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Probing the Standard Model via Rare Pion Decays. E. Velicheva, V. Baranov JINR, DUBNA. Plan of Talk. Introduction Decay Anomaly PIBETA Experiment in 1999 – 2001 PIBETA Experiment in 2004 Preliminary results of SM minimizations. What Decay?.
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Probing the Standard Model via Rare Pion Decays E. Velicheva, V. Baranov JINR, DUBNA
Plan of Talk • Introduction • Decay Anomaly • PIBETA Experiment in 1999 – 2001 • PIBETA Experiment in 2004 • Preliminary results of SM minimizations
What Decay? The radiative decay is regarded as a valuable source of pion structure information because the inner bremsstrahlungis strongly suppressed as a result of small value of the electron mass. Precise measurement of the radiative pion decay (RPD) branching ratio provides an excellent source of information on the value of the weak axial and vector form factors respectively, together with limits on the non-(V - A) contributions to Standard Model Lagrangian. • For the long period the radiative pion decay has been considered a unique system for searching physics beyond SM.
:Differential Branching Ratio The probability of the decay is (D. A. Bryman et. al., Phys.Rep. 88 (1982), 151): where is the inner bremsstrahlung; and are structure-dependent terms parametrized by two form factors describing the interaction with the vector and axial-vector weak handronic currents; and are terms describing the interference between and
:Differential Branching Ratio Here the following constants were used : ; is vector form factor calculated from the measured lifetime, using the conserved vector current (CVC); is the probability of the decay; 130.7 – is the pion decay constant; , are the masses of the positron and pion respectively. The variables x and y defined as: and are the photon and positron energies.
ISTRA Experiment The first experiment, which has alarmed about deviations from SM in RPD, was ISTRA experiment: V. N. Bolotov et al., Phys.Lett. B 243 (1990) 308. In the ISTRA experiment the radiative pion decay has been performed with a secondary 17 GeV negative pion beam on the IHEP machine with the ISRTA detector of the Institute for Nuclear Research. The high energy beam has enabled to investigate this decay in the wide range of kinematic variables: , , which include events with .
Results of ISTRA experiment The vector form factor has been determined in a model independent way: .The axial-to-vector form factor ratio has been determined: . The probability of the decay was found to be B.R.=(1.61+0.23)×10-7 for the phase space region under consideration. In ISTRA has been found that there is a good agreement for the IB and SD+ contributions. The discrepancy for total branching ratio (more than 3 standard deviations) is related to the negative (unphysical) value of the SD- contribution. It has been found that the measured number of events is about 30% smaller than expected.
Nikitin’s Radiative Corrections The radiative corrections has been calculated by I.N. Nikitin (Sov. J. Nucl. Phys. 54, (1991) p. 621). The RC had small positive values and did not explain discrepancy.
Interpretation of ISTRA Experiment’s Results: Poblaguev’ s Model The interpretation of ISTRA result in the framework of SM brought to a violation of CVC hypothesis. In order to describe this strange result a new interaction with a tensor lepton current with was introduced by A.A. Poblaguev (A.A. Poblaguev, Phys. Lett. B 238 (1990) p.108). Here and is the photon polarization vector.
Interpretation of ISTRA Experiment’s Results: Poblaguev’ s Model • Such type of phenomenologically introduced amplitude can be induced by a four-fermion tensor interaction of quark and lepton currents As far as tensor intermediate bosons are absent in SM and its popular extensions, the conclusion was made that such a type of interaction can be generated only by leptoquark exchange (P. Herczeg, Phys. Rev D 49 (1994) 247).
Problems • According to the Grand Unified Models (GUM) the leptoquark should be vary massive 1015 GeV and their influence at the electroweak scale should be negligibly small. The introduction of the new tensor interaction leads to another problem: • on the one hand for kinematic reasons the tensor interaction does not contribute directly to semileptonic two particle pion decay but on the other hand, owing to electromagnetic radiative corrections, the pseudotensor current leads to the generation of a pseudoscalar quark current , to which the pion decay is very sensitive. • Hence, the value of tensor form factor should be two orders of magnitude smaller than its required value for the explanation of ISTRA results (M. V. Voloshin, Phys. Lett. B 283 (1992) 2753).
Interpretation of ISTRA Experiment’s results: Chizhov’s Model The solution of these problems was offered by M. Chizhov (Mod. Phys. Lett A 8 (1993) 2753; hep-ph/0402105) via introduction in addition to local quark-lepton current a new non-local quark-lepton current The pseudotensor term does not appear in the sum if are positive dimensionless coupling constants. The tensor term does not contribute to pseudoscalar pion decay because of parity conservation in electromagnetic interactions.
Interprtation of ISTRA Experiment’s Results: Chizhov’s Model This type of interaction can arise due to an exchange of new spin = 1 chiral bosons which interact anomalously with matter.
