K+ - Scattering from Nuclear Targets Ed Hungerford University of Houston hunger@uh.edu E. V. Hungerford University of Houston Panic 11/10-14/08

What does a Nucleon Look Like in the Nuclear medium? The EMC effect shows that the nuclear medium modifies nuclear structure 1) Measured at high momentum transfer ( Q^{2} ≈ 2Mν ) 2) This is an assumed consequence of Nuclear density Early measurements of K+ total cross sections were enhanced, ---- Interpreted as : ----- nuclear “swelling” dibaryon structures change in the effective mass of mesonic coupling The K+ was proposed as a hadronic “replacement” for the electron E. V. Hungerford University of Houston Panic 11/10-14/08

K+ Mean Free path Useful K+ beams E. V. Hungerford Panic 11/10-14/08 University of Houston Panic 11/10-14/08

K+ Amplitude and Cross Section Im f K+ p σT Im(f) fm σT mb Re f L=0,1 L=0 Re(f) fm Because the Amplitudes are weak and relatively momentum independent the tρ approximation for construction of the optical potential is expected to be valid K+ p/n Amplitudes Soild s Dashed p E. V. Hungerford University of Houston Panic 11/10-14/08

Elementary K+-Nucleon Interaction K+ Nucleon (particularly the K+- n) interaction is not well known The spin dependence is weak L=0 is dominated by K+- p, L=1 dominated by K+- n S wave dominates for momenta less than 800 MeV/c Cross section relatively flat for momenta less than 800 MeV/c Because amplitudes show no resonance behavior they should be easily modeled Implications Should be sensitive to the Nuclear Volume K - much more diffractive – deeper minimum at lower Q2 E. V. Hungerford University of Houston Panic 11/10-14/08

Elastic and Total Cross Sections Additional data taken for Ca An Early Example of Elastic and Total Cross Sections Additional data taken for Ca 12C(K+,K+) 800 MeV/c PR 168(68)1466 x Phase Shift Increase by 25 % Cross Section increase by 25 % Ratio σc/(6σD) Elastic PR C25(82)2619 PRL 65(90)2110 Analysis PR C45(92)2019 E. V. Hungerford University of Houston Panic 11/10-14/08

Initial K+ -- e Comparison 40Ca Target Radius = 4 fm K+ 550 MeV/c Incident Momentum λK = 0.39 fm Scattered at 80º Q2 = (540 MeV/c)2  = 156 MeV x = q2/2M  = 0.91 e 1500 MeV/c Incident Momentum λK = 0.20 fm Scattered at 20º Q2 = (515 MeV/c)2  = 140 MeV x = q2/2M  = 0.93 Obviously DIS can’t be explored with these kinematics, but they are appropriate for QHD E. V. Hungerford University of Houston Panic 11/10-14/08

K+ Scattering Enhancements Scattering from C shows an increase of 36% in the 2-body amplitude – in Ca it is about 64% Can be explained by: Increasing the elementary phase shifts Decrease the effective mass of the exchanged mesons (effective mass varies with density [1 – λρ/ρ0]) Other Density dependence Calculations are not sensitive to common corrections (energy shifts, multiple scattering, etc) Data are limited but there is a consistent discrepancy between data and theory. E. V. Hungerford University of Houston Panic 11/10-14/08

K+ C Total Cross Section Ratio Compared to Calculations Increase Vector Meson Mass PRL 60(88)2723 Scaled Swelling PRC31(84)2184 Optical Models PRC31(84)2184 Optical +MEX PRC46(92)2462 E. V. Hungerford University of Houston Panic 11/10-14/08

A Second Series of Experiments PR C49(94)2569 Ratio σ/(x σD) Scaled Optical Model E. V. Hungerford University of Houston Panic 11/10-14/08

Cross Section Ratios to [x D] Re-Analysis of Ratios Cross Section Ratios to [x D] PR C(97)1304 PL B396(97)21 Super Ratio Total Reaction ρSi >ρCa>ρC E. V. Hungerford University of Houston Panic 11/10-14/08

