Dirac vs. Majorana HNLs (and their oscillations) at SHiP arXiv: - PowerPoint PPT Presentation

Dirac vs. Majorana HNLs (and their oscillations) at SHiP arXiv: 1912.05520 Inar Timiryasov (EPFL) Spaatind 2020 — Nordic conference on Particle Physics January 03, 2020 1 Speaker 1 / 15 Jean-Loup Tastet 1 (NBI)

Feebly interacting particles frontier , let’s explore the intensity frontier using low-energy, high-intensity experiments. → C.f. Oleg’s talk this morning. coupling. The new degrees of freedom are typically SM singlets . FIP candidates 1 Spin 0 : scalar portal (dark Higgs). 2 : neutrino portal (heavy neutral lepton). 3 Spin 1 : vector portal (dark photon). Axion-like particles. ... 2 / 15 • While we wait for the next hadron collider (FCC-hh: 2040–2060) to probe the energy • Feebly interacting particles (FIPs): particles interacting with the SM with a suppressed • Renormalizable portals (mix with interacting SM states, or interact with small coupling): 2 Spin 1 • Non-renormalizable portals (interact through higher dimensional operators):

Heavy Neutral Leptons (HNLs) → 𝛽𝑗 3 / 15 • HNLs can explain neutrino masses and oscillations (maybe: baryogenesis, dark matter). • They interact via mixing with fmavor eigenstates: 𝜉 𝛽 = 𝑉 PMNS 𝜉 𝑗 +Θ 𝛽𝐽 𝑂 𝐽 , Θ ≪ 1 . • Largely constrained below the kaon mass, the neutrino portal will be probed at the GeV scale by the proposed SHiP experiment.

SHiP ( S earch for Hi dden P articles) What else can we learn about the properties of HNLs at SHiP? 4 / 15 • Low-background ( 0.1 evts.) beam-dump experiment @ 400GeV SPS; 2 ⋅ 10 20 POT in 5yr. • Comprehensive Design Study for SHiP and Beam Dump Facility submitted last December. • SHiP aims to observe HNLs, and measure their mass and mixing angles.

Detour: realistic HNL benchmarks Sensitivity study [1811.00930] / PBC 𝜉 MSM , their mixing angles can be large. generations. HNLs are needed, mixing with at least two 𝑁 𝐽 Θ 𝛽𝐽 Θ 𝛾𝐽 𝐽 But: 5 / 15 [1901.09966] assume one Majorana HNL, • 𝜉 masses generated by see-saw mechanism: mixing with one generation only. ����� 𝑛 𝛽𝛾 ≅ −∑ ����� ��� ����� • For one HNL, the seesaw limit is a prediction: �� - � 2 ∼ 10 −10 ! � � μ E.g. for a 1 GeV HNL, we expect |Θ| ���� �� - � • To generate two distinct Δ𝑛 2 , at least two �������� �� - � ���� ��� - �� ��� �� - �� ������ • If multiple HNLs are degenerate as in the ��� ��� � � �� �� ��� ���� [ ��� ]

Majorana HNLs ⇒ Can violate lepton number. Kersten and Smirnov [0705.3221]). be suppressed (Shaposhnikov [hep-ph/0605047], masses, lepton number violating (LNV) efgects may 6 / 15 h ′ • New states: SM singlets w/ Majorana mass term. l + α H • Massive states: Majorana particles . W + ∗ N l + • If we want large mixing angles and correct neutrino β q W −∗ h ′′ • Is there any hope of observing LNV at all? At SHiP? • Yes & yes! • We might even measure the mass splitting!

Main idea LNC rate ∝ 1+ cos (𝜀𝑁𝜐) LNV rate ∝ 1− cos (𝜀𝑁𝜐) Consequences of HNL oscillations ⇒ existing bounds relying on LNV might not be valid. 7 / 15 • If there are two quasi-degenerate HNLs, they can oscillate among themselves. 2 ≫ 𝑛 𝜉 /𝑁 𝑁 , • Oscillations in the sterile sector can be lepton number violating. For |Θ| • To observe them, we need to remember that HNLs are long-lived . • Whether LNV is observable depends on the mass splitting 𝜀𝑁 and proper lifetime 𝜐 : 𝜀𝑁𝜐 ≪ 2𝜌 ⇒ LNC only 𝜀𝑁𝜐 ≫ 2𝜌 ⇒ LNC + LNV with equal integrated rates 𝜀𝑁𝜐 ∼ 2𝜌 ⇒ Potentially resolvable oscillations • LNV may be suppressed (especially at large mass, cf. Drewes, Klarić, Klose [1907.13034]). • Observation of LNV (or LNC only) constrains the number and mass splitting of HNLs.

