Unravelling New Physics in nonleptonic Charm Decays

Unravelling New Physics in nonleptonicCharm Decays

Stefan Schacht

CHARM 2013

Manchester, 01/09/2013

in collaboration with Gudrun Hiller and Martin JungPhys. Rev. D 87, 014024 (2013), arXiv:1211.3734

and in preparation

Can we distinguish new physics in D decaysfrom the Standard Model?

Data from LHCb, CDF, Belle,BABAR, CLEO and FOCUSRed: Post Moriond 2013 Update

Observable Measurement

SCS CP asymmetries∆adir

CP(K+K−, π+π−) −0.00329 ± 0.00121Σadir

CP(K+K−, π+π−) +0.0014 ± 0.0039ACP(D0 → KSKS) −0.23 ± 0.19ACP(D0 → π0π0) +0.001 ± 0.048ACP(D+ → π0π+) +0.029 ± 0.029ACP(D+ → KSK+) −0.0011 ± 0.0025ACP(Ds → KSπ

+) +0.012 ± 0.007ACP(Ds → K+π0) +0.266 ± 0.228

Indirect CP violationaind

CP (−0.010 ± 0.162) · 10−2

δL ≡ 2Re(ε)/(1 + |ε|2) (3.32 ± 0.06) · 10−3

K+π− strong phase differenceδKπ 18.25◦ ± 9.85◦

Observable Measurement

SCS branching ratiosB(D0 → K+K−) (3.96 ± 0.08) · 10−3

B(D0 → π+π−) (1.401 ± 0.027) · 10−3

B(D0 → KSKS) (0.17 ± 0.04) · 10−3

B(D0 → π0π0) (0.80 ± 0.05) · 10−3

B(D+ → π0π+) (1.19 ± 0.06) · 10−3

B(D+ → KSK+) (2.83 ± 0.16) · 10−3

B(Ds → KSπ+) (1.21 ± 0.08) · 10−3

B(Ds → K+π0) (0.62 ± 0.21) · 10−3

CF branching ratiosB(D0 → K−π+) (3.88 ± 0.05) · 10−2

B(D0 → KSπ0) (1.19 ± 0.04) · 10−2

B(D0 → KLπ0) (1.00 ± 0.07) · 10−2

B(D+ → KSπ+) (1.47 ± 0.07) · 10−2

B(D+ → KLπ+) (1.46 ± 0.05) · 10−2

B(Ds → KSK+) (1.45 ± 0.05) · 10−2

DCS branching ratiosB(D0 → K+π−) (1.47 ± 0.07) · 10−4

B(D+ → K+π0) (1.83 ± 0.26) · 10−4

Stefan Schacht Manchester September 2013 2 / 13

Symmetry emergency kit: SU(3)F

States and operators = representations of SU(3)F

States(D0 = − |cu〉 , D+ =

∣∣∣cd⟩, Ds = |cs〉

)= 3

Pions and Kaons: [(8) ⊗ (8)]S = (1) ⊕ (8) ⊕ (27)

Operators

Heff ∼ VudV∗cs (ud) (sc)︸︷︷︸CA

+ VusV∗cs (us) (sc) + VudV∗cd (ud)(dc

)︸︷︷︸SCS

+ VusV∗cd (us)(dc

)︸︷︷︸DCS

HSCSeff ∼ VusV∗cs

(15 + 6

)︸︷︷︸CKM leading

+ VubV∗cb (15 + 3)︸︷︷︸CKM suppressed, CPV


Is this a sign of new physics?


SU(3)F analysis of new physics models

Many possible NP models to explain measured ∆adirCP.

[Grossman Kagan Nir 2006, Hochberg Nir 2011, Altmannshofer Primulando Yu Yu 2012, Giudice Isidori Paradisi 2012, Hiller

Hochberg Nir 2012, Da Rold Delaunay Grojean Perez 2012]

SU(3)-Flavor perspective:Dirac structure not explicit, just additional dofs.

Example: scalar operators give 15NP in addition to SM 15.

Introduce NP models with specific SU(3)F structure.Can we recognize them by correlations of B and adir

CP?


