Tau Physics at SuperB

A.Lusiania∗

aScuola Normale Superiore and INFN, Pisa, Italy

The BABAR and Belle B-factories, which ended data-taking in the recent years, have analysed large samplesof tau pairs produced in e+e− annihilations at and around the Υ (4S) peak to test the Standard Model and tosearch for signs of New Physics. With the goal of producing 100 times larger tau pairs samples, the proposedSuperB Super Flavor Factory will provide several unique opportunities to verify the Standard Model and to lookfor signs of theories beyond it.

1. THE SuperB PROJECT

A high luminosity e+e− Super Flavor Factorywith a luminosity ∼100 times higher than theBABAR and Belle B-factories would be a power-ful tool to test the Standard Model (SM) and tosearch for New Physics (NP) with several uniquefeatures, which are complementary to high energypp machines, the ILC and other smaller scale highenergy physics experimental enterprises such asMEG [1]. The SuperB project [2] proposes toachieve the required luminosity of 1036 cm−2s−1

using about the same electrical power of the exist-ing B-factories and exploiting unprecedented lowemittance beams [3] such as those that are beingstudied for the ILC. SuperB would be an asym-metric e+e− collider at and around the Υ (4S)peak like BABAR, Belle and the companion similarproject Belle II, but will have two additional fea-tures: it will be possible to have an 80%-polarizedelectron beam, and to lower the center-of-massenergy at the charm and tau thresholds. Thebaseline design is aimed at collecting 15 ab−1 ofluminosity per-year, corresponding to a total of75 ab−1 in 5 years.While the B-factories were primarily aimed at

precision measurements of CP violation in the Bsector, they proved to be effective also for tauphysics and NP searches. SuperB and Belle II willbe the best facilities for tau physics measurementsin the medium term both for precision measure-ments and for NP searches; the LHC experiments

∗representing the SuperB collaboration.

offer no actual competition in this area and, withrespect to Belle II, SuperB will have the advan-tages provided by polarized beams, especially use-ful for Lepton Flavor Violation (LFV) searches,and for the measurement of the tau g−2, EDMand CP violation (CPV ) in the decay.

2. LEPTON FLAVOR VIOLATION INTAU DECAYS

LFV tau decays are allowed in the SM onceneutrino masses and mixing are introduced, butare suppressed to undetectable levels [4] by theexperimental bounds on neutrino mass differ-ences. Most NP models predict much largerrates up to the existing experimental bounds [5].Some of the most straightforward models be-yond the SM, minimal Supersymmetry (MSSM)and Non-Universal-Higgs-Masses Supersymmetry(NUHM), predict tau LFV rates that are ob-servable at SuperB in part of their parameterspace [6,7]. MSSM models predict that LFV oc-curs mainly through slepton mixing and that thelargest tau LFV branching ratio is τ → μγ; wefound that this mode is the most powerful Su-perB probe for LFV NP even if the experimen-tal sensitivity is better for other modes such asτ → 3� with � = e, μ and τ → μη. In NUHMmodels with large tanβ and relatively light Higgsmasses, Higgs-mediated LFV can become impor-tant and cause rates for τ → μρ, τ → μη andτ → μf1(980), f1(980) → π+π− to be close orslightly larger than τ → μγ [8], and hence more

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www.elsevier.com/locate/npbps

doi:10.1016/j.nuclphysbps.2011.06.054

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BR

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→ e

γ)

BR (τ → μ γ)

SPS 1amN1 = 1010 GeV, mN2 = 1011 GeVmν1 = 10-5 eV0 ≤ |θ1| ≤ π/4

0 ≤ |θ2| ≤ π/4θ3 = 0

mN3 = 1012 GeVmN3 = 1013 GeV

mN3 = 1014 GeV

θ13 = 1°θ13 = 3°θ13 = 5°θ13 = 10°

mN3 = 1012 GeV

Figure 1. B(τ → μγ) vs. B(μ → eγ) in SPS 1a,for three reference values of the heavy right-handed neutrino mass and several values of θ13.The horizontal dashed (dotted) line denotes thepresent experimental bound (future sensitivity)on B(μ → eγ). All other relevant parameters areset to the values specified in Ref. [6].

