Rare Pion Decays and Tests of the Standard Model

Rare pion decays and tests of the Standard Model

Dinko Poˇcani´c

University of Virginia

7 November 2019 Fundamental Symmetries Research with Beta Decay Institute for Nuclear Theory University of Washington, Seattle 4 – 8 November 2019 Known and measured pion and muon decays

decay B.R. physics interest + + π → µ ν 0.9998770 (4) (πµ2) + −4 µ νγ 2.00 (25) × 10 (πµ2γ) + −4 e ν 1.230 (4) × 10 (πe2) ⇐ `U, BSM (T ,. . . ) + −7 (π) (π) e νγ 7.39(5) × 10 (πe2γ) ⇐ BSM (T ,. . . ), FA , FV ,. . . 0 + −8 π e ν 1.036 (6) × 10 (πe3) ⇐ q`U(Vud ), BSM loops + + − −9 e νe e 3.2 (5) × 10 (πe2ee)

π0 → γγ 0.98798 (32) ⇐ χ anomaly e+e−γ 1.198 (32) × 10−2 (Dalitz) e+e−e+e− 3.14 (30) × 10−5 e+e− 6.2 (5) × 10−8

µ+ → e+νν¯ ∼ 1.0 (Michel) ⇐ BSM weak int. terms e+ννγ¯ 0.014 (4) (RMD) e+νν¯e+e− 3.4 (4) × 10−5

D. Poˇcani´c(UVa) Rare π decays: Study subjects 7 Nov ’19/INT 2 / 34 The electronic (πe2) decay: π+ → e+ν(γ)

BR ∼ 10−4

D. Poˇcani´c(UVa) Rare π decays: The πe2 decay 7 Nov ’19/INT 3 / 34 ∼ 2.5 × 10−5

I Strong SM helicity suppression ampliﬁes sensitivity to PS terms (“door” for New Physics) by factor2 mπ/me (mu + md ) ≈ 8000. Rπ I e/µ tests lepton universality: in SM e, µ, τ diﬀer by Higgs couplings only; there could also be newS or PS bosons with non-universal couplings (New Physics); repercussions also in the neutrino sector, SUSY, ALPS...

I Experimental world average is 23× less accurate than SM calculations! [1.2327(23) × 10−4]

πe2 decay: SM calculations, lepton universality

I Early evidence for V − A nature of weak interaction. 2 2 2 2 2 π Γ(π → eν¯(γ)) ge me (1 − me /mµ) Re/µ = = 2 2 2 2 2 1 + δRe/µ Γ(π → µν¯(γ)) gµ mµ (1 − mµ/mπ)

π Γ(π → eν¯(γ)) I Modern SM calculations: R = = e/µ Γ(π → µν¯(γ))  CALC 1.2352(5) × 10−4 Marciano and Sirlin, [PRL 71 (1993) 3629]  1.2354(2) × 10−4 Finkemeier, [PL B 387 (1996) 391] 1.2352(1) × 10−4 Cirigliano and Rosell, [PRL 99 (2007) 231801]

D. Poˇcani´c(UVa) Rare π decays: Motivation 7 Nov ’19/INT 4 / 34 Rπ I e/µ tests lepton universality: in SM e, µ, τ diﬀer by Higgs couplings only; there could also be newS or PS bosons with non-universal couplings (New Physics); repercussions also in the neutrino sector, SUSY, ALPS...

I Experimental world average is 23× less accurate than SM calculations! [1.2327(23) × 10−4]

πe2 decay: SM calculations, lepton universality

I Early evidence for V − A nature of weak interaction. ∼ 2.5 × 10−5 2 2 2 2 2 π Γ(π → eν¯(γ)) ge me (1 − me /mµ) Re/µ = = 2 2 2 2 2 1 + δRe/µ Γ(π → µν¯(γ)) gµ mµ (1 − mµ/mπ)

I Strong SM helicity suppression ampliﬁes sensitivity to PS terms (“door” for New Physics) by factor2 mπ/me (mu + md ) ≈ 8000.

