probing the standard model via rare pion decays

Probing the Standard Probing the Standard Model via Rare Pion Model via Rare Pion

DecaysDecays

E. Velicheva, E. Velicheva, V. BaranovV. Baranov

JINR, DUBNAJINR, DUBNA

Plan of TalkPlan of Talk• Introduction• Decay Anomaly• PIBETA Experiment in 1999 – 2001• PIBETA Experiment in 2004• Preliminary results of SM

minimizations

e

What Decay?What Decay? The radiative decay is regarded as a valuable source

of pion structure information because the inner bremsstrahlung is 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.

e

e

e

AF VF

:: Amplitude of DecayAmplitude of Decay e

::Differential Branching RatioDifferential Branching RatioThe 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

e

,)y,x(S1)y,x(S1f

mF

)y,x(SD)1()y,x(SD1mf2

mF)y,x(IB

2dxdy

d

intintV

22

2

e

2V

ee

1yxx

y11)y1()y,x(IB

2

2

21yxx1)y,x(SD 211),( yxyxSD

AFVF

yxx

yxS 111

,(int

1yx

xx1y1

x

1)y,x(S

2

int

),( yxSD ),( yxIB

::Differential Branching RatioDifferential 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.

e

V

A

F

F VF

ef

em m

m

E2y,

m

E2x e

E eE

e

ISTRA ExperimentISTRA ExperimentThe 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 .

e

MeV21E MeVE8.070E e o

e 60

Results of ISTRA experimentResults 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.

09.0014.0FV

23.041.0 e

Nikitin’s Radiative Nikitin’s Radiative CorrectionsCorrections

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 Interpretation of ISTRA Experiment’s Results: Poblaguev’ s ModelResults: 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.

)1(eq)q(F2

eGM 5

TT 3T 10)7.16.5(F

udF VGG )q(

Interpretation of ISTRA Experiment’s Interpretation of ISTRA Experiment’s Results: Poblaguev’ s ModelResults: 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).

)1(ed)1(uf2

G5

5T TL

ProblemsProblemsAccording 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).

e

du 5

du 5

Interpretation of ISTRA Experiment’s Interpretation of ISTRA Experiment’s results: Chizhov’s Modelresults: 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.

)1(eQ

QQd)1(uf

2

G452

5T TL

du 5

TT LL TT ff

Interprtation of ISTRA Experiment’s Interprtation of ISTRA Experiment’s Results: Chizhov’s ModelResults: 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 - 2001PIBETA 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.

Me7.51E,E e

MeV6.55E,MeV0.20E e

MeV0.20E,MeV6.55E e

3T 10)3.08.1(F


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

015.0443.0 )4(0115.0FA

0259.0FV

)6(0116.0FA


Table of Results

PIBETA Experiment in 2004PIBETA Experiment in 2004Since 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. e

e0

e

e

PIBETA Experiment in 2004PIBETA Experiment in 2004Experiment R–04–01 collaboration members:

Data Analysis : Data Analysis : Theoretical ModelTheoretical 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.

e

RC

Txfff22Tffff22

SD)ff(SDff2

SD)ff(SDffIB2dxdy

d

2TTT12TTTT

int2

AVintAV

2AV

2AVe

e

5e 1034.1m

m

T,T,A,Ve

2

T,T,A,V Ffm2

mf

x

y1T

1yxy1T

2

1

Data Analysis : Data Analysis : Radiative CorrectionsRadiative 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 group was

received by E. Kuraev and Y.Bystritsky

(Phys. Rev. D 69, (2004), 114004)

e

)y,x(IB

Data Analysis : Data Analysis : Radiative CorrectionsRadiative 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

e

A: B: C: LORC )B( 9108.0 910704.0 91074.3 NLORC )B( 910008.0 91011.0 910037.0

B

)B( LORC , % -3.56 -1.56 -4.74

B

)B( NLORC , % 0.036 -0.24 -0.05

Calculation was made using Fortran code for the three kinematic regions: A: MevEMevE

e7.51,7.51 ,

B: MevEMevEe

0.20,4.56 , C: MevEMevE

e4.56,0.20 . The results are given

in the table where the following value are given for each kinematic region: B = non-corrected rate

LORCB )( is absolute value of integrated leading order radiative corrections

NLORCB )( is absolute value of integrated radiative corrections with nonleading contributions.

B

B LORC )( is amount of change in percent where

the leading order radiative corrections are applied

B

B NLORC )( is amount of change in percent where

the nonleading order radiative corrections are applied

The kinematics of decayThe kinematics of decay e

Data AnalysisData AnalysisIn 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.

The decay was used for normalization of the decay.

e

decaynorm

decaynorm

normexpdecay AN

NABB

normB

decayN

decayA

e

Data AnalysisData AnalysisIn 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

e

Data AnalysisData 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.

e

e

normnorm N/A

The Positron Energy Spectrum for the The Positron Energy Spectrum for the Decay Decay e

Data AnalysisData 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).

e

MeV0.56E,E e

MeV0.56E,MeV0.20E e

MeV0.20E,MeV0.56E e 0

e0.40

Value of the Form Factors: Value of the Form Factors: Theoretical PredictionsTheoretical 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)

)0(FV

0

0270.0F

m

4

1)0(F

2V

)9(0262.0m

)(21)0(F

0

0

V

)9(0259.0m

21)0(F

0

V

qq22 – Dependence of Weak Form – Dependence of Weak Form

FactorsFactors

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

)0(F)q(F AA

)(026.0)(014.0025.0 syststat a

054.0026.0a

0026.00026.00326.0a

Available Data on Pion Form Available Data on Pion Form FactorFactor

Experimental History Experimental History of Pion Form Factors of Pion Form Factors

Scheme of MinimizationScheme of MinimizationTo 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

VF AF

i 2

i

expi

theori(

2sinm

E2 e2e

x

1yx

DistributionsDistributions of the RPD as a Functions of Parameter of the RPD as a Functions of Parameter λλ

Preliminary Results of SM Preliminary Results of SM MinimizationsMinimizations

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)

0259.0FV

4T 101.5F

70127.0FA

149.0

Preliminary Results of SM Preliminary Results of SM MinimizationsMinimizations

The Table of results

Thank you for attention

Results of Virginia GroupResults of Virginia Group

probing the standard model via rare pion decays

Documents