Real Photon Point Research Articles

Unitarity constraints on meson electroproduction at backward angles

At large virtuality $Q^2$, the coupling to the $\rho$ meson production channels provides us with a natural explanation of the surprisingly large cross section of the $\omega$, as well as the $\pi^+$, meson electroproduction recently measured at backward angles, without destroying the good agreement between the Regge pole model and the data at the real photon point. Together with elastic re-scattering of the outgoing meson it also provides us with a way to explain why the node, that appears at $u\sim -0.15$ GeV$^2$ at the real photon point, disappears at moderate virtuality $Q^2$. Predictions are given for the electroproduction of the $\pi^0$ meson.

Transition form factors: γ*+p→Δ(1232) , Δ(1600)

Electroproduction form factors describing the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1232)$, ${\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ transitions are computed using a fully dynamical diquark-quark approximation to the Poincar\'e-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the $\mathrm{\ensuremath{\Delta}}(1600)$ is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the $\mathrm{\ensuremath{\Delta}}(1232)$. Precise measurements of the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1232)$ transition already exist on $0\ensuremath{\le}{Q}^{2}\ensuremath{\lesssim}8\text{ }\text{ }{\mathrm{GeV}}^{2}$, and the calculated results compare favorably with the data outside the meson-cloud domain. The predictions for the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to ${Q}^{2}\ensuremath{\approx}6{m}_{p}^{2}$, enabling a meaningful direct comparison with experiment once analysis of existing data is completed. In both cases, the electric quadrupole form factor is particularly sensitive to deformation of the $\mathrm{\ensuremath{\Delta}}$-baryons. Interestingly, while the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1232)$ transition form factors are larger in magnitude than those for ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ in some neighborhood of the real photon point, this ordering is reversed on ${Q}^{2}\ensuremath{\gtrsim}2{m}_{p}^{2}$, suggesting that the ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Delta}}}^{+}(1600)$ transition is more localized in configuration space.

Measurements ofep→e′π+nat1.6<W<2.0 GeV and extraction of nucleon resonance electrocouplings at CLAS

Differential cross sections of the exclusive process $e p \to e^\prime \pi^+ n$ were measured with good precision in the range of the photon virtuality $Q^2 = 1.8 - 4.5$ GeV$^2$, and the invariant mass range of the $\pi^+ n$ final state W = 1.6 - 2.0 GeV using the CEBAF Large Acceptance Spectrometer. Data were collected with nearly complete coverage in the azimuthal and polar angles of the $n\pi^+$ center-of-mass system. More than 37,000 cross section points were measured. The contributions of the isospin $I = {1\over 2}$ resonances $N(1675){5\over 2}^-$, $N(1680){5\over 2}^+$ and $N(1710){1\over 2}^+$ were extracted at different values of $Q^2$ using a single-channel, energy-dependent resonance amplitude analysis. Two different approaches, the unitary isobar model and the fixed-$t$ dispersion relations, were employed in the analysis. We observe significant strength of the $N(1675){5\over 2}^-$ in the $A_{1/2}$ amplitude, which is in strong disagreement with quark models that predict both transverse amplitudes to be strongly suppressed. For the $N(1680){5\over 2}^+$ we observe a slow changeover from the dominance of the $A_{3/2}$ amplitude at the real photon point ($Q^2=0$) to a $Q^2$ where $A_{1/2}$ begins to dominate. The scalar amplitude $S_{1/2}$ drops rapidly with $Q^2$ consistent with quark model prediction. For the $N(1710){1\over 2}^+$ resonance our analysis shows significant strength for the $A_{1/2}$ amplitude at $Q^2 < 2.5$ GeV$^2$.

Momentum transfer dependence of the proton’s electric and magnetic polarizabilities

The Q^2-dependence of the sum of the electric and magnetic polarizabilities of the proton is calculated over the range 0 \leq Q^2 \leq 6 GeV^2 using the generalized Baldin sum rule. Employing a parametrization of the F_1 structure function valid down to Q^2 = 0.06 GeV^2, the polarizabilities at the real photon point are found by extrapolating the results of finite Q^2 to Q^2 = 0 GeV^2. We determine the evolution over four-momentum transfer to be consistent with the Baldin sum rule using photoproduction data, obtaining \alpha + \beta = 13.7 \pm 0.7 \times 10^{-4}\, \text{fm}^3.

