CP Violation in the B0s System at the Tevatron

Joseph Boudreau, for the CDF and D0 Collaborations

Dept. of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA, USA 15260

Abstract

We discuss two important measurements from the Tevatron experiments which constrainthe CP violation parameters of the B0

s system φs and assl.

Keywords: B Physics, CP Violation

The violation of CP symmetry is of greatinterest in physics because it sheds light onthe underlying dynamics of elementary par-ticles. An excellent example is the first dis-covery of CP violation in 1964 [1], whichmotivated in 1973 the prediction of a thirdgeneration by Kobayashi and Maskawa [2].The standard model predicts very smallCP violation in the B0

s system, which atthe Tevatron experiments CDF and D0 hasrecently become experimentally accessible.Appreciable CP violation in B0

s mesonscould indicate a variety of new phenom-ena such as heavy exotic particles whoseeffects enter through quantum loop correc-tions. The search for CP violation in B0

s

decays has a fascinating connection to cos-mology, as well: it has been noted [3] that afourth generation can greatly promote elec-troweak baryogenesis, raising the standardmodel expectation of the baryon to photonratio of our universe nB/nγ ≈ O(10−20) byten orders of magnitude in some scenariosand bringing it into line with the observedvalue of 5.1+0.3

−0.2 × 10−10 [4]. The presenceof the fourth generation in such a scenarioalso introduces observable CP violation ef-

fects into the B0s sector.

The most interesting studies of CP vio-lation occur when clean measurements canbe confronted with precise theoretical pre-dictions. In the B0

s system there are twosuch cases: the flavor-tagged analysis of thedecay B0

s → J/ψφ; and the measurement ofthe dilepton charge asymmetry Ab

sl.

Two quantities will prove relevant to bothanalyses, the first is called φs and secondΓs

12. The B0s system, is a two-state system

governed by a Hamiltonian H = M + iΓ,where M and Γ are Hermitian 2x2 matri-ces. In the Standard Model, the mixing ofmass and flavor eigenstates occurs throughbox diagrams which respect CP symme-try. The “heavy” and “light” mass eigen-states are CP -odd and even, respectively.Decays of B0

s to CP -even final states suchas B0

s → D+s D−

s shorten the lifetime ofthe CP -even mass eigenstate relative to theCP -odd mass eigenstate. The decay widthdifference is ΔΓs ≡ ΓL − ΓH = ΔΓs =2|Γs

12|, where Γs12 is the off-diagonal ele-

ment of the decay matrix; theory predicts|Γs

12| = 1/2 · (0.090± 0.024) ps−1 [5].

New Physics, by altering the amplitude

Nuclear Physics B (Proc. Suppl.) 207–208 (2010) 387–390

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doi:10.1016/j.nuclphysbps.2010.10.101

M s12, can produce “mixing-induced” CP vi-

olation. The two mass eigenstates can thenbe written as

|BHs 〉 = p |B0

s 〉 − q |B̄0s 〉,

|BLs 〉 = p |B0

s 〉+ q |B̄0s 〉,

which are linear superpositions of odd andeven CP eigenstates. The admixture isquantified by the mixing phase φs =arg (q/p), which when zero indicates thatthe light eigenstate is purely CP even; whenπ/2 indicates that it is equally odd andeven, and when π indicates that it is pureCP odd1. When the eigenstates are fullymixed (φs = π/2), the lifetime differenceis erased, since both CP even and odd fi-nal states are equally accessible to long andshort-lived mass eigenstates. More gener-ally, mixing-induced CP violation dilutesthe decay width difference according to:

ΔΓs = 2 · |Γs12| cos (φs) (1)

while maintaining the ratio |q/p| very closeto unity. The small departure from unity isthe source of an asymmetry

assl ≡

|Γs12|

|M s12|

sin (φs) =1− |q/p|41 + |q/p|4 (2)

which is direct CP violation – one of the fla-vor eigenstates (B0

s or B̄0s ) is preponderant

in both mass eigenstates, a situation thatgenerates a charge asymmetry in semilep-tonic decays. With theoretical values of|Γs

12|/|M s12| from [5], as

sl = (49.7 ± 9.4) ·10−4 sin (φs), which cannot exceed aboutone half of one percent. Differential rates in

1We simplify by pretending that nonzero weakphases are absent in decay amplitudes.

a flavor-tagged sample of B0s → J/ψφ de-

cays are sensitive to both the real and imag-inary part of q/p, however, usually the mag-nitude is constrained to unity and only thephase is measured.

In reality, the quantity φs appearing inEqs. 1 and 2 includes a small offset fromthe phase of Γs

12, while the CP phase mea-sured in B0

s → J/ψφ decays includes an-other small offset from the phase of the de-cay amplitudes in that channel. If we ceaseto ignore the CP phases in the decay, theseare different quantities [6], and we use the

nomenclature φJ/ψφs to distinguish the lat-

ter from the former. The standard modelpredicts that φs = (4.2 ± 1.4) · 10−3, while

φJ/ψφs = (−3.8± 0.2) · 10−2, which can also

be written as −2βs, where

βs ≡ arg

(−VtsV

∗tb

VcsV ∗cb

)

is an angle of the “squashed” (bs) unitaritytriangle, Vij being elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.

