Search for new spin-0 particles near π⁰ mass produced in association with τ pairs at BABAR

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Search for new spin-0 particles near π0_{mass produced in association with τ pairs at}

BABAR

by

Alexandre Beaulieu

BEng, Université de Sherbrooke, 2009 MASc, Université de Sherbrooke, 2011

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science

in the Department of Physics and Astronomy

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Search for new spin-0 particles near π0_{mass produced in association with τ pairs at}

BABAR

by

Alexandre Beaulieu

BEng, Université de Sherbrooke, 2009 MASc, Université de Sherbrooke, 2011

Supervisory Committee

Dr. J. M. Roney, Supervisor

(Department of Physics and Astronomy)

Dr. M. Pospelov, Departmental Member (Department of Physics and Astronomy)

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Supervisory Committee

Dr. J. M. Roney, Supervisor

(Department of Physics and Astronomy)

Dr. M. Pospelov, Departmental Member (Department of Physics and Astronomy)

Abstract

This research project searches for new physics in the τ sector that would resolve the tension between BABARmeasurement for the pion-photon transition form factorF_π0 Q2

and the standard model asymptotic prediction.

This behaviour could be explained by a new light pseudo-scalar state that mixes with the π0_{and enhances its coupling to the c and b quarks or the τ lepton, or by a new spin-0}

particle with mass very close to the π0_.

We examine one channel to test for existence of such objects: their creation in associ-ation with τ pairs in e+_e− _{collisions. The analysis uses a typical cut-based approach as}

the large predicted cross-sections and the kinematics of the final states allow for a direct selection of signal events and background suppression.

Current simulation studies predict a 90% CL limit on the production cross-section on the order of 100 fb in case of no signal, while the theory predicts production cross-sections on the order of 1pb to 100pb depending on the model.

Search for new spin-0 particles near π0_{mass produced in association with τ pairs at B}_A_B_AR

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List of Figures

1.1 Diagram of the linear accelerator and PEP-II ring. . . 2

1.2 Diagram of the BABARdetector . . . 3

2.1 General P→γ∗γ∗ vertex . . . 7

2.2 A Feynman diagram for e+_e−_→_e+_e− γγ∗→e+e−π0 . . . 8

2.3 The γγ∗_→ π0transition form factor times Q2from CELLO, CLEO and BABAR 9 2.4 The γγ∗ _→ π0transition form factor times Q2from the Belle experiment . . 9

2.5 Photon-impostor transition through a τ loop . . . 12

2.6 Diagram for impostor production in association with τ+ τ−pair in e+e− col-lisions . . . 13

2.7 The best-fit total form factors in the pseudo-scalar impostor, scalar impostor, and hard-core pion cases when fitted to the data from BABAR CLEO, and CELLO . . . 14

2.8 Diagram of the leading QED process for the standard model π0 _radiation off a τ lepton . . . 15

3.1 Neutral pion (π0_{) efficiency correction . . . 23}

3.2 Definition of the α− and α+angles in the collision centre-of-mass frame . . 25

3.3 α−vs α+distribution (from SP truth) for the phase-space model . . . 25

3.4 α−vs α+distribution (from SP truth) for the scalar model . . . 26

3.5 α−vs α+distribution (from SP truth) for the pseudo-scalar model . . . 27

3.6 Energy distribution of the expected signal π0_{’s . . . 27}

3.7 Energy of the reconstructed π0_{(Cut # 3 removed). . . 31}

3.8 Energy of lowest energy track and reconstructed π0_{(Cut # 4 removed) . . . 32}

3.9 Invariant mass of the µ-identified track and π0_{system (Cut # 5 removed) . . 33}

3.10 Invariant mass of the reconstructed π0_{(Cut # 6 removed). . . 33}

3.11 Invariant mass of the reconstructed π0_{(Cut # 6 removed). Detail . . . 34}

3.12 Missing transverse momentum (Cut # 7 removed) . . . 34

4.1 Simulated signal mass spectra after all selection criteria except the require-ment on mγγ. . . 41

4.2 Different background models to calculate Nbkg from the data sidebands . . 43

4.3 Different background models to calculate Nbkg from the SP collections . . . 45

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4.5 Probability density function of observed Nsig assuming the

background-only hypothesis . . . 48 5.1 Toy MC results for the mγγspectrum . . . 50

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List of Tables

2.1 Couplings best-fit values in the 8 GeV2_{to 40 GeV}2_{range. . . 13}

3.1 Background filters cut parameters . . . 17

3.2 The on- and off-resonance integrated luminosities of each BABARΥ(4S)run . 18 3.3 Number of data events before and after pre-selection . . . 18

3.4 Number of generated events in the simulated background samples . . . 20

(a) SP mode #3429: τ+ τ− . . . 20 (b) SP mode #1005: cc . . . 20 (c) SP mode #3981: µ+ µ− . . . 20 (d) SP mode #2400: BhaBha . . . 20 (e) SP mode #1237: B0_B0 _{. . . 20} (f) SP mode #1235: B+_B− _{. . . 20}

3.4 Number of generated events in the simulated background samples (cont’d) 21 (g) SP mode #998: uu, dd, ss . . . 21

3.5 Particle selectors used in the analysis. . . 21

3.6 Neutral pion selection criteria . . . 22

3.7 Number of generated and preselected signal events . . . 24

3.8 Summary of the signal selection requirements . . . 32

4.1 Efficiency εi for the two different signal models . . . 41

4.2 Contributions to signal selection efficiencies (εi) uncertainties. . . 42

4.3 Number of background-only events from the data sidebands with different models . . . 43

4.4 Number of background-only events from the SP collections with different models . . . 44

4.5 Number of background-only events Nbkgfrom simulation with different bin-nings . . . 46 5.1 Comparison of the fitted values Nfit

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Acknowledgements

I would like to thank:

My partner, Audrey, for her constant love and indefectible support, even when my

re-search limited my availability to her. Je t’aime.

My family, for providing me with invaluable role models that pushed me, by both their

good words and their good example, to reach my goals and ambitions.

Dr. J. Michael Roney, for mentoring, much appreciated teaching skills and patience. The BABARCollaboration, for the positive feedback on my analysis and for providing the

best environment, tools and data I could think of.

Dr. David McKeen, for his help in understanding the theoretical model and multiple

ad-vice throughout the project.

My fellow colleagues and office mates (and friends, in some cases ), for making the

usually lonely life of a graduate student much more pleasurable and gratifying. It is an honour to work in your company.

Il est temps que les années passées dans le système éducatif leur apparaissent non comme une préparation à une soumission, mais comme le début de la construction par chacun de la personne qu’il choisit d’être Albert Jacquard

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1 Introduction

1.1 The B

A

B

AR

experiment

The BABARexperiment was designed to study charge-parity (CP) violation in the B meson system with the help of an asymmetric electron-positron collider operating at nominally the Υ(4S)mass: a bb resonance of 10.58 GeV/c2which just above the BB meson pair

produc-tion threshold. This B-Factory, PEP-II, is located at SLAC Naproduc-tional Accelerator Laboratory in California and the multipurpose detector — if optimised for B physics — can accom-modate a wide range of studies. It is for example excellent at tau (τ) and charm (c) physics since B-Factories also produce these species in large quantity.

