1

Vishal Bhardwaj IISER Mohali

DAE 2020 14-18 Dec. 2020

Minnie-review

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https://www.dnaindia.com/india/photo-gallery-tribute-to-corona-warriors-this-is-how-india-is-gearing-up-for-independence-day-celebrations-2020-2836461

Saving us ! [up, down, bottom, top]nothing matches their[ strange, charm]

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A series of fortunate events

1964CPV in Kaon system𝐾𝐿 → 𝜋+𝜋− , 45 events23 x 103 in 𝐾𝐿 → 𝜋+𝜋−𝜋0

J. Cronin, V. Fitch 1980

2001 CPV in Beauty systemLarge CPV in 𝐵0 system𝐵0 → 𝐽/𝜓𝐾𝑠 ~ 700 events

M. Kobayashi, T. Maskawa 2008

2019 CPV in Charm system𝐷0 → 𝜋𝜋 ~ 14000000 events

As one can see, CPV in charm requires large data sample along with good control of systematic uncertainty.

Strange

Beauty

Charm

Charm is the new strange.

We have saved the worst for the last

Beauty is the new strange

Charm is really strange !

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CP violation in the Standard Model

𝑑′𝑠′𝑏′

=

𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏

𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏

𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏

𝑑𝑠𝑏

1 − Τ𝜆2 2 − Τ𝜆4 8 𝜆 𝐴𝜆3(𝜌 − 𝑖𝜂)

−𝜆 + 𝐴2 Τ𝜆5[1 − 2 𝜌 + 𝑖𝜂 ] 2 1 − Τ𝜆2 2 − Τ𝜆4(1 + 4𝐴2) 8 𝐴𝜆2

𝐴𝜆3[1 − 𝜌 + 𝑖𝜂 1 − Τ𝜆2 2 ] −𝐴𝜆2 + 𝐴 Τ𝜆4[1 − 2 𝜌 + 𝑖𝜂 ] 2 1 − Τ𝐴2𝜆4 2

+ 𝒪 𝜆6

Here l=sin(qc), and A, r, h are all real This representation is easy for relating CP violation to specific decay rates.

𝜂 is the only CPV source in the Standard Model.

Unitarity condition VꝉV=1 gives six relations between the CKM matrix elements.𝑉𝑢𝑑

∗ 𝑉𝑢𝑠 + 𝑉𝑐𝑑∗ 𝑉𝑐𝑠 + 𝑉𝑡𝑑

∗ 𝑉𝑡𝑠=0 𝑉𝑢𝑑∗ 𝑉𝑐𝑑 + 𝑉𝑢𝑠

∗ 𝑉𝑐𝑠 + 𝑉𝑢𝑏∗ 𝑉𝑐𝑏=0 [𝓞 𝛌 + 𝓞 𝛌 + 𝓞 𝛌𝟓 = 𝟎]

𝑉𝑢𝑠∗ 𝑉𝑢𝑏 + 𝑉𝑐𝑠

∗ 𝑉𝑐𝑏 + 𝑉𝑡𝑠∗ 𝑉𝑡𝑏=0 𝑉𝑐𝑑

∗ 𝑉𝑡𝑑 + 𝑉𝑐𝑠∗ 𝑉𝑡𝑠 + 𝑉𝑐𝑏

∗ 𝑉𝑡𝑏=0 [𝓞 𝛌𝟒 + 𝓞 𝛌𝟐 + 𝓞 𝛌𝟐 = 𝟎]

𝑉𝑡𝑑∗ 𝑉𝑢𝑑 + 𝑉𝑡𝑠

∗ 𝑉𝑢𝑠 + 𝑉𝑡𝑏∗ 𝑉𝑢𝑏=0 𝑉𝑢𝑏

∗ 𝑉𝑢𝑑 + 𝑉𝑐𝑏∗ 𝑉𝑐𝑑 + 𝑉𝑡𝑏

∗ 𝑉𝑡𝑑=0 [𝓞 𝛌𝟑 + 𝓞 𝛌𝟑 + 𝓞 𝛌𝟑 = 𝟎]

Each of these relations can be visualized as triangle in the complex plane.

One side is still small, angles not that large. Related to physics in BS system. All sides almost equal. Angles (relative phases) are large. Related to physics in Bd

system.

relating elements which appear in strange and charmed particles, are flat (despite having same area), so that one of the angles representing the relative phases of the CKM matrix elements is tiny . Related to K & D meson system

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Why the Charm ?• SM larger CP violation effects are expected with heavy quarks, in which complex

phase of CKM matrix can appear directly rather through virtual transitions.

• 𝐷0dominated by first two quarks families, and therefore large CP-violating effectsare not expected.

• Top quark loops which provide largest effects in 𝐾 and 𝐵 decays are absent for 𝐷.

• Many channels are possible for 𝐷 mesons, which are not suppressed by smallmixing angles.

• Leading to large decay widths making observation of small effects a bit difficult.

• SM actually predicts very small mixing and CP violation.• 0.1 % CP violation in decays can be searched in single cabibbo suppressed as

SM predicts small asymmetries.

❖ Decays of charmed mesons are currently the only way to probe flavor violation inthe up-quark sector.➢ Non SM effects might show different patterns for the u and d.

Within SM, CP violation is expected to be small in charm sector. But, it is promising to study single Cabibbo-suppressed decays where direct CP asymmetry may be large enough to be detected.First evidence of CP violation in charm sector is observed in SCS decays 𝐷0 → 𝐾+𝐾− and 𝐷0 → 𝜋+𝜋−at LHCb.

