Summary of Analysis for the Transverse Asymmetry Measurement in Δ Resonance March 13, 2015 Nuruzzaman Endorsement Talk at the Q-weak Collaboration Meeting Tech Note:

 Overview of the transverse dataset  Regressed transverse asymmetries in the N-to-Δ transition on H 2  MD sensitivities, differences and corrections  Cancellation of HCBA with IHWP  Overview of systematic uncertainties  details - two examples  Extraction of B n from measured asymmetry  polarization  background corrections  multiplicative corrections - one example  Comparison of B n with calculation  B n from off peak datasets Outline 2

Asymmetry ϕ Beam Normal Single Spin Asymmetry 3 Measured asymmetry M ( ϕ ) = N − N N + N = − B n P T.n = B n P T sin( ϕ - ϕ 0 ) ∧ n = ∧ k × k’ |k × k’| where, P T is transverse polarization Beam Normal Single Spin Asymmetries (B n ) are generated when transversely polarized electrons scatter from unpolarized targets B n is parity conserving and also known as transverse asymmetries B n = 2T 1γ × Im T 2γ |T 1γ | σ − σ σ + σ = T 1γ – amplitude for 1-photon exchange T 2γ – amplitude for 2-photon exchange Contains information about the Intermediate states of the proton B n provides direct access to the imaginary part of the two-photon exchange amplitude

Imaginary Part of the Two-Photon Exchange 4 Unique tool to study  *ΔΔ form factors Potential to measure charge radius and magnetic moment of Δ ! Physics Motivation: For p and Δ intermediate hadrons, vertices are known - except for  ΔΔ electromagnetic vertex from Carl Carlson γ *ΔΔ form factors

Transverse Data Set 5 Simulation by A.Subedi Data on both side of the inelastic peak were taken to constrain simulation Data on 3 types of targets Hydrogen Aluminum Carbon Transverse polarization: Vertical Horizontal Δ peak Other datasets: in the →Δ region (Al, C) in the →Δ region (H 2, GeV) elastic scattering (H 2, Al, C) elastic Moller scattering (H 2 ) in the DIS region (3.3 GeV) in pion photoproduction Main focus of this analysis: Inelastic e-p scattering with a Δ(1232) final state at E = 1.16 GeV Simulation at E = 1.16 GeV

Regressed Transverse Asymmetries on H 2 ~ 9% statistical measurement of regressed transverse asymmetry in the N-to-Δ transition Regressed asymmetry reg = ± (stat) ppm  Error weighted (H and V) regressed (std.) asym.  Not corrected for backgrounds and polarization 6 ~ 90 o phase offset the polarization dependence of measured asymmetry reg = raw - ∂ raw ∂T i ∆T i ∑ i Ref: Figure 3.7 (p. 12)

MD Sensitivities T i = X, X´, Y, Y´ & E reg = raw - ∂ raw ∂T i ∆T i ∑ i ∂ raw ∂T i 7 Ref: Figure 3.1 (p. 5)

Differences and Corrections T i = X, X´, Y, Y´ & E reg = raw - ∂ raw ∂T i ∆T i ∑ i Beam position differences (∆T i ) Corrections: ∂ raw ∂T i ∆T i Small corrections, compared to the size of the asymmetry 8 Ref: Figure 3.1, 3.5 (p. 6,10)

Cancellation of HCBA with IHWP 9 An Insertable Half Wave Plate (IHWP) can flip the electron spin. Inserting IHWP: Sign of some helicity correlated false asymmetries remains unchanged Physics asymmetries change sign (IN+OUT)/2 shows a good cancellation of helicity correlated false asymmetries Horizontal Transverse Ref: Figure 3.6 (p. 11)

Overview of Uncertainties on reg 10 reg = ± (stat) ± (sys) ppm uncertainty is dominated by statistics All other systematics are under control Ref: Figure 4.3 (p. 16)

Horizontal transverse Corrections were small (0.15% <<10% stat error) Vertical transverse Corrections were small (1.7% <<18% stat error) Regression scheme dependence is ~ ppm (0.1%) Horizontal Vertical Regression Scheme Dependence 11

