Measurement of Generalized Form Factors near the Pion Threshold

Measurement of Generalized Form Factors near the Pion Threshold
In high momentum transfer square Sep. 26, 2009 CLAS Hadron Spectroscopy Meeting What we can learn from this experiment ? What is the meaning of Q2 dependence ? K. Park

CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Previous Summary and plans * Last collaboration Jun. 2009 First time extracting preliminary E0+/GD multipole near the pion threshold through nπ+ channel Real part contribution is dominated In experiment side : - Asymmetry data is important to determine L0+ - Cross check is needed by multipoles analysis - Direct use the F.F. of Gmn from CLAS instead parameterization In theory side : - Second order correction of pion mass - More serious study for error estimation (one-loop correction) - Improved radiative correction in sum rule - DA’s parameters from LQCD become available In this analysis, acceptance and radiative corrections are issued for this kinematic regime. We verified these issues with careful study, Pion threshold region : real part that is BG contribution should be strong which mean imaginary part of resonance contribution is strongly supressed. This summary has been driven last June CLAS collaboration meeting, snd Today I would like to givr you an update report. Expasion of pion mass involve the two parameters: m_pi/M_N and m_piQ^2/m_N^3 CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Previous Summary and Plans * Today’s Sep. 2009 First time extracting preliminary E0+/GD multipole near the pion threshold through nπ+ channel Real part contribution is dominated In experiment side : - Asymmetry data is important to determine L0+ - Cross check is needed by multipoles analysis - Direct use the F.F. of Gmn from CLAS instead parameterization In theory side : - Second order correction of pion mass - More serious study for error estimation (one-loop correction) - Improved radiative correction in sum rule - DA’s parameters from LQCD become available Long term plan with high stat. data Since I would like to give you an update report based on works during last couple of months. I want to remind you what I could check as an cross check. Mulatipole analysis Direct use of FF of Gmn from CLAS measurement. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Quick Review... If we take into account near pion threshold region and pion angular momentum up to 1. Six amplitudes could be written with 7 multipoles like E0+, E1+, M1+,M1-, S0+, S1- ans S1+ And helicity amplitudes are consist of six amplitudes functions with its angle. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Perspective of soft pion in terms of Q2 at threshold Q2=0 GeV2 Low-Energy Theorem (LET) for Q2=0 1954 Kroll-Ruderman Restriction to the charged pion Chiral symmetry + current algebra for electroproduction 1960s Nambu, Laurie, Schrauner Q2 << Λ/mπ ~ 1GeV2 1970s Re-derived LETs Vainshtein, Zakharov Current algebra + PCAC 1990s Chiral perturbation theory Scherer, Koch Q2~ GeV2 ??? Question is already arised in the intermid-state of energy or momentum transfer square. This analysis has been studied with LCSR frame work which allows us to access relatively high Q2 region between 1 and 10GeV2. LCSR is the extension of stand QCD sum rule which allows us to access high Q2 region and to interpret the soft contribution to hardon form factor in terms of DA’s that enter into pQCD calculation witout any non-perturbative parameters. Q2 >> Λ/mπ pQCD factorization methods Brodsky, Lepage, Efremov, Radyunshkin, Pobylitsa, Polyakov, Strikman, et al CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

LCSR (Light Cone Sum Rule) Constructed relating the amplitude for the radiative decay of Σ+(pγ) to properties of the QCD vacuum in alternating magnetic field. An advantage of study because soft contribution to hadron form factor can be calculated in terms of DA’s that enter pQCD calculation without other nonperturbative parameters. New technique : the expansion of the standard QCD sum rule approach to hadron properties in alternating external fields. Em current operator acts on nucleon wave function with different momenta p and p’, this could be written by separable two term if applying chiral limit (m_pi-> 0). But involves ambiguities in contribution pion mass. S-wave dominance contribution in pion threshold expected in large momentum transfer from corresponding predictions of LET and suggestion from QCD model should be applicable in the intermediate Q2 region. In contrast, P-wave contribution for all Q2 are dominated in pion mass -> 0 by the pion emission from the final state nucleon. This expression is not suitable a transition to photoproduction limit due to breaking gauge invariance....[V.Braun] CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Differential Cross Section No D-wave contribution CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Legendre moments vs. Form Factors V. Braun PRD 77(2008) CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Prediction LCSR symbol index Dashed Lines : pure LCSR Solid Lines : LCSR using experimental EM form factor as input Let’s say....Pure calculation and advanced calculation : pure means pure theoretical calculation and advanced mean pure calculation + form factor parametrization from experimental result. As it shown alreay, the difference is about more or less 20% depending on Q2 region. Since first time LCSR calculation is about order of magnitude level prediction. Once experimental form factors as its input the deviation is around 30% .... Therefore, experimental measurement and extraction are crucial. Or at least experimental result give them more precise calculation by providing strong constraint. Upper : Electric Lower : Longitudinal partial wave at threshold normalized to the dipole fomular LCSR has an advantage of study because soft contribution to hadron form factor can be calculated in terms of DAs that enter pQCD calculation without other nonperturbative parameters. LCSR : sum rule are constructed relating the amplitude for the decay Sigma+ to proton gamma to properties of the QCD vacuum in alternating magnetic field. This is new technique : the expansion of the standard QCD sum rule approach to hadron properties in alternating external fields. Alternatively, using string operator expansion in singularities near light cone to Wilson expansion in local operator. From the theory point of view, the interest is because in the approximation of pion mass to ZERO , chiral symmetry supplimented by the current algebra allows one to predict the threshold cross section, LET V. M. Braun et al., Phys. Rev. D 77:034016, 2008. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