1.1.1 The accelerator: PEP-II

The accelerator facility, shown in figure 1.1, comprises a 3.2 km linear accelerator that injects electrons (e−_{) at 0.6 GeV and positrons (e}+_{) at 3.1 GeV into two rings: a}

high-energy ring storing the electrons and a low-high-energy ring storing the positrons. Electrons and positrons collide with a centre-of-mass energy nominally at the Υ(4S)mass which

de-cays almost entirely — at a rate greater than 95% — to B+

B−or B0B0[2]. Around 424 fb−1of data was recorded at that energy, translating into≈470×106 BBpairs. Moreover, 44 fb−1 were recorded just under the Υ(4S) peak, mainly to study events from the continuum.

The latter encompass all non-resonant processes: e+_e− _{→ `}+_`− ₍_{` =} _{e, µ, τ) and e}+_e− _→

qq(q=u, d, s, c), and are all background for B physics studies. Lower energy data was also

taken: 28 fb−1_{and 14 fb}−1_{at the Υ}₍_3S₎_{and Υ}₍_2S₎_{masses respectively.}

Finally, and more relevant to the present study, the τ pair production cross-section at 10.58 GeV is fairly large at 0.919 nb, meaning more than 480×106 τ+τ− events can be found in the entire BABARdata set. This explains why B-Factories also function as τ-Factories.

1.1.2 The detector: BABAR

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ver-Figure 1.1:Diagram of the linear accelerator and PEP-II ring. From the BABARimage gallery

[1]

tex detector, a tracking drift chamber, a Čerenkov light detector, an electromagnetic (elec-tron/photon) calorimeter and the instrumented flux return for detecting muons and hadrons. Below is an overview of each subsystem, based on references [1, 5].

The silicon vertex detector (SVD) : This sub-detector is the closest to the interaction point

(IP) and is used to reconstruct the position of the beam spot and the decay vertices, and to provide a precise measurement of the initial angle of the tracks. Because of the boosted centre-of-mass, these quantities determine the time difference between the decays which is crucial in measuring CP or T violations. The SVD consists of five double-sided layers of silicon, where the two inner ones are used to locate the vertices, the two outer ones, to match the tracks with the DCH and the middle one to allow for some tracking capabilities using the SVD alone. The position resolution in z and φ is 10-12 µm, except for the two farther layers which have a z resolution of 25 µm.

The tracking drift chamber (DCH) : Surrounding the SVD is the drift chamber. Its main

role is to track charged particles and allow measurement of their momentum through the curvature of the tracks in the 1.5 T magnetic field. It is a cylindrical chamber, filled

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Figure 1.2: Diagram of the BABARdetector. From the BABARimage gallery [1].

with a 80:20 mixture of helium and isobutane, and strung with tens of thousands of wires. Some of them, the field wires, are held at low voltage — either grounded or at few hundred volts — and serve to maintain a known electric field. The sense wires are held just under 2 kV to amplify, gather and detect ionisation liberated by an incoming charged particle as it travels through the gas. Since the field, hence the drift velocity, is known, this arrangement allows precise reconstruction of the tracks given the position and timing of the hits. Moreover, the amount of ionisation liberated depends on the particle velocity. Since the mass of a particle determines the momentum-velocity relation, the DCH, by measuring both dE/dx and momentum, also serves as a particle identification (PID) device.

The Čerenkov light detector (DIRC) This sub-detector is the primary PID system. It

con-sists of an array of 144 synthetic fused silica bars and a large water tank surrounded by photo-multiplier tubes (PMT’s). When a particle travels through the quartz at a speed greater than the speed of light in this material, it emits a light cone whose an-gle is directly related to its speed. This is the Čerenkov radiation. The light travels down the cylinder through total internal reflection and the angle is measured by the PMT’s just outside the tank. Combined with the momentum measurement from the DCH and, to a lesser extent, the SVD, knowing the velocity gives direct information

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on the particle mass.

The electromagnetic calorimeter (EMC) Built from thallium-doped caesium iodide CsI(Tl)

crystals, the main purpose of the calorimeter is determining the energy of electro-magnetic particles by absorbing them in the crystal and measuring the light output of the resulting electromagnetic shower with photo-diodes. However, different parti-cles shower differently: electrons and photons (γ) are completely absorbed and pro-duce a very narrow shower. Hadrons do not deposit all of their energy and propro-duce a wider shower, whereas muons travel through the EMC without showering and only deposit ionisation energy. Consequently, the EMC was optimised to measure the lo-cation and energy of electrons, photons, and neutral pions (π0_{). The latter are most}

often reconstructed via the π0_→

γγprocess.

The instrumented flux return (IFR) Since the muons don’t shower in the EMC, there is

a need for a more dense sub-detector to identify them. The iron and steel magnetic flux return yoke layers are interleaved with an active detector material that locates charged particles or the hadronic showers generated in the iron. While optimised for muons, the IFR can also detect high-momentum pions (which penetrate the EMC), other mesons such as long-lived kaons (KL) and neutrons. The active material was

originally resistive plate chambers (RPC), which unfortunately aged prematurely and were replaced by limited streamer tubes (LST) between 2004 and 2006. The LST is a single cell wire chamber filled with a mixture of organic and inert gas, where an incoming charged particle liberates ions which are then accelerated and collected by the anode wire.

1.2 Pion-photon transition form factor issue

As introduced earlier, B-Factories are in fact very versatile experiments that allow many kinds of measurements. Amongst the very interesting studies outside of B physics that were conducted at BABAR, the pion-photon transition form-factor (F_π0 Q2) gave rise to much controversy. Hadronic form factors describe the relationship between the momen-tum and the coupling between photons and hadrons. For an elementary particle, this cou-pling is constant and determined by only a few parameters. For hadrons such as the π0

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the constituents, thus giving information on the structure of the particle [6]. More detailed information about the pion-photon transition form-factor is found in section 2.1.

According to perturbative chromodynamics (pQCD), any momentum-dependence should vanish at high energies. In fact for high squared momentum transfers such as Q2_>₁₅₍_GeV/c₎2_,

F_π0 Q2

should converge towards the Brodsky-Lepage limit of 185 MeV/Q2 _{which is}

a highly reliable prediction of the scale of pQCD [7]. However, BABAR measurement of theF_π0 Q2

shows continued increase well past that limit for momentum transfers up to 40(GeV/c)2.

Many theories tried to explain that discrepancy, yet the problem remains open. A recent hypothesis is that there may exist a new particle which have a mass very close to that π0 and similar decay modes, thus mimicking it. Those objects were temporarily named “impostors”, and their measurement instead of real π0 _{would be what give rise to the}

increase in the F_π0 Q2

. A mixed state between a π0 _{and an new light pseudo-scalar}

state would also enhance its coupling to the τ, and this model was called a “hardcore pion”. For reasons described in more details in the original theory article [8], a coupling between these particles and the τ lepton is not strongly constrained either by other theories or experiment, and therefore needs to be explored. Section 2.3 reviews the key aspects of this exotic theory. The present project consists of a direct search for these states in BABAR data.

1.3 The research question

The research question is formulated as follows:

Are there hardcore pions or pion impostors produced in association with tau pairs that would account for the discrepancy observed in BABARfor the pion-photon transition form factor?

1.4 Goals of the project

1.4.1 General goal

Search for the production of hardcore pions, scalar or pseudo-scalar pion impostors (π0 HC,

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1.4.2 Specific goals

Retrieve B_AB_ARdata and official simulated background. Apply pre-selection to get a usable data set.

Generate realistic signal simulation in order to obtain signal selection efficiency. Define the selection procedure using simulated data to select signal events with as

low background as possible.

Apply the selection to experimental data and measure the production cross-section of these objects.

1.5 Thesis outline

A deeper description of the physics motivations for this search and more general back-ground information are found in section 2. The objectives of the project are stated explicitly in section 1.4 while the methodology associated with each goal is described in section 3. Measurement of the production cross-section based on BABARdata is exposed in section 5. This section also contains upper limits on the cross-sections and the new couplings re-quired by the proposed theory.