Results from the N* Program at Jefferson Lab

We discuss the results on the fundamental degrees of freedom underlying the nucleon excitation spectrum and how they evolve as the resonance transitions are investigated with increasingly better space-time resolution of the electromagnetic probe. Improved photocouplings for a number of resonant states, those for the N(1720)P13 being significantly changed, have been determined and entered into the 2008 edition of the RPP. Strong sensitivity to the N(1900)P13 state, listed now as a 2-star state in the same edition of RPP, has been observed in KΛ and KΣ photoproduction. None of the earlier observations of a Θ+5(1540) was confirmed in a series of three Jefferson Lab high statistics dedicated measurements, and stringent upper limits on production cross sections were placed in several channels. For the four lowest excited states, the Δ(1232)P33, N(1440)P11, N(1520)D13, and N(1535)S11, the transition amplitudes have been measured in a wide range in photon virtuality Q2. The amplitudes for the Δ(1232) show the importance of the pion-cloud contribution and do not show any sign of approaching the pQCD regime for Q2 < 7 GeV2. For the Roper resonance, N(1440)P11, the data provide strong evidence for this state as a predominantly radial excitation of the nucleon as a 3-quark ground state. For the N(1535)S11, comparison of the results extracted from π and η photo- and electroproduction data allowed one to specify the branching ratios of this state to the πN and ηN channels; they entered into the 2010 edition of the RPP. Measured for the first time, the longitudinal transition amplitude for the N(1535)S11 became a challenge for quark models and can be indicative of large meson-cloud contributions or alternative representations of this state. The N(1520)D13 clearly shows the rapid changeover from helicity-3/2 dominance at the real photon point to helicity-1/2 dominance at Q2 > 0.5 GeV2 confirming a long-standing prediction of the constituent quark model. The search for undiscovered but predicted states continues to be pursued with a vigorous experimental program. While recent data from Jefferson Lab and elsewhere provide intriguing hints of new states, final conclusions will have to wait for the results of the broad experimental effort currently underway with CLAS, and subsequent analyses involving the EBAC at Jefferson Lab.

SHAPE OF PION DISTRIBUTION AMPLITUDE AND TRANSVERSE MOMENTUM IN HARD EXCLUSIVE PROCESSES

Inclusion of transverse momentum effects into the description of the pion-photon transition form factor is discussed. At low k⊥, a consistent description may be obtained within the light-front formalism. On the other hand, the large-k⊥ limit is most conveniently treated within the Sudakov parameterization framework. The third way of introducing k⊥ is based on the "local duality" approach motivated by QCD sum rules. It is shown that, while the local duality gives a correct (coinciding with the axial anomaly based prediction) result for the real photon point, a straightforward extension of the formulas of the modified factorization approach into the small virtualities domain produces a divergent result. It is pointed out that such lessons should be taken into account while constructing transverse-momentum-dependent schemes for inclusive processes.

Unitarity constraints on neutral pion electroproduction

At large virtuality Q2, the coupling to the vector meson production channels provides us with a natural explanation of the surprisingly large cross section of the neutral pion electroproduction recently measured at Jefferson Laboratory, without destroying the good agreement between the Regge pole model and the data at the real photon point. Elastic rescattering of the π0 provides us with a way to explain why the node, that appears at t∼−0.5 GeV2 at the real photon point, disappears as soon as Q2 differs from zero.

Formula omitted] program at CLAS

The Nlow asterisk program is one of the major goals of CLAS experiments in Jefferson Lab and many outstanding results have been carried out. In this note, I will present some highlight recent measurements of nucleon resonance transition form factors from electro-production as the second resonances. The new pion electro-production data resolve a longstanding puzzle of the nature of the Roper resonance, and confirm the assertion of the symmetric constituent quark model of the Roper as the first radial excitation of the nucleon. The single pion electro-production data for high Q2 confirms the slow fall off of the S11(1535) transition form factor with Q2, and better constrain the branching ratios βNπ:βNη=0.50:0.45. For the first time, the longitudinal transition amplitude to the S11(1535) was extracted from the nπ+ data. Also, new results on the transition amplitudes for the D13(1520) resonance are presented showing a rapid transition from helicity 3/2 dominance seen at the real photon point to helicity 1/2 dominance at higher Q2.

