High Precision Measurement of the Pion Form
Factors via Radiative Pion Decay π + → e+ νe γ
Maxim A. Bychkov, University of Virginia
• Brief review of rare pion decay modes
• Radiative pion decay: π + → e+ νe γ (πe2γ ) in more detail
• Apparatus and data analysis method
• Results, predictions and conclusions
MENU 2007
Forschungzentrum Juelich, September 13 2007
2
Known and Measured Pion and Muon Decays (PDG 2006)
Decay
π + → µ+ ν
0.9998770 (4)
(πµ2 )
µ+ νγ
2.00 (25) × 10−4
(πµ2γ )
e+ ν
1.230 (4) × 10−4
(πe2 )
e+ νγ
1.61 (23) × 10−7
(πe2γ )
π 0 e+ ν
1.025 (34) × 10−8
(πe3 , πβ )
e+ νe+ e−
π 0 → γγ
e+ e− γ
B
3.2 (5) × 10−9
0.98798 (32)
1.198 (32) × 10−2
e+ e− e+ e− 3.14 (30) × 10−5
e+ e−
6.2 (5) × 10−8
X
(πe2ee )
µ+ → e+ νν
e+ ννγ
∼ 1.0
0.014 (4)
e+ ννe+ e− 3.4 (4) × 10−5
3
Physics Goals in Radiative Pion Decay
◦ Structure of the pion by measuring pion form factors. Independent
measurement of pion polarizibility αE with real photon
◦ Deviations from V − A form of Lweak by measuring absolute
branching ratio
◦ Check of the CVC hypothesis by precise determination of the
vector form factor FV and its momentum transfer dependence
◦ Comprehensive input to the χPT expansion coefficients
4
π → eνγ:
Standard IB and
V − A terms
SM
A tensor
interaction, too?
Exchange of S=0 leptoquarks
P Herczeg, PRD 49 (1994) 247
5
π → eνγ: Differential Branching Ratio
2
theor
d B
dxdy
m2π
4 m2e
2
=
µ
2
2
d BIB
d BSD
d Bint
α
Bπ→eν
+
+
=
dxdy
dxdy
dxdy
2π
FV
fπ
¶2
½
IB(x, y)+
[(1 + γ)2 SD+ (x, y) + (1 − γ)2 SD− (x, y)]+
FV
+
−
[(1 + γ)SDint
(x, y) + (1 − γ)SDint
(x, y)]
fπ
¾
,
±
are analytical functions of
where IB, SD ± , SDint
x ≡ 2Eγ /mπ+ ≡ 1 − q 2 and y ≡ 2Ee /mπ+ and γ = FA /FV
FA (q 2 )= FA (0) is the axial-vector form factor
FV (q 2 )= FV (0)(1 + a × (1 − x)) is the vector form factor
6
1
Theoretical Description: π + → e+ νe γ Decay
1
18
15
0.9
0.1
12
0.8
0.8
0.3
9
0.6
0.7
y=2Ee/mπ
y=2Ee/mπ
6
0.6
3
0.6
SD ×10
+
0.5
4
0.4
1
SD ×10
-
4
0.2
0.4
0.3
0.9
1.2
1.5
1.8
0
0.2
0.4
0.6
0.8
1
0
0.2
x=2Eγ /mπ
0.4
0.6
0.8
1
x=2Eγ /mπ
1
1
+
0.8
y=2Ee/mπ
0.8
−
SD
SD
IB
Leyenda
y=2Ee/mπ
0.6
0.6
0.4
0.4
IB≈1.5 at (x,y)=(0.2,0.8)
0.2
0.2
0
0
0
0.2
0.4
0.6
x=2Eγ /mπ
0.8
1
0
0.2 0.4 0.6 0.8
x=2Eγ /mπ
1
7
Available Data on Pion Form Factors
cvc
|FV | =
1
α
s
2~
= 0.0259(9) .
πτπ0 mπ
FA × 104
reference
note
106 ± 60
Bolotov et al. (1990)
(FT = −56 ± 17)
135 ± 16
Bay et al. (1986)
60 ± 30
Piilonen et al. (1986)
110 ± 30
Stetz et al. (1979)
116 ± 16
world average (PDG 2004)
CVC relates slope a for π 0 → γγ ∗ to FV slope
a = 0.041+0.004
−0.007 (Portoles, Mateu 2007)
8
π → eνγ: Pion form factors and polarizability in χPT
To first order in χPT the pion weak form form factors fix:
FA
= 32π 2 (Lr9 + Lr10 ) ,
FV
while the pion polarizability is given by
αE =
4α
r
r
(L
+
L
9
10 ) ,
2
mπ F π
so that
αE =
α
FA
FA
−4
3
×
'
6.24
×
10
fm
×
.
