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Measurements of CP violation and mixing in Charm decays at LHCb

Olli Lupton on behalf of the LHCb collaborationDepartment of Physics, University of Oxford, Keble Road, Oxford, United Kingdom

LHCb has collected the world’s largest sample of charmed hadrons. This sample is usedto search for both direct and indirect CP violation in D0 decays, and to measure D0 mixingparameters. Recent results are presented on these topics, and on related charm system studies.

1 Introduction

The search for CP violation (��CP ) in the charm system is motivated by the fact that CP violatingeffects are predicted to be tiny in the Standard Model (SM), but several theories of physicsbeyond the SM predict enhanced effects.1,2,3 Searches for��CP in charm can probe very high energyscales, and are complementary to energy-frontier searches. Singly Cabibbo-suppressed (SCS)decays can have significant contributions from loop diagrams, making them a promising targetfor direct ��CP searches,4 with multi-body decays particularly appealing due to the possibility ofenhanced CP violating effects in local regions of phase space. Here I discuss some recent ��CPsearch results from LHCb, of course there are many others already published and still to come.

The LHCb experiment is well-suited for charm mixing and ��CP measurements for a varietyof reasons. The cc production cross-section is around 1.4 mb at 7 TeV,5 so O(5 × 1012) ccpairs were produced in LHCb during 2011-12. These huge statistics ensure LHCb has world-leading sensitivity to many charm ��CP observables. Additionally, the large beam energy at theLHC ensures the D0 mesons produced are highly boosted and, therefore, well-suited for time-dependent studies. Searches for ��CP tag the D0 flavour at production using either D∗+→ D0π+

or semileptonic B meson decays.

2 Direct ��CP searches

This section describes two decay-time-integrated analyses searching for local CP asymmetriesin the phase space of 3-body SCS D0 decays. These are interesting places to search for ��CPbecause of potential enhancements by interference effects in the Dalitz plots, and the two analyseshighlight two very different ways such analyses can be carried out.

2.1 Model-independent: D0→ π+π−π0

This analysis6 uses an unbinned, model-independent method to search for direct ��CP in a sampleof 6.6× 105 D∗+–tagged candidates of around 85% purity, shown in Fig. 1(a). The analysis usesthe “energy test” statistic T 7,8, applied to a Dalitz plot analysis as outlined by M. Williams.9 Thisstatistic is related to the average distances between D0 and D0 tagged events in the data. Theexpected distribution of the statistic for the null hypothesis of no ��CP is obtained by repeatedlyrandomising the assigned D0 flavours in the signal dataset and calculating T . This distribution

(a) Dalitz plot showing thefull data sample.

]-6T value [10-2 0 2 4 6

)-8

10×E

ntri

es/(

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(b) No-��CP distribution of Tand the measured value (red).

(c) Local asymmetry in contribu-tion to T value.

Figure 1 – Model-independent search for direct��CP in D0→ π+π−π0 decays.

is shown in Fig. 1(b), together with the measured value of T , and is used to estimate the p-valueof the observed value as (2.6 ± 0.5)%. There is, therefore, no evidence for direct ��CP . Finally,Fig. 1(c) illustrates the local contributions to the T -value, showing that – while there is nosignificant effect – there is a local excess of around 1σ significance in the ρ± interference region.

2.2 Model-dependent: D0→ K0SK±π∓

Searches for ��CP can also be performed by model-dependent methods. Isobar models decomposea decay amplitude into a sum of contributions from intermediate resonances

A =∑

R

aReiφRAR. (1)

In this analysis,10 such models are first constructed for the decays D0→ K0SK−π+ and

D0→ K0SK+π− using around 105 D∗+–tagged candidates in each case and assuming CP . Dalitz

plots of the two modes are shown in Fig. 2. The m2Kπ data distributions and fit curves for these

models are shown in Fig. 3. It should be noted that these models have many other uses in theirown right, such as future measurements of the CP -violating Cabibbo-Kobayashi-Maskawa11,12

angle γ and charm mixing parameters, and other interesting results can be obtained directly fromthe models. Nonetheless, using these models the search for ��CP is carried out by substituting

