Probing CP violation in h→ τ − τ + at the LHC
PProbing CP violation in h → τ − τ + at the LHC Kaoru Hagiwara,
1, 2, ∗ Kai Ma,
3, 1, 4, † and Shingo Mori ‡ KEK Theory Center and Sokendai, Tsukuba, Ibaraki 305-0801, Japan Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA School of Physics Science, Shaanxi University of Technology, Hanzhong 723000, Shaanxi, China Department of Particle and Nuclear Physics, The GraduateUniversity for Advanced Studies (Sokendai), Tsukuba 305-0801, Japan (Dated: November 14, 2018)We propose a novel method to reconstruct event by event the full kinematics of the cascade decayprocess, h → τ + τ − → ( π + ¯ ν )( π − ν ), which allows us to measure the τ + τ − spin correlation, a measureof the CP property of the Higgs boson. By noting that the τ ± momenta lie on the plane spanned bythe accurately measured impact parameter and momentum vectors of charged pions, we can obtainthe most likely momenta of the two missing neutrinos by using the probability distribution functionsof the (cid:126)p/ T vector and the location of the primary vertex. A simple detector level simulation showsan excellent agreement between the reconstructed and the true kinematics, both in the τ + τ − andthe π + π − rest frames. The method can be tested in Z → τ + τ − events, which should exhibit nocorrelation. CP property of the observed Higgs particle h (125) [1, 2]is a window of the physics of mass generation. In generalthe mass eigenstate h (125) can be a mixture of CP-evenand CP-odd scalar particles. While only one CP-evenscalar particle exists in the Standard Model (SM), manyof its extensions not only modify the Higgs couplings togauge bosons and fermions, but also predict additionalscalars and pseudo-scalars. If the Higgs sector is CP con-serving, all the neutral mass eigenstates should have def-inite CP parity. The pure CP eigenstate assumption hasbeen investigated experimentally by both ATLAS andCMS collaborations [3–5], and the CP-odd hypothesis isdisfavored by nearly 3 σ .However, if the h (125) particle is a mixture of the CP-even and CP-odd states, the bound on the mixing pa-rameter is rather weak and a large mixing in the Higgssector is still allowed [6–8]. (For the recent review see [9]and references there in.) There are several channels thatcan be used to measure the CP property of h (125). Thegolden channel h → ZZ ∗ /Zγ ∗ /γ ∗ γ ∗ → ( (cid:96) ¯ (cid:96) )( (cid:96) (cid:48) ¯ (cid:96) (cid:48) ) hasbeen analyzed in Refs. [10–14]. The sensitivity is ratherlow because of the dominance of the tree-level (CP-even) hZZ (cid:63) amplitudes and the small (loop suppressed) hZγ ∗ and hγ ∗ γ ∗ amplitudes. Processes pp → hjj [15], pp → ht ¯ t [16], and h → τ + τ − [17, 18] have also beenanalyzed. In Ref. [19], it was pointed out that thecorrelation between planes spanned by π ± and π fromthe τ ± → ρ ± ν τ → π ± π ν τ decays can be used to mea-sure CP violation, and the experimental sensitivity canbe improved by using the impact parameters [20]. Al-ternatively, without using of the impact parameter, re-construction of the internal substructure of those decaymodes can also enhance the sensitivity [21].In Ref. [22], the 3-prong decay mode of tau was pro-posed to measure CP violation, for which the tau mo-mentum direction can be reconstructed directly, but thesensitivity is low, because of small 3-prong decay rate and the necessary spin projection to the longitudinal po-larized state. In Refs. [23–25], a new observable madeof the impact parameters and the momenta of chargeddecay products was proposed.In this letter we report our study on the process pp → h → τ + ( π + ¯ ν τ ) τ − ( π − ν τ ), in which the impact parametervectors of the π + and π − in τ + and τ − decays are usedto reconstruct event by event the full kinematics.In the analysis below we assume for simplicity the mea-sured Higgs particle h (125) is a mixture of CP-even andCP-odd scalars, denoted by H and A respectively, h = cos ξ H + sin ξ A , (1)where ξ is the Higgs mixing angle that has been assumedto be real. We also assume the Yukawa interactions of H and A with tau-lepton pair are CP conserving, L = − g Hττ H ¯ τ τ − ig Aττ A ¯ τ γ τ , (2)such that the only source of CP violation is in the mixing(1). The interactions between the mass eigenstate h (125)and the tau-lepton pair are then described as L = − g hττ h (cid:0) cos ξ hττ ¯ τ τ + i sin ξ hττ ¯ τ γ τ (cid:1) , (3)where g hττ = (cid:112) ( g Hττ cos ξ ) + ( g Aττ sin ξ ) , (4) ξ hττ = tan − [( g Aττ /g Hττ ) tan ξ ] , (5)are, respectively, the magnitude and the CP-odd phaseof the hτ ¯ τ coupling. Although the CP-violating inter-actions alter the branching ratios. However, we use inthis report the SM branching ratio of B ( h → τ + τ − ) =6 .