D. Poˇcani´c(UVa) Rare π decays: Motivation 7 Nov ’19/INT 4 / 34 I Experimental world average is 23× less accurate than SM calculations! [1.2327(23) × 10−4]

πe2 decay: SM calculations, lepton universality

D. Poˇcani´c(UVa) Rare π decays: Motivation 7 Nov ’19/INT 4 / 34 πe2 decay: SM calculations, lepton universality

I Experimental world average is 23× less accurate than SM calculations! [1.2327(23) × 10−4]

D. Poˇcani´c(UVa) Rare π decays: Motivation 7 Nov ’19/INT 4 / 34 The PEN/PIBETA apparatus • πE1 beamline at PSI • stopped π+ beam PEN detector • active target counter Runs 2-3

• 240 module spherical pure pure CsI calorimeter CsI • central tracking • beam tracking PH • digitized waveforms MWPC1 π+ mTPC VACUUM PMT beam AD AT BC MWPC2

~3 m flightpath

10 cm BC: Beam Counter PH: Plastic Hodoscope (20 stave cylindrical) AD: Active Degrader MWPC: Multi-Wire Proportional Chamber (cylindrical) T C i i T m r j c i n C a b rT Active Target mTPC: mini-Time Projection ChamberAT:

D. Poˇcani´c(UVa) Rare π decays: Experimental method 7 Nov ’19/INT 5 / 34 π-exp Experimental branching ratio (Re/µ ) Recognizing that:

I timing gates aﬀect the analyzed number of πe2 and π → µ → e events;

I MWPC eﬃciency depends on energy, peak π-exp Nπ→eν (1 + tail) fπ→µ→e(Te) (Eµ→eνν¯)MWPC Aπ→µ→e we have: Re/µ = Nπ→µν fπ→eν (Te) (Eπ→eν )MWPC Aπ→eν rf r rA

16000

14000 Ec Ec = cutoﬀ energy 12000 N = number of events 10000

Counts A = acceptance 8000

6000 tail(Ec ) = tail to peak ratio

4000 π → µ → e π → eν (E)MWPC = eﬃciency of MWPC

2000 −3 ×10 f (Te) = decay probability during 0 10 20 30 40 50 60 70 80 90 observation time window E CsI (MeV) D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 6 / 34 Branching ratio/uncertainties

peak π Nπ→eν fπ→µ→e(Te) (Eµ→eνν¯)MWPC Aπ→µ→e Re/µ = (1 + tail) Nπ→µν fπ→eν(Te) (Eπ→eν)MWPC Aπ→eν | {z } | {z } | {z } | {z } rN rf r rA | {z } blinded

Uncertainties: s δR δr 2 δ 2 δr 2 δr 2 δr 2 = N + tail + f + + A R rN 1 + tail rf r rA

MWPC(E): chamber eﬃciencies. rA: acceptances

PEN goal: δR/R ' 5 × 10−4

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 7 / 34 Discriminating πe2 and πµ2 in TGT

+ e+ t(e ) in AT predicted from t(PH) mTPC mTPC ⇒ (x, y) of πstop in AT ToF from B0 π+ PMT E(π+) AD AT Edep(AD) ⇒ Edep, z of πstop in AT t(π+) in AT predicted from t(AD) Predicted π+ and e+ energies agree VERY well with observations: 11 7 + 10.5 e 6 10 9.5 5 9 4 (MeV)

(MeV) 8.5 tgt obs e tgt obs π

8 E E 3 7.5 2 7 + 6.5 π 1 6 1 2 3 4 5 6 7 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 pred pred E (MeV) Eπ tgt (MeV) e tgt

⇒ E and t predictions are used for πe2/πµ2 discrimination.

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 8 / 34 Target waveforms and event type discrimination

Measurement |raw| 0.07 20000 π → eν simulation ﬁltered π → µν simulation predicted 0.06 15000 µ found 0.05 0.04 10000 target waveform

yield 0.03 (2GS/s) 5000 0.02

0.01 0 0 400 450 500 550 600 650 700 750 800 -2 -1.5 -1 -0.5 0 0.5 1 time (0.5 ns/bin) ∆χ2 0.030 Measurement 2 π → eν simulation ∆χ uses predicted and observed 0.025 π → µν simulation timings and energies. Steps: 0.020 2 1. evaluate 2 peak fit ⇒ χ2, 0.015 2 2. evaluate 3 peak fit ⇒ χ3, yield 0.010 2 2 2 3. find ∆χ = χ2 − χ3 (normalized). 0.005 Best of ∼ dozen similar observables at 0.000 discriminating π / π event classes. -4 -2 0 2 4 6 8 e2 µ2 pred-obs ∆Etgt D. Poˇcanić(UVa) Rare π decays: Method 7 Nov ’19/INT 9 / 34 Realistic simulation of beam det’s vs. measurement π → µν → eνν¯

60000 0.022 0.020 55000 Measurement e+ 0.018 Simulation 50000 0.016 + 45000 µ 0.014

Yield 0.012 40000 0.010 Amplitude 35000 0.008 π+(B0) 30000 0.006 π+(Tgt) 0.004 25000 + π (Deg) 0.002 20000 0.000 0 500 1000 1500 2000 2500 3000 4 4.5 5 5.5 6 6.5 7