Models have specific signatures

SM: HSM ∼ VusV∗cs

(15 + 6

)+ VubV∗cb (15 + 3)︸︷︷︸

HCPV

Model Operator HCPV

Triplet (uc)∑

qq, uσµνGµνc ∼ 3NP

HN [Hochberg Nir 2012] (uRcL)(uLuR) ∼ 15NP + 3NP

∆U = 1 (sRcL)(uRsL) ∼ 15NP + 6NP + 3NP

SU(3)F prediction: ACP(D0 → KSKS)/ACP(D0 → K+K−) ∼ 1/δX.

“Triplet model”: (uc)∑

qq, uσµνGµνc ∼ 3NP

Enhanced chromomagnetic dipole or QCD penguin operatorse.g. in SUSY [Grossman Kagan Nir 2007, Giudice Isidori Paradisi 2012, Hiller Hochberg Nir 2012]

No 15 in HCPV. ⇔ SM: 15 fixed by B’s.No disentangling possible with nonleptonic decays.


“HN model”: (uRcL)(uLuR) ∼ 15NP + 3NP

Specific Two-Higgs doublet model.

Operators 15 32 ,

12 ,

13

and 15NP32 ,

12 ,

13

coming with a relative weak phase.

Smoking gun: aCP(D+ → π+π0) , 0⇒ ∆I = 3/2 NP [Grossman Kagan Zupan 2012]

Very important channel for beauty and charm factories!

MFV/SM A1527 A15

8 A68 A3

1 A38

D+ → π0π+ ∆−12 0 0 0 0

Strong and weak phase difference needed for aCP(D+ → π+π0) , 0.


“∆U = 1 model”: (sRcL)(uRsL) ∼ 15NP + 6NP + 3NP

(sc)(us) but no corresponding operator (dc)(ud).

Breaking of discrete U spin symmetry d ⇔ s of H .

Violation of U spin limit sum rules beyond SU(3)F-X. [Hiller Jung StS 2012]

adirCP(D0 → K+K−) + adir

CP(D0 → π+π−) , 0

adirCP(D+ → K0K+) + adir

CP(Ds → K0π+) , 0

Present data, pure SU(3)F: NP and SM not distinguishable.


How to find the new physics

1 Obtain significantly improved future data.

2 Gain insights in the strong dynamics.Use structural (not quantitative!) input from QCD Factorization.

[Hiller Jung StS 2013]


NP models with gedanken data, pure SU(3)FProof of Principle

Future scenario with significantly improved hypothetical data.

Prediction of sizable CPVin D0 → π0π0 in tripletmodel (including SM).

Measurementadir

CP(D0 → π0π0) =

ΣadirCP(K+K−, π+π−) = 0

⇒ SM excluded.-0.008 -0.007 -0.006 -0.005 -0.004

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

S aCPdir HK+ K-, Π+ Π-L

a CP

dir ID

0®

Π0Π0 M

Exp

.tr

iple

tsD

U=

1H

N


NP models with structural input from QCDFUsing QCDF sum rules in SU(3)F for current data

Matching of SU(3)F and QCDF for CP conserving part.QCDF sum rules for matrix elements of CP conserving H .

CP Violation parametrized by additional SU(3)F matrix elements.

Considered NP models: Same CP conserving Hamiltonian as in SM.QCDF sum rules are still valid !

Here: Scenario B sum rules⇒ Martin’s talk.Assumptions: Flavor-universal a1, b2/b1 = C2/C1.

3 sum rules.


NP models with structural input from QCDFUsing QCDF sum rules in SU(3)F for current data

Left: Plain SU(3)F including linear breaking.

Right: Using additionally the QCDF sum rules. [preliminary results]


Summary

First comprehensive SU(3)F analysis of D→ PP decay datawithout bias.

Charm Physics remains suspense-packed after Moriond 2013 (!).

Future data could differentiate new physics from the SM.

QCDF sum rules can help a lot in this respect.

With more data one can reduce theory errors (!).

Key observables:ACP(D0 → KSKS), ACP(Ds → K+π0), ACP(D+ → π+π0), B(Ds → Klν),all SCS CP asymmetries.

Exciting time for searching for New Physics in Charm!