1% [26] to estimate the experimental sensitivity. Itwas shown in Ref. [21] that experimental sensitivity of∆ ξ hττ is about 0 . − . The sensitivity can reach 0 .
05 for ILC at √ s = 500GeV with 1 ab − [25]. a r X i v : . [ h e p - ph ] A p r In our approximation of neglecting potential CP viola-tion in τ decays, the CP-odd spin correlation of τ + and τ − can be measured by studying their decay correlations.One of the observables with maximum sensitivity to thespin correlation is the azimuthal angle correlation in theHiggs rest frame, which has a simple form,1Γ d Γ dφ = 12 π (cid:18) − π
16 cos( φ − ξ hττ ) (cid:19) , (6)in the m τ /m h → φ is the azimuthal angleof π − about the τ − momentum as the z -axis, when the x -axis is chosen along the π + transverse momentum. Ex-actly the same distribution (6) is found for the azimuthalangle φ of τ − momentum in the π + π − rest frame, wherethe z -axis is along the π − momentum and the x -axis isalong the τ + transverse momentum. The advantage ofthe latter frame is that the z -axis can be directly re-constructed by the accurately measured π + and π − mo-menta. In both frames, we should determine the τ ± mo-menta (cid:126)p τ ± accurately.If the π ± momenta are measured accurately, two pa-rameters of the τ ± momenta can be determined by usingthe on-shell conditions. We take remaining four param-eters as the magnitude of the momentum vector of taus, | (cid:126)p τ ± | , and the azimuthal angle of the taus, φ τ ± , in thelab frame where the pion momentum, (cid:126)p π ± , is along the z (polar)-axis and the x ( p xτ ± = 0)-axis in the scatteringplane spanned by the beam and the π ± momenta.If we constrain the sum of the transverse momenta ofthe two neutrinos by the observed missing transverse mo-mentum, the most likely values of p τ ± distributes aroundtheir true values, allowing us to estimate the invariantmass of tau pair, m ττ (cid:39) | (cid:126)p τ − || (cid:126)p τ + | (1 − cos( θ π + π − )) inthe collinear approximation [27]. However, the optimalvalues of the azimuthal angle, φ τ ± , show virtually no cor-relation with their true values [41]. The azimuthal anglecorrelation (6) in the π + π − rest frame is smeared out.Fortunately, the τ ’s from Higgs decay have large de-cay lengths | (cid:126)l τ ± | , typically of cτ τ ( m h / m τ ) ∼ . (cid:126)b π ± of π ± can bemeasured with a significant efficiency, providing us withthe desired construction of the azimuthal angle, φ τ ± , inthe lab frame.For single tau decay, τ − → π − ν τ , once the impactparameter vector (cid:126)b π − is measured, the decay plane is ac-curately determined by (cid:126)b π − and (cid:126)p π − , which are orthog-onal (cid:126)b π − · (cid:126)p π − = 0. The τ momentum (cid:126)p τ − should lie onthis plane and the opening angle between (cid:126)p τ − and (cid:126)p π − isconstrained by the on-shell conditioncos θ τ − π − = 2 E τ − E π − − m τ − m π − | (cid:126)p τ − || (cid:126)p π − | , (7)where | (cid:126)p τ − | is the only unknown. The orientation of the τ − momentum can be solved directly (cid:126)p τ − | (cid:126)p τ − | = (cid:126)b π − + | (cid:126)b π − | tan θ τ − π − (cid:126)p π − | (cid:126)p π − | (cid:12)(cid:12)(cid:12)(cid:12) (cid:126)b π − + | (cid:126)b π − | tan θ τ − π − (cid:126)p π − | (cid:126)p π − | (cid:12)(cid:12)(cid:12)(cid:12) , (8)where the sign of the second term is fixed by the condition( (cid:126)p τ − · (cid:126)p π − ) > . The same applies for τ + → π + ¯ ν τ decay,leaving only two free parameters | (cid:126)p τ − | = p τ − and | (cid:126)p τ + | = p τ + to reconstruct the full kinematics of the process.It is at this stage we impose the (cid:126)p/ T constraint with theprobability distribution function (PDF), ρ (cid:126)p/ T ( p τ ± ) = 1 N exp (cid:20) −
