Status Report from Tau subgroup of the HFAG

0.13 MB·English

by  Swagato Banerjee

Status Report from Tau subgroup of the HFAG
1
1
0 Swagato Banerjeea, Kiyoshi Hayasakab, Hisaki Hayashiic, Alberto Lusianid, J. Michael Roneya, Boris
2 Shwartze

n
aUniversity of Victoria, Canada.
a
J
bNagoya University, Japan.
6
2
cNara Womana’s University, Japan.

x] dScuola Normale Superiore and INFN Pisa, Italy.
e
- eBudker Institute of Nuclear Physics, Russia.
p
e
The aim of Tau subgroup of the HFAG is to provide average values of the mass and branching fractions of
h
[ thetau lepton. Using thebranchingfractions, we present tests of charged current lepton universality and obtain
estimatesfor|Vus|. Wealsosummarizethestatusofsearchesforleptonflavorviolatingdecaysofthetaulepton.
1
v
8
3
1 The latest averages from the HFAG have
5 been published in Ref. [1]. Online up-
.
1 dates of the Tau Section are available at
DELCO 1978
0 http://www.slac.stanford.edu/xorg/hfag/tau/. 1783.00 +3.00
1 ARGUS 1 -94.9002
1 1776.30 ± 2.40 ± 1.40
: 1. Mass of the τ lepton BES 1996
v 1776.96 +0.18 +0.25
-0.21 -0.17
i The mass of the τ lepton has recently been CLEO 1997
X 1778.20 ± 0.80 ± 1.20
measured by the BaBar [2] and Belle [3] exper- OPAL 2000
ar iments using the end-point technique from the 1775.10 ± 1.60 ± 1.00
Belle 2007
pseudo-massdistributioninτ− →π−π−π+ντ de- 1776.61 ± 0.13 ± 0.35
cays,aswellasbytheKEDRexperiment[4]from BaBar 2009
astudyoftheτ+τ− cross-sectionaroundthepro- 1776.68 ± 0.12 ± 0.41
KEDR 2009
duction threshold. In Figure 1, we present the 1776.69 +0.17 ± 0.15
-0.19
measurements and average values of m . PDG’10 Average
τ 1776.82 ± 0.16
HFAG Average
1776.77 ± 0.15 (CL = 57.0%)
2. τ Branching Fractions:
HFAG-Tau
Average values of the τ branching fractions 1 Summer 2010
are obtained from a global unitarity constrained 1770 1775 1780
fit. We account for correlations due to common m [MeV/c2]
τ
dependenceofnormalizationontheτ−paircross-
section [5] and assumed branching fractions for
thebackgroundmodes. Thedetector-specificsys-
tematics uncertainties are considered to be fully
correlatedbetweenmeasurementsofthesameex- Figure1. Measurementsandaveragevalueofm .
τ
1chargeconjugateτ decays areimpliedthroughout
1
2
periment. Allofthese153measurementsareexpressedas
We use 131 measurements from non-B-factory a linear function of the form ( iαiPi) of “base”
experiments, which includes the set used in the (PjβjPj)
global fit performed by the PDG [6]. The mea- branching fractions (Pi), which are chosen such
P
surements from non-B-factories include 37 mea- that they sum up to unity. The results of the
surements from ALEPH, 2 measurements from fit are shown in Table 1, which has χ2/ndof =
ARGUS, 1 measurement from CELLO, 36 mea- 143.4/117(CL = 4.9%).
surements from CLEO, 6 measurements from
CLEO3,14measurementsfromDELPHI,2 mea-
surements from HRS, 11 measurements from L3, 5
19 measurements from OPAL, and 3 measure-
ments from TPC. Finally, we include the follow-
BaBar
ing measurements from the B-factories (BaBar
4 Belle
and Belle):
• 12 measurements from BaBar:
5
0. 3
r
B(τ− →µ−ν¯µντ)/B(τ− →e−ν¯eντ) [7], r pe
B(τ− →π−ντ)/B(τ− →e−ν¯eντ) [7], be
m
B(τ− →K−ντ)/B(τ− →e−ν¯eντ) [7], Nu 2
B(τ− →K−π0ν ) [8]
τ
B(τ− →K¯0π−ν ) [9]
τ 1
B(τ− →K¯0π−π0ν ) [10]
τ
B(τ− →π−π−π+ν (ex. K0)) [11]
τ
B(τ− →K−π−π+ντ (ex. K0)) [11] 0-3 -2 -1 0 1 2 3
B(τ− →K−π−K+ντ) [11] Sigma Difference
B(τ− →K−K−K+ν ) [11]
τ
B(τ− →3h−2h+ν (ex. K0)) [12]
τ
B(τ− →2π−π+ην (ex. K0)) [13]
τ
Figure2. NormalizeddifferenceofB-factorymea-
surements w.r.t average of non-B-factory mea-
• and 10 measurements from Belle:
surements.
