ɣ βα

The CKM phase ɣ

Daniel Johnson, University of Oxfordon behalf of the LHCb Collaboration

Physics @ LHC Conference, Vancouver, 4th - 9th June 2012

CLEO

d.johnson1@physics.ox.ac.uk

Observation of CP violation in B±→D0K± decays at LHCb

Vertex Locator and Si strip/straw trackers:Determination of vertex positions and momenta

RICH detectors:K/π separation

Magnet

CP violation enters the Standard Model through the complex phase in the CKM matrix.Unitarity of the CKM matrix can be represented via ‘unitarity triangles’ where the sides represent the amplitudes of CKM elements and the angles represent relative phases.

Of the phases, ɣ is the least well known:� = (66± 12)� CKMfitter, direct measurements

Precise measurement of ɣ tests CKM unitarity: α+β+ɣ=180 ?∘

Measuring ɣ in B→DKSensitive to ɣ through interference between B±→D0 (→f) K± and B±→D0 (→f) K±

B�

D0

D0

FrDe�i�DrBei(�B��)

B�

D0

D0

FrDe�i�DrBei(�B��)

B �

D 0D 0

FrD e �i�D

rB e i(�B ��)B-D0K-

D0K-B �

D 0D 0

FrD e �i�D

rB e i(�B ��) f K-

rB ei(δB-ɣ)

Studied decays of the D0 to two daughters:

ADS: (flavour eigenstates)D0→Kπ

GLW: (CP eigenstates)D0→KK,ππ

RADS =�(B± ! [⇡K]DK±)�(B± ! [K⇡]DK±)

RCP+ =�(B± ! [KK,⇡⇡]DK±)

�(B± ! [K⇡]DK±)ACP+ =

�(B� ! DCP K�)� �(B+ ! DCP K�)�(B� ! DCP K�) + �(B+ ! DCP K+)

Candidate selectionEmploy full 2011 LHCb dataset (1fb-1) and apply a 20-variable boosted decision tree, trained on signal MC and 2010 data sidebands.

The most effective variables are flight distances (of the B± and D0), impact parameters, requirements on pt and on B± and D0 vertex qualities.

ResultsADS analysis: B±→D0 (→Kπ) K±

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Figure 1: Invariant mass distributions of selected B± ! [K±!!]Dh± candidates. The left plots are B"

candidates, B+ are on the right. In the top plots, the bachelor track passes the DLLK! > 4 cut and the Bcandidates are reconstructed assigning this track the kaon mass. The remaining events are placed in thesample displayed on the bottom row and are reconstructed with a pion mass hypothesis. The dark (red)curve represents the B ! DK± events, the light (green) curve is B ! D!±. The shaded contributionare partially reconstructed events and the total PDF includes the combinatorial component.

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Figure 2: Invariant mass distributions of selected B± ! [K+K"]Dh± candidates. See the caption ofFig. 1 for a full description. The contribution from !b ! !±

c h! decays is indicated by the dashed line.

7

Combined non-zero B±→DK± CPV significance is 4.5σ

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Figure 3: Invariant mass distributions of selected B± ! [!+!!]Dh± candidates. See the caption of Fig. 1for a full description.

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]-K+π[→+B

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Figure 4: Invariant mass distributions of selected B± ! [!±K"]Dh± candidates. See the caption ofFig. 1 for a full description. The dashed line here represents the partially reconstructed, but Cabibbofavoured, B0

s ! D0K!!+ and B0s ! D0K+!! decays where the pions are lost. The pollution from

favoured mode cross feed is drawn, but is too small to be seen.

8

GLW analysis: B±→D0 (→hh) K± h=π,K KK

ππ

Summary1) CKM phase ɣ is the least well known CKM phase: 12 2) Observe direct CPV in B→D(Kπ)K at 5.8σ and non-zero B→D(hh)K CPV at 4.5σ3) Prepare to reduce ɣ ambiguities using Dalitz analysis of B→D(KS π π)K

∘

PLB 712 (2012) 203-212

Outlook for ɣ measurementA four-fold ɣ ambiguity is intrinsic to the ADS/GLW approach. This can be reduced using other final states of the D0 meson, e.g. KSπ+π -

Study of B±→D0 (→KSπ+π -) K± ⇒ Dalitz plot analysis.Dalitz Plots display multi-body phase space. They are constructed by taking two pairs of the three final particles, adding their four-momenta, and then determining the invariant mass squared of the sum.

As well as the ‘weak phase’ ɣ, a ‘strong phase’ enters from the strong decay of the D0. This phase dependsupon position in the Dalitz plot. The strong phase can be taken from a model or averaged in regions (see right) of the Dalitz plot from charm studies at the CLEO experiment, independent of a model. A Dalitz analysis can then be performed at LHCb to obtain ɣ.

PRD 82 (2010) 112006

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Figure 3: Invariant mass distributions of selected B± ! [!+!!]Dh± candidates. See the caption of Fig. 1for a full description.

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)2c) (MeV/±Dh(m5200 5400 5600

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+πD

]-K+π[→+B

LHCb

Figure 4: Invariant mass distributions of selected B± ! [!±K"]Dh± candidates. See the caption ofFig. 1 for a full description. The dashed line here represents the partially reconstructed, but Cabibbofavoured, B0

s ! D0K!!+ and B0s ! D0K+!! decays where the pions are lost. The pollution from

favoured mode cross feed is drawn, but is too small to be seen.

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Partially reconstructed decays, modelled in MCB→D0π

B→D0K signal

mis-ID

Very low combinatorics

signal

Direct CP violation observed in B-→D0K- with 5.8σ significance

PLB 712 (2012) 203-212

First observation of the suppressed ADS mode

B→D0K signal

B→D0K signal