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𝐷0 − ഥ𝐷0 mixingc u

D0

c u

ഥ𝑫𝟎

Mass : (1864.83±0.05) MeV τD0 = (410.1±1.5) x10-15 s

Time evolution : | ൿ𝐷1,2 𝑡 = 𝑒−𝑖𝑚1

,2𝑡𝑒−

Γ1,2𝑡

2 | ൿ𝐷1,2(𝑡 = 0)

Phenomenon of mixing can be described as a decaying two-component quantum state.

Mass eigenstates (D1, D2) ǂ Flavor eigenstates (D0, D0).

𝑚1 𝑚2 and Γ1 (Γ2) are the mass and decay width of 𝐷1(𝐷2)

Flavor states

| 𝐷0 𝑡 =1

2𝑝[| 𝐷1 𝑡 + | 𝐷2 𝑡 ] and | ഥ𝐷0 𝑡 =

1

2𝑞[| 𝐷1 𝑡 − 𝐷2 𝑡

At t=0, states are produced as pure D0 or D0

| 𝐷0 𝑡 = |𝐷0 cosh𝑖𝑥+𝑦

2തΓ𝑡 −

𝑞

𝑝| ഥ𝐷0 sinh

𝑖𝑥+𝑦

2തΓ𝑡 𝑒−𝑖𝑚𝑡−

ഥΓ

2𝑡

| ൿ𝐷0 𝑡 = |ഥ𝐷0 cosh𝑖𝑥 + 𝑦

2തΓ𝑡 −

𝑞

𝑝| 𝐷0 sinh

𝑖𝑥 + 𝑦

2തΓ𝑡 𝑒−𝑖𝑚𝑡−

ഥΓ2𝑡

At later time can be 𝐷0 or 𝐷0, depending on the value of mixing parameter x, y:

𝑥 ≡𝑚1 − 𝑚2

തΓ; 𝑦 ≡

Γ1 − Γ2

2തΓ; തΓ ≡

Γ1 + Γ2

2; ഥ𝑚 ≡

𝑚1 + 𝑚2

2

* under CPT conservation assumption: |p|2+|q|2 = 1

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D0

c

u d,s,b d,s,b

u

c ഥ𝐷0

W+

W-

D0

c

u

u

c ഥ𝐷0

K+K-,π+π-π0,K+π-, π+π- , etc

In SM, D0 meson can change to D0 via

Double weak boson exchange(Short distance effects)

Intermediate state common to both (Long distance effects)

SM predictions for 𝑥 and 𝑦 suffers from larger uncertainties.Generally, Mixing in charm system strongly suppressed : |𝑥|, |𝑦| ~ 1%

Sensitive to New Physics effects : 𝒙 ≫ |𝒚|

00

20

,

2

)(

DfADfA

tAyix

p

qAe

dt

fDdN

ff

ff

t

==

+

+→ −

20

2

)(tA

yix

q

pAe

dt

fDdNff

t +

+→ −

Observables at B factories :

dN(D0 →f)/dt is different function of 𝑥, 𝑦 (and 𝑞, 𝑝) for different Af, Af

Decay time distribution of accessible states D0, D0 are sensitive to mixing parameters (𝑥 and 𝑦), depending on the final state.

D0 - ഥ𝐷0 mixing

Doubly Cabibbo Suppressionvanishes in exact SU(3)FLAVOR

Difficult to calculate

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CP violation in charmed mesonsDirect CPV (neutral and charged, mode dependent)

𝑫𝒇

ഥ𝑫ത𝒇

2 2≠

𝐴(𝐷 → 𝑓)

𝐴(ഥ𝐷 → 𝑓)≠ 1

CP violation in decay appears on the amplitude level. Occurs if two different amplitude contribute to a single decay

Indirect CPV (neutral, common for all decay modes)In Mixing : CP violation in mixing occurs if a particle D0 can’t decay into a final state f buts CP-

conjugate D0 can. 𝑫𝟎 ⟶ ഥ𝑫𝟎 ⟶ 𝒀+𝑿− ↚ 𝑫𝟎 ഥ𝑫𝟎 ⟶ 𝑫𝟎 ⟶ 𝒀−𝑿+ ↚ ഥ𝑫𝟎

𝒓𝒎 = 𝒒/𝒑 ≠ 𝟏

In interference of decays with and without mixing: If mixing followed by decay and direct decay interfere. Final state must be common to D0

and D0.Two conditions :

𝒙 =∆𝑴

𝜞≠ 𝟎

𝒂𝒓𝒈𝒒ഥ𝑨𝒇

𝒑𝑨𝒇≠0

𝑫𝒇

ഥ𝑫ത𝒇2 2

≠ഥ𝑫 𝑫

𝑫𝒇

ഥ𝑫𝒇

2 2

𝑫𝒇

ഥ𝑫≠

𝒇ഥ𝑫 𝑫

q/p

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Where one can study charm ?𝒆+𝒆− colliders

CLEO (3.77, 4.17 GeV) 3.5 × 106 (𝐷), 2.3 × 106(𝐷+)

BESIII (3.77, 4.18, 4.6 GeV) 10.5 x 106 (D), 8.4 x 106(D+) 3x106(Ds+), 1x105(Λ𝑐

+)

Clean environment

Pure sample with no background.Quantum Coherence.No T-dependent analyses.

Belle (1 ab-1), 1.3 x 109 (D), 1.5 x 108 (Λ𝑐

+)

BaBar 0.5 ab-1

6.5 x 108 (D),

High efficiency detection of neutral.Time-dependent analysis.High statistics control sample.Higher trigger event.

𝒑ഥ𝒑 colliders

Tevatron (1.96 TeV)1.3 x 1011

LHCb (7 TeV,8 TeV)5 x 1012

Large production cross-sectionLarge boostExcellent time resolution.Dedicated trigger required

휀~10 − 30%

휀~5 − 10%

휀 < 0.5%Large production

Belle II (0.08 ab-1), ~1.0 x 108 (D),

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Some results from BESIII𝐷𝑠

+ → 𝜇+𝜈𝜇

Constaints on LQCD calculations

Test on Lepton flavor universality

Global fit in SM𝐷𝑠+ → 𝜇+𝜈𝜇LQCD calculation

Recently, lot of hints of LFU violation has emerged in semileptonic B- decays.One can also expect to have similar in 𝑐 → 𝑠 transitions.