PIBETA Experiment in 1999 - 2001 Decay events acquired in the PIBETA experiment (R-89-01) revealed a discrepancy with theoretical expectations (E. Frlež et al., Phys. Rev. Lett. 93, 181804 (2004); PSI Scientific Report 2003, vol. 1, 10). The RPD data were grouped into three kinematic regions: A: B: C: The overall good agreement between PIBETA data and predictions based on SM was spoiled by statistically significant (7) deficiency in the measured branching ratio in region B. Inclusion of would account the anomaly observed in R-89-01.
PIBETA Experiment in 1999 - 2001 The best CVC fit to experimental data: or with This consistent with chiral Langrangian calculated by G.Q. Grend et. al., Nucl. Phys. B 684, (2004), 281; J. Bijnens and P. Talavera, Nucl.Phys. B 489, (1997), 387; PDG, Phys. Lett B 592, (2004), 1
PIBETA Experiment in 1999 - 2001 Table of Results
PIBETA Experiment in 2004 • Since both collaborations have observed a deficit of events in comparison with SM expectation it became one of the reasons for a new PIBETA experiment. PIBETA collaboration has used a detector system based on non-magnetic pure CsI calorimeter at Paul Scherrer Institute to collect the world’s largest sample of rare pion and muon decays. PIBETA collaboration has measured the absolute decay branching ratio with a 0.55% total uncertainly. The data set were used to extract weak axial and vector pion form factor. The data were used to find the improved value of Michel parameter. • Now we will discuss only decay.
PIBETA Experiment in 2004 Experiment R–04–01 collaboration members:
Data Analysis : Theoretical Model The theoretical model including tensor interaction and suggested by Chizhov (Phys. Part. Nucl. Lett., 2, (2005), 7) has been used to analyze the experimental data. The formula for differential branching rate was the following: Here , ; are the terms describing the tensor interaction.
Data Analysis : Radiative Corrections RC to the inner bremsstrahlung obtained by Nikitin allow taking into account only the contributions of soft photon emission and virtual corrections. The precise formula contains hard and collinear photons emission in addition to contributions of Nikitin’s formula and founded on methods of renormalization groupwas received by E. Kuraev and Y.Bystritsky (Phys. Rev. D 69, (2004), 114004)
Data Analysis : Radiative Corrections We have calculated the integrated radiative corrections to radiative pion decay rate. Results are given in the Table . All the values of RC are negative sign
Data Analysis In order to reduce the systematic uncertainty related to the number of stopped pions, the radiative pion decay was used to normalize the yields of the decays under study as follows: where is branching ratio of the normalizing decay, is the number of events detected for a given decay, is the acceptance for same decay. • Thedecay was used for normalization of the decay.
Data Analysis In order to extract the number of detected decays we used the time spectra of the positrons registered in CsI calorimeter. The fig. 1 shows the quality of the minimizations. FIG.1
Data Analysis To reconstruct the full response of detector we used a GEANT3 based simulation of the PIBETA detector. Fig 2 shows the match between the simulated and detected shapes of the positron energy spectrum for the decay. These methods allowed to calculate the normalizing constants with 0.5% precision.
Data Analysis Radiative pion events have been recorded in three overlapping phase space regions: A: B: C:and opening angle The region A is the most sensitive to the structure parameters of the pion. The region C can be used to determine the dependence of the pion form factors on the momentum squared transferred to the lepton pair (N. B. Skachkov, hep-ph/0206183).
Value of the Form Factors: Theoretical Predictions Theoretical predictions for the value of the form factors are some what model dependent. Assuming CVC hypothesis the vector form factor is directly related to the amplitude and can be extracted from the experimental width of the decay or (V. G. Vaks& B. L. Ioffe, Nuovo Cimento 10, (1958), 342). These values are in fair agreement with the calculation in the relativistic quark model (RQM) and with the leading order calculations of the chiral perturbation theory (CHPT) (C.Q. Geng et al., Nucl. Phys B 684, (2004), 281)
SINDRUM I Collaboration Phys. Rev. D, 45, (1992), 1439 Vector dominance model F.Farzanpay et al., Phys.Lett. B, 278, (1992), 413 CELLO Collaboration Z. Phys. C, 49, (1991), 401 q2 – Dependence of Weak Form Factors
Scheme of Minimization To analyze the data in regions A, B and C the following minimization scheme has been used: • 1) we fixed value of and the value of parameter was free • 2) fit where or
Preliminary Results of SM Minimizations fixed (M. A. Bychkov, Ph.D. thesis, University of Virginia, 2005) at the 90% confidence limit. This limit is more than an order of magnitude smaller than the ISTRA collaboration re-analysis result reported by Poblaguev (Phys. Rev. D, 68, (2003), 054020)
Preliminary Results of SM Minimizations The Table of results
