Direct CP violation in D meson decays - Rencontres de Moriond

Direct CP violation in D meson decays 

Joachim Brod 

in collaboration with Yuval Grossman, Alexander L. Kagan, Jure Zupan 

Recontres de Moriond, QCD session 

March 13th, 2012 

arXiv:1111.5000 [hep-ph]; arXiv:1203.xxxx [hep-ph] 

see also A. Kagan, talk at FPCP 2011, May 2011 

Joachim Brod (University of Cincinnati) CP violation in D decays 1 / 26

Introduction 

Singly Cabibbo-suppressed (SCS) D-meson decays D 0 → π + π − ,D 0 → K + K − 

CP violation in SCS D-meson decays is 

c 

ū 

V ∗ uq 

Vcq W 

sensitive to new physics (NP) in the up-quark sector 

suppressed in the standard model (SM): 

two-generation dominance 

loop suppression (penguin amplitudes) 

GIM mechanism 

Naively, expect effects of O 

VubVcb 

VusVcs 

u 

¯q 

q 

ū 

 

αs 

π ∼ 0.01%. 


Definitions 

Af ≡ A(D 0 → f) = A T f 1+rfe i(δf−φf) , 

Āf ≡ A(D0 → f) = A T i(δf+φf) 

f 1+rfe 

rf relative magnitude of subleading (penguin) amplitude with relative 

strong phase δf, weak phase φf. 

A dir 

Āf| 2 

f := |Af| 2 −| 

|Af| 2 +|Āf| 2 = 2rf sinφf sinδf 

(Universal) indirect contribution A ind 

f cancels to good approximation in 

∆ACP := A dir 

K + K− −Adir 

π + π− Joachim Brod (University of Cincinnati) CP violation in D decays 3 / 26

Measurements 

First significant measurements of CP violation in the up-quark sector 

LHCb [R. Aaij et al., 1112.0938]: 

CDF [La Thuile 2012]: 

∆ACP = (−0.82±0.21±0.11)% 

∆ACP = (−0.62±0.21±0.10)% 

leading to new world average [La Thuile 2012]: 

∆ACP = (−0.67±0.16)% 

Can it be standard model (SM)? 

Can it be new physics (NP)? 

Can we distinguish NP from SM? 


So, can it be SM? 

“There one typically finds asymmetries ∼ O(10 −4 ), i.e. somewhat smaller than 

the rough benchmark stated above. Yet 10 −3 effects are conceivable, and even 

1% effects cannot be ruled out completely.” 

[D. Benson et al., hep-ex/0309021] 

“This would lead to gigantic CP violations, an asymmetry of order 1. This is of 

course very unlikely [...]” 

[M. Golden, B. Grinstein, Phys. Lett. B 222] 

Can we be more specific? 


SM weak effective Hamiltonian 

Integrate out MW, mb, evolve down to charm scale µc, use GIM: 

H SCS 

eff = GF 

√2 

⎧ 

⎨ 

 

⎩ VcsV ∗ us Ci 

i=1,2 

Wilson coefficients: perturbative 

 

Q ¯ss 

i −Q ¯ 

dd 

i −VcbV ∗ ub 

6 

i=3 

CiQi +C8gQ8g 

Matrix elements: leading power and power corrections in 1/mc 

Estimate tree amplitude A T from data 

Relate penguin amplitude A P to A T 

 

+h.c. 


P/T at leading power 

Leading power (“Naive factorization” + O(αs) corrections): 

r LP 

 

 

f = 

A 

 

P f (leading power) 

AT f (experiment) 

 

 

 

 

r LP 

K + K− ≈ (0.01−0.02)%, rLP 

π + π− ≈ (0.015−0.03)% 

Expect sign Adir K + K− 

dir = −sign A 

Cf. global averages [HFAG] 

π + π − 

(if SU(3)F breaking is not too large). 

A K + K − = (−0.23±0.17)%, A π + π − = (0.20±0.22)% 

For φf = γ ≈ 67 ◦ and O(1) strong phases 

∆ACP(leading power) ∼ 4rf = O(0.1%). 

Order of magnitude below measurement! 


