Measurement of the Beam Polarization Using Single-Boson Processes at - - PDF document

Measurement of the Beam Polarization Using Single-Boson Processes at e−e+ Linear Colliders

Graham W. Wilson University of Kansas, Dept. of Physics and Astronomy, Malott Hall, Lawrence KS 66045, USA Standard model physics processes involving the production of single bosons (γ, W−, W+ and Z) accompanied by missing transverse momentum are investigated as a way to precisely measure the absolute beam polarization in collision at CLIC and ILC. At high energy these processes are dominated by contributions involving the V-A structure of the W-e-ν coupling and can thus provide high purity samples of collision events with known helicity structure leading to measurement of the beam polarization at the per mille level.

1 Introduction

One of the unique strengths of e−e+ linear colliders is the expected ability to provide high longitudinal polarisation of the electron beam and also to longitudinally polarise the positron

• beam. This leads to a direct way to explore e−e+ collisions with potentially all four helicity

combinations: e−

L e+ R, e− Re+ L , e− L e+ L and e− Re+ R, henceforth denoted LR, RL, LL, RR collisions.

It is expected that three methods to measure the beam polarization after acceleration to collision energy may be available: upstream and downstream Compton polarimetry and by using suitable physics events in collision. All three are expected to be useful for ILC [1] with the upstream polarimeter expected to have the highest counting rate, the downstream polarimeter can measure the depolarization in the interaction, and the collision data should provide an absolute calibration. For CLIC, a downstream polarimeter is currently excluded. Previous studies for ILC [2] have focussed on two methods for measuring the beam polarisation from collision data: i) using the Blondel scheme with both beams polarised and using two-fermion annihilation events and ii) using W-pair production which needs only electron beam polarisation. Both physics processes used have cross-sections which scale as 1/s. This study investigates the measurement of beam polarisation from collision data using single-boson processes which are particularly suited to high energy e−e+ collisions. There are four main processes which depend on the well-known pure V-A W-e-ν coupling: WW, single-photon, single-W and single-Z productiona. The single-boson processes are t-channel dominated processes with cross-sections which grow rapidly with √s in contrast to WW which falls as 1/s. It is expected that these processes and this study will be especially pertinent to CLIC and so in the first instance the studies have been carried out for 3 TeV CLIC. For definiteness, the basic single-boson processes of interest are:

• Single-photon: e−e+ → γνeνe
• Single-W−: e−e+ → W−e+νe
• Single-W+: e−e+ → W+e−νe

aFor this purpose we are considering Zνeνe and not Ze−e+

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• Single-Z: e−e+ → Zνeνe

The three different types of single-boson process are complementary and are discussed in detail in the following sections. The single-photon and single-Z processes only occur through LR (dominant) and RL helicity combinations. The single-W process has some unique features: the W charge can essentially tag the helicity of the corresponding beam particle and the LL (for W−) and RR (for W+) cross-sections are of the same order as the normally dominant LR cross-section. Basically single-W− is produced by left-handed electrons and single-W+ is produced by right-handed electrons and the process allows either helicity for the other beam particle. For now, the studies have focussed on the leptonic W and Z decays. In the single-W case, the experimental topology is a single lepton with missing transverse momentum where the ”beam-electron” escapes detection at low polar angle. The three processes experimentally consist of: photon + ET , lepton + ET , di-lepton + ET , and can be selected with high purity by placing suitable cuts on the kinematics

• f the observed visible system. The signal final states - essentially ννX, can be mimicked

by final states like e−e+X where particles such as electrons scattered at relatively small angles actually balance the transverse momentum. Such events should be removed very effectively by vetoing events with additional detected electrons in the forward calorimetry. However a detailed estimate of the rejection power of such a veto by full simulation is not currently available nor expected to be representative of achievable performance. Therefore the approach has been to set relatively conservative kinematic cuts on the visible system which should force at least one of the electrons to be easily vetoable under the background

• hypothesis. For all final states we have required that the visible system has a transverse

momentum exceeding 4% of the beam energy (60 GeV for CLIC 3 TeV). This implicity requires that for events with one beam energy electron carrying the tranverse momentum, the beam energy electron is scattered at a polar angle above 40 mrad. For events with two beam energy electrons, the implicit requirement is that at least one is above 20 mrad. The processes have been studied at the WHiZard generator level incorporating beam- strahlung and ISR effects. Where possible the cuts are defined using scaled variables so that they are still relevant to other centre-of-mass energies. Normally in event selections one is focussed on separating signal events from background

• events. What is most relevant here is selecting a sample of events with high and understood

helicity combination purity. The eventual systematic error will be dominated by how well we know the helicity combination impurity. The impurity can come from wrong helicity states in the signal process, or from wrong helicity states in background processes. Correct helicity states in background processes help increase the “signal” statistics.