experimentally powerful with SuperB. Rates ofτ → 3� comparable or larger than τ → μγ canalso happen in non-SUSY NP frameworks, suchas Little Higgs models with T parity (LHT) [5].For the MSSM with parameters set to the Snow-mass benchmark point SPS 1a [9], figure 1 showsthe complementarity of τ → μγ with μ → eγfor the purpose of constraining the NP parame-ter space, a feature that holds for a large varietyof NP models.The SuperB sensitivity for tau LFV searches

can be estimated from the published BABAR anal-yses. To a first approximation, the SuperBdetector will have performances comparable toBABAR, except for momentum and vertex reso-lution, which will be significantly better thanksto an additional silicon layer close to the interac-tion region [10]. Furthermore, improvements inphoton detection efficiency could be of the orderof 20%.LFV searches count candidates and look for an

excess over the expected background. By run-ning a BABAR analysis unchanged on a larger sta-

tistical sample, all expected upper limits scalewith at least the square root of the luminosityincrease (∝1/

√L). BABAR tau LFV searches areoptimized for the best expected upper limits, i.e.to a first approximation by maximizing the signalefficiency while keeping the expected backgroundevents of the order one or less, when the analysisis not background dominated. If it is possible tomaintain the BABAR efficiencies while keeping theexpected amount of background events negligible,then the LFV sensitivity will scale linearly withthe integrated luminosity (∝1/L). According toour studies, approximately linear scaling appearspossible for tau LFV decays into three leptons,or into a lepton and two hadrons in the finalstate (where the two hadrons may come through ahadron resonance). On the other hand, searchesfor τ → �γ suffer higher backgrounds and scaleapproximately like ∝1/

√L.The SuperB sensitivity for τ → μγ and τ → eγ

has been estimated starting from the BABAR sen-sitivity in Ref. [11] for the cut&counting search ina 2σ region in the ΔM−ΔE plane. It is assumedthat the improved tracking resolution will reducethe signal region by 35% and that the signal ef-ficiency will be 20% higher. A different strat-egy has been used to extrapolate from BABARand SuperB for the τ → 3� LFV search: theBABAR analysis has been re-optimized in order toget the lowest expected 90% CL upper limit withthe 75 fb−1 SuperB design integrated luminosity.For these channels, no improvement has been as-sumed for the experimental resolutions and effi-ciencies. Fig. 2 shows the SuperB extrapolatedsensitivities for τ → 3� compared with the linearand square-root extrapolations.

In both LFV searches, beam polarization is use-ful to increase the sensitivity for specific NP mod-els, since the polarized tau leptons in the finalstate will be associated to distinctive decay an-gular distributions; studies are ongoing to quan-tify the gain. Beam polarization will also pro-vide the ability to discriminate between NP mod-els for tau LFV production through the measure-ment of the angular distributions of the tau de-cay products [12,11]. Table 1 summarizes the ex-pected SuperB sensitivities. The figures can becompared with MSSM predictions at the refer-

A. Lusiani / Nuclear Physics B (Proc. Suppl.) 218 (2011) 335–340336

Figure 2. Expected SuperB 90% CL upper limitsfor τ → ��� LFV decays compared with the mostrecent BABAR expected upper limits. The upperand lower bands indicate the 1/

√L and 1/L ex-trapolations, respectively.

Table 1Expected 90% CL upper limits and 3σ evidencereach on LFV decays with 75 ab−1.

ProcessExpected 3σ evidence

90%CL upper limit reachB(τ → μγ) 2.4 · 10−9 5.4 · 10−9

B(τ → e γ) 3.0 · 10−9 6.8 · 10−9

B(τ → ���) 2.3−8.2 · 10−10 1.2−4.0 · 10−9

ence SPS points in the range of 0.02−97 · 10−9

for B(τ → μγ) and up to 2.2 · 10−10 for B(τ →μμμ) [11].

3. TAU g−2

The precise experimental measurement ofthe muon anomalous magnetic moment aμ =(gμ−2)/2 disagrees by about 3σ with the SM pre-diction [13]: Δaμ = aexpμ − aSMμ ≈ (3± 1)× 10−9.If the discrepancy is explained by the NP ef-fects of the MSSM with tanβ >∼ 10 and μ > 0, amuch larger effect is predicted for the tau anoma-lous magnetic moment, Δaτ/Δaμ ∼ m2

τ/m2μ, i.e.