12 (∆ (cid:126)p/ T ( p τ ± )) T V − (∆ (cid:126)p/ T ( p τ ± )) (cid:21) , (9) V = R ( φ (cid:126)p/ T ) σ (cid:126)p/ T | (cid:126)p/ obs T | σ φ (cid:126)p/T R − ( φ (cid:126)p/ T ) , (10)where N = 2 π √ det V , for the ∆ (cid:126)p/ T ( p τ ± ) = (cid:126)p/ T ( p τ ± ) − (cid:126)p/ obs T is the difference between the observed and the ex-pected (cid:126)p/ T vectors, R ( φ ) is the rotation about the beam( z )-axis. This PDF measures the likelihood that the ob-served (cid:126)p/ obs T is compatible with the sum of (cid:126)p ν + (cid:126)p ¯ ν , whichis a function of p τ ± . Here, the (cid:126)p/ T resolution is repre-sented by the covariance matrix V , which is, in principle,estimated on an event-by-event basis in the detector-levelsimulation, following the algorithm of [28].Below we explain how we simulate the process pp → h → τ + τ − → ( π + ¯ ν τ )( π − ν τ ). The events are generatedat LO for √ s = 14 TeV by using MadGraph5 [33]. TheHiggs production process is simulated by the HC modelfile [34], and the τ + τ − spin correlation is obtained byusing the TauDecay package [35]. The generated eventsare then showered by Pythia8 [36], and the detector ef-fects are simulated by using Delphes3 [37]. The jets areclassified by using the FastJet package [38] with anti- k T algorithm and a distance ∆ R = 0 . τ -jets are tagged by using the Delphes3 algorithmwhich has a reconstruction efficiency of about 0 . . Z → τ + τ − events. We multiply this ef-ficiency by the τ -identification efficiency which is about0 . π ± momenta are chosen as the exactin first, and then smeared by using the current resolu-tions of tracks [39]. The magnitudes of π ± momenta aresmeared to be the corresponding τ -tagged jets momen-tum. Using tracks inside of the τ -tagged jets is essentialbecause the soft particles inside of the τ ± -tagged jetscould completely wash out the relative orientation be-tween τ ± and π ± .The observed missing transverse momentum (cid:126)p/ obs T iscalculated on an event-by-event basis by using theDelphes3. We determine the resolution of the missingtransverse momentum σ (cid:126)p/ T and its azimuthal angle σ φ (cid:126)p/T by comparing the sum of neutrino momenta at partonlevel with the observed (cid:126)p/ T and φ (cid:126)p/ T at detector level. Wehave checked these errors are consistent with those cal-culated from errors of all visible tracks [41].The exact impact parameter vectors (cid:126)b π ± are derivedusing exact decay length vectors of tau (cid:126)l τ ± given byPythia8. For those events with p τ ∼ m h /
2, we find theimpact parameter distribution to be exponentially fallingwith the mean of | (cid:126)b π ± | ∼ µ m. In practice, the loca-tion of the primary vertex is not known accurately [39],and we should compute the impact parameter vectorsfrom the most likely location at the primary vertex. Al-though the error might be smaller for those events withtwo isolated π + and π − trajectories that we study, weintroduce a Gaussian smearing distribution with resolu-tions σ b T = 20 µ m and σ b Z = 40 µ m in the transverseand in the beam directions [39]. Therefore, we obtain thesmeared impact parameter vectors (cid:126)b obs π ± from exact decaylength vectors (cid:126)l τ ± and the smeared primary vertex.For background, we consider here only the dominantirreducible process, pp → Z → τ τ . Fake backgroundsfrom QCD jets may also contribute. It is shown inRef. [30] that at √ s = 7 , √ s = 14TeV, those values may grow, but since we em-ploy only the double single π decay modes and since thefake background does not give azimuthal angle correla-tion, we believe that our estimate based on Z → τ τ isvalid especially after improving the impact parametercuts. The efficiencies and number of events are sum-marized in Table I. The production cross sections of thesignal σ ( pp → h + anything) = 62 . σ ( pp → Z + anything) = 62 . . × and 7 . × events for the signal ( h → τ + τ − → π + π − ν ¯ ν ) and the background ( Z → τ + τ − → π + π − ν ¯ ν )at 3 ab − , respectively. The double tau-tag efficiency isabout (0 . × . ∼ . . × . ∼ . | (cid:126)p obs π ± ,T | , | η obs π ± | , and | (cid:126)p/ obs T | reduce the events by a factorof 0 .