8 / 15 Distinguishing LNC / LNV events at SHiP • Most production processes are 𝐼 → [ℎ ′ ]𝑚 𝛽 𝑂 . • We select the fully reconstructible decay channels 𝑂 → 𝑚 𝛾 𝜌 . • Can we compare the lepton charges? → No! Because the primary decay takes place inside the target. • HNLs carry not only lepton number, but also spin 1 2 ⟶ look at angular distributions. • It turns out LNC / LNV processes have very difgerent kinematics! E.g. for 2-body decays:

Complications over matrix elements compared to what Pythia provides. 9 / 15 • Not all production processes are 2-body decays. • Decay products ( 𝑚 𝛽 , 𝑚 𝛾 , 𝜌 ) are not massless ⇒ helicity fmips are possible. • Heavy mesons are not monochromatic ⇒ smears out the distribution of decay products. • We need to take geometrical acceptance into account. • To handle these complications, we need a Monte-Carlo simulation! • We use our own Monte-Carlo because we need fjner control (tracking spin correlations)

LNC / LNV distributions acceptance cuts. distinguished given enough events. 10 / 15 experiment at the SPS @ 400 GeV. LNC LNV 0 200 40 2 ) [GeV] 20 E ( 0 • Most 2/3-body decays implemented. 0 50 0 200 • 𝐸 -meson spectra from the LEBC-EHS 0.5 0.5 2 ) [GeV] 0.0 0.0 p x ( 0.5 0.5 • Basic propagation and geometrical 0 50 0 20 2 0 2 1 2 ) [GeV] 0.5 0.5 0 0.0 0.0 • Difgerent distributions ⟹ can be 0.5 0.5 p y ( 1 0 50 0 20 0.5 0.0 0.5 2.5 0.0 2.5 0.5 0.5 0.5 [GeV] 0.0 0.0 0.0 0.0 p CM z 0.5 0.5 0.5 0.5 0 50 0 20 0.5 0.0 0.5 0 1 0.5 0.0 0.5 E ( N ) [GeV] E ( 2 ) [GeV] p x ( 2 ) [GeV] p y ( 2 ) [GeV] p CM [GeV] z

We can discriminate these processes using boosted decision trees 11 / 15 • Generate 3⋅10 6 events for each mass, split 0.5 ∶ 0.2 ∶ 0.3 into training / validation / test. • We use the LightGBM gradient boosting algorithm. • Accuracy is highest when the HNL kinetic energy in CM ≳ heavy meson 𝑞 𝑈 spread. 0.64 e Classification accuracy a 0.62 e + 0.60 0.58 0.56 0.54 0.52 0.50 0.8 1.0 1.2 1.4 1.6 1.8 HNL mass M N [GeV]

How to quantitatively distinguish Majorana / Dirac? Hypotheses we want to distinguish Model-selection sensitivity sensitivity curve where SHiP has a 1/2 probability of excluding this hypothesis at 90% CL 12 / 15 1 ℋ 1 (Dirac-like): HNLs are Dirac or quasi-Dirac with 𝜀𝑁𝜐 ≪ 2𝜌 (LNC only). 2 ℋ 2 (Majorana-like): HNLs are Majorana or quasi-Dirac with 𝜀𝑁𝜐 ≫ 2𝜌 (LNC + LNV). 𝑓 ∶ 𝑉 2 • Assumptions: The mass 𝑁 𝑂 and 𝑉 2 𝜈 ratio have roughly been measured. • Compute the likelihood of each hypothesis based on the classifjer decisions and accuracy. • Considering in turn each hypothesis as the null hypothesis, draw the “model-selection” if the other is true, after 5 years of nominal operation i.e. 2⋅10 20 POT.

Model-selection sensitivity reconstruct the HNL mass. report (arXiv: 1901.09966) Source: Physics Beyond Colliders seesaw lower bound. 13 / 15 experiments that can existing exclusion bounds model-selection sensitivity. SHiP (LNV) Seesaw (IH) NUTEV SHiP (det.) BBN CHARM NA62 + + (det.) E949 Belle PS191 Seesaw (NH) 10 2 3 • Dashed line: 10 10 4 • Colored areas: 10 5 10 6 • Dotted lines: future | 2 10 7 | 10 8 • Hatched areas: 10 9 10 10 10 11 0.25 0.50 0.75 1.00 1.25 1.50 1.75 HNL mass M N [GeV]

Resolving HNL oscillations 14 / 15 could be resolved at SHiP (Canetti and Shaposhnikov [1208.4607]). • Simultaneous requirement of BAU and DM production in the 𝜉 MSM suggests 𝜀𝑁 that • Bin events in proper time, weight them by 𝑄( LNV ) and subtract the sample average: • Period of oscillations is 2𝜌/𝜀𝑁 . Allows measuring the mass splitting. 7 eV 2579 events, M N = 1 GeV, M = 4 10 p LNV inferred using LightGBM with accuracy 0.639 10.0 7.5 p LNV ) 5.0 2.5 ( p LNV, i 0.0 bin 2.5 i 5.0 7.5 0 2 4 6 8 10 12 14 Proper time [m]

Conclusion In this region, SHiP can: 2 ). 15 / 15 2 ≳ 10 −9 – 10 −8 , we can expect many fully reconstructed HNL events. For mixing angles |Θ| • Test the Majorana nature of HNLs, • If we are lucky, resolve the mass splitting 𝜀𝑁 , ... even if current / next-generation experiments like NA62 ++ do not observe any HNLs. This could help determine the number of nearly-degenerate HNLs (needed to measure |Θ 𝛽 | Along with the HNL mass / mixing angles, this would make the 𝜉 MSM cosmology predictive.