𝑅𝐷(𝑠)+ = 3.21 ± 0.64 ± 0.43(9.98 ± 0.52)

Results agree with the SM prediction (but still statistically limited).

Τℬ(𝐷0 → 𝜋−𝜇+𝜈𝜇) ℬ 𝐷0 → 𝜋−𝑒+𝜈𝑒 = 0.922 ± 0.030 ± 0.022

Τℬ(𝐷+ → 𝜋0𝜇+𝜈𝜇) ℬ 𝐷+ → 𝜋0𝑒+𝜈𝑒 = 0.964 ± 0.037 ± 0.026

1.7𝜎 consistent0.5𝜎 consistent

Strength of BESIII

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Quantum correlated measurement of 𝐷0 hadronic decays.

Quantum correlation of the 𝐷0 ഥ𝐷0 meson pair produced at 𝜓 3770 provides a unique way to probe amplitude of the D decays.Determination of the strong-phase difference between the CF and DCS amplitudes in decay of quantum-correlated 𝐷 pairs➢ Essential inputs to extract the angle 𝜙3/γ of the CKM unitarity triangle.➢ Relating measured mixing parameters in hadronic decay (𝑥′, 𝑦′) to the mass and

width difference parameters (𝑥, 𝑦).

Uniqueness of BESIII

Recenty, BESIII has presented measurement of the strong-phase

difference in 𝐾𝑆,𝐿0 𝜋+𝜋− and 𝐾𝑆,𝐿

0 𝐾+𝐾− decays.

✓ Expected uncertainty on 𝜙3/𝛾 to be 0.8°.

BESIII, PRL 124, 241802(2020),arXiv:2007.07959

BESIII, arXiv:1912.05983

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Different ways of identifying 𝐷0

𝐷0

𝜋𝑠𝑙𝑜𝑤+

𝐷∗+

Belle (II), LHCb

𝐷∗+ → 𝐷0𝜋𝑠𝑙𝑜𝑤+

Charged of the slow𝜋 tell the flavor of DFor signal extraction and background reduction

Δ𝑀 = 𝑀 𝐷0𝜋𝑠𝑙𝑜𝑤+ − M(𝐷0)

or 𝑞 = Δ𝑀 − 𝑚 𝜋𝑠𝑙𝑜𝑤+

휀 𝐷∗ ~80%, 𝜔 𝐷∗ ~0.2%

Belle II ( Rest of Events)

휀 𝐷∗ ~27%, 𝜔 𝐷∗ ~13%3 × more produced 𝐷0

Increase sample by ~40%𝜎 𝐴𝐶𝑃 reduced by ~15%

LHCb (Semileptonic 𝑩 decays)𝑏 → 𝑐𝜇− ҧ𝜈𝜇

𝐵−

𝐷0𝜇−

𝐾

ҧ𝜈

𝐾

휀: 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝜔: 𝑀𝑖𝑠𝑡𝑎𝑔𝑔𝑖𝑛𝑔

20% of the prompt tagging

+ - 0

𝑫𝟎(𝒄ഥ𝒖)

e+ e-

Fragmentation

c

ത𝒄

ത𝒄𝑞

𝑲+(ത𝒔𝒖)Other daughters

Daughterparticles

Rest of events

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First observation of CP violation in charm

Measurment of time-integrated CP asymmetries in 𝐷0 → 𝐾+𝐾− and 𝐷0 → 𝜋+𝜋− decays

14 × 10644 × 106

9 × 106 3 × 106

𝐷0

𝜋𝑠𝑙𝑜𝑤+

𝐷∗+

𝐵−

𝐷0

𝐾

ҧ𝜈

𝐾

14

𝐴𝐶𝑃 =Γ 𝐷 → 𝑓 − Γ(ഥ𝐷 → ҧ𝑓)

Γ 𝐷 → 𝑓 + Γ(ഥ𝐷 → ҧ𝑓)𝐴𝑟𝑎𝑤 =

𝑁𝐷0 − 𝑁ഥ𝐷0

𝑁𝐷0 + 𝑁ഥ𝐷0

𝐴𝑟𝑎𝑤 = 𝐴𝐶𝑃 + 𝐴𝑝𝑟𝑜𝑑 + 𝐴𝑑𝑒𝑡

If the kinematics are similar then one can expect same to cancel.

Δ𝐴𝐶𝑃 = 𝐴𝑟𝑎𝑤 𝐾𝐾 − 𝐴𝑟𝑎𝑤 𝜋𝜋 = 𝐴𝐶𝑃 𝐾𝐾 − 𝐴𝐶𝑃 𝜋𝜋

Not simple, one need to perform reweighting procedure to match kinematics of 𝐷0 → 𝐾+𝐾− and 𝐷0 → 𝜋+𝜋−

Run2 result:

Δ𝐴𝐶𝑃 = −18.2 ± 3.2 stat. ± 0.9 syst. × 10−4

Δ𝐴𝐶𝑃 = −9.0 ± 8.0 stat. ± 5.0 syst. × 10−4

Run1 result:

Δ𝐴𝐶𝑃 = −10 ± 8 stat. ± 3 syst. × 10−4

Δ𝐴𝐶𝑃 = −14 ± 16 stat. ± 8 syst. × 10−4

Combining the two modes + Run1 measurement:Δ𝐴𝐶𝑃 = −15.4 ± 2.9 × 10−4

First observation of charm CPV at 5.3𝜎

PRL 122, 211803 (2019)

JHEP 07,041 (2014)PRL 116, 191601 (2016)

SM estimate

Δ𝐴 𝐶𝑃𝑆𝑀~

𝛼𝑠

𝜋

𝑉𝑢𝑏𝑉𝑐𝑏∗

𝑉𝑢𝑠𝑉𝑐𝑠∗ ~10−4

But can also be as large as

Δ𝐴 𝐶𝑃𝑆𝑀~few − several × 10−3

15

How one might interpret CPV ? Stolen from B. Golob, Alexey A Petrov,U. Nierste

Difficult to estimate in SM.