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2 Physics motivation and theoretical background

2.1 Meson transition form factors

P

γ(∗) γ(∗)

Figure 2.1:General P→γ∗γ∗vertex, P is a pseudo-scalar meson here.

In processes including a Pγ∗

γ∗ vertex (P is a pseudo-scalar meson in this context) such as in figure 2.1, the transition form factorF_π0 q2, Q2

is a scalar kinematic quantity that describes the dependence of the transition amplitude on the momenta q2_{, Q}2 _{of the two}

photons. Studying such form factors is important because the momentum-dependence of the amplitude indicates the compositeness of the particle and provides information on the charge and currents distributions inside it. At sufficiently high momentum transfer, the transition is dominated by the nature of the hadronic state [6]. Hadronic form factors therefore provide a direct route to compare quantum chromodynamics (QCD) theoretical predictions with experimental data [9].

In particular, the pion-photon transition form factor is defined with respect to in the π0_→

γγ∗transition amplitude Aπ0→γγ∗ =ieF_π0 q2, Q2eµνρσe µ 1e2νk ρ 1kσ2 (2.1) where _e

µνρσ is the totally antisymmetric tensor,

_eµ

1, eν2are the polarisation 4-vectors of the two photons,

kρ

1, kσ2 are their momentum 4-vectors (k21= −Q2and k22= −q2). F_π0 q2, Q2

is assessed experimentally using the two-photon fusion process e+_e−_→_e+_e− γγ∗→e+e−π0, represented in figure 2.2, in a frame where q2=0such that the form factor is a function of the momentum transfer Q only.

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k2 k1 e∓ e±(p) e∓ π0 e±(p0)

Figure 2.2:A Feynman diagram for e+_e−_→_e+_e−

γγ∗ →e+e−π0. k1= −Q2= (p−p0)2 is

the squared momentum transfer, k2= −q2≈0.

What is interesting for the present investigation is thatF_π0 Q2

should converge for high momentum transfer towards the Brodsky-Lepage limit [10]

lim Q2_→_∞Q 2_F π0 Q2=√2 fπ (2.2)

where fπ '131MeV is the pion decay constant. For Q2 >15GeV2, this limit is a highly

reliable prediction, well beyond the non-perturbative QCD regime.

2.2 Comparing experimental results for the pion-photon transition form

factor

2.2.1 Results from the BABARexperiment

As outlined in the introduction, the BABARcollaboration published a measurement ofF_π0 Q2 for Q2 _{in the 4 to 40 GeV}2 _{range [11]. It is in tension with perturbative QCD calculations}

in the high Q2 _{(above 10 GeV}2_{) region. This is shown in figure 2.3 where B}_A_B_AR_{data, yet}

compatible with results from CELLO [12] and CLEO [13] at low Q2_{, don’t show any sign}

of convergence towards the Brodsky-Lepage limit of√2 fπ/Q2 '185MeV/Q2 indicated

by the horizontal dashed line.

2.2.2 Results from the Belle experiment

Due to the excitement that BABARresult raised in the QCD community — the paper received over 180 citations — another experiment measuredF_π0 Q2 between Q2 = 4GeV2 and Q2 =40GeV2[14]. They used a 759 fb−1 data sample obtained with the Belle detector at

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Figure 2.3:The γγ∗ → π0 transition form factor multiplied by Q2 from CELLO, CLEO and

BABARdata [11]. The dashed line indicates the asymptotic limit for the form factor.

the KEKB e+_e− _{collider. As shown in figure 2.4, their data don’t show the same rapid}

increase with Q2_{as B}_A_B_AR_{’s and remain compatible with perturbative QCD predictions.}

Figure 2.4:Results for the π0 _{transition form factor from the Belle measurement [14]. The}

error bars are statistical only. The dashed line shows the asymptotic limit from

pQCD (∼0.185GeV).

To get a more quantitative insight on the measurement, the Belle collaboration fitted an asymptotic functional form

Q2 Fπ0 Q2 = BQ2 Q2₊_C (2.3)

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to the data. They obtained B=0.209±0.016GeV and C =2.2±0.5GeV2 with χ2/dof=

7.07/13.

2.2.3 Comparison of the two measurements

Dr. David McKeen, a postdoctoral researcher at the University of Victoria, reproduced the fit on equation (2.3) with BABAR data1 to get B = 0.230±0.008GeV and C = 2.5±

0.3GeV2with χ2/dof=25.6/15. Both experimental results are compatible within a∼1.2σ difference on the fitted parameters. This difference is very similar to the 1.5σ one obtains using the BABARparametrisation

Q2 Fπ0 Q2 =A Q2 10GeV2 β . (2.4)

with data from both experiments [14].

Moreover, when combining Belle and BABARdata to fit equation (2.3) we obtain B=0.219±

0.007MeV and C =1.2±0.1GeV2 with χ2/dof =76.3/50. The asymptotic value B from

the combination is 4.9σ above the pQCD limit.

Lastly one can conduct a simple non-parametric test to check if the two samples can possi-bly be drawn from the same distribution even if BABARresult is systematically higher than Belle’s. We conducted a Wald-Wolfowitz runs test [15] comparing the two data sets with

+: F_π0 Q2 BABAR> Fπ0 Q 2 Belle −: F_π0 Q2 BABAR< Fπ0 Q 2 Belle.

5 runs were observed with N+ = 13, N− = 2, which is compatible with the null (same

distribution) hypothesis that predicts 4±0.65runs.

The compatibility between the two measurements, and the higher precision of “anoma-lous” BABAR result produce a combined measurement that still exceeds the predictions. This justifies continuing efforts on explaining this observation, including exploring more exotic theories.

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2.3 Motivation of the search: the hypothesis of new pion-like particles

2.3.1 General idea

Because of the theoretical robustness of the perturbative QCD asymptotic prediction, the anomaly observed in BABARdata could be a sign of physics beyond standard model (SM). Different hypotheses were considered to account for these results, but we focus here on examining the consequences of hypothetical new pion-like particles coupling with the τ leptons [8]. More precisely, two classes of models were proposed: mixing of the π0_{with a}

new light pseudo-scalar state P that enhances its coupling to c, b quarks and the τ lepton, but also a new particle – scalar or pseudo-scalar – with a mass very close to the π0_mass.

The first model is denoted “hardcore pion” (π0

HC) while the second class was named “pion

impostors” (ιS and ιP for the scalar and pseudo-scalar, respectively).

2.3.2 Interactions with SM particles

Coupling of ιS and/or ιPto the τ lepton would enhance observedFπ0 Q

2

. The transition amplitude for γγ∗_→_(ι

S,ιP) via τ loops, represented in figure 2.5, would add to the one for

the real π0_{due to their similar mass. In the case of the hardcore pion model, the π}0 _itself

would be coupled to the τ via its mixing with the new pseudo-scalar state. There would then be an apparent excess of produced π0_{via the π}0

HCalso arising from a fermion-triangle

diagram process as in figure 2.5. π0

HC being a superposition of states that include the SM

π0, a fraction of the π0_HC will collapse as SM π0at the detection. The ιP and π0_HC scenarios

therefore only differ by whether or not the Yukawa couplings to u and d quarks allow for mixing between the pseudo-scalar state and the SM π0_.

