) 7

16 Theoretical stimates Hadronic (elastic) Dominated b correction to..blunden et al., hs.rev.c7: 0346 (005) eneral arton Distribution Dominated b F 3 correction and correction to. A.Afanasev et al., hs. Rev.D7:03008 (005) Born from / Born value calculated from the / fit of the olarization data Both theories describe Rosenbluth data but have oosite rediction for /. 8

17 QCD Calculations One hoton exchange: at least two hard gluons are exchanged between the quarks: OX amlitudes of order: s 6 Q 9

18 QCD Calculations One hoton exchange: at least two hard gluons are exchanged between the quarks: OX amlitudes of order: s 6 Q Two hoton exchange: one hard gluon exchange TX amlitudes of order: s 6 Q order relative to the Born amlitude α s 9

19 QCD Calculations One hoton exchange: at least two hard gluons are exchanged between the quarks: OX amlitudes of order: s 6 Q Two hoton exchange: one hard gluon exchange TX amlitudes of order: s 6 Q order relative to the Born amlitude α s At large Q, leading order behavior: δ ~ F~ and / 3 go as : / 4 Q δf ~ behaves as: / 6 Q 9

20 QCD Calculations One hoton exchange: at least two hard gluons are exchanged between the quarks: OX amlitudes of order: s 6 Q Two hoton exchange: one hard gluon exchange TX amlitudes of order: s 6 Q order relative to the Born amlitude α s At large Q, leading order behavior: QCDSF δ ~ F~ and / 3 go as : / 4 Q BLW COZ δf ~ behaves as: / 6 Q Calculations with 3 different roton distribution amlitudes: COZ, BLW and QCDSF N. Kivel and. Vanderhaeghen hs.rev.lett.03:09004 (009) 9

21 Ke idea: fixed Q. same sin transort. (sin recession fixed) same analzing ower. ( fixed) unlike Rosenbluth, ver small.t. sstematics: A, h cancel out in the t / l ratio. 80μA beam current. 85% ol. 0cm LH target. The -γ xeriment We look for a kinematical deendence of t / l to detect a ossible two-hoton exchange effect in the e-scattering. recision limited onl b statistics (~ 0.0 for a ratio value of 0.7) e, ev e θ, deg θ e ε range <Q >

22 Ke idea: fixed Q. same sin transort. (sin recession fixed) same analzing ower. ( fixed) unlike Rosenbluth, ver small.t. sstematics: A, h cancel out in the t / l ratio. 80μA beam current. 85% ol. 0cm LH target. The -γ xeriment We look for a kinematical deendence of t / l to detect a ossible two-hoton exchange effect in the e-scattering. recision limited onl b statistics (~ 0.0 for a ratio value of 0.7) e, ev e θ, deg θ e ε range <Q >

23 Ke idea: fixed Q. same sin transort. (sin recession fixed) same analzing ower. ( fixed) unlike Rosenbluth, ver small.t. sstematics: A, h cancel out in the t / l ratio. 80μA beam current. 85% ol. 0cm LH target. The -γ xeriment We look for a kinematical deendence of t / l to detect a ossible two-hoton exchange effect in the e-scattering. recision limited onl b statistics (~ 0.0 for a ratio value of 0.7) e, ev e θ, deg θ e ε range <Q >

24 Ke idea: fixed Q. same sin transort. (sin recession fixed) same analzing ower. ( fixed) unlike Rosenbluth, ver small.t. sstematics: A, h cancel out in the t / l ratio. 80μA beam current. 85% ol. 0cm LH target. The -γ xeriment We look for a kinematical deendence of t / l to detect a ossible two-hoton exchange effect in the e-scattering. recision limited onl b statistics (~ 0.0 for a ratio value of 0.7) e, ev e θ, deg θ e ε range <Q >

25 HS with Focal lane olarimeter Two HS drift chambers for tracking--measure roton momentum and define incident trajector for F. Scintillator hodoscoes S0 and S for trigger and timing. HS Drift Chambers S0 and S CH analzers Focal lane olarimeter - Two CH analzers, 55 cm thick - Two sets of drift chambers track rotons scattered in analzer. F Drift Chambers

26 BigCal Calorimeter 744 channels electromagnetic calorimeter easure electron angles and energ Searate elastic from inelastic background From 6.8% to 3% energ resolution ( in ev) due to radiation damage osition resolution not ver sensitive to radiation damage ~5 mm

