Pion beta decay,Vud and π → `νγ

Emil Frlez

for the PIBETA Collaboration

University of Virginia

4th International Workshop on

CHIRAL DYNAMICS 2003

Theory and Experiment

Bonn, GERMANY

8–13 September, 2003

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The PIBETA Collaboration:

M. Bychkov, E. Frlez, W. Li, R.C. Minehart, D. Pocanic,L.C. Smith, W.A. Stephens, B.A. Vandevender,

Y. Wang, K.O.H. Ziock

University of Virginia, Charlottesville, VA 22904, USA

W. Bertl, J. Crawford, Ch. Bronnimann, M. Daum,R. Horisberger, S. Ritt, R. Schnyder, H.-P. Wirtz

Paul Scherrer Institut, CH-5232 Villigen, Switzerland

T. Kozlowski

Institute for Nuclear Studies, PL-05-400 Swierk, Poland

B. G. Ritchie

Arizona State University, Tempe, AZ 85287, USA

V.V. Karpukhin, N.V. Khomutov, A.S. Korenchenko,S.M. Korenchenko, N.P. Kravchuk, N.A. Kuchinsky

Joint Institute for Nuclear Research, Dubna, Russia

D. Mzhavia, Z. Tsamalaidze

Instit. for High Energy Physics, Tbilisi St. Univ., Georgia

I. Supek

Rudjer Boskovic Institute, Zagreb, Croatia

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The PIBETA Experiment: MOTIVATION

Provide precision tests of Standard Model and

QCD predictions:

• π+ → π0e+νe – main goal

◦ SM tests from CKM unitarity

• π+ → e+νeγ(ee)

◦ FA/FV , π polarizability (χPT prediction)

◦ tensor coupling besides V − A

• µ+ → e+νeνµγ(ee)

◦ departures from V − A in Lweak

• π+ → e+νe – 2nd phase

◦ e-µ universality

◦ pseudoscalar coupling besides V − A

◦ massive neutrino, Majoran, ...

Pion Beta (πβ) Decay: Theory

Quark-Lepton Universality

The basic weak-int. V -A form (e.g., µ decay):

〈e|lα|νe〉 → ueγα(1 − γ5)uν

is preserved in hadronic weak decays

〈p|hα|n〉 → upγα(GV − GAγ5)un with Gi ' 1 .

Departure from GV = 1 (plain CVC) comes from

weak quark mixing (Cabibbo 1963):

GV = Gµ cos θC(= GµVud) cos θC ' 0.97

which with 3 q generations is generalized in the

Cabibbo-Kobayashi-Masakawa matrix (1973):

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

CKM unitarity cond.: |Vud|2 + |Vus|

2 + |Vub|2 ?

= 1,

provides a means of testing the limits of the SM.

Status of CKM Unitarity

|Vus| ' 0.2196 ± 0.0026 from Ke3 decays.

|Vub| ' 0.0036 ± 0.0007 from B decays.

(a) Superallowed Fermi nuclear β decays

1990 Hardy reconciled discrepancies between Ormand

& Brown and Towner et al. ft values:

|Vud|2 + |Vus|

2 + |Vub|2 = 0.9962 ± 0.0016,

or 1 − 2.4σ.

(b) Neutron β decay

3∑

i=1

|Vui|2 = 1.0096 ± 0.0044, or 1 + 2.3σ,

[after Erozolimskiı et al. (1990)]

3∑

i=1

|Vui|2 = 0.9917 ± 0.0028, or 1 − 3.0σ.

[Abele et al, PRL, May 2002]

(c) Pion β decay – this work

Pion Beta Decay:

π± → π0e±ν BR ' 1 × 10−8

Pure vector transition: 0− → 0−

Theoretical decay rate at tree level:

1

τ0=

G2F |Vud|

2

30π3

(

1 −∆

2M+

)3

∆5f(ε, ∆)

= 0.40692 (22)|Vud|2 (s−1) .

With radiative and loop corrections we get:

1

τ=

1

τ0(1 + δ) ,

so that the branching ratio is

BR(πβ) =τ+

τ0(1 + δ)

= 1.0593 (6) × 10−8(1 + δ)|Vud|2 .

