Precise measurement of πand πͺ - ias.ust.hkias.ust.hk/program/shared_doc/2020/202001hep/...2...
Transcript of Precise measurement of πand πͺ - ias.ust.hkias.ust.hk/program/shared_doc/2020/202001hep/...2...
Precise measurement of ππΎ and πͺπusing threshold scan method
Peixun Shen, Paolo Azzurri, Zhijun Liang, Gang Li, Chunxu Yu
NKU, INFN Pisa, IHEP
IAS Program on High Energy Physics 2020
2020/1/18, HKUST
1IAS Program on High Energy Physics 2020 [email protected]
Outline
Motivation
Methodology
Statistical and systematic uncertainties
Data taking schemes
Summary
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Motivation
The mW plays a central role in precision EW
measurements and in constraint on the SM model
through global fit.
πΊπΉ =ππΌ
2ππ2 sin2 ππ
1
(1+Ξπ)
Ξπ is the correction, whose leading-order
contributions depend on the ππ‘ and ππ»
Several ways to measure ππ:
The direct method, with kinematically-constrained or mass
reconstructions
Using the lepton end-point energy
π+πβ threshold scan method (used in this study )
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W.J. Stirling, arXiv:hep-ph/9503320v1 14 Mar 1995
ILC, arXiv:1603.06016v1 [hep-ex] 18 Mar 2016
FCC-ee, arXiv:1703.01626v1 [hep-ph] 5 Mar 2017
Methodology
Why?
πππ(ππ, Ξπ, π )= ππππ
πΏππ(π =
πππ
πππ+ππππ)
so ππ, Ξπ can be obtained by fitting the ππππ , with the theoretical formula πππ
How?
In general, these uncertainties are dependent on π , so it is a optimization problem
when considering the data taking.
If β¦, then?
With the configurations of πΏ, ΞπΏ, ΞπΈ β¦, we can obtain: ππ~?Ξπ βΌ?
Ξππ, ΞΞπππππ πΏ π Nπππ πΈ ππΈ β¦β¦
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Theoretical Tool
The πππ is a function of π , ππ and Ξπ,
which is calculated with the GENTLE
package in this work (CC03)
The ISR correction is also calculated by
convoluting the Born cross sections with
QED structure function, with the radiator
up to NL O(πΌ2) and O(π½3)
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Statistical and systematic uncertainties
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Statistical uncertainty
Ξπππ = πππ ΓΞπππ
πππ= πππ Γ
πππ+ππππ
πππ
=πππ
πΏππ(π =
πππ
πππ+ππππ)
Ξππ =ππππ
πππ
β1Γ Ξπππ =
ππππ
πππ
β1Γ
πππ
πΏππ
ΞΞπ =ππππ
πΞπ
β1Γ Ξπππ =
ππππ
πΞπ
β1Γ
πππ
πΏππ
With πΏ=3.2ππβ1, π=0.8, π=0.9:
Ξππ=0.6 MeV, ΞΞπ=1.4 MeV (individually)
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Statistical uncertainty
When there are more than one data point, we can measure both ππ and Ξπ.
With the chisquare defined as:
the error matrix is in the form:
When the number of fit parameter reduce to 1:
Ξππ =ππππ
πππ
β1
Γ Ξπππ =ππππ
πππ
β1
Γπππ
πΏππ
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Statistical uncertainty
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Systematic uncertainty
To
tal
Uncorrelated
E
ππΈ
ππππ
Correlated
πππ
πΏ
π
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Energy calibration uncertainty
With ΞπΈ, the total energy becomes:
πΈ = πΊ πΈπ, ΞπΈ + πΊ(πΈπ, ΞπΈ)
Ξππ =πππ
ππππ
ππππ
ππΈΞπΈ
The ΞmW will be large when ΞπΈ
increase, and almost independent
with π.
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Energy spread uncertainty
With πΈπ΅π, the πππ becomes:
πππ πΈ = 0βπππ πΈβ² Γ πΊ πΈ, πΈβ² ππΈβ²
= π πΈβ² Γ1
2ππΏπΈπ
β πΈβπΈβ²2
2ππΈ2
ππΈβ²
ππΈ + ΞππΈ is used in the simulation, and ππΈ is for
the fit formula.
The ππΎ insensitive to πΉπ¬when taking data
around πππ. π GeV
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Background uncertainty
The effect of background are in two different ways
1. Stat. part: Ξππ(ππ΅) =πππ
ππππβ
πΏππ΅ππ΅
πΏπ
2. Sys. part: Ξππ(ππ΅) =πππ
ππππβ πΏππ΅ππ΅
πΏπβ Ξππ΅
With L=3.2abβ1, ππ΅ππ΅ = 0.3pb, Ξππ΅ = 10β3οΌ
Ξππ(ππ΅)~0.2 MeV, which has been embodied in the product of π β π,
and Ξππ(ππ΅) is considerable with the former.
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Correlated sys. uncertainty
The correlated sys. uncertainty includes: ΞπΏ, Ξπ, Ξπππβ¦
Since ππππ = πΏ β π β π, these uncertainties affect πππ in same way.