27 f -f f HYSICAL ASYTRIS hsical asmmetries (helicit deendent) are obtained b taking the difference between the angular distributions of events of the two helicit states: f (θ, φ)-f (θ,φ) Focal lane asmmetr can be written as a sine function with a hase shift which is related to the ratio of the olarization comonents at the focal lane. f (θ - ) - f (θ - ) = Δφ Bsin( Δ) With the F, we measure the roton olarization after undergoing recession through the HS magnets. B = ha tanδ F F (t ) (n ) = - F t F n, F n Tgt l sin θ 3

28 The F.F. ratio is indeendent of the reconstructed target variables and δ for both Fs. δ: relative momentum of the sectrometer with resect to the central momentum 0 =.0676 ev/c Sin recession Check R = = - t l ( e e' ) tan e θ tgt (disersive) and φ tgt (nondisersive) are the angles at the target. ood understanding of the sin recession calculation through the sectrometer magnets. ood qualit of the COSY Sin transort matrix. 4

29 Analzing ower Tight analzer cuts Single track events selection. Correction for the energ loss in CH alied. Transverse momentum: T F loss = HS sinθ F ood stabilit of the analzing ower over the 3 kinematics. 6

30 Analzing ower Tight analzer cuts Single track events selection. Correction for the energ loss in CH alied. Transverse momentum: T F loss = HS sinθ F ood stabilit of the analzing ower over the 3 kinematics. ven if A cancels in the form factor ratio, it is an imortant quantit for the extraction of l since we measure ha l. hat (e ) e' θe R = μ = -μ tan ha 6

31 Analzing ower Tight analzer cuts Single track events selection. Correction for the energ loss in CH alied. Transverse momentum: T F loss = HS sinθ F ood stabilit of the analzing ower over the 3 kinematics. ven if A cancels in the form factor ratio, it is an imortant quantit for the extraction of l since we measure ha l. hat (e ) e' θe R = μ = -μ tan ha 6

32 Form Factor Ratio No evidence of an esilon deendence at a 0.0 level for a ratio of 0.7 in the olarization data at Q =.5 ev. odels redict a bigger correction (oosite sign) at small ε, not seen in the data. Theoretical redictions are with resect to the Born aroximation. (calculated from the fit to the olarization data) Q =.5 ev Validate the recoil olarization transfer technique to extract the roton form factor ratio.blunden et al., hs.rev.c7: 0346 (005) Radiative corrections calculated with ASCARAD ~ % A.Afanasev et al., hs.rev.d7:03008 (005) (Afanasev et.al, hs. Rev. D 64, N. Kivel and. Vanderhaeghen hs.rev.lett.03:09004 (009) 3009 (00)) Bstritski, Kuraev and Tomasi-ustafsson, hs.rev.c75: 0507 (007) 7

33 X focal lane (cm) Longitudinal olarization ε= 0.63 ε= 0.5 ε= 0.77 Y focal lane (cm) atching accetance cut : cut to match the accetance of the largest ε kinematic, to that of the ε=0.4 one. Same sin transort Normalized l / l_born to the smallest ε kinematic. Based on the assumtion that A is kinematic indeendent. 0.05% sstematic errors (oller measurements) 8

34 mirical determination of TX amlitudes Fit the ratio - μ with a constant ( ε) ε t = μ in the OX 9

35 mirical determination of TX amlitudes Fit the ratio - μ with a constant ( ε) ε t = μ in the OX Fit Born with Aε ( - ε) / / ( - ε) ε for for ε ε 0 QCD calculation 9

36 mirical determination of TX amlitudes Fit the ratio - μ with a constant ( ε) ε t = μ in the OX Fit Born with Aε ( - ε) / / ( - ε) ε for for ε ε 0 QCD calculation Fit r with a linear function in ε: a bε D 9

37 mirical determination of TX amlitudes Fit the ratio - μ with a constant ( ε) ε t = μ in the OX Fit Born with Aε ( - ε) / / ( - ε) ε for for ε ε 0 QCD calculation Fit r with a linear function in ε: a bε D xtract using the / value from t / fit 9