SM: Large penguin power corrections 

From SU(3)F fits [Cheng, Chiang, 1001.0987, 1201.0785; Bhattacharya, Gronau, Rosner, 1201.2351; 

Pirtskhalava, Uttayarat, 1112.5451] we know 

Signals breakdown of 1/mc expansion 

O(1) = Tf ∼ Ef = O(1/mc) 

Power corrections: look at two specific contributions - insertions of Q4, Q6 



Associated penguin contractions of Q1 cancel scheme and scale dependence 

Single hard gluon exchange leads to “effective Wilson coefficients” C eff 

4 and 

C eff 

6 depending on the gluon virtuality q2 . 

Setting A T (exp) = Ef in 

and Nc counting leads to 

r PC 

f = 

 

 

 

 

A P f 

(power correction) 

AT f (experiment) 

 

 

 

 

rf,1 ∼ 2Nc|VcbVubC eff 

6 |/(C1sinθc), 

rf,2 ∼ 2|VcbVub(C eff 

4 +C eff 

6 )|/(C1sinθc). 



r π + π − ,i (black) and r K + K − ,i (blue) for µ = 1GeV,mc,mD 

∆ACP(Pf,1) = O(0.3%), ∆ACP(Pf,2) = O(0.2%) 

⇒ a SM explanation is plausible. 


Uncertainties 

Extraction of annihilation amplitudes Ef from data 

Neglected contributions to Ef 

Nc counting 

modeling of penguin contraction matrix elements 

Neglected additional penguin contractions 

Cumulative uncertainty of a factor of a few; much larger effects are unlikely. 

Can we trust it? 


SM: Consistent picture 

Another observation: from Br(D 0 → K + K − ) ≈ 2.8×Br(D 0 → π + π − ) 

|A(D 0 → K + K − )| = 1.8×|A(D 0 → π + π − )| 

Should be the same in SU(3)F limit 

Usually interpreted as a sign of large O(1) SU(3)F breaking 

But note that 

|A(D 0 → K − π + )| = 1.15×|A(D 0 → K + π − )| 

for Cabibbo-favored (CF) decay D 0 → K − π + and doubly Cabibbo-suppressed 

(DCS) decay D 0 → K + π − . 

H CF 

eff = GF 

√2 VcsV ∗ ud 

 

i=1,2 

CiQ ¯ ds 

i +h.c. 


c 

ū 

Weak Hamiltonian, written differently 

TKK = T s KK +P T,s 

KK −PT,d 

KK 

Tππ = −T d ππ +P T,s 

ππ −P T,d 

ππ 

Broken penguin Pbreak violates U spin (s ↔ d) 

s+d 

−VcbV ∗ ub 

H SCS 

eff = GF 

√2 

⎡ 

⎣ 

i=1,2 

Ci 

u 

¯q 

q 

ū 

⎧ 

⎨ 

⎩ (VcsV ∗ us −VcdV ∗ ud) 

 

Q ¯ss 

i +Q ¯ 

dd 

i /2+ 

6 

i=3 

i=1,2 

c 

ū 

Ci 

s−d 

CiQi +C8gQ8g 

Penguin P violates CP 

 

Q ¯ss 

i −Q ¯ 

dd 

i /2 

⎤⎫ 

⎬ 

⎦ 

⎭ +h.c. 

Joachim Brod (University of Cincinnati) CP violation in D decays 13 / 26 

u 

¯q 

q 

ū

D 0 → K − π + ,K + K − ,π + π − ,K + π − 

U-spin decomposition 

Assume nominal U-spin breaking ∝ ǫU ∼ 0.2−0.3 

Additional assumption: T = O(1), P = O(1/ǫ), where ǫ ∼ 0.2−0.3 

For ǫ ∼ 0.3 we have naturally 

rf = |VcbVub| P 

|VcsVus| T 

Right order of magnitude to explain ∆ACP 

|VcbVub| 1 

∼ ∼ 0.2% 

|VcsVus| ǫ 

Pbreak = ǫUP ∼ ǫU/ǫ ∼ O(1) explains Br(K + K − ) = 2.8×Br(π + π − ) 

Test by performing a fit to branching ratios and CP asymmetries. 


Pbreak T 

Fit to data 

nominal ǫU 

P ∼ T/ǫ 


∆ACP from fit 


By exchanging the spectator quark, 

D + → K + K 0 

D + s → π + K 0 

receive contributions from 

Relations to other modes 

⇒ expect direct CP asymmetries of same order 


NP: viable models 

Constraints from D mixing, Kaon mixing, direct searches ... 