B(τ− →h−π0ν ) [14]
τ
B(τ− →K¯0π−ν ) [15] The differences between the global fit per-
τ
formed by PDG and us are:
B(τ− →π−π−π+ν (ex. K0)) [16]
τ
B(τ− →K−π−π+ν (ex. K0)) [16] • We expand the list of base modes from 31
τ
to37toaccountforrecentmeasurementsby
B(τ− →K−π−K+ν ) [16]
τ the B-factories with significant precision.
B(τ− →K−K−K+ν ) [16]
τ
• We use the originalcorrelationmatrixpub-
B(τ− →π−π0ην ) [17]
τ lished by ALEPH [18] between hadronic
B(τ− →K−ηντ) [17] modes instead of between pionic modes.
B(τ− →K−π0ην ) [17]
τ • We use updated background estimates to
B(τ− →K¯0π−ηντ) [17] adjust the B-factory measurements.
3
• We avoid applying the PDG-style scale
Base modes Branching fractions
factors to all our measurements. How-
(from τ− decay) (in %)
ever, the BaBar and Belle measurements
leptonic modes
of B(τ− →K−K+K−ν ) are 5.4 σ apart.
τ e−ν¯ ν 17.833 ± 0.040
We scale the errors on these 2 measure- e τ
µ−ν¯ ν 17.408 ± 0.038
ments only, following the PDG procedure µ τ
non-strange modes
for single-quantity averaging.
π−ν 10.831 ± 0.051
τ
The three-kaon decays had not been ob- π−π0ν 25.531 ± 0.090
τ
served before the B-factory era. For the re- π−2π0ν (ex. K0) 9.278 ± 0.097
τ
maining 20 B-factory measurements, Figure 2 π−3π0ν (ex. K0) 1.046 ± 0.074
τ
shows a histogram of the normalized difference h−4π0ν (ex. K0,η) 0.107 ± 0.039
τ
((B-factory value minus averaged non-B-factory K−K0ν 0.160 ± 0.016
τ
value)/estimated uncertainty in the difference). K−π0K0ν 0.162 ± 0.019
τ
The average difference between the two sets of π−K0K0ν 0.024 ± 0.005
S S τ
measurements is -0.98 σ (-1.26 σ for the 9 Belle π−K0K0ν 0.119 ± 0.024
S L τ
measurementsand-0.75σ forthe 11BaBarmea- π−π−π+ν (ex. K0,ω) 8.983 ± 0.050
τ
surements). Althoughthissystematictrendisyet π−π−π+π0ν (ex. K0,ω) 2.751 ± 0.069
τ
to be understood, the magnitude of discrepancy h−h−h+2π0ν (ex. K0,ω,η) 0.097 ± 0.036
τ
isless thanthe value ofreportedbythe PDG[6]. h−h−h+3π0ν 0.032 ± 0.003
τ
π−K−K+ν 0.144 ± 0.003
τ
3. Tests of Lepton Universality π−K−K+π0ν 0.006 ± 0.002
τ
3h−2h+ν (ex. K0) 0.082 ± 0.003
τ
From the unitarity constrained fit, we obtain
3h−2h+π0ν (ex. K0) 0.020 ± 0.002
B(τ− →µ−ν ν )/B(τ− →e−ν ν ) = 0.9762 ± τ
µ τ e τ π−π0ην 0.139 ± 0.007
τ
0.0028,whichincludesacorrelationof18.33%be-
π−ων 1.959 ± 0.064
τ
tweenthebranchingfractions. Thisyieldsavalue
h−π0ων 0.409 ± 0.042
of ggµe = 1.0019 ± 0.0014, which is consistent τ strange modes
wit(cid:16)h th(cid:17)e Standard Model (SM) value. K−ντ 0.697 ± 0.010
Using the world averaged mass, lifetime and K−π0ν 0.431 ± 0.015
τ
meson decay rates [6], we determine gτ = K−2π0ντ (ex. K0) 0.060 ± 0.022
gµ K−3π0ν (ex. K0,η) 0.039 ± 0.022
0.9966 ± 0.0030 (0.9860 ± 0.0073) from(cid:16)the(cid:17)pi- τ
