Elastic meson-nucleon and nucleon-nucleon scattering: models vs. all available data. E. Martynov *, J.R. Cudell, A. Lengyel * Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

E. Martynov2 Blois, Elastic m-n and n-n scattering …. Outline Dataset. Parametrizations. Overlapping bins method.  results of analysis  pomeron trajectory,  pomeron residues,  - and - reggeon residues. Rescatterings Global fit  without hard pomeron  with hard pomeron Conclusion

E. Martynov3 Blois, Elastic m-n and n-n scattering …. The dataset 1.All experimental data on for elastic scattering were collected from the Durham Data Base ( They were verified and uniquely formatted. The integrated file contains now more than experimental points for at all and. Some evident typos were corrected. 2.Generally, the quality of the data is quite often unknown, because in some papers the systematic errors are not given and, in others, it is unclear whether they are included in the given errors or not. 3.Moreover, some of the collected subsets strongly contradict each other in the normalization. Such subsets (not many, about 6 of more than 60 at the considered t and s ) were excluded. The rest of the subsets were used “as is”, without any corrections to their normalization. 4.We plan to analyze the problem of the relative normalizations in more details later.

E. Martynov4 Blois, Elastic m-n and n-n scattering …. Parametrization of the amplitude a+b -> a+b Contribution of a Regge pole with trajectory where Normalization:

E. Martynov5 Blois, Elastic m-n and n-n scattering …. Overlapping bins 1.Simplified parameterization were are parameters to be fitted. 2.Bins and fitting procedure. Let us define the elementary bin: If the s-dependence of the above amplitudes is more or less correct, we can determine the values of trajectories and couplings from the fit in a given bin, provided is small enough. Performing such fit for we scan all data from up to and obtain an effective t-dependence of trajectories and couplings.

E. Martynov6 Blois, Elastic m-n and n-n scattering …. 3.Some details of the method The length of the bin,, (not too big, not too small) The shift to the next bin, Minimal number of points in the bin for each process, Moderate variations of do not change the results. Interval of t where the analysis of the data was performed Interval of s where the analysis of the data was performed

E. Martynov7 Blois, Elastic m-n and n-n scattering …. - and - trajectories These trajectories at are determined in our analysis quite badly. If are free parameters they lead to big errors in their values as well as in the corresponding constants. To restrict this randomness, we used the intercepts and slopes of and trajectories from the fits at and the data from the resonance region. Maximal Minimal Average

E. Martynov8 Blois, Elastic m-n and n-n scattering …. Results Pomeron trajectory Quality of the fit First diffractive cone (?) Higher intercept, higher slope of the pomeron trajectory than the well-known and very often used DL trajectory at “f max ” “f min ”

E. Martynov9 Blois, Elastic m-n and n-n scattering …. Couplings (or residue functions or form factors) A few general remarks The behavior of the crossing-even couplings does not depend strongly on the choice of the - reggeon trajectory. Crossing-odd couplings are almost independent of the -trajectory. Crossing-odd couplings change sign at This is related with the well-known cross- over phenomena. There is quite an unexpected change of sign in the couplings of -reggeon contributions. There are no doubts about this effect in the and cases.

E. Martynov10 Blois, Elastic m-n and n-n scattering …. Rescatterings Quasieikonal form:

E. Martynov11 Blois, Elastic m-n and n-n scattering …. Results of the fit 1.Fit was performed to the data on and in the region Number of the experimental points: 2.Number of reggeon exchanges N=5 ( ). For N>5 the corrections are small numerically (at the available energies) 3. is not satisfactory even for only : Total cross sections and the ratios are not described well 4.Rescatterings in the quasieikonal form do not explain the zeros in and contributions

E. Martynov12 Blois, Elastic m-n and n-n scattering …. Global fit Parametrization the same form for hard pomeron odderon contribution is negligible at t=0

E. Martynov13 Blois, Elastic m-n and n-n scattering …. Fit was performed in two steps: 1.Fit to the data at t=0, Number of points Fit to the data at t≠0 (with fixed intercepts and couplings) Number of points a. Fit to the data at t≠0 and GeV (with fixed intercepts and couplings and with the factors ) Number of points A number of the models were considered in order to find “pro” and “con” for various contributions with and without odderon, with and without hard pomeron, with and without factors

E. Martynov14 Blois, Elastic m-n and n-n scattering …. No hard pomeron (   /DoF=1.207 for t=0) no Z  with Z  no Oddwith Oddno Oddwith Odd N par   /DoF Results: 1.Some evidence for an odderon contribution, 1.Explicit account of the cross-over points in the -contibutions improves the quality of the data description. 3. However, there is an unsatisfactory situation as for the slope of the -trajectory. (Too low (~0.6 GeV -2 ) comparing with the value known from the spectroscopy data (~0.9 GeV -2 )). 4.Despite of the improvements is quite large.

E. Martynov15 Blois, Elastic m-n and n-n scattering …. With hard pomeron (   /DoF=1.004 for t=0), with Z  and without odderon Power F for HPExp. F for HP no Z f with Z f no Z f with Z f N par   /DoF Hard pomeron contribution obviously improves the data description. Very clear signal in a favor of HP is the for the forward data. 6.The eikonalized hard pomeron also leads to a good description of all mentioned data. Hard pomeron term in pp amplitude is not zero as in the case of the bare one. (preliminary: g (h) pp ~1/3 g (h) Mp,  SP ~1.095,  HP ~1.3,  ’ HP ~ 0.1) 7.Too low slopes of the f - and  - trajectories. (Nonlinearity?) Trajectories: Fit to the data at gives Soft pomeron Hard pomeron

E. Martynov16 Blois, Elastic m-n and n-n scattering …. Conclusion  Hard pomeron contributes not only to the forward observables of pure hadronic processes ( ) but also to the differential cross sections,.  There are problems with the zeros in  - and f - contributions ( a treatment is not clear ) and with the slopes of their trajectories.  Comparison with other pomeron models ( dipole pomeron, tripole pomeron ) is necessary.  The new, more precise data, especially at high energy ( RHIC, LHC ), are very much desirable.