1

Review of Charm Mixing

June 1, 2004

Kevin Flood

University of Massachusetts, Amherst

HQL 2004San Juan, Puerto Rico

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Outline

• SM & New Physics predictions

• Charm mixing formalism

• Current experimental status

• Future outlook

• Further references

3

Charm Mixing in the Standard Model

• Box diagram SM charm mixing rate naively expected to be very low (Rmix~10-10) (Datta & Kumbhakar)

• Z.Phys. C27, 515 (1985)

– CKM suppression → |VubV*cb|2

– GIM suppression → (m2s-m2

d)/m2W

– di-penguin mixing, rmix~10-10 (Petrov)• Phys. Rev. D 56, 1685 (1997)

• Recent SM predictions can accom-modate high mixing rate (Falk et al.)

• x,y ≈ sin2 C x [SU(3) breaking]2 ~1%– y: Phys.Rev. D 65, 054034 (2002)– x: hep-ph/0402204 (2004)

d, s, bV*ci Vui

Vuj V*cj

D0 D0

c

u

W

d, s, b

W

c

u

SM Mixing: box diagram

SM Mixing: a long-range contribution

D0

D0

c

u

c

u

u

W+

d

d

u

u

d

d

u

W-

(Plot courtesy of A. Petrov, hep/ph 0311271)

: y=/2

mix

ing

ra

te =

|am

pli

tud

e|2 SM Mixing Predictions

best exp. limit on |y|

: x=/

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New Physics Charm Mixing Predictions

(Plot courtesy of A. Petrov, hep/ph 0311271)

• Possible enhancements to mixing due to new particles and interactions in new physics models

• Most new physics predictions for x– extended Higgs, tree-level FCNC– fourth generation down-type quarks– supersymmetry: gluinos, squarks– lepto-quarks

x=M/

mix

ing

ra

te =

|am

pli

tud

e|2

New Physics Mixing Predictions

c

u

u

c

H0

b´b´

c

u

u

c

qq

c

u

u

c

~ ~

g~

g~

FCNC

fourth generation quark

supersymmetry

l,

c

u

u

c

LQ

leptoquarks

LQl,

current mixing experimental sensitivity

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Measuring Mixing with D*+ D0 +tag WS Decays

• WS D0 decays from many sources• Mixing, DCS amplitudes interfere in

non-CP hadronic final states• No DCS decays in semileptonic final

states• Identical final state in SCS decays

c

u

c

u

l+, u

l, d

u

s

Mixing followedby CF or semi-leptonic decay

c

u

u

s

u

dsin c

sin c

cos c

1, cos c

DCS decayK

e/,

tag

other charmed hadron

D*+ decay at interaction point

beamspot D0

e+ e- event topology

near-future Babar SL analysis will hadronically reconstruct opposite charm in order to double-tag mixed events

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Experimental Methods

• In contrast to B mixing, cannot measure time-dependent flavor oscillations in charm mixing

• Measure charm mixing using D*+ tagged decays:

– WS D0 decays to hadronic (w/DCS interference) or semileptonic final states (B factories, FOCUS)

– Compare ratios of lifetime from K to tagged D0, D0 decays into CP=+1 final states (B factories, FOCUS)

– Time-integrated measurements exploiting coherent DD production at (3770) (CLEO-C only)

D*+ D0 +tag

D0 K+−

Wrong-sign tag decays

D*+ D0 +tag Right-sign

tag decaysK−+

(D0/D0 K+−)

(D0 +− or K+K−)

(D0 +− or K+K−)

D0 tag decays

D0 tag decays

(D0/D0 K+−)

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Time Dependence of DCS/Mixed Hadronic & Semileptonic Final States

• Mixing implies that the physical states are not pure flavor states

002,1 DqDpD 1

22 qp,

• Charm mixing values most often quoted using scaled parameters x, y

2

, yM

x12 MMM

1221

12 • For |x|, |y| << 1, time-dependence of WS hadronic final states with mixing and DCS amplitudes