Analysis σR less model dependent than σT An optical potential is required to extract σR from the transmission experimental data The results are not self-consistent Need elastic data to get the optical potential While a tρ approximation should be valid, it appears that potential is repulsive at low density but less so or attractive at high density Energy dependence of K+-Li is similar to more complex nuclei Super ratio removes Energy dependence [σR(exp) /σR(cal)]/[σR(exp) /σR(cal)] Meson Exchange is energy dependent E. V. Hungerford University of Houston Panic 11/10-14/08

Elastic Scattering on C and Li at 635 and 715 MeV/c C/Li Ratio PL B382(96)29 NP A625(97)251 Elastic PL B382(96)29 Li λ = 1.0 C λ = 1.2 DWIA λ= 1.0, 1.3 PRL 55(85)592 PR C51(95)857 λ = 1.0 Analysis PRL 55(85)592 PR C51(95)857 E. V. Hungerford University of Houston Panic 11/10-14/08

Analysis Using a fit to σR and σT does not produce self consistent results, i.e. optical potentials constructed to fit σR and σT are not self consistent Need an increase of ~15% of Im Vopt for Li plus an additional 17-25 % of nuclear dependence A density threshold is needed – use a linear density dependence for Im Vopt of the form α = 1 + β(ρ – ρo)Θ(ρ – ρo) ρo = 0.088; Β = 13.0 ρ the average nuclear density Vopt → Re Vopt + Im Vopt [ α ] ρo > ρ (Li) = 0.049 Self consistent fits possible PR C(97)1304 PL B396(97)21 E. V. Hungerford University of Houston Panic 11/10-14/08

Inelastic Scattering Transition density < ρo PL B382(96)29 ρ (C) = 0.104 ρ (T) = 0.063 DWIA λ = 1.0 DWIA uses Transition Strength from π Scattering DWIA λ = 1.3 Transition density < ρo Simple density dependence does not work E. V. Hungerford University of Houston Panic 11/10-14/08

Quasi_free Scattering On D, C, Ca, and Pb PRL 71(93)2571 PR C51(95)669 Note Data Quality and Resolution Normalization ±11% E. V. Hungerford University of Houston Panic 11/10-14/08

Number of Effective Nucleons Aeff = N0 Aα N0 ≈ 2 ; Α ≈ 0.6 Compare to π+/π- -- 0.44/0.56 e -- ≈1 A large σT increases Aeff but each cross section increases – Resulting Aeff insensitive K+ reaches 55% of Central Nuclear Density in Pb Verifies K+ Long mean free path E. V. Hungerford University of Houston Panic 11/10-14/08

K+ Ca Quasi Free Compared to EM Theory q = 500 MeV/c Developed relativistic response in analogy to EM Scattering EM response (Dirac V-A) expressed in Coulomb/Transverse – Coulomb quenched 4-vector current-current formulation for K+ uses scalar, vector, tensor forms and IA for nuclear response Nuclear current obtained from the Walecka model with ρ, ω, σ exchange Relativistic RPA applied to get the coherent nuclear response EM quenching due to the polarization of Nucleon sea – relativistic RPS effect K+ quenching sensitive to cancellation of kinematics and Relativistic RPA Still need some renormalization so Aeff(exp) is used but shape is correct PR C51(95)806 E. V. Hungerford University of Houston Panic 11/10-14/08

A Possible Round of New Experiments Previous Experimental Parameters Momentum -- 500- 800 MeV/c K+ flux -- 3 x 105 instantaneous; 0.5 x 105 avg π/K – 1 Acceptance – 15% Beam Dimensions – 8 x 3 cm2 Targets – Mostly Natural 2-4 g/cm2 ΔE – 3-4 MeV (FWHM) Δθ – 2-4 Deg PID especially for pions and protons Normalizations carefully handled Dominated by systematics – 15% E. V. Hungerford University of Houston Panic 11/10-14/08

We need more data and more inspired theory Conclusions Reaction, total, elastic, inelastic, quasi-free all seems to have the same problem While it appears that the issue is related to nuclear density, some simple, direct dependence does not seem to work What the data seems to indicate is an increase in the Im Vopt with perhaps a more attractive real component A. Gal NP A639(98)485c suggests that there are “missing” medium effects Have we asked the right questions about the K+-nuclear interaction ? We need more data and more inspired theory E. V. Hungerford University of Houston Panic 11/10-14/08

The End E. V. Hungerford University of Houston Panic 11/10-14/08