In SM, need to estimate size of penguin vs tree !

Δ𝐴𝐶𝑃 = −15.4 ± 2.9 × 10−4 First observation of charm CPV at 5.3𝜎

Within 𝑆𝑈(3)𝐹𝑙𝑎𝑣𝑜𝑟: 𝐴𝐶𝑃𝐾𝐾~ − 𝐴𝐶𝑃

𝜋𝜋

But then data shows 𝑆𝑈(3)𝐹𝑙𝑎𝑣𝑜𝑟 violated at 𝒪(30%) in amplitudes

SM prediction for desired CP asymmetry

𝐴𝐶𝑃𝑓

∝ 𝐼𝑚2𝑉𝑐𝑏

∗ 𝑉𝑢𝑏

𝑉𝑐𝑠∗ 𝑉𝑢𝑠 − 𝑉𝑐𝑑

∗ 𝑉𝑢𝑑~ − 6 × 10−4

∆𝐴𝐶𝑃~(2.0 ± 0.3) × 10−4

A. Petrov, PLB 774, 295 (2017)

Physics beyond SM may well affect ∆𝐴𝐶𝑃

Smaller than experimental value by a factor of 7

In order to pin-point the reason for this, one need to measure precise CP asymmetries in other charm decays.

QCD dynamics enhancing P and PA ?

QCD dynamics enhancing P and PA by factor of 7 can’t enhance |𝐴𝐶𝑃𝑑𝑖𝑟 𝐷0 → 𝐾𝑠𝐾𝑠 | or

|𝐴𝐶𝑃𝑑𝑖𝑟 𝐷0 → ഥ𝐾∗0𝐾𝑠 | by same factor of 7.

16

Search for CP violation in D0→ KSKS

➢ SM limit 1 % for direct CPV in D0 → KS0KS

0

➢ SCS decays (such as D0 → KS0KS

0 ) are special interest: possible interference with

NP amplitude could lead to larger nonzero CPV

Method:

𝐴𝐶𝑃 𝐷0 → 𝐾𝑠𝐾𝑠 = 𝐴𝑟𝑎𝑤 𝐷0 → 𝐾𝑆𝐾𝑆 − 𝐴𝑟𝑎𝑤 𝐷0 → 𝐾𝑠𝜋0 + 𝐴𝐶𝑃 𝐷0 → 𝐾𝑆𝜋0 + 𝐴𝐾0/ ഥ𝐾0

𝐴𝐾0/ ഥ𝐾0: Asymmetry originating from the different strong interaction of K0 and K0 mesons

with nucleons of the detector material = (−0.11 ± 0.01)%

ACP (D0 → KS0π0) = (−0.20 ±0.17)%

Ko et al PRD 84, 111501 (2011)

PRD92,054036 (2015)

D0 D0

ACP (D0 → KS0KS

0 ) = (− 0.02±1.53±0.17 )%

In Belle II, we expect to reach sensitivity of ±0.23% with 50 ab-1.

5399±87

PRL119,171801(2017)

The Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

17

𝐴𝐶𝑃 sensitivity

0.13 ± 0.19 ± 0.05

−0.009 ± 0.065 ± 0.048

0.005 ± 0.042 ± 0.029

LHCb, PRL 122,191803 (2019).

Belle II compliment LHCb in neutralsThe Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

Search for CP violation in FCNC D0→V, V=φ, K*0, r0

Radiative charm decays are dominated by long-range non-perturbative processes▪ enhance B.F. up to 10-4, ▪ whereas short-range interactions are predicted to yield rates at the level 10-8.

❖ In some SM extensions sizeable CP asymmetry expected in radiative charm decays:

▪ 𝐴 𝐶𝑃𝑉𝛾

> 3 % signal of New Physics

PRD 52, 6383 (1995) arXiv:1509.01997

PRL 109, 171801 (2012), arXiv:1210.6546

ACPsig = Araw

sig - Arawnorm + ACP

norm

𝐴𝑟𝑎𝑤 =𝑁 𝐷 → 𝑉 − 𝑁(ഥ𝐷 → 𝑉)

𝑁 𝐷 → 𝑉 + 𝑁(ഥ𝐷 → 𝑉)= 𝐴𝐶𝑃+𝐴𝐹𝐵+𝐴 𝜖

𝜋𝑠 𝑎

𝐴𝐹𝐵, 𝐴𝜖𝜋𝑠 eliminated through relative measurement of ACP .

ACP : independent of all kinematic variablesAFB : due to -Z0 interference; an odd function of cosθ* in CM frame𝑨𝝐

𝝅𝒔 : independent of final state,

943fb-1

PRL118,051801(2017)

The Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

19

Rare D decays➢ In case, the believed enhancement of CPV in charm decay is due to the New Physics.

➢ One expect it to have effect in other charm decays.➢ Rare charm decays seems to be the other way to confirm this.