K¯0π−ν 0.831 ± 0.018
onic and kaonic branching fractions, with a cor- τ
K¯0π−π0ν 0.350 ± 0.015
relation of 13.10%. Combining these results, we τ
K¯0π−2π0ν 0.035 ± 0.023
obtain ggµτ = 0.9954 ± 0.0029,which is consis- K¯0h−h−h+τντ 0.028 ± 0.020
tent wit(cid:16)h (1(cid:17).6 σ below) the SM expectation. K−π−π+ν (ex. K0,ω) 0.293 ± 0.007
τ
We also test lepton universality between τ K−π−π+π0ν (ex. K0,ω,η) 0.041 ± 0.014
τ
and µ (e), by comparing the averaged electronic K−φν (φ→KK) 0.004 ± 0.001
τ
(muonic)branchingfractionsoftheτ leptonwith K−ην 0.016 ± 0.001
τ
the predicted branching fractions from measure- K−π0ην 0.005 ± 0.001
τ
mentsoftheτ andµlifetimesandtheirrespective K¯0π−ην 0.009 ± 0.001
τ
masses [6]. This gives ggµτ = 1.0011 ± 0.0021 K−ωντ 0.041 ± 0.009
Sum of strange modes 2.8796 ± 0.0501
and gτ = 1.0030 ±(cid:16)0.00(cid:17)21. The correlation
ge Sum of all modes 100.00
co-effi(cid:16)cien(cid:17)t between the determination of gτ
gµ Table 1
from electronic branching fraction with the(cid:16)one(cid:17)s Results of unitarity constrained fit.
obtained from pionic and kaonic branching frac-
4
tions are 48.16% and 21.82%, respectively. Av-
eraging the three values, we obtain gτ = LEP EW WG (W → µ νµ)/(W → e νe)
gµ 0.9970 ± 0.0100
1.0001± 0.0020,whichisconsistentwith(cid:16)the(cid:17)SM FlaviaNet (K → π µ νµ)/(K → π e νe)
value. In Figure 3, we compare these determi- 1.0010 ± 0.0025
nations with the values obtained from pion [19], NA62, KLOE (K → µ νµ)/(K → e νe)
kaon [20] and W decays [21]. 0.9980 ± 0.0025
TRIUMF, PSI (π → µ νµ)/(π → e νe)
4. Measurement of |V | 1.0017 ± 0.0015
us
HFAG Fit (τ → µ νµ ντ)/(τ → e νe ντ)
Using the unitarity constraint on the 1.0019 ± 0.0014
first row of the CKM matrix and |V | =
ud
0.97425 ± 0.00022 [24], one gets |V | = HFAG-Tau
us
Summer 2010
0.2255 ± 0.0010. Here we present 3 ex-
0.9 0.95 1
tractions for |Vus| using B(τ− →K−ντ), |g /g|
B(τ− →K−ν )/B(τ− →π−ν ), and inclu- µ e
τ τ
sive sum of τ branching fractions having net
LEP EW WG (W → τ ντ)/(W → µ νµ)
strangeness of unity in the final state. 1.0390 ± 0.0130
We use the value of kaon decay constant HFAG Fit (τ → e νe ντ) × τµ/ττ
1.0011 ± 0.0021
f = 157 ± 2MeV obtained from Lattice calcu-
laKtions [22], and our value of B(τ− →K−ντ) = H0.F9A96G6 F±i t0 (.τ0 →03 0π ντ)/(π → µ νµ)
G2FfK2|1V6uπsh¯|2m3τττ 1− mm2K2 2SEW, where SEW = H0.F9A86G0 F±i t0 (.τ0 →07 3K ντ)/(K → µ νµ)
1.0201 ± 0.000(cid:16)3 [23],τ (cid:17)to determine |Vus| = H0.F9A95G4 A±v 0e.r0a0g2e9 (τ → π ντ, K ντ)
0.2204 ± 0.0032, which is consistent with (1.5 σ HFAG Average (τ → e νe ντ, π ντ, K ντ)
below) the value from CKM unitarity. 1.0001 ± 0.0020
Weextract|V |using|V |,Latticecalculation
us ud