Coupling to other SM particles than the τ are ruled out by other experimental results. The first requirement for a particle to couple to these hypothetical objects is that it must be elec-trically charged in order to affect the coupling of pions to photons. The other constraints on coupling to non-τ particles are that

coupling to non-SM objects would need an impostor mass greater than 100 GeV to escape collider bounds on pair-production;

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τ τ τ γ∗ γ π0_HC, ιP, ιS

Figure 2.5:Photon-impostor transition through a τ loop

such mass requires an unrealistically large coupling to explain observed π0 be-haviour

coupling to light quarks would have to be stronger than π0−u, d, scoupling and is also unrealistic;

coupling to c: the branching ratioB(

ψ0→γπ0) = (1.58±0.42) ×10−6[16] requires

couplings between the c quark and ιP, π0_HC, ιS respectively meeting

|gc|,|gπc |,|hc|.0.023 (2.5)

which can’t explain BABARdata forF_π0 Q2;

coupling to b: the branching ratio B(_Υ(2S) → _Υ(1S)_π0) < 1.8×10−4[17] requires couplings between the b quark and ιP, π0_HC, ιS respectively meeting

|gb|,|gπb| . 0.055 (2.6a)

|hb| . 0.0055 (2.6b)

which can’t explain BABARmeasurement neither;

coupling to e would mean that γγ is no longer the primary decay mode for π0 coupling to µ: muon(g−2)puts limits on couplings around 10−3−10−4.

2.3.3 Production cross-sections

Relevant to searching for these new objects in the BABARdata set are the production cross-sections for e+_e−_→

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e+ e− τ+ π0_HC, ιP, ιS τ−

+

e+ e− τ+ π0_HC, ιP, ιS τ−

Figure 2.6:Diagram for impostor production in association with τ+

τ−pair in e+e−collisions

With gπ

τ, gτ and hτ being respectively the couplings to the π0_HC, ιP and ιS, the expected

cross-sections at√s=10.58GeV are [8]

σ(e+e−→τ+τ−π0_HC) ' 9.8(g_τπ)2 pb, (2.7a) σ(e+e−→τ+τ−ιP) ' 9.8g2τ pb, (2.7b)

σ(e+e−→τ+τ−ιS) ' 110h2τ pb. (2.7c)

Fitting the couplings to BABARdata for F_π0 Q2

gives results presented in figure 2.7. Ta-ble 2.1 contains the best-fit values together with their confidence intervals at various con-fidence levels. Note that the value for hτ is limited to the largest fit value consistent with

the(g−2)_τ constraint: 0.840.

Table 2.1: Couplings best-fit values in the 8 GeV2 to 40 GeV2 range. Confidence intervals

(CI) determined as intervals where χ2 _≤_χ2

min+∆χ2, with ∆χ2 =1.00, 3.84, and

6.63respectively for the 68.3%, 95% and 99% confidence level.

Coupling Best fit 68.3% CI 95% CI 99% CI

gπ

τ 0.25 0.22–0.27 0.16–0.29 0.12–0.31

gτ 0.70 0.61–0.79 0.51–0.84 0.46–0.87

hτ 1.09 0.94–1.21 0.79–1.30 0.71–1.34

In the entire Υ(4S) BABARdata set, these predicted cross-sections translate respectively to

O(105), O(106)or O(107)events for the hardcore pion, pseudo-scalar impostor or scalar

impostor model in the τ+

τ−(ιP, ιS, π0_HC) final state. Such particles should therefore

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Figure 2.7:The best-fit total form factors (from QCD and hypothesised model contributions) in the pseudo-scalar impostor (solid), scalar impostor (dashed), and hard-core

pion (dotted) cases when fit to the data from BABAR, CLEO, and CELLO. The

re-sultant couplings are gτ = 0.63, hτ = 0.84 and gπτ = 0.18. The shaded region

indicates the range of QCD-predicted form factors. The scalar impostor coupling

is limited by the constraint brought from(g−2)τ. From reference [8].

2.3.4 e+e− → ä+ä− á0 _{in the standard model}

It is instructive to estimate the rate of π0_{production in association with τ pairs in e}+

e− col-lisions from the standard model to put these new couplings in perspective. To lowest order in quantum electrodynamics (QED) and quantum chromodynamics (QCD), the standard model process where a π0_{is radiated off a τ lepton is represented in figure 2.8.}

We note the presence of the Pγγ vertex of figure 2.1 so the matrix element will involve the amplitude from equation (2.1) as well as an additional suppression factor arising from the two-photon loop and the τ propagator. The calculation of the matrix element for such diagram with lepton`in the final state [18, 19] yields an effective coupling between the π0

and the lepton

g``= − m` 2 fπ _α π 2 ·R (2.8)

where m` =mτ '1.8GeV in the present case, fπ '0.093GeV is the pion decay constant,

and α'1/137is the fine-structure constant. R is a dimensionless amplitude that is a func-tion of the pion form-factorF_π0 k2,(p_π0 −k)2integrated over the virtual photon

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momen-

τ− π0

τ− P

Figure 2.8:Diagram of the leading QED process for the standard model π0_{radiation off a τ}

lepton

tum k, and the mass ratio mτ/mπ0.

As a first approach, neglecting the contribution from R gives

g_``e.m.∼ O10−5 (2.9)

which is roughly 5 orders of magnitude smaller than the couplings we expect from the im-postor model. With an efficiency comparable with the present search, the expected signal for SM production would be less thanO 10−2

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3 Analysis methodology

Each major step of the analysis corresponds to a specific goal of the research project. First pre-selection was applied to BABARdata and background simulation, then the resulting files were transferred from SLAC to the mercury cluster at the University of Victoria. Details about which collections were used, the pre-selection and the total number of events are found in section 3.1.

In parallel, e+_e− _→

τ+τ− ιP and e+e−→τ+τ− ιS signal events were generated according

to the methodology explained in section 3.2; they will be used to calculate the selection efficiency.

These background and signal simulated samples were then used to define the selection criteria, improve the data-simulation agreement in the sidebands regions and maximise the signal selection efficiency while minimising background level. Basically, this selection consists of requiring each event to have a τ pair and a π0_{, where the latter is not the result of}

a τ decay. The tau pair was identified by requiring the event to have two charged particles, one electron and one muon as per BABARrecommended PID selectors as well as one pair of neutrals having an invariant mass compatible with the π0_{. Section 3.3 exposes the details}

of the selection criteria and the rationale behind them.

The analysis is developed and optimised using simulation and data in the sideband regions (regions that will be excluded from the analysis by the selection criteria). The protocol is “frozen” before looking at the signal data so as to respect the standards of a blind analysis. When the criteria were set, the analysis was applied to the complete data set and the im-postor production cross-section was calculated. This chapter explains in more detail each step of the experimental method.

3.1 B

A

B

AR

data and background simulation

3.1.1 Pre-selection and software configuration

The analysis uses ROOT [20] ntuples generated on the Long-Term Data Access (LTDA) sys-tem [4]. It utilises the analysis-52 software release and TauMiniUser package to produce the ntuples from the AllEvents skim (R24f skim cycle) [21].

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The TauMiniUser package reads the input collections, process events that pass (BGFMuMu || BGFTau || BGFTwoProng) background filters where the requirements of these filters are found in table 3.1. TauMiniUser then select all events that pass the 1N (N≥1)

topol-ogy requirement: the net charge must be zero, one hemisphere must contain one prong and the other hemisphere either contains one or three prongs. A “prong” is defined as a GoodTrackVeryLoosetrack that does not overlap with a pair of tracks identified as coming from γ→e+e− converted in the material of the detector [22].

Table 3.1: Background filters cut parameters. From reference [23].