(More) Model-independent operator analysis 

[Isodori, Kamenik, Ligeti, Perez 1111.4987] 

Supersymmetric examples (Q8g = −gs/4π 2 mcūLσµνG µν cR) 

[Grossman, Kagan, Nir hep-ph/0609178; Giudice, Isidori, Paradisi 1201.6204] 

[Diagrams by A. Kagan] 

Tree-level exchanges 

[Hochberg, Nir 1112.5268; Altmannshofer, Primulando, Yu, Yu 1202.2866] 


How to distinguish NP from SM 

NP models that have ∆I = 3/2 contributions: 

SM tree operators have both ∆I = 1/2 and ∆I = 3/2 contributions 

SM penguin operators (∝ ¯qq,g) have only ∆I = 1/2 contributions 

E.g. D + → π + π 0 has I = 2 final state ⇒ no SM contribution to A dir . 

Can construct more sophisticated sum rules [Grossman, Kagan, Zupan; work in progress] 

Example: Single scalar exchange could explain both AFB(t¯t) and ∆ACP 

[Hochberg, Nir 1112.5268] 

NP models that have only ∆I = 1/2 contributions: 

Build models and look for collider signatures. In many cases allowed 

parameters are close to experimental sensitivity 

[Altmannshofer, Primulando, Yu, Yu 1202.2866; see also Feldmann, Nandi, Soni 1202.3795] 

Example: LR contributions to Q8g in SUSY 

[Grossman, Kagan, Nir hep-ph/0609178; Giudice, Isidori, Paradisi 1201.6204] 


Conclusion 

Enhanced penguin contributions in the SM can naturally explain both ∆ACP 

and Br(K + K − ) = 2.8×Br(π + π − ) – plausible and consistent 

NP contributions not excluded, viable and testable models exist 


Backup slides 


Experiments measure 

CDF: A ind 

f 

Definitions 

Af := Γ(D0 → f)−Γ(D 0 → f) 

Γ(D0 → f)+Γ(D 0 ≈ Adir f + 

→ f) 〈t(f)〉 

τ Aind f 

= (−0.02±0.22)% 


Penguin matrix elements 

Pf,1 = GF 

√2VcbV ∗ ubC6 ×〈f|−2(ūu)S+P ⊗ A (ūc)S−P|D 0 〉 

Pf,2 = GF 

√2VcbV ∗ ub2(C4 +C6)×〈f|(¯qαqβ)V±A ⊗ A (ūβcα)V−A|D 0 〉 

C eff 2 

4(6) µ,q = C4(6)(µ)+C1(µ) αs 

 

1 1 

+ 

2π 6 3 log 

 

mc 

− 

µ 

1 

8 G 

2 ms m2 c 

〈f|(ūu)S+P ⊗A (ūc)S−P|D 0 〉 

〈f|(¯sαsβ − ¯ dαdβ)V−A ⊗A (ūβcα)V−A|D 0 = O(Nc), 

〉 

〈f|(ūαuβ)V±A ⊗A (ūβcα)V−A|D 0 〉 

〈f|(¯sαsβ − ¯ dαdβ)V−A ⊗A (ūβcα)V−A|D 0 = O(1). 

〉 

, m2 d 

m2, c 

q2 

m2 

c 


CP asymmetries from fit 


U-spin decomposition 

A( ¯ D 0 → K + π − ) =VcsV ∗ udT(1− 1 

2 ǫ′ 1T), 

A(¯D 0 → π + π − ) = 1 

A(¯D 0 → K + K − ) = 1 

2 (VcdV ∗ ud −VcsV ∗ us) T(1+ 1 

1 

2ǫ1T)−Pbreak(1− 2ǫ(2) sd ) 

−V ∗ cbVub(T/2(1+ 1 1 

2ǫ1T)+P(1− 2ǫP)), 2 (VcsV ∗ us −VcdV ∗ ud) T(1− 1 

1 

2ǫ1T)+Pbreak(1+ 2ǫ(2) sd ) 

−V ∗ cbVub(T/2(1− 1 1 

2ǫ1T)+P(1+ 2ǫP)), A( ¯ D 0 → π + K − ) =VcdV ∗ usT(1+ 1 

2ǫ′ 1T). 


(Barbieri-Giudice-) Fine tuning

Direct CP violation in D meson decays - Rencontres de Moriond

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