We show that an endpoint-overlap model can explain the scaling laws observed in exclusive hadronic reactions at large momentum transfer. The model assumes one of the valence quarks carries most of the hadron momentum. Hadron form factors and fixed-angle scattering are related directly to the quark wave function, which can be directly extracted from experimental data. A universal linear endpoint behavior explains the proton electromagnetic form factor, proton-proton fixed-angle scattering, and the t-dependence of proton-proton scattering at large s >> t. Endpoint constituent counting rules relate the number of quarks in a hadron to the power-law behavior. All proton reactions surveyed are consistent with three quarks participating. The model is applicable at laboratory energies and does not need assumptions of asymptotically high energy regime. A rich phenomenology of lepton-hadron scattering and hadron-hadron scattering processes is found in remarkably simple relationships between diverse processes. Experimental regularitiesThe experimental study of differential cross sections of hard exclusive hadronic reactions at high energy reveals a remarkable pattern: They are described by power laws [1][2][3]. A model explanation exists [4][5][6][7], yet it is not satisfactory [8] at the energies of experimental measurements. We are driven to find a consistent explanation of experimental regularities by re-examining all the facts from a fresh point of view."Hard" reactions are those which depend on a single large scale Q 2 > GeV 2 , or several large scales with a fixed ratio. It is remarkable that the proton electromagnetic form factor a e-mail: sumeetkd@iitk.ac.in b e-mail: pkjain@iitk.ac.in c e-mail: ralston@ku.edu F 1 (Q 2 ) agrees well with a decreasing power of Q 2 for Q 2 5 GeV 2 [9]. For large momentum transfer, it is remarkable that pp → pp fixed-angle cross section dσ/dt agrees well with a decreasing power of Q 2 ∼ s [10], where √ s is the center of mass energy. There are many other examples.We have re-evaluated the phenomenology of power-law dependence or "scaling laws" for exclusive reactions. Due to history, the most simple and plausible explanation failed to be developed. The model appears in the literature as the Feynman process, also known as the Drell-Yan model, also known as the endpoint-overlap model [11][12][13]. There is much to be learned and much that is new when the model is objectively explored. The endpoint-overlap modelBefore engaging the technical analysis, a brief synopsis of history is appropriate. It is fair to observe that relatively few papers in recent years have supported the short-distance model that dominated attention earlier. How and why did consideration of soft processes in hard scattering take so long to develop? In their evaluation of the endpoint region, Brodsky and Mueller [14] wrote that "its contribution depends sensitively on the hadronic wave functions". The discussion discovered no actual fault in the endpoint contribution. Instead of finding a flaw, the section end...

The presence of charged scalars is almost inevitable in most of the beyond standard model scenarios. They are expected to be detected easily if they are there due to their electromagnetic charge. These charged scalars can be produced at the LHC and their decays may lead to interesting signals-multilepton final states, displaced vertices, etc. These charged particles also play crucial roles in low energy rare processes. Thus apart from the collider searches in low energy rare processes their presence can be smelled. Here, we have noted the impact of doubly charged scalars in rare meson decays. As the mesons are lighter these heavy scalars always appear off shell. Due to their off-shell structure the phase space is relatively complicated to deal with. In this paper we have supplemented a general proposal to compute these decays that involve off-shell doubly charged scalars. We have argued that our prescription can be used for any process involving off-shell heavy scalars. Using the prescribed method we have computed two possible meson decays: M ± -► I f l j M '11, M ± -» I f ljlfJ n M '^. We have also estimated the numerical values of the branching ratios in different channels for different charged mesons.

We compute the momentum-transfer dependence of the proton Pauli form factor F 2 in the Endpoint overlap Model. We find the model correctly reproduces the scaling of the ratio of F 2 with the Dirac form factor F 1 observed at the Jefferson Laboratory. The calculation uses the leadingpower, leading-twist Dirac structure of the quark light-cone wave function and the same endpoint dependence previously determined from the Dirac form factor F 1 . There are no parameters and no adjustable functions in the Endpoint Model's prediction for the scaling behavior of F 2 . The model's predicted momentum dependence of the ratio F 2 (Q 2 )/F 1 (Q 2 ) is quite insensitive to the endpoint wave function, which explains why the observed ratio scales like 1/Q down to rather low momentum transfers. We also fit the magnitude of this ratio by adjusting the parameters of the wave function. The Endpoint Model appears to be the only comprehensive model consistent with all form factor information as well as reproducing fixed-angle proton-proton scattering at large momentum transfer. Any one of the processes is capable of predicting the others.

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