Filter name Quantity Default_value

BGFMuMu

Minimum momentum for highest-momentum track 4.0 GeV/c Minimum momentum for second highest-momentum track 2.0 GeV/c Minimum θ1+θ2of the two highest-momentum tracks 2.8 rad

Maximum θ1+θ2of the two highest-momentum tracks 3.5 rad

Maximum electromagnetic calorimeter energy associated

with the two highest-momentum tracks 2.0 GeV

BGFTau

Required number of charged “tight” tracks 2

Total charge of the event 0

Maximum momentum|p1| + |p2|of the two tracks 9 GeV/c

Maximum energy sum of the clusters associated with the

two tracks 5 GeV

Maximum E/p for one of the two tracks 0.8c Minimum value of |p1+p2|⊥

ECM/c−|p1|−|p2| 0.07

BGFTwoProng

Required number of charged “tight” tracks 2

Maximum cluster energy for the two tracks 3.0 GeV Minimum momentum for one of the two tracks 1.0 GeV Minimum separation of the two tracks|θ1+θ2| 0.1 rad

Minimum θ for track with highest|pCM| −0.75rad

or

Minimum|p⊥|for at least one track 4.0 GeV/c

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3.1.2 Data sets used in the analysis

Table 3.2 shows the recorded luminosities for BABARruns 1 to 6, used in the present analysis. The total time-integrated luminosity is [24]

L_int= (468.1±1.8) fb−1.

The data efficiency of the pre-selection described in §3.1.1 is detailed in table 3.3.

Table 3.2: The on-resonance (L_on) and off-resonance (L_off) time-integrated luminosities of

the individual BABARΥ(4S)runs, and the ratio between the on- and off-resonance

integrated luminosities. The first uncertainties are statistical and the second un-certainties are systematic. From reference [24].

Run Nº Lon(fb−1) Loff(fb−1) Lon/Loff

1 20.37 ±0.01±0.09 2.564±0.002±0.014 7.946±0.006 ±0.027 2 61.32 ±0.01±0.26 6.868±0.004±0.034 8.928±0.006 ±0.023 3 32.28 ±0.01±0.13 2.443±0.003±0.012 13.213±0.015 ±0.037 4 99.58 ±0.02±0.41 10.016±0.007±0.043 9.943±0.007 ±0.012 5 132.33±0.02±0.59 14.278±0.008±0.066 9.268±0.005 ±0.012 6 78.31 ±0.02±0.35 7.752±0.006±0.036 10.102±0.008 ±0.013

Table 3.3: Number of data events in the AllEvents skim (N_AllEvts), after pre-selection (Npre),

and pre-selection efficiency (ηpre)

Peak Run # NAllEvts Npre ηpre

(×106) (×106) (%) on 1 292.782 50.380 17.2 2 958.854 158.996 16.5 3 501.277 83.650 16.6 4 1593.488 251.899 15.8 5 2104.338 327.803 15.5 6 1262.797 195.071 15.4 off 1 33.809 6.415 18.9 2 101.137 17.985 17.7 3 35.184 6.352 18.0 4 149.077 25.430 17.0 5 208.389 35.869 17.2 6 115.335 19.583 16.9

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3.1.3 Background simulation collections

The analysis uses all “official” BABARbackground sources: e+e− →τ+τ−, e+e− →µ+µ−, e+e− → qq (q = u, d, s, c, b), and Bhabha scattering events. Each simulated background

event is weighted to match data luminosity according to

wLix=

σxLi_int

Ni gen, x

(3.1) where σxcorresponds to the production cross-section for a given process x,Li_int is the

in-tegrated data luminosity for Run i and Ni

gen, xis the number of generated events of process

x according to run i conditions. On-peak and off-peak were treated as two different run conditions, so wi

L can take up to 12 different values for each process, each of which are

given in table 3.4.

3.1.4 Particle identification (PID) and weighting

Table 3.5 lists the selectors used in the analysis and references the BABAR Analysis Doc-uments (BADs) that describes them in more detail. Even though the PidLHElectrons (tight)selector is superseded by the more recent Kalanand Mishra (KM) selectors [27], the former is preferable in the current analysis since it has a lower “pion-as-electron” mis-identification rate than the electron KM selector in “tight” mode. The rate is four to six times lower in the chosen likelihood-based selector than in the KM one [28]. Charged pi-ons mis-identified as leptpi-ons is predicted to be an important background source in the analysis. The choice of PID selectors was guided by BABAR’s recommendations only; how-ever a further optimisation study to confirm that choice would be appropriate.

Moreover, in the current analysis, we accept an “electron track” as soon as an event passes the electron selector. Remaining events that pass the muon selector are identified as “muon tracks”. As such, PID efficiencies from BABAR’s PidTables package were used to correct for known differences between data and simulation. The weight applied to all simulated events is the product of the weights for the electron track and the muon track.

wPID =wePID(q, p, θ, φ) ·w

µ

PID(q, p, θ, φ) (3.2)

where q is the charge of the particle (+1or−1), p is the magnitude of its momentum with

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Table 3.4: Number of generated events in the simulated background samples

(a)SP mode #3429: τ+

τ−

Peak σ Run Ngen Npre ηpre wL

(nb) # (×106) (×106) (%) on 0.919 1 19.687 7.637 38.7 0.9509 2 57.194 22.545 39.4 0.9853 3 49.002 19.293 39.3 0.6054 4 180.077 73.596 40.8 0.5082 5 237.094 96.598 40.7 0.5129 6 139.424 56.278 40.3 0.5162 off 0.919 1 1.926 0.750 38.9 1.2234 2 6.830 2.700 39.5 0.9241 3 4.499 1.777 39.5 0.4990 4 14.494 5.931 40.9 0.6351 5 25.788 10.539 40.9 0.5088 6 14.062 5.721 40.7 0.5066 (b)SP mode #1005: cc

(nb) # (×106) (×106) (%o) on 1.30 1 55.254 0.308 5.58 0.4793 2 164.722 0.966 5.87 0.4839 3 88.321 0.485 5.50 0.4751 4 267.308 2.126 7.96 0.4843 5 344.579 2.846 8.26 0.4992 6 208.664 1.712 8.21 0.4879 off 1.30 1 5.585 0.031 5.62 0.5968 2 17.560 0.099 5.67 0.5085 3 6.532 0.035 5.50 0.4862 4 21.292 0.154 7.27 0.6115 5 37.813 0.294 7.80 0.4909 6 20.540 0.160 7.80 0.4906 (c)SP mode #3981: µ+_µ−

(nb) # (×106) (×106) (%) on 1.147 1 24.597 16.791 68.2 0.9499 2 74.079 50.123 67.6 0.9494 3 38.890 26.653 68.5 0.9520 4 121.574 81.752 67.2 0.9395 5 153.551 102.662 66.8 0.9885 6 94.085 62.310 66.2 0.9547 off 1.147 1 2.477 1.704 68.8 1.1873 2 7.849 5.397 68.7 1.0036 3 2.912 2.001 68.7 0.9625 4 9.409 6.338 67.3 1.2210 5 16.724 11.222 67.1 0.9792 6 10.268 6.857 66.7 0.8659 (d)SP mode #2400: BhaBha

(nb) # (×106) (×106) (%) on 40 1 21.313 0.320 1.50 38.23 2 64.118 1.011 1.57 38.25 3 35.227 0.543 1.54 36.65 4 106.363 1.258 1.18 37.45 5 133.569 1.539 1.15 39.63 6 81.040 0.902 1.11 38.65 off 40 1 2.165 0.033 1.54 47.37 2 6.848 0.112 1.64 40.12 3 2.534 0.039 1.57 38.56 4 8.189 0.094 1.15 48.92 5 14.547 0.168 1.16 39.26 6 7.900 0.092 1.16 39.25 (e)SP mode #1237: B0_B0