18 for the signal and 0 .
01 for the background.It is these selected events we find the most likely valuesof p τ − and p τ + by using the smeared (cid:126)b π ± vectors and thePDF (9) of the missing p T vector. The method gives agood resolution for the invariant mass of the τ -pair [41],(other method for the mass reconstruction can be foundin Refs. [30–32]), and we impose | m obs ττ − m h | <
10 GeV.We find that 0 .
49 of signal survives the cut, while thebackground is suppressed by 0 . φ rec distribution of Z → τ + τ − → π + π − ν ¯ ν events is shown, where the black-solidline is obtained after the smearing in the impact param-eter vector is introduced. The pink-dotted line is found TABLE I: Efficiency and expected number of events for thesignal process pp → h → τ + τ − → ( π + ¯ ν τ )( π − ν τ ), and themajor irreducible background process pp → Z → τ + τ − → ( π + ¯ ν τ )( π − ν τ ), at 14 TeV with an integrated luminosity3 ab − . Eff. Evt.( h ) Eff. Evt.( Z )No cuts 1 .
000 1 . × .
000 7 . × tau-tag 0 .
225 3 . × .
120 8 . × | η obs π ± | < . | (cid:126)p obs π ± ,T | ) >
15 GeVmax( | (cid:126)p obs π ± ,T | ) >
35 GeV | (cid:126)p/ T | >
45 GeV 0 .
180 5 . × .
010 8 . × | m ττ − m h | <
10 GeV 0 .
492 2 . × .
075 6 . × min( | (cid:126)b obs π ± ,T | ) > µ m 0 .
150 422 0 .
240 1 . × (rec) fD - - - fD ( / N ) d N / d FIG. 1: The reconstructed azimuthal angle distribution of Z → τ + τ − events after the smearing in the impact parame-ter. The black-solid line denotes the case without | (cid:126)b obs π ± ,T | cut,the pink-dotted line denotes min( | (cid:126)b obs π ± ,T | ) > µ m, and thegreen-solid line shows min( | (cid:126)b obs π ± ,T | ) > µ m. The data pointscorrespond to an integrated luminosity 3 ab − . after imposing the cut | (cid:126)b obs π ± ,T | > µ m, and the green-solid line for | (cid:126)b obs π ± ,T | > µ m. After the last cut thedistribution becomes flat as the theoretical prediction.This is because those events whose true | (cid:126)b π ± | are smallerthan experimental resolution cannot be resolved, andour reconstruction procedure via Eq. (8) tends to give∆ φ rec ∼ | (cid:126)b true π ± | (cid:28) | (cid:126)b obs π ± | [41].Fortunately, as is shown in Fig. 1 this systematic bias canbe reduced by applying cuts on | (cid:126)b obs T | . As shown in thebottom line of Tab. I, the efficiency of impact-parameterscut for the Higgs decay 0 .
15 is smaller than the one for Z → τ + τ − → π + π − ν ¯ ν events 0 .