38 mirical determination of TX amlitudes Fit the ratio - μ with a constant ( ε) ε t = μ in the OX Fit Born with Aε ( - ε) / / ( - ε) ε for for ε ε 0 QCD calculation Fit r with a linear function in ε: a bε D xtract using the / value from t / fit Y Y γ γ Y = Re(δ ~ / ) = Re(δ ~ / ) 3 = Re(δF ~ / ) / γ 3 best constrained are at the % level, oosite sign, cancel artiall in the observables Vanderhaeghen, Kivel, uttmann 9

39 CONCLUSION The form factor ratio is indeendent of the target variables. ood stabilit of the analzing ower over the 3 kinematics. No evidence of an esilon deendence at a 0.0 level for a form factor ratio of 0.7 at Q of.5 ev. Results statisticall consistent with a constant for the longitudinal olarization observable. The γ correction to is the best constrained, the corrections to and F 3 have oosite sign and are of the order % 0

40

41 BACK-U SLIDS

42 Analzing ower CH data Dubna and aou combined fit xerimental result from the Dubna (Azhgire et al.) data. Single track events and F onl. aximum of analzing ower follows the / lab trend of the Dubna and aou results but with a sstematic shift. Track multilicit???

43 Standard Radiative Corrections

44 Analzing ower CH data Dubna and aou combined fit xerimental result from the Dubna (Azhgire et al.) data. Single track events and F onl. aximum of analzing ower follows the / lab trend of the Dubna and aou results but with a sstematic shift. Track multilicit???

45 Zclose deendence (cm) (cm) Analzer Chamber The analzing ower is not constant within the whole width of the analzer. The form factor ratio is constant within the analzer for the 3 kinematics. Dilution of the analzing ower from bad reconstructed events.

46 Reconstructed Scatterings Zclose z-coordinate of the oint of closest aroach between incident and scattered track Cone-test exhibits the razor blade shae of the events in the z- θ lan

47 Reconstructed Scatterings Distance of closest aroach (sclose), θ and φ distributions for rotons scattered in the CH analzers. eak at small angle due to Coulomb scattering. Ticall 50% as man events undergo scattering in F as in F.

48 mirical determination of TX amlitudes Fit the ratio - μ with a constant Fit Born with aε ( ε) ε ( - ε) t / = μ in the OX / ( - ε) ε for for ε ε QCD calculation 0 Fit r with a linear function in ε: a bε xtract / Y Y D γ γ Y = = / D value from Re(δ ~ Re(δ ~ / / = t ) a b ( / )( ) / 3 = Re(δF ~ / ) / γ 3 fit / ) best constrained using the are at the % level, oosite sign, cancel artiall in the observables Vanderhaeghen, Kivel, uttmann 9

49 The angular distribution is given b: N 0 FALS ASYTRIS Number of incident roton with helicit state. ε(, θ) Fraction of roton with momentum scattered with an angle θ. A (, θ) Analzing ower of the CH reaction. N f x c (, θ, ), f ε(, θ) = N [ (c 0 π s sin( )...] )cos olarization comonents at the focal lane. A )sin cos( ), s,... Fourier coefficients of helicit indeendent instrumental asmmetries. (sum of N and N -, cancelled in first order) aximizing the Likelihood function: (S ij COSY sin transort matrix elements) L( f N event (i) (i) (i) (i) (i) (i) (i) t, ) = [ hεia (Stt S )cos l l l i - hεia (Sxtt S )sin xl l i λ ] 0 i= (s A f x c Small negative correction at the nd order in the F.F. ratio for the 3 kin. : ΔR 0.0 5

50 The angular distribution is given b: N 0 FALS ASYTRIS Number of incident roton with helicit state. ε(, θ) Fraction of roton with momentum scattered with an angle θ. A (, θ) Analzing ower of the CH reaction. N f x c (, θ, ), f ε(, θ) = N [ (c 0 π s sin( )...] )cos olarization comonents at the focal lane. A )sin cos( ), s,... Fourier coefficients of helicit indeendent instrumental asmmetries. (sum of N and N -, cancelled in first order) aximizing the Likelihood function: (S ij COSY sin transort matrix elements) L( f N event (i) (i) (i) (i) (i) (i) (i) t, ) = [ hεia (Stt S )cos l l l i - hεia (Sxtt S )sin xl l i λ ] 0 i= (s A f x c Small negative correction at the nd order in the F.F. ratio for the 3 kin. : ΔR 0.0 5