2 Single-photon

The e−e+ → γνeνe process is already fully specified at the stable particle level and is by far the simplest process under study. This involves three types of Feynman diagram: W- exchange in the t-channel (LR only), W-W-fusion (WWγ coupling) (LR only), Zγ production (LR and RL). Additionally, the experimental signature of a single photon and missing trans- verse momentum, is indistinguishable from other processes leading to neutrinos, obviously e−e+ → γνµνµ and e−e+ → γντντ but also potentially four-neutrino and six-neutrino final states with a photonb.

bThese should be checked - expected to be small

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Process σLR σRL LR-purity γνeνe 3072 ± 32 8.4 ± 0.1 γνµνµ 13.1 ± 0.2 8.5 ± 0.1 γντντ 13.1 ± 0.2 8.5 ± 0.1 Total 3098 ± 32 25.3 ± 0.2 99.190 ± 0.006% Table 1: Accepted cross-sections (fb) and the accepted LR purity for the single-photon selection 2.1 Event Selection Currently only acceptance cuts on the photon are applied.

• Photon xT = pT /Ebeam > 0.04
• Photon sin θ > 0.12
• Photon x = E/Ebeam < 0.5

The photon energy cut rejects about 50% of the radiative-return to the Z events while retaining about 90% of the LR events. The resulting cross-sections for the various helicity combinations and processes are listed in Table 1. As one can see the accepted cross-section is large (3 pb) and results in about 99.2% LR helicity combination purity.

3 Single-Z

In practice, the e−e+ → Zνeνe process needs to be studied at the “four-fermion” level for specific final states. The main source of events of interest is WW-fusion to Z through the WWZ coupling. It is expected that the final state corresponding to the Z → µ−µ+ decay mode will be the cleanest albeit with a somewhat lower cross-section. Therefore this initial study focusses on the process e−e+ → µ−µ+νeνe. It is expected that the e−e+ → e−e+νeνe process also deserves study and may contribute with similar precision. Other four-fermion final states which are indistinguishable experimentally, µ−µ+νµνµ and µ−µ+ντντ can also contribute. 3.1 Event Selection

• Di-muon, xT = pT /Ebeam > 0.04
• Muon sin θ > 0.12
• Di-muon mass within 10 GeV of MZ

The resulting cross-sections for the various helicity combinations and processes are listed in Table 2. As one can see the accepted cross-section is about 0.16 pb and results in about 99.7% LR helicity combination purity. The non-signal final states contribute relatively little

• mainly from ZZ type processes and so give equal contributions to the RL cross-sections for

each neutrino flavour. The Z mass cut keeps 85% efficiency for LR signal while accepting

• nly 4% of the WW dominated µ−µ+νµνµ.

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Process σLR σRL LR-purity µ−µ+νeνe 158.5 ± 1.7 0.152 ± 0.002 µ−µ+νµνµ 0.49 ± 0.02 0.159 ± 0.003 µ−µ+ντντ 0.364 ± 0.005 0.154 ± 0.002 Total 159.4 ± 1.7 0.465 ± 0.004 99.709 ± 0.003% Table 2: Accepted cross-sections (fb) and accepted LR purity for the di-muon selection for single-Z production The selection purity can and should be further improved by rejecting events where the di-muon is highly energetic (typical of ZZ rather than Zνeνe).

4 Single-W

The e−e+ → W−e+νe and e−e+ → W+e−νe processes also need to be studied at the “four- fermion” level for specific final states. The main source of events of interest is γW-fusion to W through the WWγ coupling. The final states corresponding to W’s decaying to electrons and muons appear most promising as it is experimentally improbable to reliably measure the W charge in hadronic decays. Therefore this initial study focusses on three four-fermion processes to select single-W− and single-W+ in the electron and muon channels.

• CC18: e−e+ → µ−νµe+νe : Single-W− with W− decay to µ−
• CC18: e−e+ → µ+νµe−νe : Single-W+ with W+ decay to µ+
• MIX56: e−e+ → e−e+νeνe : Single-W− and single-W+

The latter one ( e−e+ → e−e+νeνe) can be separated into kinematic regions dominated by single-W− and single-W+ using kinematic cuts. Various four-fermion processes were extensively studied at LEP2 leading to various clas- sifications of the processes. The muon channels belong to the so-called CC18 set of 18 charged-current based Feynman diagrams. The e−e+ → e−e+νeνe process (MIX56) has contributions from all five main production mechanisms (WW, Weν, ZZ, Zee, Zνeνe) and so in principle can be quite complicated. One essential element of estimating cross-sections for the region of phase space of interest for single-W production is to allow the outgoing unobserved beam electron to remain close to the original beam direction corresponding to the case of very low momentum transfer by

• photons. For the Whizard generation samples used for standard ILC and CLIC studies the