2

22

4t

yxtRyRet DCSDCS

tWS

where + (-) correspond to initial D0 (D0), and in the limit of no CP violation

KK yxx sincos KK xyy sincos ,with K being the relative strong phase between DCS and mixing amplitudes

• Semileptonic final states retain only the term proportional to (t)2 with no possible strong phase

pq

mr

0

0

argDHf

DHf

pq

D

D

rm ≠ 1 CP-violation in mixing

φ ≠ 1 CP-violation in interference

between mixing and decay

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Time Dependence of DCS/Mixed Hadronic & Semileptonic Final States

2

22

4t

yxtRyRet DCSDCS

tWS

• Hadronic WS time-dependence:– RDCS ≡ 1, y´ = −0.3, |x´| = 0.3– analyses using hadronic final

states must fit time-dependence possibly close to a pure exponential

• WS time-dependence for semi-leptonic analyses is well-distinguished from exponential

2

22

4t

yxet t

WS

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• Combined fit to M(D0), lifetime, M(D*+)-M(D0)

• ~120,000 unmixed D0 events provide model from data for mixed signal pdf’s

• Fit for RWS, RDCS, x´2, y, CP asym– NWS ~ 430 evts– Results consistent with no mixing,

no CP asymmetries– Obtained unphysical result, x´2 < 0– Upper limits calculated with toy MC

using frequentist approach

Hadronic K Mixing (Babar: 57 fb-1 )

WS M(K)in M sgnlregion

WS M in M(K) sgnlregion

WS M(K)in M sideband

WS M in M(K) sideband

Year Exper. y´ (95% CL) x´2/2 (95% CL)

2003 Babar −5.6 < y´ < 3.9 % < 0.11%

2001 FOCUS −12.4 < y´ < −0.5 % < 0.076 %

2000 CLEO −5.8 < y´ < 1.0 % < 0.041%

Babar Babar

Babar Babar

WS lifetime in M(K)+ M sgnl region

WS lifetime in M(K)+ M side-band

Babar Babar

PDG 2004

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• Combined fit to lifetime, M(D*+)-M(D0)– statistics-limited measurement– D0 lifetime+error consistent w/PDG value

• Neural network D0 reconstruction• ~50,000 unmixed D0 events provide

model for mixed decays• submitted to ICHEP 2004

Preliminary Babar Semi-electronic Mixing (87 fb-1)

D+

D0 bkgdzero life

RSM signal region

D0 sgnl

RSlifetimeD+

D0 bkgdzero life

D0 sgnl

random D+

random D0

zero life

WSM D0 sgnl

pkng D+

BabarPrelim.

BabarPrelim.

BabarPrelim.

Year Exper. Final State(s) Rmix (95% CL)

2002 FOCUS K+− < 0.13%

2002 CLEO K*+e− < 0.86 %

1996 E791 K+e−, K+− < 0.5% (90% CL)

2004 Babar K+e−incl.) 0.12% (1sens.)

2004 Babar K+e−incl.+double tag) ~0.06% (1sens.)PDG 2004 (w/ICHEP+future Babar)

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Time Dependence of Decays to CP-Even Final States

• For |x|, |y| << 1, the time-dependence of D0 → K+K- or D0 → K+K- or can be written

txyreKKD mt sincos1)( 0

txyreKKD mt sincos1)( 10

• For decays to non-CP eigenstates have

teKDKD )()( 00

• The ratio of CP to non-CP lifetimes then becomes

sincos1)(

)(0

00

xyrKKD

KDm

sincos1)(

)( 10

00

xyrKKD

KDm

• If CP is conserved then the ratios are equal and CPy 1

00

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Mixing Using CP-Even Eigenstates (Lifetime Ratio)