➢ Forbidden at tree level in SM and CKM suppressed.➢ Expected to be dominated by long distance tree-level contributions➢ Potential for enhancements from BSM physics PRD101,115006 (2020)

20

𝐷+𝐷𝑠

+

arXiv:2011.00217

Search for rare decay D0→ PRD 93, 051102 (2016)(R)

Decay is sensitive to search for new Physics :

mediated by FCNC (𝑐 → 𝑢), forbidden in the tree level and highly suppressed due to

GIM in SM

SM Prediction : B ~ 10-8 PRD 66,014009 (2002)

In MSSM B ~ 10-6 with gluinos exchange PLB 500, 204 (2001)

D→π0π0, ηη

ηπ0, KSπ0, K

Lπ0

CLEO 2003

BESIII 2015BaBaR 2012Belle 2016

Signal: 4±15

Set world’s best limit at 8.5×10−7 in absence of a signal

In Belle II, with 50 ab-1, one might expect to reach : 10-7-10-8.

More in Latika’s talk

The Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

Search for D → invisible decay

NP contributions such as scalar Dark matter, right-handed neutrino or

Majorana fermion could substantially enhance the value up to 10-15

DM search associated with D meson : alternative way for search for DM.

In the Standard Model (SM), D meson decay to helicity suppressed by a

factor of PRD 82, 034005 (2010)

Method is based on the Belle previous techniques for DS leptonic decay.

+ - 0

D(*)tag

D*-sig

s- D0

e+ e-

Xfrag

D(*)

tag

Xfrag : fragmentation up to three at most one 0

: tag side, product of one c-jet

: Slow pion decay from ഥ𝐷𝑠𝑖𝑔∗−

Full reconstruction

πs

−

Signal side information:

Missing momentum against 𝐷𝑡𝑎𝑔(∗)

, 𝑋𝑓𝑟𝑎𝑔 𝑎𝑛𝑑 𝜋−

JHEP 09, 139 (2013)

PLB 651, 374 (2007)

PR 117, 75 (1985)

Search for D → invisible decay

inclusive

D

sig

N

fDNfDB

0

)()(

0

0

→=→

924fb-1

90% CL upper limit at 9.4×10−5

PRD95, 011102 (2017)(R)

Luminosity, ab-1

Inclusive D yield, in 106

Belle 0.9 0.6

Belle II 50 38

Reconstruct 𝐷𝑡𝑎𝑔(∗)

, 𝑋𝑓𝑟𝑎𝑔 𝑎𝑛𝑑 𝜋−. Get Mmiss to get inclusive D0 sample.

The Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

24

D0→K+π- wrong sign analysis

D0 K+π-

DCS

D0Mixing CF

u

uc

s

W-

d

u

D0 K+

π-V*

ud

Vcs

u

cD0

u u

c d

W+u

s

D0 π -

K+V*

us

Vcd

Doubly Cabibbo Suppressed (DCS)

Mixing

Cabibbo Flavored (CF)

𝑅 𝑡 =𝑁𝑊𝑆(𝑡)

𝑁𝑅𝑆(𝑡)= 𝑅𝐷 + 𝑅𝐷𝑦′Γ𝐷0 𝑡 +

𝑥′2 + 𝑦′2

4(Γ𝐷0 𝑡)2

𝑅𝐷 =𝐴𝐷𝐶𝑆

𝐴𝐶𝐹

2

𝑥′ = 𝑥 cos 𝛿 + 𝑦 sin 𝛿 , 𝑦′ = −𝑥 sin 𝛿 + 𝑦 cos 𝛿

𝛿 = 𝑎𝑟𝑔𝐴𝐷𝐶𝑆

𝐴𝐶𝐹𝑥 =

∆𝑚𝐷0

Γ𝐷0𝑦 =

∆Γ𝐷0

2Γ𝐷0

d → strong phase not directly measurable at B-factories

Same initial-and final stateInterference between the two amplitude will occur

In the limit of CP conservation

y’ and x’2 accessible

D0 K-π+

CF

D0Mixing DCS

Right sign CF dominates the Right Sign decay amplitude

Normalize wrong sign rate to the right sign to obtain

25

𝐷0 − ഥ𝐷0 mixing at B factories

200 mm

100 mm

Experimental method

Tag and suppress background➢ D*+

→D0π+slow

➢ Flavor of D0→using charge of πslow

➢ 𝑝𝐶𝑀𝑆

𝐷∗> 2.5 GeV/c to eliminate D0 from B decay

Measure D0 proper time 𝑡, its error 𝜎𝑡 by reconstructing D0 momentum and flight length 𝑙

𝒕 =𝒍𝒅𝒆𝒄

𝒄𝜷𝜸𝜷𝜸 =

𝒑𝑫𝟎

𝑴𝑫𝟎

σt calculated from vtx error matrices

Mixing parameters (x’2,y’) extracted by the fit to the time-dependent ratio of wrong sign to right sign decays

𝑅 𝑡/𝜏𝐷0 =∞−

+∞Γ𝑊𝑆 𝑡′/𝜏𝐷0 ℛ 𝑡/𝜏𝐷0 − 𝑡′/𝜏𝐷0 𝑑(𝑡′/𝜏𝐷0 )

∞−

+∞Γ𝑅𝑆 𝑡′/𝜏𝐷0 ℛ 𝑡/𝜏𝐷0 −𝑡′/𝜏𝐷0 𝑑(𝑡′/𝜏𝐷0 )

ℛ 𝑡/𝜏𝐷0 −𝑡′/𝜏𝐷0 is resolution function of the real decay time t’.