"default_q_cut" was set at 4 GeV. This cut has been relaxed for this study to 0.511 MeV resulting in an increase in the estimated cross-section by a factor of four. Such behaviour is expected - but quantitative checks of the veracity of the calculation assumptions are warranted and we are in communication with the Whizard authors to check that the program is being used in a suitable manner for these final states. 4.1 Single-µ− Event Selection

• Muon xT = pT /Ebeam > 0.04

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Process σLR σRL σLL σRR LX purity µ−νµe+νe 570.9 ± 10.5 0.0004 ± 0.0001 657.4 ± 10.0 µ−µ+νeνe 6.35 ± 0.29 0.0204 ± 0.0008 µ−µ+νµνµ 3.58 ± 0.09 0.0235 ± 0.0011 µ−µ+ντντ 0.045 ± 0.002 0.0214 ± 0.0008 Total 580.9 ± 10.5 0.0657 ± 0.0016 657.4 ± 10.0 99.9947 ± 0.0001% Table 3: Accepted cross-sections (fb) and accepted LX purity for the single-µ− selection for single-W− production using “standard” muon veto acceptance Process σLR σRL σLL σRR XR purity µ+νµe−νe 570.9 ± 10.5 0.0004 ± 0.0001 657.4 ± 10.0 µ−µ+νeνe 0.78 ± 0.10 0.0038 ± 0.0003 µ−µ+νµνµ 0.48 ± 0.03 0.0038 ± 0.0005 µ−µ+ντντ 0.0073 ± 0.0006 0.0031 ± 0.0003 Total 572.2 ± 10.5 0.0111 ± 0.0007 657.4 ± 10.0 99.99910 ± 0.00006% Table 4: Accepted cross-sections (fb) and accepted XR purity for the single-µ+ selection for single-W+ production using the extended muon veto acceptance for illustration

• Muon sin θ > 0.12
• No electron/positron with sin θ > 0.04
• No additional muon with sin θ > 0.12

The electron veto removes contributions dominated by WW. The additional muon veto removes di-muon events with genuine ET and keeps the event selection mutually exclusive with respect to the single-Z selection discussed above. Estimated cross-sections are shown in Table 5. The selected events have a LX purity (fraction of unpolarized cross-section coming from LR or LL collisions) of about 99.995%. The estimated impurity is dominated by events where an associated muon is scattered below 120 mrad. If the LCAL (40 to 120 mrad) can be used to veto muons and so extend the polar angle range of the muon veto to about 40 mrad the purity can be further increased and the RL background decreased by about a factor of six. 4.2 Single-µ+ Event Selection Selection criteria are of course the same and the results are basically the same except that right-handed positrons rather than left-handed electrons are favoured. For completeness, instead of just inserting a mirror-image of the above results, the results are shown in Table 4 assuming that the muon veto can be extended to 40 mrad resulting in an XR purity of 99.999%. 5 LCWS11

Process σLR σRL σLL σRR LX purity e−e+νeνe 454.4 ± 5.2 3.29 ± 0.06 554.5 ± 6.2 4.05 ± 0.07 e−e+νµνµ 5.17 ± 0.09 3.36 ± 0.06 6.28 ± 0.10 3.99 ± 0.07 e−e+ντντ 5.11 ± 0.09 3.35 ± 0.06 6.28 ± 0.10 3.99 ± 0.07 Total 464.7 ± 5.2 10.00 ± 0.11 567.1 ± 6.2 12.03 ± 0.12 97.910 ± 0.015 % Table 5: Accepted cross-sections (fb) and accepted LX purity of the single-e− selection for single-W− production Process σLR σRL σLL σRR XR purity e−e+νeνe 591.0 ± 5.9 9.96 ± 0.10 10.97 ± 0.11 685.7 ± 6.9 e−e+νµνµ 15.7 ± 0.2 9.97 ± 0.10 10.81 ± 0.11 16.6 ± 0.2 e−e+ντντ 15.4 ± 0.2 9.89 ± 0.10 10.81 ± 0.11 16.6 ± 0.2 Total 622.1 ± 5.9 29.8 ± 0.2 32.6 ± 0.2 718.9 ± 6.9 95.55 ± 0.02% Table 6: Accepted cross-sections (fb) and accepted XR purity of the single-e+ selection for single-W+ production where the −q cos θ cut has been removed for illustration 4.3 Single-e− Event Selection

• Electron xT = pT /Ebeam > 0.04
• Electron sin θ > 0.12
• No additional electron or positron with sin θ > 0.04
• Electron −q cos θ < 0.75

In addition to the cuts developed for the muon channel, the last cut is added to help reject Bhabha-like events with forward electrons (Zee) which would otherwise reduce the helicity purity. The LX purity is about 97.9%. 4.4 Single-e+ Event Selection Selection criteria are the same and the results are basically the same except that right- handed positrons rather than left-handed electrons are favoured. For completeness, instead

• f just inserting a mirror-image of the above results, the results are shown in Table 6 if one

were to remove the −q cos θ cut resulting in a lower purity of 95.6%.