2
2
8π mπ Fπ
FV
FV
[To resolve Lr9 and Lr10 one needs
1 2
2
1
hrπ i = 2 Lr9 −
6
Fπ
96π 2 Fπ2
Ã
ln
m2π
µ2
+
1
ln
2
m2K
µ2
+
3
2
!
,
w.a. 1.1 %; most accurate data, NA7 1986. ; last revisited at selex in 2001]
9
The PIBETA Experiment:
◦
◦
◦
◦
◦
◦
◦
stopped π + beam
segmented active tgt.
240-det. CsI(p) calo.
central tracking
digitized PMT signals
stable temp./humidity
cosmic µ antihouse
pure
CsI
PV
π+
AC1
MWPC1
beam
BC
AD
AC2
AT
MWPC2
10 cm
10
Data Analysis Method
In order to reduce the systematic uncertainties we use
π + → e+ νe (πe2 ) decay for normalization:
exp
Bπe2γ
Aπe2 × Nπe2γ
= Bπe2 ×
Nπe2 × Aπe2γ
B(A)πe2 is branching ratio (acceptance) of π + → e+ νe decay
Nπe2γ is the number of the detected πe2γ events
Aπe2γ is the acceptance of the πe2γ decay
11
Available Results: π + → e+ νe Decay
Marciano and Sirlin,
[PRL 71 (1993) 3629]:
Γ(π → eν̄(γ))
= (1.2352 ± 0.0005) × 10−4
Γ(π → µν̄(γ)) calc
Cirigliano and Rosell,
[hep-ph/07073439v1 (2007)]:
Γ(π → eν̄(γ))
= (1.2352 ± 0.0001) × 10−4
Γ(π → µν̄(γ)) calc
Decker and Finkemeier,
[NP B 438 (1995) 17]:
Γ(π → eν̄(γ))
= (1.2356 ± 0.0001) × 10−4
Γ(π → µν̄(γ)) calc
Experiment, world average
(PDG 2006):
Γ(π → eν̄(γ))
= (1.230 ± 0.004) × 10−4
Γ(π → µν̄(γ)) exp
12
Data Analysis: π + → e+ νe
Number of Events
25000
•
20000
π→eν
Simulation
Measurement
15000
10000
5000
0
45
50
55
60
65
Positron Energy (MeV)
Number of Events
π → eν +
10
background
µ
-50
75
Measurement
Monte Carlo
4
10 3
70
π
SUM
µp
0
50
tCsI - tπ-gate (ns)
100
150
13
Data Analysis Method: π + → e+ νe γ
π →e νeγ Region A
+
+
Θeγ=180
A
Ee+ >50 MeV
Eγ >50 MeV
Θe+γ >40o
0
Θeγ=180
0
π →e νeγ Region B
+
B
0
+
⊗
⊗
C
0
1
+
1
x=2Eγ/mπ+
⊗
SDMAX
0
z=2Eν/mπ+
Θeγ=180
y=2Ee+/mπ+ 1
0
Θeγ=0
IBMAX
0
1
1
x=2Eγ/mπ+
-
⊗
SDMAX
0
z=2Eν/mπ+
0
2Ee+/mπ+
+
y=2Ee+/mπ+ 1
⊗
⊗
IBMAX
0
⊗
⊗
Θeγ=180
0
Θeγ=0
0
Ee+ >50 MeV
Eγ >10 MeV
o
Θe+γ >40
0
SDMAX
0
Θeγ=180
0
-
IBMAX
π →e νeγ Region C
+
Θeγ=180
SDMAX
y=2Ee+/mπ+ 1
Θeγ=0
Ee+ >10 MeV
Eγ >50 MeV
o
Θe+γ >40
0
+
SDMAX
0
+
1
1
2Eγ /mπ+
x=2Eγ/mπ+
-
⊗
SDMAX
z=2Eν/mπ+
0
2Eν/mπ+
14
Data Analysis Method: π + → e+ νe γ
To extract the values of the FF’s we minimize:
χ2 =
X
i=A,B,C
(Biexp (FA , FV , a) − Bithe (FA , FV , a))2
σi2 (FA , FV , a)
Both experimental and theoretical B’s depend on FA , FV , a.
Region
Stat. uncert. (%)
Syst. uncert. (%)
A
0.54
0.79
B
2.0
0.58
C
1.2
1.38
15
Data Analysis: π + → e+ νe γ
4000
Region A
P/B = 73
2000
Number of events
0
-10
3000
-7.5
-5
-2.5
0
2.5
Region B
5
7.5
10
P/B = 2.2
©
©©
¼
2000
Acc. bgr.
