a higher precision measurement of the d (2010) d mass di erence · 2017. 8. 1. · august 1, 2017...

A higher precision measurement of theD∗(2010)+ − D+ mass difference

⇒ a higher precision measurement of m(D+)−m(D0)

Michael D. Sokoloff

University of Cincinnati, on behalf of the BaBar Collaboration

August 1, 2017

Michael D. Sokoloff University of Cincinnati

A higher precision measurement of the D∗(2010)+ − D+ mass difference 0 / 12

Mass difference measurements constrain theoryfrom Goity and Jayalath

Chiral perturbation theory and lattice QCD calculations of heavy-lightmesons start in the limit of infinitely heavy b- and c-quark masses andSU(3) flavor symmetry for the light quarks and consider symmetrybreaking associated with (i) the finite masses of the heavy quarks, (ii) thedifferent light quark masses, and (iii) the electromagnetic interactions.

The symmetry-breaking associated with these sources can be related tomass differences [see, e.g., Goity and Jayalath, PLB 650 (2007)].

Improving mass difference measurements allows more preciseunderstanding of the symmetry-breaking, and should lead to more precisepredictions of other quantities.



http://www.sciencedirect.com/science/article/pii/S0370269307005114

The data come from the BaBar detectorran 1999 - 2008; Lint ≈ 468 fb−1 recorded at, and 40 MeV below, the Υ (4S) resonance



D∗+ → D+π0: the D+ and π0 candidates

(GeV)ππKm1.84 1.86 1.88 1.9

Eve

nts

/ (1

.0 M

eV)

0

5000

10000

15000

20000

BABAR

BABAR Preliminary

These are the D+ → K−π+π+

candidates from which the D∗+

candidates are built.

The vertical red lines indicate themass range used for the nominal fit.

As a sanity check, we vary the masswindow used in the analysis and findno significant variation.

)(GeV)γγM(0.12 0.125 0.13 0.135 0.14 0.145 0.15

Arb

itra

ry u

nit

0

0.01

0.02

0.03

0.04

0.05 Real Data

MC w/ EMC Corr.

MC w/ EMC Corr.

& 0.3% rescaling

MC w/o EMC Corr.

BABARPreliminary

The background-subtracted γγinvariant mass spectrum from realdata is shown in red.

The truth-matched MC spectrumwith no energy scale corrections isshown in black.

The MC spectra with nominalenergy corrections and with anadditional 0.3% rescaling are shownin blue and magenta, respectively.



Simulated ∆m+ ≡ m(D∗+)−m(D+)

M (GeV)∆0.135 0.14 0.145 0.15 0.155 0.16

Eve

nts

/ 50

keV

210

310

410

510 0.030 ± = -0.735 α 0.100 ±n = 5.194 0.014 ± = 0.202 1f 0.022 ± = 0.573 2f

0.034 MeV± = 1.161 3Lσ

0.016 MeV± = 0.875 3Rσ

3.053 keV± = 16.663 m∆δ 0.013 MeV± = 1.683 1σ 0.014 MeV± = 0.669 2σ

: 605/491ν/2χ

M (GeV)∆0.135 0.14 0.145 0.15 0.155 0.16N

orm

. Res

idu

al

4−

2−

0

2

4

BABAR Preliminary (MC)

M (GeV)∆0.135 0.14 0.145 0.15 0.155 0.16

Eve

nts

/ 50

keV

0

5000

10000

15000

20000

0.030 ± = -0.735 α 0.100 ±n = 5.194 0.014 ± = 0.202 1f 0.022 ± = 0.573 2f

0.034 MeV± = 1.161 3Lσ

0.016 MeV± = 0.875 3Rσ

3.053 keV± = 16.663 m∆δ 0.013 MeV± = 1.683 1σ 0.014 MeV± = 0.669 2σ

: 605/491ν/2χ

M (GeV)∆0.135 0.14 0.145 0.15 0.155 0.16N

orm

. Res

idu

al

4−

2−

0

2

4 BABAR

BABAR Preliminary (MC)

Signal shape parameters are derived from truth-matched Monte Carlosimulation. When fitting the real data, most of the fit model parametersare taken directly from the MC. However, several of the resolution termsare allowed to vary to account for possible differences between data andsimulation.