51 The angular distribution is given b: N 0 FALS ASYTRIS Number of incident roton with helicit state. ε(, θ) Fraction of roton with momentum scattered with an angle θ. A (, θ) Analzing ower of the CH reaction. N f x c (, θ, ), f ε(, θ) = N [ (c 0 π s sin( )...] )cos olarization comonents at the focal lane. A )sin cos( ), s,... Fourier coefficients of helicit indeendent instrumental asmmetries. (sum of N and N -, cancelled in first order) aximizing the Likelihood function: (S ij COSY sin transort matrix elements) L( f N event (i) (i) (i) (i) (i) (i) (i) t, ) = [ hεia (Stt S )cos l l l i - hεia (Sxtt S )sin xl l i λ ] 0 i= (s A f x c Small negative correction at the nd order in the F.F. ratio for the 3 kin. : ΔR 0.0 5

52 The angular distribution is given b: N 0 FALS ASYTRIS Number of incident roton with helicit state. ε(, θ) Fraction of roton with momentum scattered with an angle θ. A (, θ) Analzing ower of the CH reaction. N f x c (, θ, ), f ε(, θ) = N [ (c 0 π s sin( )...] )cos olarization comonents at the focal lane. A )sin cos( ), s,... Fourier coefficients of helicit indeendent instrumental asmmetries. (sum of N and N -, cancelled in first order) aximizing the Likelihood function: (S ij COSY sin transort matrix elements) L( f N event (i) (i) (i) (i) (i) (i) (i) t, ) = [ hεia (Stt S )cos l l l i - hεia (Sxtt S )sin xl l i λ ] 0 i= (s A f x c Small negative correction at the nd order in the F.F. ratio for the 3 kin. : ΔR 0.0 5

53 The angular distribution is given b: N 0 FALS ASYTRIS Number of incident roton with helicit state. ε(, θ) Fraction of roton with momentum scattered with an angle θ. A (, θ) Analzing ower of the CH reaction. N f x c (, θ, ), f ε(, θ) = N [ (c 0 π s sin( )...] )cos olarization comonents at the focal lane. A )sin cos( ), s,... Fourier coefficients of helicit indeendent instrumental asmmetries. (sum of N and N -, cancelled in first order) aximizing the Likelihood function: (S ij COSY sin transort matrix elements) L( f N event (i) (i) (i) (i) (i) (i) (i) t, ) = [ hεia (Stt S )cos l l l i - hεia (Sxtt S )sin xl l i λ ] 0 i= (s A f x c Small negative correction at the nd order in the F.F. ratio for the 3 kin. : ΔR 0.0 5

54 The angular distribution is given b: N 0 FALS ASYTRIS Number of incident roton with helicit state. ε(, θ) Fraction of roton with momentum scattered with an angle θ. A (, θ) Analzing ower of the CH reaction. N f x c (, θ, ), f ε(, θ) = N [ (c 0 π s sin( )...] )cos olarization comonents at the focal lane. A )sin cos( ), s,... Fourier coefficients of helicit indeendent instrumental asmmetries. (sum of N and N -, cancelled in first order) aximizing the Likelihood function: (S ij COSY sin transort matrix elements) L( f N event (i) (i) (i) (i) (i) (i) (i) t, ) = [ hεia (Stt S )cos l l l i - hεia (Sxtt S )sin xl l i λ ] 0 i= (s A f x c Small negative correction at the nd order in the F.F. ratio for the 3 kin. : ΔR 0.0 5

55 The angular distribution is given b: N 0 FALS ASYTRIS Number of incident roton with helicit state. ε(, θ) Fraction of roton with momentum scattered with an angle θ. A (, θ) Analzing ower of the CH reaction. N f x c (, θ, ), f ε(, θ) = N [ (c 0 π s sin( )...] )cos olarization comonents at the focal lane. A f )sin cos( ), s,... Fourier coefficients of helicit indeendent instrumental asmmetries. (sum of N and N -, cancelled in first order) λ = c 0 icos i sisin aximizing the Likelihood function: (S ij COSY sin transort matrix elements) L( N event (i) (i) (i) (i) (i) (i) (i) t, ) = [ hεia (Stt S )cos l l l i - hεia (Sxtt S )sin xl l i λ ] 0 i= (s A f x i c i Small negative correction at the nd order in the F.F. ratio for the 3 kin. : ΔR 0.0 5