A →∑

R

aR(1±∆aR)ei(φR±∆φR)AR, (2)

where the signs of the ∆ terms are set by the D0 flavour tag. A χ2 test is performed withrespect to the no-��CP hypothesis (∆aR = ∆φR = 0), with the result χ2/n.d.f. = 32.3/32 = 1.01,corresponding to a p-value of 45%. No evidence for direct��CP is, therefore, found in these decays.This is the most precise study to date with around one hundred times greater statistics thanthe preceding CLEO analysis.13

3 AΓ with D0→ π+π− and D0→ K+K−

The charm system is of particular interest as it is the only up-type system where mixing andindirect ��CP can be probed. Mixing itself is now well-established, helped by several LHCbresults,14,15,16 but indirect ��CP is not. The LHCb result17 presented here is a measurement of AΓ,which is given, approximately, by

ACP (t) ≡ Γ(D0→ f; t)− Γ(D0→ f; t)

Γ(D0→ f; t) + Γ(D0→ f; t)≈ Adir

CP −AΓt

τ. (3)

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

m2Kπ [ GeV2/c4 ]

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m2 K

0 Sπ

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Figure 2 – Dalitz plots showing the full D0→ K0SK

−π+ (left) and D0→ K0SK

+π− (right) data samples.

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0m2

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K∗(892)+

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(K0Sπ)−S-wave × a0(980)+

(Kπ)0S-wave

K∗(1410)−

K∗(1410)− × K∗(892)−

LHCb preliminary

Figure 3 – D0→ K0SK

−π+ (left) and D0→ K0SK

+π− (right) m2Kπ projections.

The analysis uses D0 decays to K+K− (2.3× 106 signal candidates) and π+π− (0.8× 106 signalcandidates) where the D0 flavour is tagged by a semileptonic B decay and the full dataset from2011-12 is used. For each mode the time-dependent CP asymmetry ACP (t) is computed in 50bins of D0 decay time optimised to have approximately equal sensitivity and AΓ is extractedwith a straight line fit. The fits are shown in Fig. 4, and the resulting values of AΓ are:

AΓ(K−K+) = (−0.134± 0.077 (stat)+0.026−0.034 (syst))%

AΓ(π−π+) = (−0.092± 0.145 (stat)+0.025−0.033 (syst))%

There is also an older LHCb result18 using promptly produced, D∗+–tagged D0 recorded only in2011 that has slightly better precision.

0 1000 2000 3000 4000 5000

[%

]ra

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Figure 4 – Time-dependent CP asymmetry ACP (t) for D0→ K−K+ (left) and D0→ π−π+ (right) decays.

4 Summary

There is lots of activity in LHCb searching for ��CP in the Charm sector! Many different methodsare available, particularly for direct ��CP searches, here I have only presented a selection withrecent results. We have also seen how measurements of promptly-produced, D∗+–tagged Charmcomplement those using semileptonic B meson decays.

There are many more exciting results still to come from the 2011-12 dataset, such as ameasurement of AΓ with the full prompt, D∗+–tagged dataset and mixing measurements fromthe “golden modes” D0→ K0

Sπ+π− and D0→ K0

SK+K−.Run 2 of the LHC is also now underway, and with even higher Charm production cross

sections at 13 TeV, the huge datasets are about to get even bigger.

References

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2. Marina Artuso, Brian Meadows, and Alexey A. Petrov. Charm meson decays.Ann.Rev.Nucl.Part.Sci., 58:249–291, 2008.

3. Franco Buccella, Maurizio Lusignoli, Alessandra Pugliese, and Pietro Santorelli. CPviolation in D meson decays: Would it be a sign of new physics? Phys.Rev., D88(7):074011,2013.

4. Yuval Grossman, Alexander L. Kagan, and Yosef Nir. New physics and CP violation insingly Cabibbo suppressed D decays. Phys.Rev., D75:036008, 2007.

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decays. JHEP, 04:043, 2015.18. R. Aaij et al. Measurements of indirect CP asymmetries in D0 → K−K+ and D0 → π−π+

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