Both CDF and D0 have carried out flavor-tagged analyses of the decay B0

s → J/ψφ.The CDF analysis [7] uses 6500 signalevents from 5.2 fb−1 of data and both same-side and opposite side flavor tagging, whichtogether give an effective tagging efficiencyεD2 = 4.8%. The CDF analysis now allowsa contribution [8] from B0

s → J/ψK+K−,where the kaons are in an S-wave state.Results are shown in Fig. 1. The S-wavecontamination is small and has little impacton the result. CDF also has produced con-straints on the real and imaginary part [8] ofλ = q/p, but without allowing S-wave con-tamination. Likelihood contours are shownin Fig. 2. D0 has recently updated their pre-vious result [9] based on 2000 signal eventsfrom 2.8 fb−1 with εD2 ≈ 4.7%. The up-dated analysis [10] based on 6.1 fb−1 ob-

J. Boudreau / Nuclear Physics B (Proc. Suppl.) 207–208 (2010) 387–390388

Figure 1: From the CDF analysis of B0s → J/ψφ,

Ref. [7], confidence regions in the βs and ΔΓs pa-rameter space constrained such that |λ| ≡ |q/p| =1, shown with a band representing Eq. 1 and using|Γ12| = 1/2 · (0.090± 0.024) ps−1.

Figure 2: From the CDF analysis of B0s → J/ψφ,

Ref. [7], the likelihood profile for the real and imag-inary part of λ, “cos (2βs)” and “sin (2βs)”.

serves 3400 signal events but uses only op-posite side tagging, with εD2=2.5%, so theincrease in statistical power from the sam-ple size comes with a loss of tagging power.D0 constrains the strong phases in the decayto those measured in B0 → J/ψK∗0 [11] toobtain a point estimate φs = (−44+22

−21)◦, or

equivalently (βs = −22+11−10)

◦; the justifica-tion for the constraint is given in Ref. [12].

Figure 3: From Ref. [13], the allowed region in theas

sl and adsl parameter space from the dimuon charge

asymmetry analysis (red band), together with theworld average value of ad

sl from the B-factories [11](vertical gray band), and an independent directmeasurement of as

sl from D0 [14] (horizontal grayband). Also shown is the standard model predic-tion.

D0 reports evidence of an anomalousdimuon charge asymmetry Ab

sl, a linearcombination of the asymmetries as

sl andad

sl in strange and nonstrange B mesons.The study [13], based on 1.495 · 109 in-clusive muons and 3.371 · 106 dimuonsfrom 6.1 fb−1 of data, measures Ab

sl =−00957 ± 0.00251(stat.) ± 00146(syst.),about 3.2σ from the standard model expec-

J. Boudreau / Nuclear Physics B (Proc. Suppl.) 207–208 (2010) 387–390 389

tation Absl(SM) = (−2.3+0.5

−0.6) · 10−4. Re-sults are shown in Fig 3. A rather involvedanalysis is required to extract Ab

sl from rawasymmetries, using data to estimate back-ground contamination and its charge asym-metry. With B-factory world average valuesfor ad

sl, D0 obtains assl = −0.0146± 0.0075.

The result is consistent with D0’s directmeasurement as

sl = −0.0017 ± 0.0091 us-ing B0

s → μ+D−s X events [14]; an average

of the two results gives assl = −0.0094 ±

0.0059, which does not strongly indicatenew physics in the B0

s sector. D0 draws fur-ther conclusions on the parameter φs withthe aid of Eq. 1 without theoretical input on|Γs

12|/|M s12|, shown in Fig. 4; but the bigger

anomaly here is that the central value of assl

from Ref. [13] would require |Γs12|/|M s

12| tohave at a minimum three times its expectedvalue. Ref. [15] suggests that New Physicscontributing to Γs

12, would normally alterthe τ(B0

s )/τ(B0) lifetime ratio (predicted tobe 1.00 ± 0.01) and calls for a new preci-sion measurement. The CDF J/ψφ analysis(Ref. [7]) now furnishes a 2% measurementτs = 1.53 ± 0.025 ± 0.012 ps deviating byonly 0.3% from the PDG world average B0

lifetime of 1.525± 0.009.

In summary, CDF’s direct measurementof βs in the channel, B0

s → J/ψφ is 1σ fromβs(SM) while D0’s measurement is 2σ away,and a recent D0 measurement of Ab

sl devi-ates from the standard model expectationat 3.2σ, but additional anomalies besides ahigh value of φs are required in order for CPviolation in the B0

s sector to be the sourceof the discrepancy.

The author wishes to thank the organiz-ers for an enjoyable workshop.

Figure 4: From Ref. [10], confidence regions in thespace of parameters ΔΓs and φJ/ψφ

s ≡ −2βs, shownwith a green band denoting the allowed region infrom the Ab

sl measurement, Ref. [13], and a lightblue band (added by the author) representing Eq. 1using |Γ12| = 1/2 · (0.090± 0.024) ps−1.

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