(nb) # (×106) (×106) (%o) on 0.525 1 34.941 0.013 0.38 0.3060 2 104.348 0.040 0.39 0.3085 3 57.888 0.021 0.37 0.2927 4 169.801 0.102 0.60 0.3078 5 216.089 0.141 0.65 0.3215 6 135.224 0.089 0.66 0.3040 (f)SP mode #1235: B+_B−

(nb) # (×106) (×106) (%o) on 0.525 1 34.878 0.019 0.56 0.3066 2 105.561 0.061 0.58 0.3049 3 56.035 0.030 0.55 0.3024 4 166.784 0.130 0.78 0.3134 5 215.168 0.177 0.82 0.3228 6 130.336 0.108 0.83 0.3154

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Table 3.4: Number of generated events in the simulated background samples (continued)

(g)SP mode #998: uu, dd, ss

(nb) # (×106) (×106) (%) on 2.09 1 44.588 0.854 1.91 0.9548 2 185.904 3.610 1.94 0.6894 3 137.541 2.631 1.91 0.4905 4 421.799 9.040 2.14 0.4934 5 554.300 12.035 2.17 0.4990 6 327.032 7.059 2.15 0.5005 off 2.09 1 4.478 0.086 1.92 1.1967 2 20.213 0.394 1.95 0.7101 3 10.283 0.199 1.93 0.4965 4 34.028 0.711 2.09 0.6152 5 60.329 1.317 2.18 0.4946 6 32.950 0.718 2.18 0.4917

Table 3.5: Particle selectors used in the analysis.

Particle Name of the selector

Electrons PidLHElectrons (tight) [25] Muons BDTLooseMuonSelection [26]

3.1.5 Neutral pion (á0_{) reconstruction and weighting}

The π0_{’s were reconstructed using the method described in reference [29] and outlined}

below. The photons were first selected using the GoodPhotonLoose and GammaForPi0 crite-ria, but with a tighter requirement on raw energy to ensure better purity of photons from π0 decays. These photons were in turn combined by adding their four-momenta, and candidates meeting pi0Loose requirements were selected. All photon and neutral pion requirements are listed in table 3.6.

The lateral moment(LAT)used for selecting π0candidates is defined as

LAT≡ ∑ Ncry i=3 Eir2i E1r2₀+E2r2₀+∑ Ncry i=3 Eiri2 , (3.3) where

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Table 3.6: Neutral pion selection criteria. From reference [29].

Candidate

particle Quantity Requirement

Photon (γ) Raw energy (ELateral moment (LATraw) γ)† 0.01Eraw<>LAT75MeVγ <0.8

Polar angle (θγ) 0.473 rad< θγ < 2.36rad

Neutral pion (π0₎

Invariant mass (mγγ) 100MeV<mγγ<160MeV/c

Energy (Eγγ) Eγγ>200MeV

If sharing a photon Keep candidate with smallest|mγγ−mπ0| ‡ †_{: As defined by equation (3.3)}

‡_{: m}

π0 =134.98MeV/c

2_[2]

Ei: Raw energy deposited in crystal i in decreasing order (i.e. E1<E2<...ENcry), ri: Distance between the cluster centroid and the position of crystal i,

r0: Average distance between two crystals (r0=5cm).

When processing simulated events — either background or signal —, a weighting factor is used to reflect data/simulation efficiency differences based on control samples studies. Again, we used the weighting found in reference [29] since the selection is identical to the current analysis. However, as shown in figure 3.1, we used a linear regression to calculate the weight to apply to each event as a function of the π0_{momentum instead of}

interpolat-ing between bin values. Moreover, in the cited analysis, the authors estimated systematic uncertainties affecting π0 _{efficiency to}_±_{0.009, independent of the π}0_{momentum. In the}

present case, an uncertainty component≤3.8×10−3is added by the regression statistics, so the weights applied to the simulated events to compensate for data/simulation differ-ences in π0_{reconstruction efficiency were given by}

w_π0 = (0.9322+0.0131p_π0) ±0.01. (3.4) This result is also compatible with a previous, more exhaustive π0 _{efficiency study that}

states a pi0Loose efficiency of

η_π0 = (0.934±0.008) + (0.019±0.004)p_π0 (3.5) where the uncertainties include both statistical and systematic components [30].

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[GeV/c] 0 π p 1 2 3 4 5 6 0 π p,r-av w 0.85 0.9 0.95 1 1.05 1.1 1.15

Figure 3.1:Time-averaged neutral pion efficiency corrections from reference [29]. Error bars

show statistical uncertainty only. Red curve shows linear regression wπ0(pπ0) =

a0 + a1pπ0 with a0 = 0.9322± 0.0012(stat) and a1 = 0.0131± 0.0006(stat).

χ2/dof=28.42/11.

3.2 Producing simulated signal

The signal was simulated by first generating e+_e−_→

τ+τ−π0events where the three-body final state is distributed according to allowed phase space and the τ leptons decay generi-cally. Each of these events were then re-weighted so their angular distribution reflects the processes described in figure 2.6: e+

e− →τ+τ−π0_HC, e+e− →τ+τ−ιPand e+e−→τ+τ− ιS. Since the π0_HCand ιPmodels both involve a new pseudo-scalar state and differ only by

their production cross-section, the weights for these two models are identical.

3.2.1 Simulation generation tools and configuration Around two million e+_e− _→

τ+τ− π0simulated events were requested to the Simulation Production (SP) group. They were generated assuming pure phase-space decay of the virtual photon, generic decay modes for the τ+

τ− pair and the π0. This model was im-plemented in EvtGen [31] and includes the effect of initial state radiation but no final state radiation. A sample of events incorporating final state radiation [32] is currently being generated, but we expect no important effect to be observed.

Table 3.7 lists the number of generated events that are present in BABAR collections, the number of preselected events and the pre-selection efficiency. The weight applied to scale the simulated signal to the data luminosity is also calculated using equation 3.1. We used

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the lower bound of the 95% confidence interval for the couplings to calculate the appro-priate cross-sections for scaling the simulated signal. However, since this signal will only be used to establish the selection efficiency, this choice does not affect the final result but only the signal/background ratio seen in the intermediate plots.

Table 3.7: Number of generated and preselected signal events for SP mode # 11372: e+_e−_→

τ+τ−π0. σ is the lower bound of the 95% confidence interval on the ιPproduction

cross-section obtained from couplings in table 2.1 and was used to scale the signal SP to data luminosity. The total number of generated events is 2,127,000.

(pb) # (×103) (×103) (%) on 2.549 1 97.000 34.574 35.6 0.5352 2 238.000 87.133 36.6 0.6567 3 128.000 46.530 36.4 0.6428 4 519.000 200.792 38.7 0.4891 5 570.000 219.090 38.4 0.5918 6 377.000 144.660 38.4 0.5295 off 2.549 1 5.000 1.933 38.7 1.3071 2 30.000 11.203 37.3 0.5835 3 9.000 3.293 36.6 0.6919 4 23.000 8.974 39.0 1.1100 5 89.000 34.471 38.7 0.4089 6 42.000 16.138 38.4 0.4705

3.2.2 Signal angular distribution re-weighting

The phase-space generated events were then re-weighted to reflect that the impostors are in fact radiated off one of the τ leptons. If any spin correlations is neglected, weighting each event by the corresponding matrix element will give the exact signal distributions. Each signal weight was also normalised by the sum of all signal weights to maintain proper data/simulation scaling.