𝑫𝟎 → 𝑲+𝝅−

26

2980710±1885 events 11478±177 events

Gaussian + Johnson SU

WS decay D0→ K+π-

D0→ K-π+ D0

→ K+π-

RWS: (0.385±0.006) %

976fb-1

Belle, PRL 112, 111801(2014)

ΔM=M(D*+→D0(→Kπ)πs

+)-M(D0

→Kπ)

with mixingwithout mixing

τ = 1/Γ𝐷0

Divide sample into N bins of decay time and fit M

Fitting ratios less sensitive to resolution function

Belle, PRL 112, 111801(2014)

N=10N=5

BaBar, PRD 98, 211802(2007)

3.9σ5.1σ

384fb-1

976fb-1

27

Most precise measurement by LHCb PRD97, 031101 (R)(2018)

The Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

28

CP eigenstates decays D0→ K+K- / π+π-

Mixing in D0 decays to CP eigenstates, give rise to an effective lifetime τ that differs from that in the decays to flavor eigenstates such as D→K+π-.Observables

𝑦𝐶𝑃 =𝜏 𝐷0 → 𝐾−𝜋+

𝜏 𝐷0 → 𝐾−𝐾+ − 1

𝑦𝐶𝑃 is equal to the mixing parameter 𝑦 if CP is conserved.Otherwise, effective lifetimes of ഥ𝐷0 and 𝐷0 decaying to the same CP eigenstate differ and the asymmetry

𝐴Γ =𝜏 ഥ𝐷0 → 𝐾−𝐾+ − 𝜏 𝐷0 → 𝐾+𝐾−

𝜏 ഥ𝐷0 → 𝐾−𝐾+ + 𝜏 𝐷0 → 𝐾+𝐾−≠ 0

In absence of direct CP violation, 𝑦𝐶𝑃 and 𝐴Γ are related to 𝑥 and 𝑦 as

𝑦𝐶𝑃 =1

2

𝑞

𝑝+

𝑝

𝑞𝑦𝑐𝑜𝑠𝜙 −

1

2

𝑞

𝑝−

𝑝

𝑞𝑥𝑠𝑖𝑛𝜙

𝐴Γ =1

2

𝑞

𝑝−

𝑝

𝑞𝑦𝑐𝑜𝑠𝜙 −

1

2

𝑞

𝑝+

𝑝

𝑞𝑥𝑠𝑖𝑛𝜙

where 𝜙 = arg(𝑞

𝑝)

PLB 486, 418 (2000)

PLB 486, 418 (2000)JHEP 0705, 102 (2007)

We measure:Difference in proper decay time distributions of D0

→f and D0→f

CP eigenstates decays D0→ K+K- / π+π- 976fb-1

Tag D0 flavor by charge of πS from D*Belle, PLB 753, 412 (2015)

Proper decay time distribution summed over cosθ*where θ* polar angle of D0 in CMS with respect to the direction of e+

Measure 𝑦𝐶𝑃 and 𝐴Γ in bins of cosθ*

𝑦𝐶𝑃 = +1.11 ± 0.22 𝑠𝑡𝑎𝑡 ± 0.09 𝑠𝑦𝑠𝑡 % (4.7σ)𝐴Γ = −0.03 ± 0.20(𝑠𝑡𝑎𝑡) ± 0.07(𝑠𝑦𝑠𝑡) %

Open (full) circle for 3 (4)-layer SVD

Least Square fit

32% C.L. 40% C.L.

Fitted D0 Lifetime:(408.46±0.54)fs(stat only)

World Average:(410.1±1.5) fs

30

𝑦𝐶𝑃 = 0.57 ± 0.13 ± 0.09 %Result is consistent with the known value of the mixing parameter

𝑦 = 0.62 ± 0.07 %Showing no evidence for CP violation in 𝐷0 − ഥ𝐷0 mixing.

312K

878K

4579K

3fb-1

𝑦𝐶𝑃 = 0.38 ± 0.28 ± 0.15 %

𝑦𝐶𝑃 = 0.63 ± 0.15 ± 0.11 % 𝐷0 → 𝐾+𝐾−

𝐷0 → 𝜋+𝜋−

CP eigenstates decays D0→ K+K- / π+π-

Observable Stats Systematic Total

𝑦𝐶𝑃(%) Reducible Irreduc.

976 fb-1 0.22 0.07 0.07 0.24

5 ab-1 0.10 0.03-0.04 0.07-0.04 0.11-0.12

50 ab-1 0.03 0.01 0.07-0.04 0.05-0.08

Source ∆𝑦𝐶𝑃(10−2)

Acceptance 0.050

SVD misalignments 0.060

Mass window position

0.007

Background 0.059

Resolution function 0.030

Binning 0.021

Total syst. Error 0.220

Prospectus in Belle II The Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

31

CP-odd decays: ℬ 𝐷0 → 𝐾𝑠𝜔 = 5 times ℬ 𝐷0 → 𝐾𝑠𝜙 in PDGMeasure 𝑦𝐶𝑃 in 𝐷0 → 𝐾𝑠𝜔 for the first time.

Utilizes the full Belle data set.Parameter 𝑦𝐶𝑃 is determined by

𝑦𝐶𝑃 = 1 − 𝜏(𝐷0 → 𝐾−𝜋+)/𝜏(𝐷0 → 𝐾𝑠𝜔)

Lifetime fitting is performed with resolution (triple Gaussians) and background (with nonzero- and zero-lifetime components),

We get 𝑦𝐶𝑃 = 0.96 ± 0.91 ± 0.62−0.00

+0.17 %Statistical, systematic, and from possible CP-even decays in the final state.

91K 1375K

𝑦𝐶𝑃 in 𝐷0 → 𝐾𝑠𝜔 Belle PRD 102, 071102(R) (2020)

32

Mixing in three body D0→KS

0π+π-

CF : D0→K*-π+

DCS : D0→K*+π-

CP : D0→ρKS

0

𝒜 amplitude for | 𝐷0

➢ Interference between intermediate resonance provide sensitivity to both magnitude and sign of the mixing parameters.