Fit scheme dependence is ~ ppm (1.0%) Horizontal Transverse Vertical Transverse Fit Function reg H [ppm] reg H (n) – reg H (1) [ppm] 1 reg H sin( ϕ + ϕ 0 ) + C 5.343± reg H sin( ϕ + ϕ 0 ) 5.344± reg H sin( ϕ ) + C 5.303±0.533− reg H sin( ϕ ) 5.304±0.533−0.039 Fit Function reg V [ppm] reg V (n) – reg V (1) [ppm] 1 reg V cos ( ϕ + ϕ 0 ) + C 4.525± reg V cos( ϕ + ϕ 0 ) 4.510±0.806− reg V cos ( ϕ ) + C 4.458±0.807− reg V cos ( ϕ ) 4.442±0.807−0.083 Small fit scheme dependence for horizontal transverse, slightly higher for vertical transverse. Probably low statistics! The PV contamination to the transverse asymmetry is buried under this uncertainty. Fit Scheme Dependence of reg 12 C = A PV + background

Extraction of B n from Measured Asymmetry 13 Beam Normal Single Spin Asymmetry: Extracting B n from the experimental measured asymmetry by  removing false asymmetries  correcting for the beam polarization  removing background asymmetries  correcting for radiative tails and other kinematic correction Al. window background Beam line scattering Other neutral background Elastics B bi = Background asymmetries f bi = dilution factors   M total = M RC M Det M Q2 M ϕ Detector Bias Radiative Cor. Q 2 Precision Det. Acceptance  reg = raw - ∂ raw ∂T i ∆T i ∑ i = ± (stat) ± (sys) ppm

Summary of Systematic Uncertainties Extracted Physics Asymmetry 14 Beam Normal Single Spin Asymmetry: B n = ± ppm Biggest contribution is from elastic dilution Ref: Figure 5.6 (p. 26)

Extraction of Physics Asymmetry 15 Beam Normal Single Spin Asymmetry: DayIHWPAvgStat Error 51Out In Polarization from Moller polarimeter P = ± 0.28 (stat) ± 0.74 (sys)  Polarization using Møller polarimeter runs after transverse [Anc. ELOG 91]Anc. ELOG 91  Systematic uncertainty is from Run 2 studies [DocDB 1955]DocDB 1955 Polarization Correction Ref: Section 5.1 (p. 17)

Extraction of Physics Asymmetry 16 Beam Normal Single Spin Asymmetry: Error weighted (H and V) asym. reg DS-Al =8.419 ± (stat) ± (sys) ppm B Al = ± ppmf Al = ± [DocDB 2042]DocDB 2042  Corrected measured asym. for: US/DS Al windows acceptance correction polarization Background Corrections Al. window Ref: Figure 5.1 (p. 18)

Extraction of Physics Asymmetry 17 Beam Normal Single Spin Asymmetry: [J. Leacock thesis]J. Leacock thesis  Polarization independent mechanical asymmetry hence lumped with regression correction. The beamline scattering produces light in MD and there is a contribution in the dilution.  assumed 50% uncertainty in dilution to allow for azimuthal dependence f BB = ± Background Corrections Beamline scattering Ref: Section (p. 19) Expect an updated approach in near future

Extraction of Physics Asymmetry 18 Beam Normal Single Spin Asymmetry: B QTor = ± ppm f QTor = ± [DocDB 1549]DocDB 1549 Background Corrections Neutral scattering  Soft neutral background from secondary interaction of scattered electrons in the transport line  May be from Moller scattering, e-p elastic scattering. Don’t have much idea about the asymmetry, assumed to be zero with large uncertainty Ref: Section (p. 19) Expect an updated approach in near future

Extraction of Physics Asymmetry 19 Beam Normal Single Spin Asymmetry: B el = ± ppm f el = ±  Corrected asym. for √Q 2 [Anc. ELOG 59]Anc. ELOG 59  10% additional uncertainty in f el is due to discrepancy between data and simulation BNSSA in elastic e-p scattering B n el = ± (stat) ± (sys) ppm Kinematics = GeV = 7.9° = GeV 2 Background Corrections Elastic radiative tail [DocDB 1886]DocDB 1886 Ref: Section (p. 20)

Extraction of Physics Asymmetry 20 Beam Normal Single Spin Asymmetry: [Anc. ELOG 59]Anc. ELOG 59 Background Corrections Elastic radiative tail Δ peak B el = ± ppm f el = ±  10% additional uncertainty in f el is due to discrepancy between data and simulation (incomplete) Residual = (data – sim.) data Δ peak Ref: Figure 5.2,5.3 (p. 20,22)

Asymmetry is Diluted by Elastic Radiative Tail 21 Physics asymmetry depends strongly on the elastic radiative tail Careful study is ongoing Ref: Figure 5.4 (p. 23)