Bin (0.5 ns/bin) EDegrader (MeV)

10-1 Measurement 0.025 Measurement Simulation Simulation 10-2 0.020

Yield 10-3 Yield 0.015

0.010 10-4 0.005

10-5 0.000 1 2 3 4 5 6 7 8 9 10 26.5 27 27.5 28 28.5 2nd peak Etgt (MeV e.e) ∆tDEG-B0 (ns)

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 10 / 34 Z t 1 0 0 0 −t/τµ −t/τπ fπ-µ-e(t)= fπ→µ(t − t )fπ→e(t )dt = e − e . 0 τµ − τπ 2 w w t+w −t/τµ −t/τπ |fπ-µ-e|t−w = τµe sinh − τπe sinh τµ − τπ τµ τπ 2δt w w −t/τµ −t/τπ δfπ-µ-e = e sinh − e sinh τµ − τπ τµ τπ π → eν(γ) timing selection:

1 Z t2 f (t , t ) = e−t/τπ = e−t1/τπ − e−t2/τπ π→eν 1 2 τ π t1 δt −t2/τπ Choose t1 < 0: δfπ→eν = e . τπ

Analysis requires: δt, w, t and t2.

Choice of time interval, f (Te)

π → µ → e (“Michel”) timing selection: symmetric time window.

0.5

0 0 50 100 150 200 t (ns)

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 11 / 34 π → eν(γ) timing selection:

1 Z t2 f (t , t ) = e−t/τπ = e−t1/τπ − e−t2/τπ π→eν 1 2 τ π t1 δt −t2/τπ Choose t1 < 0: δfπ→eν = e . τπ

Analysis requires: δt, w, t and t2.

Choice of time interval, f (Te)

π → µ → e (“Michel”) timing selection: symmetric time window. Z t 1 0 0 0 1 −t/τµ −t/τπ fπ-µ-e(t)= fπ→µ(t − t )fπ→e(t )dt = e − e . 0 τµ − τπ 2 w w t+w −t/τµ 0.5 −t/τπ |fπ-µ-e|t−w = τµe sinh − τπe sinh τµ − τπ τµ τπ 2δt w w δf = e−t/τµ sinh − e−t/τπ sinh π-µ-e 0 τµ − τπ τµ τπ 0 50 100 150 200 t (ns)

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 11 / 34 1 Z t2 f (t , t ) = e−t/τπ = e−t1/τπ − e−t2/τπ π→eν 1 2 τ π t1 δt −t2/τπ Choose t1 < 0: δfπ→eν = e . τπ

Analysis requires: δt, w, t and t2.

Choice of time interval, f (Te)

0.5

0 0 50 100 150 200 t (ns) D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 11 / 34 Choice of time interval, f (Te)

1 1 Z t2 f (t , t ) = e−t/τπ = e−t1/τπ − e−t2/τπ π→eν 1 2 τ π t1

0.5 δt −t2/τπ Choose t1 < 0: δfπ→eν = e . τπ Analysis requires: δt, w, t and t . 0 2 0 50 100 150 200 t (ns) D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 11 / 34 rf : decay time windows ×10-3 220 0.8

200 “Michel” window 0.7

180 0.6 t + w 3 w = 50 ns 160 − 0.5 10 140 0.4 t ×

f 0.3

120 / time (ns) f 100 t − w δ 0.2 80 0.1

0 10 20 30 40 50 60 70 60 80 100 120 140 160 180 200 w (ns) tcentral (ns) 10-1 πe2 window 10-2 δt = 60 ps δt = 50 ps π → µν → eνν¯(γ) -3 f 10 / δrf /rf negligible f δt = 40 ps δ 10-4 δt = 30 ps π → eν(γ)

-5 10 δrf /rf negligible for t2 & 90 ns

0 20 40 60 80 100 120 140 160 180 200 t2 (ns) D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 12 / 34 CsI EM Calorimeter: realistic simulation Crystals are not all the same:

I diﬀerent detector response, non-uniformities, ∆Ω coverage; I 240 PMTs, with slightly diﬀerent properties, opt. couplings.