➢ Allows for probes for indirect CP violation

K*-

K*+

Powerful decay mode for flavor-tagged time-dependent D0-D0 studies ρ

ℳ 𝑚−2, 𝑚+

2, 𝑡 = 𝒜(𝑚−2, 𝑚+

2)𝑒1 𝑡 + 𝑒2 𝑡

2+

𝑞

𝑝ҧ𝒜(𝑚−

2, 𝑚+2)

𝑒1 𝑡 − 𝑒2 𝑡

2

ഥℳ 𝑚−2, 𝑚+

2, 𝑡 = ҧ𝒜(𝑚−2, 𝑚+

2)𝑒1 𝑡 + 𝑒2 𝑡

2+

𝑝

𝑞𝒜 (𝑚−

2, 𝑚+2)

𝑒1 𝑡 − 𝑒2 𝑡

2

ҧ𝒜 amplitude for | ഥ𝐷0 𝑚 ±2≡ 𝑚2(𝐾𝑆0𝜋

±)

Time dependence contained in terms 𝑒1,2𝑡 =exp[-i (m1,2 – iΓ1,2/2)t]

𝒜(𝑚−2, 𝑚+

2) = 𝑎𝑟 𝑒𝑖𝜑𝑟𝒜𝑟(𝑚−

2, 𝑚+2) + 𝑎𝑁𝑅𝑒𝑖

𝜑𝑟

Sum of intermediates states

ҧ𝒜(𝑚−2, 𝑚+

2) = 𝑎 ത𝑎𝑟 𝑒𝑖𝜑𝑟 ҧ𝒜𝑟(𝑚−

2, 𝑚+2) + 𝑎𝑁𝑅𝑒𝑖

𝜑𝑟

Simultaneous determination of x and y via t-dependent amplitude analysis

CPV

Quasi two body intermediate state

33

Measurement of x, y and q/pFit projection for CP conserved fit

D0 mean lifetime = (410.3±0.6)fs

Consistent with PDG: (410.1±1.5)fs

𝒙 = (𝟎. 𝟓𝟔 ± 𝟎. 𝟏𝟗−𝟎.𝟎𝟗−𝟎.𝟎𝟗+𝟎.𝟎𝟑+𝟎.𝟎𝟔)%

𝒚 = (𝟎. 𝟑𝟎 ± 𝟎. 𝟏𝟓−𝟎.𝟎𝟓−𝟎.𝟎𝟔+𝟎.𝟎𝟒+𝟎.𝟎𝟑)%

Significance : 2.5σ

CP conservedCPV allowed

Also search for CPV in D0/D0→KS

0π+π-

|q/p|= 𝟎. 𝟗𝟎−𝟎.𝟏𝟓−𝟎.𝟎𝟒−𝟎.𝟎𝟓+𝟎.𝟏𝟔+𝟎.𝟎𝟓+𝟎.𝟎𝟔

𝒂𝒓𝒈(𝒒/𝒑) = (−𝟔 ± 𝟏𝟏−𝟑−𝟒+𝟑+𝟑)

∘Value of x and y consistent with CP conserved fit

921fb-1

No hint for indirect CP violation

Belle PRD89, 091103 (R)(2014)

1231731±1633 signal events with purity of 95.5%

34

Mixing parameters using 𝐷0 → 𝐾𝑠𝜋+𝜋−

𝑥𝐶𝑃 =1

2𝑥 cos 𝜑

𝑞

𝑝+

𝑝

𝑞+ 𝑦 sin 𝜑

𝑞

𝑝−

𝑝

𝑞

∆𝑥 =1

2𝑥 cos 𝜑

𝑞

𝑝−

𝑝

𝑞+ 𝑦 sin 𝜑

𝑞

𝑝+

𝑝

𝑞

𝑦𝐶𝑃 =1

2𝑦 cos 𝜑

𝑞

𝑝+

𝑝

𝑞− 𝑥 sin 𝜑

𝑞

𝑝−

𝑝

𝑞

∆𝑦 =1

2𝑦 cos 𝜑

𝑞

𝑝−

𝑝

𝑞− 𝑥 sin 𝜑

𝑞

𝑝+

𝑝

𝑞

𝑥𝐶𝑃 = 𝑥

∆𝑥 = 0

𝑦𝐶𝑃 = 𝑦

∆𝑦 = 0

If no CPV

𝜑 = arg𝑞𝐴𝑓

𝑝𝐴𝑓

𝑞

𝑝= 1

Mixing is well established. No evidence of CPV in mixing

Reminder 𝑥 ≡𝑚1−𝑚2

ഥ𝛤; 𝑦 ≡

𝛤1−𝛤2

2ഥ𝛤

35

Belle II prospectus

𝒙 = (𝟎. 𝟓𝟔 ± 𝟎. 𝟏𝟗−𝟎.𝟎𝟗−𝟎.𝟎𝟗+𝟎.𝟎𝟑+𝟎.𝟎𝟔)%

𝒚 = (𝟎. 𝟑𝟎 ± 𝟎. 𝟏𝟓−𝟎.𝟎𝟓−𝟎.𝟎𝟔+𝟎.𝟎𝟒+𝟎.𝟎𝟑)%

|q/p|= 𝟎. 𝟗𝟎−𝟎.𝟏𝟓−𝟎.𝟎𝟒−𝟎.𝟎𝟓+𝟎.𝟏𝟔+𝟎.𝟎𝟓+𝟎.𝟎𝟔

𝒂𝒓𝒈(𝒒/𝒑) = (−𝟔 ± 𝟏𝟏−𝟑−𝟒+𝟑+𝟑)

∘

Systematic uncertainty start dominating at ~5 ab-1.Can this be avoided ? Measuring strong phase variation across Dalitz plane using coherent 𝐷0 ഥ𝐷0

pairs (BESIII).