Extraction of Physics Asymmetry 22 Beam Normal Single Spin Asymmetry: M ϕ = ± [Anc. ELOG 44]Anc. ELOG 44 Multiplicative Corrections A single detector measures the average asymmetry over 49% of azimuth Transverse measurement uses octant asymmetries and need to correct for the octant coverage cos ϕ = cos ϕ 0 sin Δ ϕ ΔϕΔϕ Ref: Section (p. 24) Detector acceptance

Extraction of Physics Asymmetry 23 Beam Normal Single Spin Asymmetry: M RC = ± M Det = ± M Q2 = ± [DocDB 1886]DocDB 1886 [DocDB 1886]DocDB 1886 [Anc. ELOG 44]Anc. ELOG 44 M RC and M Det are used as it is from elastic transverse calculation (has minimal impact) M ϕ = ± [Anc. ELOG 44]Anc. ELOG 44 Multiplicative Corrections Ref: Section (p ) Expect an updated approach for M RC, M Det and M Q2 in near future

Summary of Systematic Uncertainties Extracted Physics Asymmetry 24 Beam Normal Single Spin Asymmetry: Kinematics = GeV = 1.2 GeV = 8.3° = GeV 2 ~ 38% measurement of transverse asymmetry in the N-to-Δ transition Ref: Figure 5.6 (p. 26) B n = ± ppm

Inelastic Transverse Asymmetry from B. Pasquini 25 The points are from B. Pasquini’s theory calculation at E beam = GeV I fit the points with a function p 0 + p 1 /θ lab

Comparing B n with Calculation 26

B n for All H 2 Dataset 27 Data on both sides of the inelastic peak were taken to better constrain the elastic dilution Residual = (data – sim.) data [ELOG 837] 6700 A 6000 A 7300 A Ref: Figure 7.1 (p. 30)

Summary 28 The measured B n in the N-to-Δ transition on H 2 at E beam = 1.16 GeV is ± ppm Working towards the improvement in systematic uncertainty Preliminary result shows agreement with a theoretical calculation Physics implications of the model needs investigation This data has potential to extract  *ΔΔ form factors

29 Backup Slides

Summary of Input Parameters 30 Beam Normal Single Spin Asymmetry:

B n With 5% Elastic Dilution Uncertainty 31 f el = ± (5%) Same dilution, with lower uncertainty

B n Using New Elastic Dilution From Hend 32 f el = ± (10%) From Hend Anc-ELOG 167: includes El H 2, DIS H 2, DS El Al, US El Al

B n Using New Elastic Dilution From Hend 33 f el = ± (5%) From Hend Anc-ELOG 167: includes El H 2, DIS H 2, DS El Al, US El Al (with 5% uncertainty)

Scaling of Elastic Asymmetry for Bkg. Corr. 34 Beam Normal Single Spin Asymmetry: B el = ± ppm Elastic asym. from Buddhini, B n = ± ± ppm [Doc-DB2017] Elastic B n ~ √Q 2 Using Q 2 el = ± (2.4% relative uncertainty) and Q 2 in = (2.4% relative uncertainty)  But B n = B n (θ,E)  Need to modify our scaling calculation

Scaling of Elastic Asymmetry for Bkg. Corr. 35 Beam Normal Single Spin Asymmetry: The impact of elastic asymmetry on B n is small

Asymmetry ϕ Beam Normal Single Spin Asymmetry Measured asymmetry: 36 M ( ϕ ) = N − N N + N = − B n P T.n = B n P T sin( ϕ - ϕ 0 ) ∧ n = ∧ k × k’ |k × k’| where, P T is transverse polarization and B n is BNSSA B n is proportional to the interference of one and two-photon exchange amplitude Provides access to the imaginary part of the two-photon exchange amplitude As part of a program of B n background studies, we made the first measurement of B n in the N-to-Δ transition using the Q-weak apparatus Unique tool to study  *ΔΔ form factors γ *ΔΔ form factors Δ Δ p e-e- e-e- γγ

e e p p γ one photon exchange e e p p γ γ two photon exchange B n and Two-Photon Exchange 37 B n = 2T 1γ × Im T 2γ |T 1γ | σ − σ σ + σ = B n ~ α EM m e /E e ~ around E e ~ 1 GeV Observable of the imaginary part of two-photon exchange process Parity conserving, time reversal invariant T 1γ – amplitude for 1-photon exchange T 2γ – amplitude for 2-photon exchange Contains information about the Intermediate states of the proton Beam Normal Single Spin Asymmetries (B n ) are generated when transversely polarized electrons scatter from unpolarized targets

Measured Asymmetry in Nuclear Targets 38 Many of these measurement are first of their kind and carry interesting physics.