Real data: ∆m+ ≡ m(D∗+)−m(D+)

M (GeV)∆0.135 0.14 0.145 0.15 0.155

Eve

nts

/ (5

0 ke

V)

500

1000

1500

2000

2500

3000: 520/491ν/2χ

622±: 150904 sigN

6.8 keV±: 140597.6 + m∆

M (GeV)∆0.139 0.14 0.141 0.142

Eve

nts

/ 50

keV

0

1000

2000

3000

M (GeV)∆0.135 0.14 0.145 0.15 0.155 0.16N

orm

. Res

idu

al

4−

2−

0

2

4

BABAR Preliminary (real data)Fitting simulated data sets generatedwith signal and background PDFscorresponding to those in our nominal fitproduces a bias of 3.4 keV with a verysmall nominal uncertainty.

We add this bias to the directly fittedvalue and assign a systematic uncertaintyof 1.7 keV to this shift.

Thus, the central value becomes∆m+ = 140 601.0 keV

Varying the “‘fixed” fit model parametersaccording to their reported covariancematrices produces an rms spread of2.1 keV in the central fit value. We assignthis as another systematic uncertainty.



π0 candidates in data and MCdifferences, correction factors, and associated systematic uncertainties

)(GeV)γγM(0.12 0.125 0.13 0.135 0.14 0.145 0.15

Arb

itra

ry u

nit

0

0.01

0.02

0.03

0.04

0.05 Real Data

MC w/ EMC Corr.

MC w/ EMC Corr.

& 0.3% rescaling

MC w/o EMC Corr.

BABARPreliminary

The “calibrated” energy scales in the data andMC simulation, at higher energy scales thanobserved here, differ by (−0.35 ± 0.09)% [NIMA729, pp 615-701 (2013)].

Making a similar 0.3% MC photon energycorrection improves the data/MC agreement inthe mγγ distribution shown above.

Varying the correction by ±0.3%, and tryingother MC neutrals corrections, leads to a±7.0 keV systematic uncertainty in ∆m+.

(rad.)γγθ0.6 0.8 1 1.2 1.4 1.6 1.8 2

)-3

-1)

peak

pos

ition

(10

true

/P0 π

(P

2.5−

2−

1.5− BABAR Preliminary

Truth-matched π0 momentum distributionsobserved in MC samples do not peak at thegenerated momenta.

The observed variation is accounted for bymaking a momentum scale correction in each of10 bins of γγ opening angle.

As will be seen later, this largely mitigates anobserved variation of ∆m+ with θγγ .

Varying the MC π0 momentum scale valuesaccording to the errors in each bin leads to a±0.5 keV systematic uncertainty in ∆m+.





Searching for anomalous variations - Idivide the data into 10 disjoint sets of p(D∗+) and of cos θ(D∗+)

) (GeV)*+p(D1 2 3 4 5 6 7

(M

eV)

+ m∆

140.55

140.6

140.65

140.7 : 14.0/9ν/2χ-value: 0.12p

BABAR Preliminary

)*+(Dθcos 1− 0.5− 0 0.5 1

(M

eV)

+ m∆

140.55

140.6

140.65

140.7 : 18.3/9ν/2χ-value: 0.03p

BABAR Preliminary

We study variations in fit results as functions of kinematic variables to identifypossible sources of detector/simulation differences. We assign systematicsmimicking the PDG scale factor method for inflating errors.If the fit results from a given dependence study are compatible with a constantvalue, in the sense that χ2/ν < 1, where ν is the number of degrees of freedom,we assign no systematic uncertainty.

If χ2/ν > 1, we ascribe an uncertainty of σsys = σstat√χ2/ν − 1 to account

for unidentified detector effects.The variations observed as functions of p(D∗+) and cos θ(D∗+) lead to ±5.0keV and ±6.9 keV systematic uncertainties in ∆m+, respectively.



Searching for anomalous variations - IIdivide the data into 10 disjoint sets of φ(D∗+) and of m(Kππ)

) (rad.)*+(Dφ3− 2− 1− 0 1 2 3

(M

eV)

+ m∆

140.55

140.6

140.65

140.7 : 2.1/9ν/2χ-value: 0.99p

BABAR Preliminary

(GeV)ππKm1.86 1.865 1.87 1.875 1.88

(M

eV)

+ m∆

140.55

140.6

140.65

140.7

: 8.7/9ν/2χ-value: 0.47p

BABAR Preliminary

The variations seen with these variables are “consistent” with beingpurely statisical (i.e., χ2/ν < 1).