5 Event Selection Summary

The event selection results are collated in Table 7. Listed is the unpolarised cross-section, σU = 1

4(σLR + σRL + σLL + σRR) and the relevant helicity combination purity.

6 Polarisation Analysis

(still need to work on this - and write some related programs - should be straightforward) LCWS11 6

Channel σU (fb) Preferred Helicity Helicity Purity γ ET 780.8 LR 99.19% µ−µ+ ET (single-Z) 40.0 LR 99.71% µ− ET (single-W−) 309.6 LX 99.9947% µ+ ET (single-W+) 309.6 XR 99.9947% e− ET (single-W−) 263.5 LX 97.91% e+ ET (single-W+) 263.4 XR 97.91% Table 7: Event selection summary using standard cuts We use the results presented in the previous tables to assess uncertainties on the mea- surement of the beam polarisation(s) in different measurement scenarios. The measured cross-section for a particular choice of electron and positron beam polar- ization is given by the following formula (from [3]). σPe− Pe+ = 1 4{(1−Pe−)(1+Pe+)σLR+(1+Pe−)(1−Pe+)σRL+(1−Pe−)(1−Pe+)σLL+(1+Pe−)(1+Pe+)σRR} There are two main potential running scenarios: with only the electron beam polarised and with both beams polarized. We assume the electron beam polarisation is 80% and the positron beam polarisation may be 30% and a total integrated luminosity of 2ab−1. Various helicity configurations may be chosen for running. In particular if the helicity can be easily reversed while keeping the same value of |P| for each beam, the configuration with both beams polarised lends itself to use of the Blondel scheme in cases where the LL and RR cross-sections are identically zero. In this scheme one takes data with all four helicity configurations - those that favor LR, RL, LL, RR and from the measurements of the four cross-sections can solve for the absolute electron and positron polarizations, the unpolarised cross-section and ALR = (σLR−σRL/(σLR+σRL). The best statistical sensitivity is obtained when all four combinations receive equal luminosity. We also present results where 90% of the luminosity is devoted to the helicity combinations which allow s-channel vector-particle exchange (LR and RL). Under the more pessimistic (and simpler) assumption that no positron beam polarisation is available one can use the measured asymmetry with electron polarisation in the various channels and the predicted helicity purity to effectively measure the beam polarisation. As an example we give in Table 8 the expected numbers of events in the various channels for a 2ab−1 run at 3 TeV equally divided between -80% and +80% electron beam polarisation and use the measured asymmetry and expected asymmetry to extract the electron-beam polarisation. The single-W+ channels are not very useful in this context as they don’t measure the electron beam polarisation. More studies still to do ..

7 Systematics and Other Backgrounds

The “background” contribution in most channels is Z-like or ZZ-like and can be checked using suitable control channels. 7 LCWS11

Channel N− N+ Polarisation γ ET 1,395,365 166,285 80.000 ± 0.050 % µ−µ+ ET (single-Z) 71,753 8,179 80.000 ± 0.216 % µ− ET (single-W−) 557,238 61,945 80.000 ± 0.076 % µ+ ET (single-W+) 294,278 324,905

• e− ET (single-W−)

465,411 61,503 80.000 ± 0.092 % e+ ET (single-W+) 243,383 283,531

• Table 8: Expected event statistics and polarisation measurement using electron beam po-

larisation The tracker charge measurement is expected to be sufficient to guarantee negligible mis- measurement errors especially for the relatively low transverse momenta under consideration. The study has not yet exhaustively evaluated all backgrounds but has concentrated on backgrounds with genuine missing energy from prompt neutrinos. Other backgrounds which should be looked at in more detail are µ−µ+ for single-µ, radiative Bhabha for single-electron and τ −τ + for the single lepton channels and two-photon production of di-leptons. If backgrounds or charge measurement issues become more important, the selection cuts can be tightened with an expected relatively minor effect on performance. Need to discuss collision energy spectrum and different beam depolarisation issue.

8 Acknowledgments

TO DO

References

[1] B. Aurand et al., “Beam Polarization at the ILC: the Physics Impact and the Accelerator Solutions,” arXiv:0903.2959 [physics.acc-ph]. [2] K. Moenig, “Polarisation Measurements with Annihilation Data”, Proceedings of LCWS04, Paris, April 2004, LC-PHSM-2004-012. [3] G. Moortgat-Pick et al., “The role of polarized positrons and electrons in revealing fundamental inter- actions at the linear collider,” Phys. Rept. 460, 131 (2008) [arXiv:hep-ph/0507011].

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