Comparison of Measured Asymmetry 39 A PV in = ± 0.65 (stat) ± 0.73 (sys) ± 0.07 (blinding) ppm at Q 2 = ± GeV 2 E = GeV [J. Leacock thesis]J. Leacock thesis Inelastic PV Measurement

Two-Photon Exchange Form Factors 40 Form factors: Δ p, Δ, X p e-e- e-e- γγ p p γ Δ p γ X p γ Δ p γ Δ Δ γ + + FF TFF Don’t know This measurement will help Δ p, Δ, X p e-e- e-e- γγ p(n) π0(π+)π0(π+) Don’t know X Δ γ

Why B n =0 at θ =0 ? & Why B n is Large ? 41 σ − σ ∝ 2m e Q εLεL ε (1-ε) = 2m e Q Q ν (1-ε) 1/2 Q ν = 2m e ν (1-ε) ν el = ν in = ν min = 300 MeV + K. E. Private communication with Carl Carlson (1-ε) = ε(1/ε-1) ε -1 = 1+ 2 ν2ν2 Q2Q2 1+ tan 2 θeθe 2 = 2ε ν2ν2 Q2Q2 1+ tan 2 θeθe 2 B n = 2T 1γ × Im T 2γ |T 1γ | σ − σ σ + σ = ν = K  P K is the average incoming four-momenta of the electron P is the average outgoing four-momenta of the proton

Estimation of Beamline Background Asymmetry 42 B BB = ± ppm

Theory Expectations of B n in Elastic Scattering 43 Preliminary estimates of the uncertainties of the measurements looks promising Theory from Phys. Rev. C77, (2008) Pb data from PRL 109, (2012) Theory agree with exp. for all nuclei except Pb Bn ∝Bn ∝ AQ Z B n = 0 B n [ppm] Q [GeV] New Carbon data point Aluminum point will help to understand theory between A = 12 and A = 208 At forward angles

Contamination from PV Beam Spin Asymmetry 44 Bizzeti, Phys. Rev. C 33, 1837 (1986) derived the parity violating analyzing power in the scattering of transversely polarized nucleons from spin ½ targets Potential phase shift in B n due to B t ~ Too small to observe! From Blunden, Melnitchouk & Sachdeva B t = meme MpMp Q2Q2 MZ2MZ2 ϵ M ( ϕ ) = B t S cos( ϕ - ϕ 0 ) At Q-weak kinematics, B t ~ 0.01 ppb Elastic scattering

QTor Scan from Geant 3 Simulation 45 [Ana. ELOG 837]Ana. ELOG 837

46 Horizontal Transverse Vertical Transverse For now 1% systematic uncertainty has been assigned for nonlinearity. Will revisit the calculation with a better approach. Nonlinearity is ~ ppm (1.0%) HWP-IN HWP-OUT HWP-IN HWP-OUT Charge sensitivities vs octant Nonlinearity

47 Error is used as 2.4% of Q 2. More details in ELOG 44 (Ancillary) For transverse asymmetry B n ~ √Q 2 = m√Q 2 m = B n /√Q 2 dB n = ± (1/2) mdQ 2 /(√Q2) From GEANT-III Q 2 = ± (GeV/c) 2 at main detector e + p ==> e + n + π + no internal bremsstrahlung cross section weighted E’ = RANDOM()*(E in - M e ) + M e Q 2 = 4EE’sin 2 θ Q 2 Precision

48 Cuts on the helicity-correlated beam parameters were used to assign a systematic error that comes from shifts in the mean value of the regressed “5+1” asymmetry after cuts are applied. Cut Dependence of M

49 Horizontal Transverse Vertical Transverse Cut Allowed Stat. Shift [ppm] A M H Cut – NoCut [ppm] 7,6,5,4σ σ σ σ Cut Allowed Stat. Shift [ppm] A M V Cut – NoCut [ppm] 7,6,5,4σ σ σ σ A 2.5σ cuts on the helicity-correlated beam parameters were used to assign a systematic error that comes from shifts in the mean value of the regressed “5+1” asymmetry after cuts are applied that cannot be attributed to statistical shifts. Cut Dependence of M