Δaτ ≈ 10−6.The tau g−2 influences both the angular dis-

tribution and the polarization of the tau pro-duced in e+e− annihilations, and both featuresare experimentally accessible by measuring thetau decay products angular distributions. Po-larized beams enhance significantly the experi-mental sensitivity: with a 100% polarized elec-tron beam, Ref. [14] estimates that SuperB with75 ab−1 will measure the real and imaginary partof the g−2 form factor at the Υ (4S) with experi-mental resolutions in the range [0.75−1.7] ·10−6.Two measurements of the real part of g − 2 areproposed: one fitting just the polar angle distri-bution of the tau leptons, and one based on themeasurement of the transverse and longitudinalpolarization of the tau from the angular distribu-tion of its decay products. All events with tauleptons decaying either in πν or ρν are consid-ered, but no detector effects are accounted for.Preliminary investigations assuming 80%

eletron beam polarization, realistic detector ef-ficiencies and efficiencies uncertainties, and theinclusion of all tau decay channels, estimate thatthe real part of the aτ (q) form factor can be mea-sured with a statistical error of 2.4 · 10−6. At thetau mass momentum scale, the high-energy NPcontributions are with good approximation thesame as for the zero-momentum-transfer tradi-tional, ΔaNP

τ (mτ ) ≈ ΔaNPτ (0). Systematic effects

from reconstruction uncertainties are expected tobe one order of magnitude lower than the sta-tistical precision. Thus the estimated SuperBresolution is comparable to the MSSM contribu-tion required to explain the muon discrepancyand about 1% of the SM-predicted tau magneticanomaly [15].

4. TAU EDM

Within the SM, the tau EDM is predicted tobe very small and experimentally inaccessible;on the other hand NP contributions are severelyconstrained by the stringent experimental upperbound on the electron EDM, de < 1.6 ·10−27 e cmat 90% CL [16]. Under rather general condi-tions, the electron bound limits the tau EDM todτ <∼ 10−22 e cm [11].

A. Lusiani / Nuclear Physics B (Proc. Suppl.) 218 (2011) 335–340 337

Like the tau g−2, the tau EDM influences boththe angular distributions and the polarization ofthe tau produced in e+e− annihilation. Witha polarized electron beam, one can reconstructobservables from the angular distribution of theproducts of a single tau decay that unambigu-ously discriminate between the contribution dueto the tau EDM and other effects [17,18]. Accord-ing to Ref. [17], SuperB with 75 ab−1 can mea-sure the real part of the tau EDM form factorwith a resolution of ΔRe{dτ} = 7.2 · 10−20 e cm,assuming a 100% polarized electron beam collid-ing with unpolarized positrons at the Υ (4S) reso-nance, and a perfect reconstruction of all τ → πνand τ → ρν decays.That sensitivity estimate has been refined with

assumptions more close to the experimental real-ity:

• electron-beam linear polarization 80%±1%,

• 80% geometric acceptance,

• track reconstruction efficiency 97.5%±0.1%(similarly to that achieved in LEP analy-ses [19] and BABAR ISR analyses [20].

The perfect reconstruction of the tau direction isstill assumed. The tau EDM resolution is esti-mated to be ≈ 10 · 10−20e cm, corresponding toa tau angular distribution asymmetry of 3 · 10−5.Uncertainties on track reconstruction efficienciesdo not systematically limit the measurement, ac-cording to the simulations. Since also tau decaymodes other than τ → (π, ρ)ν can be used, with atheoretically equivalent statistical power [21], onecan further improve the above mentioned resolu-tion.The tau EDM can also be measured on tau

pairs that are produced by unpolarized beams,by measuring the correlations of the angular dis-tributions of both tau leptons in the same events.In this case the experimental resolution is worsebecause of the statistical dilution that arises bymeasuring one tau polarization from the angu-lar distribution of its decay products to deter-mine through entanglement the polarization ofthe other tau. Belle has published such a mea-surement [22], confirming that all tau decays, in-cluding the leptonic decays with two neutrinos,

provide statistically useful information. With29.5 fb−1 of data, the experimental resolution onthe real and imaginary parts of the tau EDM is1.7 ·10−17 e cm and 0.86 ·10−17 e cm, respectively,including systematic effects. An extrapolation toSuperB with a data sample of 75 ab−1 (assum-ing systematic effects can be reduced according tostatistics) corresponds to an experimental sensi-tivity of 34·10−20 e cm and 17·10−20 e cm, respec-tively, a two orders of magnitude improvement.