24 at 14 TeV because themomentum of the softer π ± is lower for the signal thanthe background after the | m obs ττ − m h | <
10 GeV cut, dueto the chirality flipping nature of the hτ ¯ τ coupling [41].In the end, we find S/ √ S + B ≈ . π + π − rest framebetween the true and reconstructed azimuthal angle forthe SM Higgs boson, i.e. ξ hττ = 0, after the cut (true) fD - - - (r e c ) fD - - - FIG. 2: Correlations between the true and reconstructed az-imuthal angle difference for the SM Higgs ( ξ hττ = 0) after thecut | (cid:126)b obs π ± ,T | > µ m. The 422 data points correspond to anintegrated luminosity 3 ab − . | (cid:126)b obs π ± ,T | > µ m. The reconstructed ∆ φ distributesaround the true value within about π/ φ (true) values. We find that the ∆ φ (rec)-∆ φ (true)agreement is worse [41] in the τ + τ − rest frame, becausethe reconstructed τ ± momenta have relatively larger er-ror. We, therefore, propose to use the π + π − rest frameto study the decay plane correlation. Shown in Fig. 3 arethe reconstructed ∆ φ distribution of the signal events forthe SM ( ξ hττ = 0) in blue-solid and for maximum CP vi-olation ( ξ hττ = π/
4) in pink-dashed lines, after the cut | (cid:126)b obs π ± ,T | > µ m is applied. We can measure clearly CPviolation as a phase shift in the ∆ φ distribution (6), ifthe background is absent.Fig. 4 shows histograms of ∆ φ rec for signal, back-ground and their sum after the cut | (cid:126)b obs π ∓ ,T | > µ m. Theblue-solid and pink-dashed lines denote the signal eventsfor ξ hττ = 0 and π/
4, respectively. The green-solid lineshows the background events. The red-solid and -dottedcurves show our fit to the sum of background and signalevents for ξ hττ = 0 and ξ hττ = π/
4, respectively. Thefit function is simply the sum of the function (6) and (rec) fD - - - fD ( / N ) d N / d FIG. 3: Distributions of the reconstructed azimuthal angledifference for the h → τ + τ − → π + π − ν ¯ ν events with ξ hττ =0 (blue-solid line) and ξ hττ = π/ | (cid:126)b obs π ± ,T | > µ m. The data points correspond to anintegrated luminosity 3 ab − . (rec) fD - - - / b i n p = fD N pe r FIG. 4: The ∆ φ rec distribution of the signal and backgroundand the result of fitting. The blue-solid line show the signalevents of ξ hττ = 0, the green-solid line shows the backgroundevents. The red-solid histogram shows their sum. The red-solid curve shows our fit. The dashed line and histogramsare for ξ hττ = π/
4. In both cases, we use the same back-ground events. We require | (cid:126)b obs π ∓ ,T | > µ m. The data pointscorrespond to an integrated luminosity 3 ab − . the constant background, where their normalizations andthe phase shift, ξ hττ in Eq. (6), are fitted to the binneddata as shown by the red histograms in Fig. 4. We findfor ξ true hττ = 0 and π/
4, respectively, ξ hττ = 0 . ± . χ / d . o . f = 14 . /
9, and ξ hττ = 0 . ± .
18 at χ / d . o . f = 13 . /
9. We checked the result is stableunder the change of bin size.The sensitivity of ∆ ξ hττ ≈ . τ + τ − → π + π − ν ¯ ν mode only is encouraging. And what is more, wefind that the kinematical correlation as shown in Fig. 1can be parametrized as a function of the cut-off param-eter, min( | (cid:126)b obs π ± | ). By modifying the fitting function toaccount for the kinematical bias, we find significant im-provements in the ∆ ξ hττ accuracy of possibly a factor of10, details of which will be reported elsewhere [41]. Webelieve that the method can be tested and improved byusing the side bands, e.g. for those events which satisfy | m obs ττ − m Z | <
10 GeV or m obs ττ >
150 GeV, which aredominated by Z → τ + τ − background.In summary, by employing the impact parameter vec-tors of π ± trajectories, we propose a novel method tomeasure the CP violation in h → τ + τ − → π + π − ν ¯ ν .Even through only part of the kinematical informationof tau leptons is stored in the π ± momenta and the im-pact parameters, (cid:126)p π ± and (cid:126)b π ± , the spin correlation canstill be measured by maximizing the probability densities,Eq. (9), for the missing transverse momenta, (cid:126)p/ T . We findan excellent agreement between the reconstructed andtrue kinematics in the π + π − rest frame, by using the typ-ical experimental resolutions of the LHC detectors. Theexperimental sensitivity is estimated to be ∆ ξ hττ ≈ . − at √ s = 14 TeV. Acknowledgements
K.H. is supported in part by the William F. Vilas TrustEstate, and by the U.S. Department of Energy under thecontract DE-FG02-95ER40896. K.M. is supported by theChina Scholarship Council, and the National Natural Sci-ence Foundation of China under Grant No. 11647018,and partially by the Project of Science and Technol-ogy Department of Shaanxi Province under Grant No.15JK1150. ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected][1] G. Aad et al. . (ATLAS Collaboration), Phys. Lett.
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