The expressions for the matrix elements were determined by Dr. David McKeen and are reported in appendix A. In order to visualise the effect of this re-weighting on the angular distribution of the impostors, figures 3.3, 3.4 and 3.5 show the α−vs α+distributions, where

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e− e+ τ+ τ− π0 α− α+

Figure 3.2:Definition of the α−and α+angles in the collision centre-of-mass frame

According to the phase-space model shown in figure 3.3, events where either or both α angles have high values are favoured. Being in the centre-of-mass frame, there is a strict condition that

α−+α+≥π (3.6)

so the allowed phase-space is larger when at least one of these angles is large.

0 10 20 30 40 50 + α 0 0.5 1 1.5 2 2.5 3 --α 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 -50 -40 -30 -20 -10 0

Figure 3.3: α−vs α+distribution (from simulation truth) according to the phase-space model

The scalar impostor model shows a different angular distribution in figure 3.4. Here, the impostor is preferably aligned with either the τ− _{or the τ}+ _{off which it radiates. This is}

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reflected in the 2D distribution where most of the events lie near the α−+α+=π line, or in the α− and α+projections both peaking around 0 and π.

10 20 30 40 50 + α 0 0.5 1 1.5 2 2.5 3 --α 0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 16 18 -50 -40 -30 -20 -10

Figure 3.4: α−vs α+distribution (from simulation truth) after re-weighting by the scalar

im-postor model matrix elements

The pseudo-scalar model (figure 3.5) presents an in-between angular behaviour resulting from a competition between the γ5_{to generate a pseudo-scalar in the vertex factor and the}

scalar product of the impostor and τ momenta in the calculation of the matrix elements. While the former suppresses collinear τ± _{and impostors, the latter enhances their}

proba-bility. The π0

HCmodel is also based on a new pseudo-scalar so the re-weighting is the same

as for the ιP.

Furthermore, figure 3.6 displays the energy spectrum according to the three different mod-els. While applying the pseudo-scalar model weights doesn’t notably alter the distribution, a scalar impostor would generally exhibit a much lower energy. This is expected to affect the signal selection efficiency dramatically since, as will be detailed in §3.3.1, we select only high-energy π0_{’s that could not have originated from a τ decay.}

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0 10 20 30 40 50 + α 0 0.5 1 1.5 2 2.5 3 --α 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 -50 -40 -30 -20 -10 0

Figure 3.5: α− vs α+distribution (from simulation truth) after re-weighting by the

pseudo-scalar pseudo-scalar impostor model matrix elements

(GeV)

0

π

E

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Normalized counts / 0.05 GeV

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Pseudoscalar Scalar Phase space

Figure 3.6:Energy distribution of the π0_{’s in signal simulation with the three different}

mod-els. The values are taken from simulation truth and the histograms are nor-malised.

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3.3 Definition of the signal selection

3.3.1 List of the selection criteria

The next paragraphs detail the selection criteria, also known as selection cuts, used to dis-criminate signal events together with their rationale. They are also summarised in table 3.8.

Select ä+_ä−

events As detailed in §3.1.1, the pre-selection require the event to have two oppositely-charged tracks. τ+

τ− events are selected by requiring that one track is iden-tified as an electron and the other as a muon. This provides a clean signature for τ+

τ− creation in e+

e− collision, at the cost of limiting the overall selection efficiency since the branching fraction for τ+

τ− → 2ντνeνµe ±

µ∓ is only about 6.2% [2]. The τ+τ− →2νe2ντ

e+e−mode was not selected to remove as much Bhabha scattering events as possible.Those events are not simulated in sufficient quantities in the BABAR collections. The τ+τ− → 2νµ2ντµ+µ−mode was not selected either since µ pair productions would become a large

background and would necessitate a more elaborate selection procedure to eliminate. Moreover, leptonic τ decays will necessarily imply some missing transverse momentum in the event because of the neutrinos that are created. Since the momentum of the e+

e− sys-tem is aligned with the beam axis z, the magnitude of the missing transverse momentum, pmiss_⊥ , is the total momentum of the reconstructed tracks and neutrals perpendicular to z:

pmiss_⊥ =

∑

k

pksin φk (3.7)

where pk is the magnitude of the momentum of particle k, φkis its polar angle, and index

kscans both tracks and all reconstructed neutrals.

Based on observation of signal, background and blinded data, we defined pmiss_⊥ >0.3GeV/c

as a requirement for signal events. This requirement also removes Bhabha scattering and two-photon e+

e− →e+e− π+π− π0 events where the e+e− pair escapes down the beam pipe.

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Select 1á0 _events _{Events presenting one and only one π}0_{, according to the π}0

recon-struction method outlined in §3.1.5, are selected. This criterion is trivially brought by the e+e−→τ+τ−π0signal that this analysis is aiming to observe.

Limit energy of the reconstructed á0 _{Figure 3.6 shows the energy spectra of the π}0_’s

orig-inating from signal simulation. A clear feature of these is that they will always have an energy lower than 4.7 GeV. Consequently, all reconstructed π0_{’s above that energy}

thresh-old will be discarded. Moreover after all selection criteria are applied there are no signal events that have an energy lower than 2.2 GeV as it can be seen in figure 3.7. The exact value of lower bound is therefore not dictated by any other reason than that we expect no signal compatible with the model below this energy. The π0_{energy requirement is that}

2.2GeV≤E_π0 ≤4.7GeV. (3.8)

Remove e+e− → ä+ä− → á±á0ßä +ßßä∓ background These events can be

misinter-preted as signal events when the π±_{is misidentified as a lepton. As this is expected to be}

a major source of background, two different handles are used to minimise it. Moreover the approach is useful to eliminate events where the π0_{comes from decay of a charmed}

meson.

Firstly, kinematics of such events offer a powerful way to eliminate them [8]. Let Eτ1, Eτ2 be the energies of the two tau leptons, and Etr1, Etr2 the energies of the two observed tracks coming from the decay of their respective τi. Trivially,

Eτ1 =Eτ2 =ECM/2. (3.9)

If the observed π0_{comes from τ}

1decay, we also have either

Etr1 +Eπ0 ≤ECM/2 (3.10)

or

Etr2 +Eπ0 ≤ECM/2 (3.11)

The corollary of these last two inequalities if that if

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and

Etr2 +Eπ0 >ECM/2, (3.13)

then the π0_{can not come from a τ decay. This was implemented by ordering the tracks by}

measured energy, and requiring that

Esmall+Eπ0 ≥ECM/2 (3.14)

where Esmall is the smallest of the tracks energies.

Secondly, the invariant masses of the two possible π±

π0systems were reconstructed for every identified π0_{by applying a pion mass hypothesis to the muon-identified tracks. The}

invariant mass of these systems was then required to be greater than the τ mass to ensure that the π0_{can’t result from a τ decay through τ}±_→

π±π0ν.

Require reconstructed á0_{’s to have a mass between 100 MeV/c}2_{and 160 MeV/c}2 _{This cut is}

part of the π0_{reconstruction method defined earlier (§3.1.5). It was however implemented}

separately to allow for observation of the photon pair invariant mass spectrum when this requirement is lifted. This distribution is important in the analysis to estimate the num-ber of background-only events, confirm the scaling between data and simulation in the sidebands region, but also to enable detection of possible other new particles that would couple to the τ but with a mass not necessarily close to the π0_mass.

In other words, this requirement is used as a criterion for selecting 1π0_{events and to enable}

plotting of the N−1distributions — when each cut is lifted individually —, but it is not enforced when fitting the mγγdistributions to get the signal yield.