4.1. CP Violation in tau decayNo CP violation has been observed yet in the

lepton sector, and in general CP asymmetry ratesin tau decays are expected to be very small (e.g.order of 10−12 in τ± → K±π0ν [23]). TheSM predicts a small but measurable CP asym-metry of 3.3 · 10−3 ± 2% relative for the decayτ± → KSπ

±ν [24]. The measurement of this lastasymmetry can serve as a calibration measure-ment for searches for effects in other tau decaysand any observed deviation from expected asym-metries in tau decays would indicate the existenceof NP.

Most of the known NP models cannot gener-ate observable CP -violating effects in tau decays(see e.g. Ref. [5]). The only known exceptions areR-parity violating SUSY [25,26] or specific non-supersymmetric multi-Higgs models [27–30]. Insuch frameworks, the NP contributions in tau de-cay can be significant and in some cases the CPasymmetries or the T -odd CP -violating asymme-tries in the angular distribution can be enhancedup to the level of 10−1. Such enhancements fromNP are compatible with limits from other observ-ables, and saturate at the experimental limits ob-tained by CLEO [31]. In particular, sizable asym-metries can be produced in the decays τ → Kπντ ,τ → Kη(′)ντ , and τ → Kππντ [25,27–30].

The CLEO collaboration has published asearch for CP violation in tau decay [31], look-ing for a tau-charge-dependent asymmetry of theangular distribution of the hadronic system pro-duced in τ → KSπν. The Cabibbo-suppresseddecay mode into KSπν is considered because itwould be affected by a larger mass-dependentHiggs coupling. In the CLEO analysis, eventsin the sidebands of the KS mass distribution are

A. Lusiani / Nuclear Physics B (Proc. Suppl.) 218 (2011) 335–340338

used to calibrate the detector response, assumingthere is no CPV in the τ → πππν mode. Usinga data sample of 13.3 fb−1 (12.2 · 106 tau pairs),CLEO measures the mean of the optimal asym-metry observable 〈ξ〉 = (−2.0± 1.8) · 10−3. Sincethis analysis relies on real data for detector re-sponse calibration, we can assume that SuperBwith 75 ab−1 would not be limited by systemat-ics and could reach an experimental sensitivityΔ 〈ξ〉 ≈ 2.4 · 10−5.

5. SUMMARY

The SuperB project aims at collecting 75 ab−1

of e+e− collisions with an 80% polarized electronbeam at the Υ (4S) peak in 5 years, providinginteresting opportunities to test the SM and tosearch for NP in tau production and decay.Searching for LFV in tau decays is a distinc-

tively clean and powerful tool to detect NP ef-fects and to provide information on the featuresof NP models. In this area SuperB explores phe-nomena no other running or planned facility otherthan a Super Flavour Factory can investigate; fur-thermore tau LFV searches are complementary tomuon LFV searches pursued by MEG and othermuon LFV future projects for the purpose of iden-tifying many of the most viable NP models.The large and clean tau samples provided by

SuperB permit to extend the experimental knowl-edge by about two orders of magnitude in themeasurement of the fundamental properties of thetau lepton, the g−2 and the EDM form factors.NP models meant to explain the present muong−2 discrepancy between theory and experimentpredict a larger deviation of the tau g−2 with re-spect to the SM prediction, which is close the theestimated SuperB experimental resolution.By measuring the angular distribution and

charge asymmetries of the tau decay products,SuperB can extend the experimental constraintson CP violation in tau decay by about two ordersof magnitude, with the ability to detect NP ef-fects from specific models that otherwise satisfythe known observations.For all the above mentioned observations, the

quantum entanglement of the initial τ+τ− stateand the further definition of the initial collid-

ing e+e− state with the electron beam polariza-tion provides significant additional experimentalreach. Overall, SuperB will be able to probe animportant part the parameter space of the mostviable NP scenarios, in a complementary and of-ten distinctive way with respect to the presentlyrunning and planned high energy physics facili-ties.

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