of the ratio of decay constants f /f = 1.189 ± HFAG-Tau
K π Summer 2010
0.007[22]andthelong-distancecorrectionδ =
LD 0.9 0.95 1
(0.03 ± 0.44)%, estimated using corrections to |g/g |
τ µ
τ →hν and h→µν [25], for the ratio
τ µ
m2 2
B(τ− →K−ντ) = fK2|Vus|2 1− mK2τ (1+δ ), LEP EW WG (W → τ ντ)/(W → e νe)
B(τ− →π−ντ) fπ2|Vud|2 (cid:16)1− m2π(cid:17)2 LD 1.0360 ± 0.0140
m2
τ
where short-distance ele(cid:16)ctro-wea(cid:17)k correc- HFAG Fit (τ → µ νµ ντ) × τµ/ττ
tions cancel in this ratio measured to be 1.0030 ± 0.0021
B(τ− →K−ν )/B(τ− →π−ν ) = 0.0644 ±
τ τ
0.0009. This includes a correlation of −0.49%
between the branching fractions, and yields
|V |=0.2238 ± 0.0022, which is also consistent
us
HFAG-Tau
with (0.7 σ below) |V | from CKM unitarity.
us Summer 2010
The total hadronic width of the τ normal-
0.9 0.95 1
ized to the electronic branching fraction, R = |g/g|
had τ e
B /B ,canbewrittenasR =R +
had e had non−strange
R . We can then measure
strange
R
|V |= R / non−strange −δR . Figure 3. Measurements of lepton universality
us s strange (cid:20) |Vud|2 theory(cid:21) from W, kaon, pion and tau decays.
5
Here, we use |V | = 0.97425 ± 0.00022 [24],
ud
and δR = 0.240 ± 0.032 [26] which con-
theory FlaviaNet K decays
l3
tributes to an error of 0.0010 on |Vus|. We note 0.2254 ± 0.0013
that this error is equivalent to half the differ- FlaviaNet K decays
l2
ence between calculations of |V | obtained using 0.2252 ± 0.0013
us
Hyperon decays
fixedorderperturbationtheory(FOPT)andcon-
0.2260 ± 0.0050
tourimprovedperturbationtheory(CIPT)calcu-
HFAG Fit (τ → K ντ)
lations of δRtheory [27], and twice as large as the 0.2204 ± 0.0032
theoretical error proposed in Ref. [28]. HFAG Fit (τ → K ντ)/(τ → π ντ)
AsinRef.[29],weimproveupontheestimateof 0.2238 ± 0.0022
electronic branching fraction by averaging its di- HFAG Fit (τ → s inclusive)
0.2174 ± 0.0022
rectmeasurementwithits estimatesof(17.899±
CKM Unitarity
0.040)% and (17.794 ± 0.062)% obtained from 0.2255 ± 0.0010
the averaged values of muonic branching frac-
tions and the averaged value of the lifetime of HFAG-Tau
theτ lepton=(290.6±1.0)×10−15 s[6],assum- Summer 2010
ing lepton universality and taking into account 0.2 0.21 0.22 0.23
the correlation between the leptonic branching |V |
us
fractions. This gives a more precise estimate
for the electronic branching fraction: Buni =
e
(17.852 ± 0.027)%.
Assuming lepton universality, the total
Figure 4. Measurements of |V | from kaon, hy-
hadronic branching fraction can be written us
as: B = 1 − 1.972558 Buni, which gives peron and tau decays.
had e
a value for the total τ hadronic width nor-
malized to the electronic branching fraction as
R =3.6291 ± 0.0086.
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