New approach to low energy virtual Compton scattering and generalized polarizabilities of the nucleon

Virtual Compton scattering off the nucleon (VCS) is studied in the regime of low energy of the outgoing real photon. This regime allows one to directly access the generalized polarizabilities of the nucleon in a VCS experiment. In the derivation of the low energy theorem for VCS that exists in the literature, the low energy limit taken for virtual initial photons does not match on that for real photons, when one approaches the initial photon's mass shell. While this problem has for a long time been attributed to the nonanalyticity of the Compton amplitude with respect to the photon virtuality, I demonstrate that it is merely due to an ill-defined low energy limit for VCS, on one hand, and to a particular way of constructing the VCS amplitude, used in the literature, on the other. I provide a uniform description of low energy Compton scattering with real and virtual photons by defining a Lorentz-covariant operator sub-basis for Compton scattering in that regime, which has six independent structures. Correspondingly, six new generalized polarizabilities are introduced in the Breit frame. These polarizabilities are defined as continuous functions of the photon virtuality and at the real photon point match onto the nucleon polarizabilities known from real Compton scattering.

The N* physics program at Jefferson Lab

Recent measurements of nucleon resonance transition form factors with CLAS at Jefferson Lab are discussed. The new data confirm the assertion of the symmetric constituent quark model of the Roper as the first radial excitation of the nucleon. The data on high Q2 nπ+ production better constrain the branching ratios βNπ and βNη. For the first time, the longitudinal transition amplitude to the S11(1535) was extracted from the nπ+ data. Also, new results on the transition amplitudes for the D13(1520) resonance are presented showing a rapid transition from helicity 3/2 dominance seen at the real photon point to helicty 1/2 dominance at higher Q2. I also discuss the status of the search for new excited nucleon states.

Low Q2measurements of the neutron and 3He spin structure

Thomas Jefferson National Accelerator Facility experiment E97-110 was performed to provide a precise measurement of the extended Gerasimov-Drell-Hearn integral and of moments of the neutron and of the 3He spin structure functions. The momentum transfer range 0.02 < Q2 < 0.3 (GeV/c)2 will allow us to test predictions of Chiral Perturbation Theory, and chek the GDH sum rule by extrapolating the integral to the real photon point. The data have been taken in Hall A using a highly polarized electron beam and a polarized 3He target. The status of the data analysis is discussed, and preliminary results are shown.

Electromagnetic nucleon-delta transition in the perturbative chiral quark model

We apply the perturbative chiral quark model to the gamma N -> Delta transition. The four momentum dependence of the respective transverse helicity amplitudes A(1/2) and A(3/2) is determined at one loop in the pseudoscalar Goldstone boson fluctuations. Inclusion of excited states in the quark propagator is shown to result in a reasonable description of the experimental values for the helicity amplitudes at the real photon point.

Electromagnetic form factors of the $\Delta(1232)$ excitation

In the resonance region we have precisely determined the electromagnetic properties of the $\Delta(1232)$ -resonance, in particular the E2/M1 ratio $R_{EM}=(-2.5 \pm 0.1) \%$ . For pion electroproduction recent experimental data from Mainz, Bates, Bonn and JLab for Q2 up to 4.0 (GeV/c)2 have been analyzed with the isobar model MAID. The extracted E2/M1 ratio shows, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and becomes positive with increasing Q2. This is a possible indication of a very slow approach toward the pQCD region. The C2/M1 ratio near the photon point is found as $R_{SM}(0)=(-6.5 \pm 0.5) \%$ . At high Q2, the absolute value of the ratio is strongly increasing, a further indication that pQCD is not yet reached. The electromagnetic-transition form factors of the $\Delta(1232)$ excitation are parameterized and fitted to the electroproduction data. This also shows a zero-crossing of the electric form factor G E * at $Q^2=3.6\pm 0.5$ (GeV/c)2.

PROBING Δ STRUCTURE WITH PION ELECTROMAGNETIC PRODUCTION

The Dubna-Mainz-Taipei dynamical model for pion electromagnetic production, which can describe well the existing data from threshold up to 1 GeV photon lab energy, is presented and used to analyze the recent precision data in the Δ region. We find that, within our model, the bare Δ is almost spherical while the physical Δ is oblate. The deformation is almost saturated by the pion cloud effects. We further find that up to Q2 = 4.0(GeV/c)2 the extracted helicity amplitude A3/2 and A1/2 remain comparable with each other, implying that hadronic helicity is not conserved at this range of Q2. The ratio E1+/M1+ obtained show, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and to become positive with increasing Q2. This is a possible indication of a very slow approach toward the pQCD region. Finally, we find that the bare helicity amplitude A1/2 and S1/2, but not A3/2, starts exhibiting the scaling behavior at about Q2 ≥ 2.5(GeV/c)2.

