To the Annual Report of the 02/23/99

WSU Nuclear Science Group V. L. Rykov

Search for CP-violation and new physics beyond SM in polarized proton collisions at RHIC

The measurable asymmetries due to physics beyond SM, including CP- and/or T-violation, in charged and neutral current leptoproduction at polarized colliders are discussed.

- Introduction
- Phenomenological model and asymmetries
- Discussion
- Conclusion

Just in months ahead, the first high luminosity collisions of two polarized proton beams are expected to occur at RHIC in BNL at up to 500 GeV, bringing a new quality to the collider physics. In the collisions of polarized particles, the presence of two axial vectors of initial polarizations, fully controlled by experimenters, may dramatically increase the number of available for test correlations between participating vectors, generating asymmetries, which could relatively easily be measured. In frame of Standard Model (SM), many of these asymmetries are either strongly suppressed or strictly prohibited. Therefore, if some of them were found nonzero, this could be a strong indication of new physics beyond SM.

In this paper we will show a few examples of measurable asymmetries for hadronic leptoproduction via vector - and -boson exchange:

and (1)

which are probably the cleanest processes to search for new physics beyond SM at RHIC energies. If certain criteria met, it might be difficult to explain the observed nonzero correlations in theories without CP- and/or T-violation at the energy scale of hundreds of GeV, just above the *W*- and *Z*-mass range. At this energy scale, the CP/T-violating mechanism behind these correlations could virtually be anywhere and everywhere [1,2].

In the lowest order, processes (1) are represented by the usual *s-*channel annihilation graphs. The CP- and/or T-violation may occur in either or both of two vertices. In this report, for the sake of simplicity, the presence of CP-odd phases has been assumed in the quark sector only, and the usual (*V-A*)-interactions were kept for lepton coupling to gauge bosons. To carry out some particular calculations, the phenomenological lagrangian [2] has been used. For the charged current -coupling, this lagrangian looks as follows:

(2)

where *g* is a coupling constant, presumably on the order of the electroweak one, and L
is the energy scale of the “full strength” tensor interactions. The notations and are for the “upper” (*u* and *c*) and “lower” (*d*, *s*, and *b*) quarks, respectively. The CP-symmetry of model (2) is broken if any or all formfactors are complex. In the neutral current lagrangian, , of type (2) for -interactions, three formfactors, and , must be real. The CP-violation may occur only due to tensor coupling with purely imaginary .

In model (2), the tree-level cross section for the polarized quark and antiquark annihilation (1) in their center-of-mass system of reference is:

(3)

where and are for the *W*- or *Z*-peak mass and width, respectively. With two transversely polarized quarks, the double-spin CP- and T-odd asymmetries could be generated if CP-symmetry is broken in either vector or tensor coupling or both:

(4)

(5)

In formulae (4)-(5), and are transverse polarizations of initial quark and antiquark; and where is the momentum of the initial quark and or is the momentum of the final lepton. The upper and lower signs before the T-odd term in Eq. (4) correspond to and productions, respectively. Only the main contributions to the cross-section are kept in Eqs. (4)-(5), neglecting all others, suppressed by powers of .

In the ultrarelativistic limit of , the term does not contribute into the -annihilation cross sections of unpolarized or just longitudinally polarized quarks. However, in the case of transverse polarizations, “vector-tensor” interference could generate a number of T-even and T-odd single-spin asymmetries, as well as double-spin asymmetries with one quark polarized transversely and the other one polarized longitudinally:

(6)

where and are quark and antiquark helicities, respectively; the upper and lower signs follow the convention of Eq. (4).

The double-spin T-odd correlations (4) of the vector coupling could be detected as a transverse “quadrupole” azimuthal anisotropy of lepton production. In two CP-conjugate processes of -production, these “true” CP-odd asymmetries are of the opposite signs. This makes them distinguishable from “spurious” CP-even ones because the latter do not change signs after CP-conjugation. Therefore, if this anisotropy is detected in the neutral current annihilation, it could never be “true”, but only a “spurious'” one due to some CP-even initial and/or final state interactions.

CP-violation in “tensor” coupling makes the cross section dependent on the sign of product with the measurable where cross sections are for the “right”- and “left'”-handed mutual orientations of vectors , , and , respectively. The “true” CP-odd should be of the same sign in -and -productions, but “spurious” ones change signs after CP-conjugation. In the neutral current annihilation, neither CP-even theory can generate a nonzero . Therefore, a detection of a nonzero neutral-current in quark (or lepton) and __its__ antiquark (antilepton) annihilation would be an unambiguous evidence of CP-violation.

The single-spin and double-spin asymmetries of type (6) are strongly suppressed at the tree-level of Standard Model. On the other hand, for the equal strength of unusual interactions at the quark level, the single-spin asymmetries are less diluted, compared to double-spin ones, by not so strong correlations of quark’s, but particularly antiquark’s polarizations to the proton’s one. Therefore, single-spin asymmetries could be the most sensitive to a new physics beyond SM. Like in the case of nonzero double-spin asymmetries (4)-(5), to determine, whether CP-violation takes place, the relative signs of detected asymmetries in CP-conjugated processes have to be compared. It should be underlined that CP-violation may show up not only in nonzero T-odd correlations, but also in purely T-even ones. An example is fomula (6) where CP-odd imaginary parts are before the T-even scalar products while before the T-odd products of three vectors are the real, CP-even parts of participating amplitudes. This, to some extent surprising result, is apparently the feature of the particular interaction model with the lagrangian (2), although it is probably not so difficult to invent models where CP-violation generates T-odd single-spin asymmetries as well and vice versa.

To detect, but particularly to distinguish CP-odd and CP-even asymmetries, the directions of motion of the incident quark and antiquark have to be known. In polarized - (or , or , or …)-collisions, this won’t be a problem. This is not the case at *pp-*colliders. As a result, for example, T-odd double-spin asymmetries (4)-(5) and some single-spin asymmetries integrated over the full phase space will obviously be zero. However, if a valence quark participated in the CP-odd process of *W-* or *Z-*production, the produced boson would likely be moving in the direction of the incident “hard'” valence quark rather then in the direction of a “soft” sea antiquark. As a result, the nonzero T-odd asymmetries might separately be detectable in the forward and backward hemispheres. In the most favorable case of CP-violating *udW-*coupling, the “true” CP-odd correlations in -production could even be distinguishable from the “spurious'” ones.

An expected RHIC sensitivity to the asymmetries above at *pp-*level would be ~. It is yet to be studied, how this sensitivity should be transferred back to the quark level, as well as the limitations to CP-odd amplitudes, arising from already accomplished experiments.

This work was supported in part by the U.S. Department of Energy Grant DE-FG0292ER40713. At various stages, it has been reported to a number of workshops and seminars in BNL and also in the Indiana University, to the plenary session of the STAR Collaboration Meeting at BNL in July 1998. It will be published in the Proceedings of the 13^{th} International Symposium on High-Energy Spin Physics, which had been held in Protvino, Russia, in September 1998.

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