1000
0
-10
1500
-7.5
-5
-2.5
0
2.5
Region C
5
7.5
10
P/B = 6.6
1000
500
0
-10
-7.5
-5
-2.5
0
2.5
t(e)-t(γ) (ns)
5
7.5
10
16
Data Analysis: π + → e+ νe γ
Number of events
• Measurement
1500
A
1000
B
500
0
0
0.2
0.4
0.6
0.8
2
λ ≡ (2Ee/mπ)sin (Θeγ/2)
1
1.2
π → eνγ
Simulation
2000
Number of events
π → eνγ
Simulation
2000
• Measurement
1500
A
1000
500
0
C
20
30
40
50
60
Photon Energy Eγ (MeV)
70
80
17
Results (I)
10 5
χ2 Minimization A+B+C
FA=0.0119(1)
2
χ (A+B+C)
10 4
10 3
FA≈ - 0.041
10 2
2 / χ2 ≈ 880
χ+
-
10
1
-600
-400
-200
0
FA-Axial Form Factor x104
200
18
150
χ2 Contours
140
FA Form Factor x 104
130
4σ
120
2σ
110
1σ
FV = 259 x 10-4
CVC
100
90
80
220
230
240
250
260
270
FV Form Factor x 104
280
290
19
Results (II)
for fixed CVC value of FV = 259 × 10−4
and fixed q 2 dep.
a = 0.041
improved value of
FA = (119 ± 1) × 10−4
numerical value of
FT = (−0.60 ± 2.78) × 10−4
ALTERNATIVELY
a new exp. value of
FV = (258 ± 17) × 10−4
the value of
FA = (117 ± 17) × 10−4
first meas’t of q 2 dep.:
a = 0.095 ± 0.058
improved limit on FT :
−5.2 ≤ FT × 104 ≤ 4.0 90% CL
20
Results (III)
Using fixed FV =0.0259 and a=0.041 we obtain
Eemin
+
Eγmin
(MeV)
(MeV)
50
50
10
min
θeγ
Bexp
Bthe
no. of
(×10−8 )
(×10−8 )
events
−
2.614(21)
2.599(11)
35.9 k
50
40◦
14.46(22)
14.45(2)
16.2 k
50
10
40◦
37.69(46)
37.49(3)
13.3 k
me
10
40◦
73.86(54)
74.11(3)
65.5 k
αE = (2.87 ± 0.10) × 10−4 fm3
τπ0 = (8.46 ± 1.11) × 10−17 s
21
Summary of Radiative Pion Decay Results
• We improved the precision of pion form factors FA , FV and
absolute B exp sixteen-,five- and tenfold respectively. Confirmed
the sign of the ratio FA /FV .
• We have determined for the first time the momentum dependence
of the charged pion FF’s.
• We set a new stringent limits on the tensor interaction; excellent
agreement with SM.
• We provided a sub-percent precision input data for the χPT.
• Our radiative π results provide critical input in controlling the
systematics of the approved π → eν (PEN) experiment, R-05-01.
• The PEN experiment will double the R-04-01 data set on radiative
π decays, with yet lower backgrounds.
22
Experiment R-04-01 (PIBETA) collaboration members:
V. A. Baranov,c W. Bertl,b M. Bychkov,a Yu.M. Bystritsky,c E. Frlež,a
N.V. Khomutov,c A.S. Korenchenko,c S.M. Korenchenko,c M. Korolija,f
T. Kozlowski,d N.P. Kravchuk,c N.A. Kuchinsky,c D. Mzhavia,c,e
D. Mekterović,a D. Počanić,a P. Robmann,g O.A. Rondon-Aramayo,a
A.M. Rozhdestvensky,c T. Sakhelashvili,b S. Scheu,g V.V. Sidorkin,c
U. Straumann,g I. Supek,f Z. Tsamalaidze,e A. van der Schaaf,g
B. A. VanDevender,a E.P. Velicheva,c V.V. Volnykh,c and Y. Wanga
a Dept
of Physics, Univ of Virginia, Charlottesville, VA 22904-4714, USA
b Paul
c Joint
Scherrer Institut, CH-5232 Villigen PSI, Switzerland
Institute for Nuclear Research, RU-141980 Dubna, Russia
d Institute
e IHEP,
Tbilisi, State University, GUS-380086 Tbilisi, Georgia
f Rudjer
g Physik
for Nuclear Studies, PL-05-400 Swierk, Poland
Bošković Institute, HR-10000 Zagreb, Croatia
Institut der Universität Zürich, CH-8057 Zürich, Switzerland