1 Proton and neutron electromagnetic form factors

In the framework of the new t-dependence of the General Parton Distributions (GPDs), which reproduce the electromagnetic form factors of the proton and neutron at small and large momentum transfer, the gravitational form factors of the nucleons and a separate contribution of the quarks to them are obtained.

Gravimagnetic nucleon form-factors in the impact parameter representation.

O.V. Selyugin and O.V. Teryaev

BLTPh, JINR, Dubna

As a basis, it is assumed that the form factor is dominated by a soft mechanism and the Generalized Parton distributions (GPDs)-handbag approach [1] is utilized. GPDs for provide information about the distribution of the parton in impact parameter space [4]. It is connected with -dependence of .

In [3], a simple ansatz was proposed which will be good for describing the form factors of the proton and neutron by taking into account a number of new data that have appeared in the last years. We choose the -dependence of GPDs in the form


The size of the parameter was determined by the low experimental data; the free parameters ( - for and - for ) were chosen to reproduce the experimental data in a wide region. The was taken from the MRST2002 global fit [5] wth the scale GeV. In all our calculations we restrict ourselves, as in other works, only to the contributions of and quarks and the terms in and . Correspondingly, for , as for example [2], we have


where and [2]. With standard normalization of the form factors, we have . The parameters and were chosen to obtain two possible forms of the ratio of the Pauli and Dirac form factors.

1 Proton and neutron electromagnetic form factors

The proton Dirac form factor calculated in [3] reproduces sufficiently well the behavior of experimental data not only at high but also at low . Our description of the ratio of the Pauli to the Dirac proton form factors and the ratio of shows that in our model we can obtain the results of both the methods (Rosenbluth and Polarization) by changing the slope of . Based on the model developed for proton the neutron form factors are calculated too. To do this the isotopic invariance can be used to change the proton GPDs to neutron GPDs. Hence, we do not change any parameters and conserve the same -dependence of GPDs as in the case of proton. Our calculation of shows that the variant which describes the polarization data is in better agreement with the experimental data. The calculation of more clearly shows that this variant much better describes the experimental data especially at low momentum transfer.

2 Gravitational form factors

As was shown in [6], the gravitational form factor for fermions is determined as

Figure 1: a)[left] Gravitation form factor (hard line) and Proton Dirac form factor (dashed line), both calculated in this work; the data for are from [7]. b)[right] Contributions of the (dashed line) and (hard line) to the gravitation form factor

Using this representation we can calculate the gravitational form factor for the nucleon. Our result for is shown in Fig.1a. Separate contributions of the and - quark distribution are shown in Fig.1b. At these contributions equal and ; and , . The sum of will be near zero . In accuracy of our approximations this result coincides with zero. In fig.1a we compare gravitational form factors with our calculations of electromagnetic form factors. It can be seen that at large momentum transfer they have the same -dependence. Of course, they essentially differ in size.

Figure 2: Densities of a)[left] the gravitational form factor and b)[right] the electromagnetic form factor .

3 Conclusion

We introduced a simple new form of the -dependence of GPDs. It satisfies the conditions of the non-factorization, introduced by Radushkin, and the Burkhardt condition on the power of in the exponential form of the -dependence. With this simple form we obtained a good description of the proton electromagnetic Sachs form factors. Using the isotopic invariance we obtained good descriptions of the neutron Sachs form factors without changing any parameters.

On the basis of our results we calculated the contribution of the and quarks to the gravitational form factor of the nucleons. The cancellation of these contributions at shows that the gravimagnetic form factor is zero for separate contributions, gluons and quarks, which confirms the result of [8].


  • [1] X.D. Ji, Phys. Lett. 78 , (1997) 610; Phys. A.V. Radyushkin, Phys. Rev. D 56 (1997) 5624.
  • [2] M. Guidal, M.V. Polyakov, A.V. Radyushkin, and M. Vanderhaeghen, Phys. Rev. D 72 (2005) 054013.
  • [3] O.V. Selyugin, O.V. Teryaev ArXiv:hep-ph/0712.1947.
  • [4] M. Burkardt , Phys. Rev. D 62 (2000) 119903.
  • [5] A.D. Martin et al., Phys. Lett. B 531 (2002) 216.
  • [6] A.V. Belitsky, X.D. Ji, Phys. Lett. B 538 , (2002) 289; S.J. Brodsky, Dae Sung Hwang, Bo-Qiang Ma, and Ivan Schmidt, Nucl.Phys. B 578 (2002) 326.
  • [7] A.F. Sill et al., Phys.Rev. D 48 (1993) 29.
  • [8] O.V. Teryaev, hep-ph/9803403.
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