LCSR Preliminary Q2 dependence of the Normalized E0+ Multipole by dipole F. F. Using…. Measurement of differential cross sections Extract structure functions (s T+L, s TT, s LT) Extract Legendre moments Plug into LCSR… Assumption of Im(G2)=y2=0 Assumption of GEn =0 Preliminary Red lines : LCSR solid line : pure calc. dash line :exp. F. F. input Blue line : MAID07, E0+ Black MAId07 L0+ CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Alternative way to extract multipoles near pion threshold region ?
Question ??? Alternative way to extract multipoles near pion threshold region ? If we take into account near pion threshold region and pion angular momentum up to 1. Six amplitudes could be written with 7 multipoles like E0+, E1+, M1+,M1-, S0+, S1- ans S1+ And helicity amplitudes are consist of six amplitudes functions with its angle. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Multipoles Analysis I. G. Aznauryan, PRD 57, 2727 (1998) Using six amplitudes ( Fi ) : ** if lπ = 1 F1 = E0+ + 3*cos(θ)*(E1+ + M1+) F2 = 2*M1+ + M1- F3 = 3*(E1+ - M1+) F4 = F5 = S0+ + 6*cos(θ)*S1+ F6 = S1- - 2*S1+ Helicity amplitudes ( Hi ) : H1 = (-1/sqrt(2))*cos(θ/2)*sin(θ)*(F3 + F4) H2 = -1*sqrt(2)*cos(θ/2)*(F1 - F2 - sin(θ)*(F3 - F4)) H3 = (1/sqrt(2))*sin(θ/2)*sin(θ)*(F3 - F4) H4 = sqrt(2)*sin(θ/2)*(F1 + F2 +(cos(θ/2))**2*(F3 + F4)) H5 = -1*(sqrt(Q2)/abs(k_cm))*cos(θ/2)*(F5 + F6) H6 = (sqrt(Q2)/abs(k_cm))*sin(θ/2)*(F5 - F6) If we take into account near pion threshold region and pion angular momentum up to 1. Six amplitudes could be written with 7 multipoles like E0+, E1+, M1+,M1-, S0+, S1- ans S1+ And helicity amplitudes are consist of six amplitudes functions with its angle. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Multipoles Analysis I. G. Aznauryan, PRD 57, 2727 (1998) Structure functios vs. Helicity amplitudes ( Hi ) : σT+L = (1/2)*(H1² + (H2²)*(H3²) + H4²) + ε*(H5² + H6²) σTT = H3*H2 - H4*H1 σLT = (-1/sqrt(2))*( H5*(H1 - H4) + H6*(H2 + H3) ) These helicity amplitudes are linked to structure functions which are extracted from experimental data. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Multipoles Analysis I. G. Aznauryan, PRD 57, 2727 (1998) Constraints : * E0+, S0+ are dominated in this regime. ** M1-, S1- were used from MAID2007 model prediction. *** for I=3/2 case, following correlation functions are acceptable. → GD′ =(1+Q2/mu_02)² → GM = 3.*exp(-0.21*Q2)/( *Q *Q2²)/GD′ → M1+ = (Y_O/52.437)* GM * sqrt((( Q2)/2.46)**2-0.88)* 6.786 → E1+ = * M1+ → R_sm = *Q *Q2² * sqrt(Q2) * Q2²* sqrt(Q2) → S1+ = R_sm*M1+/100. where, mu_02=0.71, Y_O is the interpolation value from SAID model. There are some constraints taht we can use. I assumed that the Isospin 3/2 is mainly contributed in this region. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Multipoles extraction Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F. Blue : E0+ using LCSR w/ zero pion mass Red : E0+ using LCSR w/ real pion mass Black : E0+ from multipole analysis Blue : E1+ from multipole analysis L0+ and E1+ error bar does not treated properly. Expasion of pion mass involve the two parameters: m_pi/M_N and m_piQ^2/m_N^3 Red lines : LCSR solid line : pure calc. dash line : exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Multipoles extraction Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F. Blue : E0+ using LCSR w/ zero pion mass Red : E0+ using LCSR w/ real pion mass Black : E0+ from multipole analysis Blue : E1+ from multipole analysis W=1.13GeV shows already E0+ is away from in high Q2 region. W> 1.13GeV does not shows much change in E0+ but E1+. Which mean p-wave contribution is already impact into. Expasion of pion mass involve the two parameters: m_pi/M_N and m_piQ^2/m_N^3 Red lines : LCSR solid line : pure calc. dash line : exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Multipoles extraction Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F. Blue : E0+ using LCSR w/ zero pion mass Red : E0+ using LCSR w/ real pion mass Black : E0+ from multipole analysis Blue : E1+ from multipole analysis Expasion of pion mass involve the two parameters: m_pi/M_N and m_piQ^2/m_N^3 Red lines : LCSR solid line : pure calc. dash line : exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