50 Slug averaged sensitivities look reasonable, similar to elastic data Used slug averaged sensitivities and differences to extract corrections Slug Averaged Corrections for Vertical Transverse

51 Polarization Runlet based A PMTavg runlet [ppm] Slug based A PMTavg slug [ppm] A PMTavg runlet - A PMTavg slug [ppm] Horizontal Vertical Regressed data manually using theses slug averaged corrections (3 rd column). Runlet vs Slug Average Corr.s for V-Transverse Runlet vs Slug Avg. Correction Dependence is ~ ppm

MD1 barsum asym MD1 RR LL MD1 signal => Weights of PMTs are matched nicely S 1L/R signal W 1L/R weight 52 MD asymmetry Hor : A M sin( ϕ + ϕ 0 ) + C Ver : A M cos( ϕ + ϕ 0 ) + C MD1 PMTavg asym PolarizationA PMTavg [ppm]A barsum [ppm]A PMTavg - A barsum [ppm] Horizontal Vertical Barsum and PMTavg Asymmetries

53 Beam parameter differences look reasonably stable Differences for Vertical Transverse

54

Extraction of Physics Asymmetry 55 Beam Normal Single Spin Asymmetry: M RC = ± M Det = ± M Q2 = ± [DocDB 1886]DocDB 1886 [DocDB 1886]DocDB 1886 [Anc. ELOG 44]Anc. ELOG 44 M RC and M Det are used as it is from elastic transverse calculation (has minimal impact) M ϕ = ± [Anc. ELOG 44]Anc. ELOG 44 Multiplicative Corrections A single detector measures the average asymmetry over 49% of azimuth Transverse measurement uses octant asymmetries and need to correct for the octant coverage. cos ϕ = cos ϕ 0 sin Δ ϕ ΔϕΔϕ B n ~ √Q 2 dB n = ± (1/2) mdQ 2 /(√Q2)

B n and Two-Photon Exchange 56 γ *ΔΔ form factors Δ Δ p e-e- e-e- γγ Unique tool to study  *ΔΔ form factors Potential to measure charge radius of Δ and magnetic moment of Δ. Possibility of measuring elastic, not just transition, electromagnetic properties of Δ ! Physics Motivation: from Carl Carlson For p and Δ intermediate hadrons, vertices are known - except for  *ΔΔ electromagnetic vertex γ *ΔΔ form factors

e e p p γ one photon exchange e e p p γ γ two photon exchange B n and Two-Photon Exchange 57 B n = 2T 1γ × Im T 2γ |T 1γ | σ − σ σ + σ = Observable of the imaginary part of two-photon exchange process Parity conserving, time reversal invariant T 1γ – amplitude for 1-photon exchange T 2γ – amplitude for 2-photon exchange Contains information about the Intermediate states of the proton B n provides direct access to the imaginary part of the two-photon exchange amplitude γ *ΔΔ form factors Δ Δ p e-e- e-e- γγ Unique tool to study  *ΔΔ form factors Possibility of measuring elastic, not just transition, electromagnetic properties of Δ

Asymmetry ϕ Beam Normal Single Spin Asymmetry Measured asymmetry 58 M ( ϕ ) = N − N N + N = − B n P T.n = B n P T sin( ϕ - ϕ 0 ) ∧ n = ∧ k × k’ |k × k’| where, P T is transverse polarization Beam Normal Single Spin Asymmetries (B n ) are generated when transversely polarized electrons scatter from unpolarized targets Also known as transverse asymmetries B n ~ α EM m e /E e ~ at E e ~ 1 GeV

e e p p γ one photon exchange e e p p γ γ two photon exchange B n and Two-Photon Exchange 59 B n = 2T 1γ × Im T 2γ |T 1γ | σ − σ σ + σ = Observable of the imaginary part of two-photon exchange process Parity conserving, time reversal invariant T 1γ – amplitude for 1-photon exchange T 2γ – amplitude for 2-photon exchange Contains information about the Intermediate states of the proton B n provides direct access to the imaginary part of the two-photon exchange amplitude

Imaginary Part of the Two-Photon Exchange 60 Unique tool to study  *ΔΔ form factors Potential to measure charge radius of Δ and magnetic moment of Δ ! Physics Motivation: For p and Δ intermediate hadrons, vertices are known - except for  ΔΔ electromagnetic vertex from Carl Carlson γ *ΔΔ form factors

Inelastic Transverse Asymmetry from B. Pasquini 61