• Some definitions

AYY00

, 1 , , 2

A

• If no CP violation in mixing (rm=1) (also, if φ=0 → Y=yCP, Y=0)

sin , cos xYyY

Year Exper. Final State(s) y (%) AΓ, ΔY (%)

2003 Belle K+− yCP = 1.15±0.69±0.38 AΓ = −0.20 ± 0.63 ± 0.30

2003 Babar K+−, +− y cos φ = 0.8 ± 0.4 +0.5-0.4 ΔY = −0.8 ± 0.6 ± 0.2

2001 CLEO K+−, +− yCP = −1.1 ± 2.5 ± 1.4 ---

2001 Belle K+− yCP = −0.5 ± 1.0 +0.7-0.8 ---

2000 FOCUS K+− yCP = 3.4 ± 1.4 ± 0.7 ---

1999 E791 K+− yCP = 0.83 ± 2.89 ± 1.03 ---

PDG 2004

Babar

sincos xyA Belle

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Current Charm Mixing Limits

(Plot courtesy of G. Burdman & I. Shipsey)

(Plot courtesy of D. Williams)

y (%)

Lifetime Ratio Results Current Mixing Limits

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Future Outlook

• Near future– FOCUS:

• Working on hadronic and semi-electronic mixing analyses (WIN 2003)

– Belle:• ~300 fb-1 total integrated

luminosity by end of current run• No hints of future charm mixing

plans at recent conferences ?

– Babar:• ~250 fb-1 total integrated

luminosity by end of current run– Plans to update hadronic K

mixing and lifetime ratio analyses– Time-dependent three-body Dalitz

plot mixing– New semileptonic analysis using

double-tagged events plus update of ICHEP result, ~linear statistical sensitivity increase

• Long-term– CLEO-C:

• DD coherent production• very clean charm samples• time-integrated msmts only

– Belle/Babar:• ~500-600 fb-1 total integrated

luminosity by end of running

– BTeV:•O(109) charm decays!

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• The following offer comprehensive and up-to-date guides, with copious citations, to the current state of charm mixing, theoretically (both articles) and experimentally (Burdman & Shipsey)– Charm Physics: Theoretical Review

• A. Petrov (2003), hep-ph/0311371

– D0 Mixing and Rare Decays• G. Burdman & I. Shipsey, Ann.Rev.Nucl.Part.Sci, 431

(2003), hep-ph/0310076

• An earlier article also systematically compiles the many charm mixing predictions as of 1999– Compilation of D0-D0 Mixing Predictions

• H.N. Nelson, in Proceedings of the 19th Intl. Symp. on Lepton and Photon Interactions at High Energy (LP99), ed. J.A. Jaros & M.E. Peskin, SLAC (1999), hep-ex/9908021

• PDG 2004 also contains a review of charm mixing with citations to all exp. results presented herein

• D. Asner (the previous speaker), updated Nov. 2003

Recent Charm Mixing Review Articles

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Backup slides

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FOCUS Semi-muonic Mixing (preliminary)

• Combined fit to lifetime, M(D*)-M(D0)

• D0 reconstruction using vertex location

• ~6700 unmixed events• -14 mixed events• Rmix < ~0.0012 (90% CL)• Presented at ICHEP 2002

“A Search for D0 Mixing in Semileptonic Decays from FOCUS”, M. Hosack, Ph.D. thesis (2003)

D0 lifetime

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Differences in Neutral Meson Mixing

• Charm mixing is negligible in comparison both to the D0 decay rate and to mixing in the neutral K and B systems

– scale of plots chosen to highlight differences

Bd

B, K Mixing

Bs

K0

D0 Mixing

E (10-9 MeV)

d

/dE

E (10-10 MeV)

E (10-9 MeV)

E (10-12 MeV)d

/dE

d

/dE

d

/dE

Md

Ms

MK

MD ≈ O(10-14)

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c

u

D0 D0

c

u

g

W

d, s, b

d, s, b

V*ci Vui

V*ciVui W

SM di-penguin diagram