CLAS Gmn measurement as input instead of using parametrization ?
Question ??? CLAS Gmn measurement as input instead of using parametrization ? Simple parametrization of form factor for neutron is based on low momentum trnsfer square region of experiments. Since we have very nice measurement of one of thiese. Magnetic formfactor of neutron from CLAS in this year. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Form factors and Multipole for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) S. Platchekov Nucl.Phys. A 70 (1990) J.J. Kelly Phys. Rev. C 70 (2004) Preliminary Preliminary As I showed this plot previously. This is the E0+ multipole extraction from LCSR frame work basis with Sach’s formfactors parametrizations. So far, CLAS has published excellent GMn measurement with covering high Q2 region where is interested in this region too. Red lines : LCSR solid line : pure calc. dash line :exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Error band : covariant matrix for non-linear least square fill circle : data using recoil or target polarization measurement (16-22) Open circle : data from the deutron quadrupole form factor (23) J. J. Kelly et al., PRC 70: (2004) CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Neutron magnetic form factor from CLAS In this year, CLAS has a great publication which is a measurement of magnetic form factor of neutron in high Q2. Psper by Jeff . 3% systematic error precision analysis, two incident beam energies using the ratio of e-n to e-p scattering off the proton and deutron target. Black solid curve : J.J. Miller’s treatment: the nucleon is treated using light front dynamics as a relativistic system of three bound quarks and a surrounding pion cloud Green band : Diehl’s treatment : GPD are parameterized and fixed by fits to the experimental data. Dashed curve : M. Guidal’s treatment : A Regge parametrization of the GPDs is used to charaterize the elastic nucleon form factors at low Q2 and extend to high Q2. J. Lachniet et al., PRL 102: (2009) CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Form factors and Multipole for nπ+channel J. Lachniet (2009) Phys. Rev. Lett. 102 CLAS DATA J.J. Kelly Phys. Rev. C 70 (2004) Preliminary J. Lachniet : Jeff Red lines : LCSR solid line : pure calc. dash line :exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Summary As first time, E0+ multipole comparison near pion threshold between two methods (LCSR, multipole fit) was performed. Multipole analysis gives us same answer for extracting E0+ multipole with LCSR method. however, the fitting chi2 should be improved ...(future plan) Direct use of neutron magnetic form factor from CLAS publication gives consistent result with F.F. parametrization. In this analysis, acceptance and radiative corrections are issued for this kinematic regime. We verified these issues with careful study, Pion threshold region : real part that is BG contribution should be strong which mean imaginary part of resonance contribution is strongly supressed. Expasion of pion mass involve the two parameters: m_pi/M_N and m_piQ^2/m_N^3 By using Gmn from CLAS published data, the uncertainty from parametrization of form factor could be reduced. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