We use the total correlated sys. uncertainty in data taking optimization:
πΏπ = ΞπΏ2 + Ξπ2
Ξππ =πππ
πππππππ β πΏπ , ΞΞπ =
πΞπ
πππππππ β πΏπ
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Correlated sys. uncertainty
Ξππ =πππ
πππππππ β πΏπ
Two ways to consider to effect:
Gaussian distribution
πππ = πΊ(πππ0 , πΏπ β πππ
0 )
Non-Gaussian (will cause shift)
πππ = πππ0 Γ (1 + πΏπ)
With πΏπ = +1.4 β 10β4(10β3) at 161.2GeV
ΞmW~0.24MeV (3MeV)
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Correlated sys. uncertainty
To consider the correlation, the scale factor method is
used,
π2 = ππ π¦πβββ π₯π
2
πΏπ2 +
ββ1 2
πΏπ2 ,
where π¦π , π₯π are the true and fit results, h is a free
parameter, πΏπ and πΏπ are the independent and
correlated uncertainties.
For the Gaussian consideration, the scale factor can
reduce the effect.
For the non-Gaussian case, the shift of the ππ is
controlled well
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β’ Smallest Ξππ, ΞΞπ (stat.)
β’ Large sys. uncertainties
β’ Only for ππ or Ξπ, without correlation
One point
β’ Measure ππ and Ξπ simultanously
β’ Without the correlation
Two points
β’ Measure ππ and Ξπ simultaneously, with the correlation
Three points
or more
Da
ta t
ak
ing
sch
emes
Data taking scheme
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Taking data at one point (just for ππΎ)
There are two special energy points :
The one which most statistical sensitivity to ππ:
Ξππ(stat.) ~0.59 MeV at πΈ=161.2 GeV
(with ΞΞπ and ΞπΈπ΅π effect)
The one Ξππ(stat)~0.65 MeV at πΈ β 162.3 GeV
(with negative ΞΞπ, ΞπΈπ΅π effects)
With ΞπΏ Ξπ < 10β4, Ξππ΅<10β3, ΞπΈ=0.7MeV,
ΞππΈ=0.1, ΞΞπ=42MeV)
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βπ(GeV) 161.2 162.3
πΈ 0.36 0.37
ππΈ 0.20 -
ππ΅ 0.17 0.17
πΏπ 0.24 0.34
ΞW 7.49 -
Stat. 0.59 0.65
Ξππ(MeV) 7.53 0.84
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Taking data at two energy points
To measure Ξππ and ΞΞπ, we scan the energies and the luminosity fraction of
the two data points:
1. πΈ1, πΈ2 β [155, 165] GeV, ΞπΈ = 0.1 GeV
2. πΉ β‘πΏ1
πΏ2β 0, 1 , ΞπΉ = 0.05
We define the object function: π = mW + 0.1Ξπ to optimize the scan parameters
(assuming ππ is more important than Ξπ).
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Taking data at two energy points
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The 3D scan is performed, and
2D plots are used to illustrate
the optimization results;
When draw the Ξπ change
with one parameter, another
is fixed with scanning of the
third one;
πΈ1=157.5 GeV, πΈ2=162.5
GeV (around ππππ
πΞπ=0 ,
ππππ
ππΈπ΅π=0)
and F=0.3 are taken as
the result.
(MeV) π ππ¬ ππ© πΉπ Stat. Total
Ξππ 0.38 - 0.21 0.33 0.80 0.97
ΞΞπ 0.54 0.56 1.38 0.20 2.92 3.32
ΞπΏ(Ξπ)<10β4, Ξππ΅<10β3
ππΈ=1 Γ 10β3, ΞπΈ=0.7MeVΞππΈ=0.1%
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Optimization of πΈ1
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The procedure of three
points optimization is
similar to two points
πΈ1 157.5 GeV
πΈ2 162.5 GeV
πΈ3 161.5 GeV
πΉ1 0.3
πΉ2 0.9
Taking data at three energy points
Ξππ~0.98 MeVΞΞπ ~3.37 MeV
ΞπΏ(Ξπ)<10β4, Ξππ΅<10β3
ππΈ=1 Γ 10β3, ΞπΈ=0.7MeVΞππΈ=0.1
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Summary
The precise measurement of ππ (Ξπ) is studied (threshold scan method)
Different data taking schemes are investigated, based on the stat. and sys.
uncertainties analysis.
With the configurations :
Thank youοΌ
ΞπΏ(Ξπ)<10β4, Ξππ΅<10β3
ππΈ=1 Γ 10β3, ΞπΈ=0.7MeVΞΞπ=42MeV, ΞππΈ=0.1
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Backup Slides
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Covariance matrix method
π¦π =ππ
π, π£ππ = ππ
2 + π¦π2ππ
2
where ππ is the stat. error of ππ, ππ is the relative error of π
The correlation between data points π, j contributes to the
off-diagonal matrix element π£ππ:
Then we minimize: π12 = πππβ1π
For this method, The biasness is uncontrollable
(MO Xiao-Hu HEPNP 30 (2006) 140-146)
H. J. Behrend et al. (CELLO Collaboration)
Phys. Lett. B 183 (1987) 400
Dβ Agostini G. Nucl. Instrum. Meth. A346 (1994)
24
Scale factor method
This method is used by introducing a free fit parameter to the π2:
π22 = π
ππ¦πβππ2
ππ2 +
πβ1 2
ππ2
ππ includes stat. and uncorrelated sys errors, ππ are the correlated errors.
The equivalence of this form and the one from matrix method is
proved in : MO Xiao-Hu HEPNP 30 (2006) 140-146 .
Both the matrix and the factor approach have bias, which may be considerably striking when the data points are quite many or the scale factor is rather large.
According to ref: MO Xiao-Hu HEPNP 31 (2007) 745-749, the unbiased π2 is constructed as:
π32 = π
π¦πβπππ2
ππ2 +
πβ1 2
ππ2 (used in our previous results)
The central value from π22 can be re-scaled, the relative error is still larger than those from π3
2 estimation.25