3.3.2 Quantitative assessment of the signal selection on simulation: (N−1) plots

The following plots — figures 3.7 to 3.12 — show the distributions of the kinematic vari-ables before the selection criteria on their value was applied and after all other criteria have been imposed (N−1plots). Data is shown only in the non-signal region for observing the degree of agreement with simulated backgrounds. It is worth noting that histograms for ιS are on a different scale and the actual event rate is 10 times higher than what is read on

the y-axis. Also, no histogram represent π0

HCsignal as it follows the same shape as ιP, but

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legends) to show to which extend re-weighting of the signal events influences the shape of the distributions. (GeV) γ γ E 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Counts / 0.1 GeV 0 10 20 30 40 50 60 70 80 DATAP Signal S Signal × 0.1 PhSp Signal SP µ µ SP τ τ cc SP uds SP B0B0bar SP B+B- SP bhabha SP ) SP stat σ ⊕ data stat σ (Data-SP) / ( -0.5 0 0.5 1 1.5 2

Figure 3.7:Energy of the reconstructed π0 _{(Cut # 3 removed). Signal region is between the}

two vertical lines. Filled histograms correspond to simulated background pro-cesses, line histograms are the simulated signals: P Signal is re-weighted for

pseudo-scalar model, 0.1×SSignal is re-weighted for scalar model and divided

by 10 to allow display in the same plot, PhSp is the pure phase-space model with-out re-weighting.

3.4 Calculation of the yield

3.4.1 Number of candidate events in the data Nsi g =Nsel− Nb kg

This number was determined by fitting a curve near the predicted signal region in the data mγγspectrum.

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distri-Table 3.8: Summary of the signal selection requirements

Cut No _Quantity _Requirement

1 Particle ID (e=0, µ=1) Trk_pid={0,1} ||

Trk_pid={1,0} 2 Number of reconstructed π0_{’s (N}

π0) Nπ0=1

3 Energy of reconstructed π0_(E

π0) 2.2GeV<Eπ0 <4.7GeV

4 Energy of lowest energy track and π0 _E

small+Eπ0 ≥ECM/2

5 Mass of µ-identified track and π0 _m

π±(µ-ID’d)+π0 ≥mτ

6 Mass of the reconstructed π0 † ₁₀₀_MeV/c2_≤_m

γγ≤160MeV/c2

7 Missing transverse momentum (pmiss

⊥ ) pmiss⊥ >0.3GeV/c

†_:_{This requirement is only enforced to plot the N}₋₁_{distributions. Yield calculations use a fit on m}

γγ after

lifting this cut.

(GeV) 0 π + E small E 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Counts / 0.0666667 GeV 0 50 100 150 200 250 300 DATA P Signal S Signal × 0.1 PhSp Signal SP µ µ SP τ τ cc SP uds SP B0B0bar SP B+B- SP bhabha SP ) SP stat σ ⊕ data stat σ (Data-SP) / ( -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Figure 3.8:Energy of lowest energy track and reconstructed π0 _{(Cut # 4 removed). Signal}

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) 2 (GeV/c µ ID's as π , ± π + 0 π M 0 1 2 3 4 5 6 7 8 9 10 2 Counts / 0.1 GeV/c 0 5 10 15 20 25 30 35 40 DATA P Signal S Signal × 0.1 PhSp Signal SP µ µ SP τ τ cc SP uds SP B0B0bar SP B+B- SP bhabha SP ) SP stat σ ⊕ data stat σ (Data-SP) / ( -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

Figure 3.9:Invariant mass of the µ-identified track and π0_{system (Cut # 5 removed). Signal}

region is at the right of the vertical line. See figure 3.7 for details on the legend.

) 2 (GeV/c γ γ M 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 Counts / 0.05 GeV/c 0 100 200 300 400 500 DATA P Signal S Signal × 0.1 PhSp Signal SP µ µ SP τ τ cc SP uds SP B0B0bar SP B+B- SP bhabha SP ) SP stat σ ⊕ data stat σ (Data-SP) / ( -4 -3 -2 -1 0 1 2 3

Figure 3.10:Invariant mass of the reconstructed π0 _{(Cut # 6 removed). See figure 3.7 for}

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) 2 (GeV/c γ γ M 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2 Counts / 0.01 GeV/c 0 20 40 60 80 100 120 140 160 180 200 220 DATA P Signal S Signal × 0.1 PhSp Signal SP µ µ SP τ τ cc SP uds SP B0B0bar SP B+B- SP bhabha SP ) SP stat σ ⊕ data stat σ (Data-SP) / ( -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Figure 3.11:Invariant mass of the reconstructed π0 _{(Cut # 6 removed). Detail of π}0 _mass

peak. Signal region is inside the rectangle. See figure 3.7 for details on legend.

(GeV/c) miss T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Counts / 0.1 GeV/c 0 5 10 15 20 25 30 35 DATA P Signal S Signal × 0.1 PhSp Signal SP µ µ SP τ τ cc SP uds SP B0B0bar SP B+B- SP bhabha SP ) SP stat σ ⊕ data stat σ (Data-SP) / ( 0 0.2 0.4 0.6 0.8 1

Figure 3.12:Missing transverse momentum (Cut # 7 removed). The signal region is at the

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bution is qualitatively represented by

nbkg(m) = p2m2+exp(a+bm) (3.15)

between≈0GeV/c2 and ≈1GeV/c2, where the exponential part describes the decreasing area at the beginning of the spectrum. p2, a and b are free parameters adjusted to each

spectrum. Moreover, figure 3.11 shows good agreement between simulation and data in the sidebands, so the interval

0.05GeV/c2≤mγγ≤0.9GeV/c2

was chosen for the fit in order to measure the background level adequately. Section 4.3.3 provides a study of the background shape using simulation and data sidebands.

The expected signal is the π0_{mass peak, and was approximated by a Gaussian. The}

equa-tion n(m) =nbkg(m) +A exp " −1 2 m−µm σm 2# (3.16) was therefore fitted to the data using ROOT’s TH1F::Fit(), where nbkg(m) comes from

equation (3.15), and A is a scale constant related to the number of selected signal events Nsel, the standard deviation of the peak σm and the bin width ∆m by

Nsel = √

2π Aσm

∆m . (3.17)

In these fits, A was left floating, while µm was constrained in the PDG value [2] plus or

minus 10 MeV/c2_{interval [8].}

0.125GeV/c2≤mγγ≤0.145GeV/c2 (3.18)

This 10 MeV/c2_{was determined as a conservative mass range for the ι}

P and ιS compatible

with the mγγ spectra (∆χ2 . 5 with the best fit value) in reference [11]. The standard

deviation was constrained in the

0.0117GeV/c2≤σm ≤0.0128GeV/c2 (3.19)

range which corresponds to the best fit value on simulated signal π0_{mass peak (see}

fig-ure 4.1) , plus or minus three standard deviations to allow for possible systematic differ-ences between data and simulated samples.

Search for new spin-0 particles near π⁰ mass produced in association with τ pairs at BABAR

Supervisory Committee

Abstract

Contents

List of Figures

List of Tables

Acknowledgements

1

Introduction

1.1

The B

B

experiment

1.2

Pion-photon transition form factor issue

1.3

The research question

1.4

Goals of the project

1.5

Thesis outline

2

Physics motivation and theoretical background

2.1

Meson transition form factors

2.2

Comparing experimental results for the pion-photon transition form

factor

2.3

Motivation of the search: the hypothesis of new pion-like particles

+

momen-

3

Analysis methodology

3.1

B

B

data and background simulation

3.2

Producing simulated signal

3.3

Definition of the signal selection

∑

3.4

Calculation of the yield