BACK-UP

Stefan Schacht Manchester September 2013 14

Measurements of ∆ACP

2008 BaBar AK+K−CP = (0.00 ± 0.34 ± 0.13)%

Aπ+π−

CP = (0.24 ± 0.52 ± 0.22)%2011 old LHCb result, D∗ (−0.82 ± 0.21 ± 0.11)%2012 Belle (−0.87 ± 0.41 ± 0.06)%2012 CDF (−0.62 ± 0.21 ± 0.10)%2013 LHCb, D∗ (−0.34 ± 0.15 ± 0.10)%2013 LHCb, B→ D0µX (0.49 ± 0.30 ± 0.14)%

Average post Moriond March 2013: [HFAG 2013]

∆adirCP = −0.00329 ± 0.00121 (2.7σ)

Average pre Moriond March 2013: [HFAG 2012]

∆adirCP = −0.00678 ± 0.00147 (4.6σ)


Can we distinguish new physics in D decaysfrom the Standard Model?

Large direct CP violation in Charm Decays (?!)Post Moriond 2013: [HFAG 2013, LHCb 2013, Belle 2012, CDF 2012, BaBar 2008]

∆adirCP = adir

CP(D0 → K+K−) − adirCP(D0 → π+π−) = −0.00329 ± 0.00121 (2.7σ)

SM contribution is suppressed. Naive expectation: ∆adirCP . O(0.001)

CKM and QCD factor: ∆adirCP ' λ

4 ·P/T ∼ 10−3 · 0.1 (?)

Problem: αs(mc) large and expansion in ΛQCD/mc doubtful.


Symmetry Emergency Kit

We do not know how to reliably calculatethe hadronic matrix elements 〈f |Oj |i〉 for charm.

What is the best we can do instead?1 SU(3)F ⇒ Relate several decay amplitudes of D→ PP.

2 Comprehensive Fit of D→ P8P8 data: 25 observables.


Perturbation from Hbreak ∼ ms s s ∝ 1 ⊕ 8e.g. , (15) ⊗ (8) = (42) ⊕ (24) ⊕ (151) ⊕ (152) ⊕ (15′) ⊕ (6) ⊕ (3)

[Table: Hiller Jung StS 2012] [Previous works: Kingsley Treiman Wilczek Zee 1975, Einhorn Quigg 1975, Altarelli Cabibbo Maiani1975, Voloshin Zakharov Okun 1975, Quigg 1980, Savage 1991, Chau Cheng 1992, Pirtskhalava Uttayarat 2011, Feldmann Nandi Soni

2012, Brod Grossman Kagan Zupan 2012, Bhattacharya Gronau Rosner 2012, Franco Mishima Silvestrini 2012, . . . ]

25 observables, 13 matrix elements⇒ FitStefan Schacht Manchester September 2013 18

Classification by Cabibbo Suppression

Cabibbo favored: c→ sdu

D0c

u

s

u

K−

u

d

π+Vud ∼ 1

V ∗cs ∼ 1

Singly-Cabibbo suppressed:c→ ssu und c→ ddu

D0c

u

d

u

π−

u

d

π+Vud ∼ 1

V ∗cd ∼ −λ

Doubly-Cabibbo suppressed:c→ dsu

D0c

u

d

u

π−

u

s

K+Vus ∼ λ

V ∗cd ∼ −λ

CPV ∝ V∗cbVub

D

c

u

b

V ∗cb Vub

u

s

s

u

K+

K−

+ Penguin contractions ofTree operators (!)


Observables vs. Degrees of Freedom

17 amplitudes of {D0,D+,Ds} to Pions/Kaons.26 observables: 17 B, 8 SCS ACP, 1 relative strong phase.

25 measured observables (B(Ds → KLK+) not measured)

3 SU(3) limit MEs coming with Σ, 2 coming with ∆.Only relative phases⇒ 9 SU(3) limit params. ∈ R.

Linear SU(3) breaking: 15 additional MEs.

17×20 matrix of Clebsch-Gordan coefficients: Not full rank.

Consider terms coming only with ∆ separately for calculating the rank.

Only 13 matrix element combinations have physical meaning.

Redefine MEs to reduce # MEs from 20 to 13.Example: B31

1,8 7→

√72 B31

1,8 −

√52 B32

1,8 .

Further similar replacements found by Gaussian elimination:Remove B62

8 , B1538 , B153

27 , B24227 and B42

27.


Direct and Indirect CP Violation

CP asymmetries with final state KS or initial state D0 havecontributions from indirect CPV.

Get pure direct CPV by removing the mixing contributionsKaon mixing: ∝ δL = 2 Re ε/

(1 + |ε|2

)= (3.32 ± 0.06) · 10−3. [PDG 2012]

D0 mixing: aindCP = (−0.010 ± 0.162) · 10−2. [HFAG 2013]

Sign depends on appearing K0 or K0 in tree level Feynman diagram.