Recent calculations of pion beta decay

radiative corrections

(1) In the light-front quark model

W. Jaus, Phys. Rev. D 63 (2001) 053009.

• total RC for pion beta decay:

δ = (3.230 ± 0.002) × 10−2 .

(2) In chiral perturbation theory

V. Cirigliano, M. Knecht, H. Neufeld and

H. Pichl, hep-ph/0209226

• χPT with e-m terms up to Oe2p2

• theoretical uncertainty of 5 × 10−4 in

extracting |Vud| from BR(

πe3(γ)

)

.

Pion Beta (πβ) Decay: Experimental Method

PIBETA Experiment:

◦ stopped π+ beam◦ segmented active tgt.◦ 240-elem. CsI(p) calo.◦ central tracking◦ digitized PMT readout◦ cosmic µ antihouse◦ stable temp./humidity

AT

MWPC1

MWPC2

PV

AD

AC1

AC2BC

CsIpure

π+beam

10 cm

PIBETA Detector Assembly (1998)

Experimental Method: Summary

• Detect π+ decays at rest (during a delayed

180 ns gate).

gate

π stop

beam veto

π

-30 0 150 ns

• Use π+ → e+ν prescaled for normalization.

• Accept every πβ trigger – unbiased (γγ

coincidences above Michel endpoint)

1

τπβ

=1

τπ+

·BReνfpresc

BRπ0→γγ

·Aeν

Aπβ

·Nπβ

Neν

Aπβ , Aeν are acceptances for the decay modes,

respectively.

Online “πβ” Energy Spectrum:

True πβ events buried deep under overwhelming

background!

πβ Signal-to-Background Ratio

πβ Timing and Angular Distributions

πβ: Normalization to π → eν Yield

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Radiative Pion Decay (π → eνγ): Theory

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REVIEW OF PARTICLE PROPERTIES

Particle Data Group

π± → l±νγ AND K± → l±νγ

FORM FACTORS

Written by H. S. Pruys (Zurich University)

“The electroweak decays of the pseudoscalar

mesons are investigated to learn something about

the unknown hadronic structure of these mesons,

assuming a standard V −A structure of the weak

leptonic current. The experiments are quite dif-

ficult, and it is not meaningful to analyse the

results using parameters for both the hadronic

structure (decay constants, form factors) and

the leptonic weak current (e.g., to add pseu-

doscalar or tensor couplings to the V − A cou-

pling).”

LAMPF: L. E. Piilonen et al.,

Phys. Rev. Lett. 57, 1402-1405 (1986)

π → eνγ Signal

LAMPF: L. E. Piilonen et al.,

Phys. Rev. Lett. 57, 1402-1405 (1986)

π → eνγ Analysis

π → eνγ Signal-to-Background Ratios

π → eνγ Invariant Masses

π → eνγ Timing Distributions

π → eνγ Axial-to-Vector Form Factor Ratio

π+ → e+νeγ Exp vs Theoretical Branching Ratios:

Glimpse at Pion Weak Form Factors

Fit Fixed Fitted χ2

Parameters Parameters

FV = 0.0170(80)PGP FA = 0.0116(16) None 2751

FT = 0

SM/ FV = 0.0259(5) FA = 0.0123(4) 275.0CVC FT = 0 γ = 0.475(18)

CVC FV = 0.0259(5) FA = 0.0141(5) 1.0FT = −0.0022(4)

π+ → e+νeγ Exp vs The Branching Ratios:

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π+ → e+νeγ: λ Distribution

PIBETA EXPERIMENT:

PROGRESS SUMMARY

• π+ → π0e+ν Branching Ratio

• Current PIBETA Statistical Uncertainty

0.4%, Systematic Uncertainty 0.7%

• Extracted Branching Ratio in Agreement

with CVC Hypothesis and Radiative

Corrections

• π+ → e+νγ Decay

• Extracted Axial-to-Vector Form Factor

Ratio in Agreement with Chiral

Prediction, γEXP = 0.475± 0.018 vs

γCHIRAL = 0.463 (B. R. Holstein 1986)

• Limit on Phenomenological Tensor Term

FT ≤ 3 · 10−3 at 95% CL