Can two-boson radiative Correction Explain the NuTeV Anomaly? - Internal Note

I discuss the possibility that two-boson radiative e ects are the reason for the fact that the rate of neutral-current divided by the rate of charged-current (NC/CC) events in the NuTeV experiment is one percent lower that the standard model prediction. Although two-boson e ects in the charged-current process are included in the Bardin radiative corrections (used by NuTeV) at the quark-parton level, interactions with spectator quarks and and spectator nucleons are not included. In the case when the second exchanged photon in a two-boson process is soft, its wavelenth is long and e ects of interaction with the other spectator-quarks in the nucleon, or the spectator nucleons in the iron target can be important. A one precent change in the NC/CC ratio can caused by an additional two-boson contribution at a level which is about half of the level which is currently needed to explain recent results in elastic electron-proton scattering. This note is written in order to motivate more theoretical e ort in the calculation of these two-boson spectator e ects, and does not claim that this e ect is the explanation the NuTeV anomaly. However, in the absense of reliable detailed calculations, this explanation cannot be rulled out at this time. TWO PHOTON EFFECTS IN ELECTRON AND MUON SCATTERING Recently, it has been suggested that the electric form factor of the proton as measured in electron scattering using the standard Rosenbluth separation technique [1], is sensitive to twophoton [2] radiative corrections. This has been proposed to explain a di erence between the Rosenbluth results and the results using the newer polarization transfer technique [3]. The polarization measurements do not directly measure the form factors, but measure the ratio GE/GM , as as shown in Figure 1. There are currently several experiments proposed at Je erson laboratory to study the magnitude of the two-photon contributions, as well as several theoretical e orts in calculating this e ect in more detail. A simple way to parametrize these two-photon e ects is in the form of an e ective additional longitudinal contribution to the elastic cross section, thus resulting in a larger electric form factor as measured via a Rosenbluth technique. For elastic scattering the ratio R is related to the ratio of elastic form factors by the following expression Relastic = (4M=Q)(GE=GM), or R p elastic = (0:481=Q )( pG p E/G p M) . For example for Q of 2.5 Gev the data in gure 1 (from Bodek, Budd and Arrington [4], show that Rpelastic= (0.19)(0:88) =0.14 0:04 from the t to the Rosenbluth separation data and Relastic= (0.192)(0:72)=0.10 0:02 from the t to the polarization transfer data. If this di erence is to be attributed to two-photon e ects, then it implies a 4% epsilon dependence in the radiative corrections and an uncertainty in R of 0.04 0.02. A xed longitudinal contribution of this order becomes much more important at larger values of Q as shown in the gure. As the electric form factor (or Relastic) becomes smaller, the two-photon contribution becomes larger than the electric form factor of the proton. The uncertainty in the longitudinal contribtution from two-photon e ects in the inelastic radiative corrections is actually lower than the above estimate because modern radiative corrections programs for inelastic electron and neutrino scattering (e.g. Bardin) already include two photon e ects at the parton level.