AdirCP(D+ → KSK+) = ACP(D+ → KSK+) + δL (with K0)

AdirCP(Ds → KSπ

+) = ACP(Ds → KSπ+) − δL (with K0)

Neglect K and D mixing in ACP(D0 → KSKS) = −0.23 ± 0.19.


How Large is the Breaking in D→ PP?

δX ≡maxij|B

ji|

max(|A1527|, |A

68|, |A

158 |)

δ′X ≡ maxd

∣∣∣∣∣AX(d)A(d)

∣∣∣∣∣δX ignores suppression byClebsch-Gordan-coefficients.

δ′X ignores possible largecancellations.

0.1 0.2 0.3 0.4 0.50.1

0.2

0.3

0.4

0.5

∆X

∆ X¢

68%

C.L

.95

%C

.L.

Data can be described by SU(3)-expansion with δ(′)X . 30%.


How Large are the Penguins/Triplets?All plots: post Moriond 2013 ∆adir

CP ' λ4 ·P/T

0 1 2 3 40

1

2

3

4

∆3¢

∆ 3

68%

C.L

.95

%C

.L.

without large ACP

0 10 20 30 40 500

5

10

15

∆3¢

∆ 3

68%

C.L

.95

%C

.L.

all data

0 1 2 3 40

1

2

3

4

∆3¢

∆ 3

68%

C.L

.95

%C

.L.

all data, zoom

δ3: max(ratios matrix elements) δ′3: max(ratios amplitudes)

Left: Without ACP(D0 → KSKS) ACP(Ds → KSπ+) ACP(Ds → K+π0)

= −0.23 ± 0.19 = 0.012 ± 0.007 = 0.266 ± 0.228


How Large are the Penguins/Triplets?Pre Moriond 2013

0 1 2 3 40

1

2

3

4

∆3¢

∆ 3

68%

C.L

.95

%C

.L.

without large ACP

0 10 20 30 40 500

5

10

15

∆3¢

∆ 3

68%

C.L

.95

%C

.L.

all data

δ3: max(ratios matrix elements) δ′3: max(ratios amplitudes)

Left: Without ACP(D0 → KSKS) ACP(Ds → KSπ+) ACP(Ds → K+π0)

= −0.23 ± 0.19 = 0.031 ± 0.015 = 0.266 ± 0.228


Future Data

Observable Future dataSCS CP asymmetries

∆adirCP(K+K−, π+π−) −0.007 ± 0.0005

ΣadirCP(K+K−, π+π−) −0.006 ± 0.0007

adirCP(D+ → KSK+) −0.003 ± 0.0005

adirCP(Ds → KSπ

+) 0.0 ± 0.0005adir

CP(Ds → K+π0) 0.05 ± 0.0005K+π− strong phase difference

δKπ 21.4◦ ± 3.8◦


SU(3)F-X Clebsch-Gordan Coefficients afterReparametrizations


Quantum Numbers and Hamiltonian

Initial states: Antitriplet of D Mesons Notation: |µ〉I, I3,Y∣∣∣D0⟩

= |cu〉 = 3 12 ,−

12 ,−

13,

∣∣∣D+⟩ =∣∣∣cd

⟩= 3 1

2 ,12 ,−

13,

∣∣∣D+s⟩

= |cs〉 = 30,0, 23

Final states from Octet of pseudoscalars: Pions and Kaons∣∣∣π+⟩ = |8〉1,1,0,∣∣∣π0

⟩= |8〉1,0,0,

∣∣∣π−⟩ = |8〉1,−1,0∣∣∣K+⟩ = |8〉 12 ,

12 ,1

,∣∣∣K−⟩ = |8〉 1

2 ,−12 ,−1,

∣∣∣K0⟩

= |8〉 12 ,−

12 ,1

,∣∣∣K0

⟩= |8〉 1

2 ,12 ,−1

Operators: Flavor Structure of Hamiltonian

Heff ∼ VudV∗cs (ud) (sc)︸︷︷︸CA

+ VusV∗cs (us) (sc) + VudV∗cd (ud)(dc

)︸︷︷︸SCS

+ VusV∗cd (us)(dc

)︸︷︷︸DCS


Documents

Unravelling New Physics in nonleptonic Charm Decays