Therefore, the systematic uncertainties in ∆m+ associated with thesevariation are zero.



Searching for anomalous variations - IIIdivide the data into 10 disjoint sets of θγγ

(rad.)γγθ0.6 0.8 1 1.2 1.4 1.6 1.8 2

(M

eV)

+ m∆

140.55

140.6

140.65

140.7

: 45.5/9ν/2χ-value: 7.4e-07p

BABAR Preliminary

This is the variation with γ γopening angle before the MCmomentum scale correction ismade.

(rad.)γγθ0.6 0.8 1 1.2 1.4 1.6 1.8 2

(MeV

)+

mΔ

140.55

140.6

140.65

140.7

: 16.2/9ν/2χ-value: 0.06p

BABAR Preliminary

This is the variation with γ γopening angle after the MCmomentum scale correction ismade.

The variations observed as a function of θγγ lead to a ±6.1 keVsystematic uncertainty in ∆m+.



Overview of Systematic Uncertainties for ∆m+

Table: Systematic errors for ∆m+, fromall considered sources.

Source syst. [keV]

Fit bias 1.7

D∗+ plab dependence 5.0

D∗+ cos θ dependence 6.9

D∗+ φ dependence 0.0

m(D+reco ) dependence 0.0

Diphoton opening angle dependence 6.1

Run period dependence 0.0

Signal model parametrization 2.1

EMC calibration 7.0

MC π0 momentum rescaling 0.5

Total 12.9

Table: These are the p-values for thehypothesis that observed variations in thevalue of ∆m+ for the disjoint subsets ofdata are consistent with statisticalfluctuation.

Source p-value

D∗+ plab dependence 0.12

D∗+ cos θ dependence 0.03

D∗+ φ dependence 0.99

m(D+reco ) dependence 0.47

Diphoton opening angle dependence 0.06

Average 0.33

⇒ ∆m+ = (140 601.0± 6.8± 12.9) keV



Previously published: ∆m0 ≡ m(D∗+)−m(D0)see Phys. Rev. Lett. 111, 111801 (2013) and Phys. Rev. D 88, 052003 (2013)

m [GeV]∆0.14 0.145 0.15 0.155 0.16 0.165

Even

ts /

50 k

eV

1

10

210

310

410

+π - K→0(a) D

Total

res. function⊗RBW

Background

Res

idua

lN

orm

aliz

ed

-4

-2

0

2

4

m [GeV]∆0.14 0.145 0.15 0.155 0.16 0.165

Even

ts /

50 k

eV

1

10

210

310

410

+π -π +π - K→0(b) D

Total

res. function⊗RBW

Background

Res

idua

lN

orm

aliz

ed

-4

-2

0

2

4

⇒ ∆m0 = (145 425.9± 0.4± 1.7) keV



https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.111801

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.88.052003

Derived value for ∆mD ≡ m(D+)−m(D0)more details of the analysis available in arXiv:1707.09328

Combining the BaBar measurements of ∆m+ and ∆m0, we find:∆m+ = (140 601.0 ± 6.8 ± 12.9) keV

∆m0 = (145 425.9 ± 0.4 ± 1.7) keV

∆mD = (4 824.9 ± 6.8 ± 12.9) keV

Table: Prior world-average (WA) values [PDG, 2016], accessed online 23July 2017, compared with our measured values.

parameter prior WA present measurement

∆m+ (140 670± 80) keV (140 601± 15) keV∆mD (4 750± 80) keV (4825± 15) keV

Other world-average measurements [PDG, 2016]:

m(D0) = (1864.83 ± 0.05) MeV

m(D+) = (1869.59 ± 0.09) MeV

∆mπ = (4 593.6 ± 0.5) keV

∆mK = (−3 934 ± 20) keV



https://arxiv.org/abs/1707.09328

http://pdg.lbl.gov/2017/html/authors_2016.html

http://pdglive.lbl.gov

http://pdg.lbl.gov/2017/html/authors_2016.html

a higher precision measurement of the d (2010) d mass di erence · 2017. 8. 1. · august 1, 2017...

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