Measurement of form factors
Introduction
Since long ago [1] decays (, ) have offered the opportunity to test several features of the electroweak interactions such as the V–A structure of weak currents, current algebra and the predictions of chiral perturbation theory. These decays have been the object of a renewed interest both on the experimental and theoretical side since they provide the cleanest [2] way to extract the CKM matrix element . decays give access to the product , where , the vector form factor at zero momentum transfer, has to be determined by theory. The recent calculations at [3] in the framework of chiral perturbation theory show how could be experimentally constrained from the slope and the curvature of the scalar form factor of the decay. In addition, the form factors are needed to calculate the phase space integrals which are another ingredient for the determination of . Finally, very recently it has been pointed out [4] how a precise measurement of the value of at the Callan–Treiman point [5] could provide a clean test of a small admixture of right-handed quark currents (RHCs) coupled to the standard W boson.
Until recently, the experimental knowledge [6] on form factors was mainly based on a certain number of old measurements dating back to the seventies. The slopes obtained from decays were less precise than those determined in decays, and a large difference between the results from charged and neutral kaon decays was present. This difference was more pronounced for the slope where, in addition, the situation was confused also by the presence of negative values. Very recent high precision experiments [7], [8], [9], [10], [11] provided a more accurate determination of these quantities with values smaller than the old PDG averages and agreement between K0 and measurements has been established. Furthermore, evidence for a quadratic term in the vector form factor was found, at the level of about 2σ, by ISTRA+ in and by KLOE in decays. A cleaner indication came also from KTeV, both in and decays, with a significance of about 3σ.
This Letter reports on a new high statistics measurement of form factors. Following this introduction Section 2 recalls the formalism about the decays, Section 3 describes the experimental set-up, Section 4 reports about the analysis, and Section 5 delineates the fitting procedure and the treatment of the systematic error.
Section snippets
The decay
Only the vector current contributes to decays. As a result the matrix element can be written in terms of two dimensionless form factors : where and are the kaon and pion four momenta, respectively, and are the lepton spinors, is the lepton mass and is the square of the four-momentum transfer to the lepton pair. The form factor is related to a scalar term proportional to the lepton
Experimental set-up
For the measurement reported here the data were taken during a dedicated run period in September 1999. A pure beam was produced by 450 GeV/c protons from the CERN SPS hitting a beryllium target. The decay region was contained in a 90 m long evacuated tube and was located 126 m downstream the target after the last of three collimators.
The NA48 detector was originally designed for a precise measurement of direct CP violation in the neutral kaon decays to two pions. A detailed description can
Event selection
The data sample consists of about 108 triggers recorded alternating the polarities of the magnetic field of the spectrometer. To identify the decays the following selection criteria were applied to the reconstructed data.
The events were required to have exactly two tracks of opposite charge forming a vertex in the decay region, defined to be between 7.5 m and 33.5 m from the exit of the final collimator and within 2.5 cm from the beam line. The distance of closest approach of these two
Fitting procedure
The measurement reported here is based on the study of the Dalitz plot density. As mentioned before, the ambiguity in the determination of the kaon energy leads to two solutions for the energy and for the CMS energies of the μ and the π. Consequently each event has a double location on the Dalitz plot. We chose to evaluate and by using only the low kaon energy solution. According to the MC simulation, this corresponds to the most probable solution, being in 61% of cases the correct
Conclusions
The decay has been studied with the NA48 detector. A sample of reconstructed events was analyzed in order to extract the decay form factors.
Studying the Dalitz plot density we measured the following values for the form factors parameters: , and .
Our results indicate the presence of a quadratic term in the expansion of the vector form factor in agreement with other recent analyses of kaon
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Cited by (0)
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Funded by the UK Particle Physics and Astronomy Research Council.
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Present address: Ottawa-Carleton Institute for Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
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Present address: High Energy Accelerator Research Organization (KEK), Tsukuba, Japan.
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Present address: Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, UK.
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Present address: Department of Physics, University of Oxford, Denis Wilkinson Building, Keble road, Oxford, OX1 3RH, UK.
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Present address: University of British Columbia, Vancouver, BC, Canada, V6T 1Z1.
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Present address: Istituto di Cosmogeofisica del CNR di Torino, I-10133 Torino, Italy.
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Present address: Scuola Normale Superiore e Sezione dell'INFN di Pisa, I-56100 Pisa, Italy.
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Present address: Northwestern University, Department of Physics and Astronomy, Evanston, IL 60208, USA.
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Present address: Dipartimento di Fisica dell'Università e Sezione dell'INFN di Ferrara, I-44100 Ferrara, Italy.