&lt;‘γ*N→Δtransition form factors: A new analysis of data onp(e,e′p)π0atQ2=2.8and4.0 (GeV/c)2

Recent JLab data of the differential cross section for the reaction ${p(e,e}^{\ensuremath{'}}p){\ensuremath{\pi}}^{0}$ in the invariant mass region of $1.1&lt;W&lt;1.4 \mathrm{GeV}$ at four-momentum transfer squared ${Q}^{2}=2.8$ and $4.0 (\mathrm{GeV}{/c)}^{2}$ are analyzed with two models, both of which give an excellent description of most of the existing pion electroproduction data below $W&lt;1.5 \mathrm{GeV}.$ We find that at up to ${Q}^{2}=4.0 (\mathrm{GeV}{/c)}^{2},$ the extracted helicity amplitudes ${A}_{3/2}$ and ${A}_{/2}$ remain comparable with each other, implying that hadronic helicity is not conserved at this range of ${Q}^{2}.$ The ratios ${E}_{1+}{/M}_{1+}$ obtained show, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and to become positive with increasing ${Q}^{2}.$ This is a possible indication of a very slow approach toward the pQCD region. Furthermore, we find that the bare helicity amplitude ${A}_{1/2}$ and ${S}_{1/2},$ but not ${A}_{3/2},$ starts exhibiting the scaling behavior at about ${Q}^{2}&gt;~2.5(\mathrm{GeV}{/c)}^{2}.$

The E2/M1 and C2/M1 ratios and form factors in N→ Δ transitions

A partial wave analysis of pion photoproduction has been obtained in the framework of fixed-t dispersion relations valid from threshold up to 500 MeV. In the resonance region we have precisely determined the electromagnetic properties of the \Delta(1232) resonance, in particular the E2/M1 ratio R_{EM}=(-2.5 +- 0.1) %. For pion electroproduction recent experimental data from Mainz, Bates and JLab for Q^2 up to 4.0 (GeV/c)^2 have been analyzed with two different models, an isobar model (MAID) and a dynamical model. The E2/M1 ratios extracted with these two models show, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and become positive with increasing Q^2. This is a possible indication of a very slow approach toward the pQCD region. The C2/M1 ratio near the photon point is found as R_{SM}(0)=(-6.5 +- 0.5) %. At high Q^2 the absolute value of the ratio is strongly increasing, a further indication that pQCD is not yet reached.

Experimental test of the Gerasimov-Drell-Hearn sum rule

The Gerasimov-Drell-Hearn (GDH) sum rule gives a prediction for the integral over the spin structure function g 1( x) of the proton at the real photon point ( Q 2 = 0). The experimental test of the sum rule will be performed at the electron accelerators MAMI in Mainz and ELSA in Bonn.

The N Delta form factors: from the real photon to pseudothreshold

We study the extrapolation of the electromagnetic N Delta transition form factors in the time-like region, from the real photon point to zero CM momentum (pseudothreshold), where the transition moments can be compared with quark model predictions. Our method consists of calculating the long-range contributions to the form factors due to the Delta -excitation by a 'quasi-real' pion photoproduced through the background. These long-range dispersive effects are of the order of 30% for the magnetic dipole and of 100% for the two electric quadrupoles. In particular, they account for the presently accepted experimental E2/M1 ratio and predict a large difference, for real photons, between the transverse and the longitudinal quadrupole moments. The imaginary parts are also investigated and found to be different from zero, through very small, only near pseudothreshold. As regards the k2 dependence, it is found that these contributions yield for the magnetic form factor a faster decrease than the dipole in the space-like region, as expected, but essentially the same for time-like photons. For the quadrupole moments, the extrapolation to pseudothreshold yields a vanishingly small value as foreseen by the naive quark model.

Off-shell electromagnetic form factors of pions and kaons in chiral perturbation theory.

The off-shell electromagnetic vertex of a (pseudo-) scalar particle contains, in general, two form factors F and G which depend, in addition to the squared momentum transfer, on the invariant masses associated with the initial and final legs of the vertex. Chiral perturbation theory to one loop is used to calculate the off-shell form factors of pions and kaons. The formalism of Gasser and Leutwyler, which was previously used to calculate the on-shell limit of the form factor F, is extended to accommodate the most general form for off-shell Green's functions in the pseudoscalar meson sector. We find that chiral symmetry predicts that the form factors F of the charged pions and kaons go off-shell in the same way, i.e., the off-shell slope at the real photon point is given by the same new phenomenological constant $\beta_1$. Furthermore, it is shown that at order $p^4$ the form factor F of the $K^0$ does not show any off-shell dependence. The form factors G are all related to the form factors F in the correct fashion as required by the Ward-Takahashi identity. Numerical results for different off-shell kinematics are presented.