Uncertainty due to Dalitz model

𝐷0 → 𝐾𝑠𝜋+𝜋−

BELLE2-NOTE-PL-2020-010

The Belle II Physics Book, PTEP2019, 12, 123C01 (2019)

36

𝐷0 → 𝐾𝑠𝜋+𝜋− bin flip methodBin-flip method → Relies on ratios between charm decays reconstructed in similar

kinematic and decay-time conditions, thus avoiding the need for an accurate modelling

of the efficiency variation across phase space and decay time.

Data is binned in Dalitz coordinates where the binning scheme is chosen to have

approximately constant strong-phase differences

PRD99,012007(2019)

𝑚±2 is squared invariant mass 𝑚2 𝐾𝑆𝜋± for 𝐷0 → 𝐾𝑆𝜋+𝜋− and 𝑚2 𝐾𝑆𝜋∓ for ഥ𝐷0 → 𝐾𝑆𝜋+𝜋−

Two sets of eight bins are formed and organized symmetrically about principal bisector 𝑚+2 = 𝑚−

2

Bins labelled with indices ±𝑏. +b refer to 𝑚+2 > 𝑚−

2 (unmixed CF 𝐷0 → 𝐾∗−𝜋+ dominate)-b refer to symmetric 𝑚+

2 < 𝑚−2 (receives larger contribution from decays following oscillation)

J. Libby et al PRD 82, 112006 (2010)

37

LHCb measure ratio 𝑅𝑖+ 𝑅𝑖

− between initially produced 𝐷0(ഥ𝐷0) meson in i bin

𝑥𝐶𝑃 = 2.7−0.15+0.17 × 10−2 Τ𝑞 𝑝 = 1.05−0.17

+0.22

𝑦𝐶𝑃 = (7.4 ± 0.37) × 10−3 𝜑 = −0.09−0.16+0.11

Combining the world average value: 𝑥 = 3.9−1.2+1.1 × 10−3

Evidence of positive mass difference b/w the 𝐷0 mass eigenstates.

PRL122, 231802(2019)

𝑅𝑏(𝑡𝑗) =𝑁−𝑏(𝑡𝑗)

𝑁𝑏(𝑡𝑗)ത𝑅𝑏(𝑡𝑗) =

ഥ𝑁−𝑏(𝑡𝑗)

ഥ𝑁𝑏(𝑡𝑗)

38

39

40

Charm result

➢ CPV is observed in Charm after Mixing.➢ Need to measure CPV in different models in order to really prove that the CPV is

due to SM or NP.➢ Exciting and difficult times ahead.➢ Stats limitation is going to over soon.➢ We will soon start getting limited by Syst. ➢ Need to be more smart. Pretty sure that next generation will be.

41

Charm result

➢ CPV is observed in Charm after Mixing.➢ Need to measure CPV in different models in order to really prove that the CPV is due

to SM or NP.➢ Exciting and difficult times ahead.➢ Stats limitation is going to over soon.➢ We will soon start getting limited by Syst. ➢ Need to be more smart. Pretty sure that next generation will be.

42

43

Using D0→ KS ππ and D0

→KS K K decaysBaBar, PRL 105 081803 (2010)

469fb-1

D0→ KS ππ D0

→ KS KK

540800±800 79900±300

𝒙, 10-3

𝒚, 10-3

+ Non Mixing

Disfavor non-mixing hypothesis with C.L. equivalent to 1.9σ

44

CP eigenstates decays D0→ K+K- / π+π- 468fb-1

BaBar, PRD 87, 012004 (2013)Measure the lifetimes

τ+ : 𝐷0 → 𝐾−

𝐾+

, 𝜋−

𝜋+ τ+: ഥ𝐷0 → 𝐾

−𝐾

+, 𝜋

−𝜋

+ τKπ : 𝐷0(ഥ𝐷0) → 𝐾∓𝜋±

Use their inverse to compute 𝑦𝐶𝑃 =Γ++ഥΓ+

2Γ− 1 and ∆𝑌 = −

𝐴Γ

2=

Γ+−ഥΓ+

2Γ

Only tagged for D0

→ππdue to poor S/N in untagged

𝑦𝐶𝑃 = 0.72 ± 𝟎. 𝟏𝟖 ± 0.12 % (3.3𝜎)

∆𝑌 = −𝐴Γ

2= 0.09 ± 0.26 ± 0.06 %

Uncertainty on 𝒚𝑪𝑷 is impressive

45

BaBar, PRD 93, 112014 (2016)Using D0→ π+π-π0 decay468fb-1

Signal identified as :∆𝑚 ≡ 𝑚 𝜋+𝜋−𝜋0𝜋𝑠

+ − 𝑚 𝜋+𝜋−𝜋0

𝑝𝜋0 > 350 MeV𝑝∗ 𝐷0 > 2.8 GeV

𝒙 = 𝟏. 𝟓 ± 𝟏. 𝟐 ± 𝟎. 𝟔 %𝒚 = 𝟎. 𝟐 ± 𝟎. 𝟗 ± 𝟎. 𝟓 %

No CPV

D0 mean lifetime = (410.2±3.8)fs

Consistent with PDG: (410.1±1.5)fs

𝒎𝝅+𝝅𝟎𝟐

𝒎𝝅−𝝅𝟎𝟐

𝒎𝝅+𝝅𝟎𝟐

𝒎𝝅−𝝅𝟎𝟐

Diff b/w data and fit model prediction

𝒎𝝅+𝝅𝟎𝟐

𝒎𝝅−𝝅𝟎𝟐 𝒎𝝅+𝝅−

𝟐

First measurement of mixing parameter of time dependent amplitude analysis.

Background from:𝐷 → 𝐾−𝜋+,𝐷 → 𝐾−𝜋+𝜋0,𝐷 → 𝐾𝑠𝜋+𝜋−and 𝐷 → 𝐾𝑠(→ 𝜋+𝜋−)𝜋0

Fit with isobar model of relativistic BW line shape~138000 events