BACKUP SLIDES In this analysis, acceptance and radiative corrections are issued for this kinematic regime. We verified these issues with careful study, Pion threshold region : real part that is BG contribution should be strong which mean imaginary part of resonance contribution is strongly supressed. Expasion of pion mass involve the two parameters: m_pi/M_N and m_piQ^2/m_N^3 CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Theoretical imrovement plans Enrgy dependent generalized form factors generated by FSI Adding D-wave contributio model Tune calculation with low Q2 and high W experimental data Systematic approach in the global PWA analysis framework in Np and g*N scattering under QCD S-, P- and D partial waves. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Legendre –moment vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Assumption in LCSR V.Braun PRD77(2008) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, threshold Scherer, Koch, NPA534(1991) Vainshtein, Zakharov NPB36(1972) CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Multipoles vs. F. F. for nπ+channel CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Prediction MAID2007 W-dependence of L0+ from MAID2007 Lower Q2, Smaller W dependence I going to show the visualized motivation which is more clear. Here you see the more interesting can be increased in pi+ channel at the threshold. In the UIM model in high Q2 region for pion angular momentum is =0, we see cusp effect around 1GeV2 of Q2 then most likely independence Q2 behavior of E0+. Meanwhile, L0+ has negative value. Bold (real) part is coming from BG. Thin(img) from resonance contribution…. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Prediction MAID2007 Bold –Real part Thin – Imaginary part I going to show the visualized motivation which is more clear. Here you see the more interesting can be increased in pi+ channel at the threshold. In the UIM model in high Q2 region for pion angular momentum is =0, we see cusp effect around 1GeV2 of Q2 then most likely independence Q2 behavior of E0+. Meanwhile, L0+ has negative value. Bold (real) part is coming from BG. Thin(img) from resonance contribution…. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Kinematical Coverage * E=5.754GeV(pol.), LH2 target (unpol.) * IB=3375/6000A, Oct Jan. 2002 Variable Unit Range # Bin Width Q2 GeV2 2.05 ~ 4.16 5 various W GeV 1.11 ~ 1.15 3 0.02 cosθ*π -1.0~ 1.0 10 0.2 φ *π Deg. 0. ~ 360. 12 30 Here is the quick review of experimentally kinematic coverage in this analysis. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Preliminary Results Preliminary Cross Section (φ*) φ* – dependent cross section in term of W, Q2, cosθ* Various physics models Blue shade : systematic uncertainty estimation Red data : CRS with new analysis CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Structure Function Preliminary sensitive ! insensitive ! CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Structure Function Preliminary sensitive ! CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Preliminary Preliminary Preliminary Legendre –moments
I apologized you because the color code is not consistent. Be careful color code is changed Preliminary Legendre –moments

Legendre moments vs. Form Factors C_pi = isospin factor = sqrt(2) F_pi = 93MeV GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

l-moments vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, threshold C_pi = isospin factor = sqrt(2) F_pi = 93MeV GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Legendre-moments vs. F. F. C_pi = isospin factor = sqrt(2) F_pi = 93MeV pion form factor GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Legendre moments vs. Form Factors * 3 Eqs. 4 parameter should be determined * Real parts x1, x2 can be determined by A1, D0 legendre coeff. * Imaginary parts y1, y2 can be determined in 2cases * Asymmetry helps to determine complete form factor S-wavve transverse component = E0+ = is only survived based on assumption of G_En=0 Where, C_pi = isospin factor = sqrt(2) F_pi = 93MeV GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Historically, threshold pion in the photo- and electroproduction is the very old subject that has been receiving continuous attention from both experiment and theory sides for many years. Pion mass vanishing approximation in Chiral Symmetry allows us to make an exact prediction for threshold cross section known as LET The LET established the connection between charged pion electroproduction and axial form factor in nucleon. Therefore, It is very interesting to extracting Axial Form Factor which is dominated by S- wave transverse multipole E0+ in LCSR CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

LCSR (Light Cone Sum Rule) Constructed relating the amplitude for the radiative decay of Σ+(pγ) to properties of the QCD vacuum in alternating magnetic field. An advantage of study because soft contribution to hadron form factor can be calculated in terms of DA’s that enter pQCD calculation without other nonperturbative parameters. New technique : the expansion of the standard QCD sum rule approach to hadron properties in alternating external fields. CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Legendre moments vs. Form Factors C_pi = isospin factor = sqrt(2) F_pi = 93MeV GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

l-moments vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, threshold C_pi = isospin factor = sqrt(2) F_pi = 93MeV GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Legendre-moments vs. F. F. C_pi = isospin factor = sqrt(2) F_pi = 93MeV pion form factor GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Legendre moments vs. Form Factors * 3 Eqs. 4 parameter should be determined * Real parts x1, x2 can be determined by A1, D0 legendre coeff. * Imaginary parts y1, y2 can be determined in 2cases * Asymmetry helps to determine complete form factor S-wavve transverse component = E0+ = is only survived based on assumption of G_En=0 Where, C_pi = isospin factor = sqrt(2) F_pi = 93MeV GM GE magnetic/ electric proton form factor CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Scaled cross section X Q6 Q2 dependence of the scaled cross section for three different W bins Preliminary Color index Rad.Corr. with MAID03 Rad. Corr. With SLee04 dash solid CLAS Hadron Spectroscopy meeting Sep. 26, K. Park

Measurement of Generalized Form Factors near the Pion Threshold

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Measurement of Generalized Form Factors near the Pion Threshold

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