0.030 0.03 0.03 0.03 0.03

0.025 Xtal 4 0.025 Xtal 14 0.025 Xtal 24 0.025 Xtal 34 0.025 Xtal 44

0.020 0.02 0.02 0.02 0.02 Meas Meas Meas Meas Meas 0.015 Sim 0.015 Sim 0.015 Sim 0.015 Sim 0.015 Sim Yield Yield Yield Yield Yield

0.010 0.01 0.01 0.01 0.01

0.005 0.005 0.005 0.005 0.005

0.0000.030 0.030 0.030 0.030 0.030 50 55 60 65 70 75 8050 55 60 65 70 75 8050 55 60 65 70 75 8050 55 60 65 70 75 8050 55 60 65 70 75 80 ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV) 0.025 Xtal 54 0.025 Xtal 64 0.025 Xtal 74 0.025 Xtal 84 0.025 Xtal 94

0.020 0.02 0.02 0.02 0.02 Meas Meas Meas Meas Meas 0.015 Sim 0.015 Sim 0.015 Sim 0.015 Sim 0.015 Sim Yield Yield Yield Yield Yield

0.010 0.01 0.01 0.01 0.01

0.005 0.005 0.005 0.005 0.005

0.0000.030 0.030 0.030 0.030 0.030 50 55 60 65 70 75 5080 55 60 65 70 75 8050 55 60 65 70 75 8050 55 60 65 70 75 8050 55 60 65 70 75 80 ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV) 0.025 Xtal 104 0.025 Xtal 114 0.025 Xtal 124 0.025 Xtal 134 0.025 Xtal 144

0.020 0.02 0.02 0.02 0.02 Meas Meas Meas Meas Meas 0.015 Sim 0.015 Sim 0.015 Sim 0.015 Sim 0.015 Sim Yield Yield Yield Yield Yield

0.010 0.01 0.01 0.01 0.01

0.005 0.005 0.005 0.005 0.005

0.000 0 0 0 0 0.03050 55 60 65 70 75 0.038050 55 60 65 70 75 0.038050 55 60 65 70 75 0.038050 55 60 65 70 75 0.038050 55 60 65 70 75 80 ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV) 0.025 Xtal 154 0.025 Xtal 164 0.025 Xtal 174 0.025 Xtal 184 0.025 Xtal 194

0.020 0.02 0.02 0.02 0.02

0.015 Meas 0.015 Meas 0.015 Meas 0.015 Meas 0.015 Meas

Yield Sim Yield Sim Yield Sim Yield Sim Yield Sim 0.010 0.01 0.01 0.01 0.01

0.005 0.005 0.005 0.005 0.005

0.00050 55 60 65 70 75 08050 55 60 65 70 75 08050 55 60 65 70 75 08050 55 60 65 70 75 08050 55 60 65 70 75 80 ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV) ECsI (MeV)

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 13 / 34 CsI simulation cont’d.

0.020 0.020 0.018 Measurement 45 degree cone 0.018 Measurement 30 degree cone 0.016 Simulation 0.016 Simulation 0.014 0.014 0.012 0.012 0.010 0.010 Yield Yield 0.008 0.008 0.006 0.006 0.004 0.004 0.002 0.002 0.000 0.000 50 55 60 65 70 75 80 50 55 60 65 70 75 80 ECsI (MeV) ECsI (MeV)

0.020 0.020 0.018 Measurement Main Xtal + 0.018 Measurement Main Xtal + 0.016 Simulation next to 0.016 Simulation nearest 0.014 nearest 0.014 neighbors 0.012 neighbors 0.012 0.010 0.010 Yield Yield 0.008 0.008 0.006 0.006 0.004 0.004 0.002 0.002 0.000 0.000 50 55 60 65 70 75 80 50 55 60 65 70 75 80 ECsI (MeV) ECsI (MeV)

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 14 / 34 Tail trigger

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 15 / 34 Experimental precision not good enough (∆R/R ∼ 10−3)! Must use MC simulation!

Measured “tail” after subtraction

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 16 / 34 Measured “tail” after subtraction

Experimental precision not good enough (∆R/R ∼ 10−3)! Must use MC simulation!

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 16 / 34 δtail/(1 + tail): photoneutron reactions

NaI(Tl) Response (BINA)

[PiENu: NIM A791 (2015) 38] 104

103 Counts 102

1 0 10 20 30 40 50 60 70 Energy [MeV] D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 17 / 34 Photoneutron cross sections, σ(γ, xn)

Bramblett, 1966 Bramblett, 1966 Bergere, 1969 140 Varlamov, 2006 Bergere, 1969 300 CHIPS, g4.9.6 Varlamov, 2016 Cascade, g4.10.2 CHIPS, g4.9.6 MSU model 120 Cascade, g4.10.2 PEN 13 fit MSU model 250 PEN 13 fit PEN avg fit PEN 13 fit 100 PEN 13 fit 200 80 (mb) (mb) σ

150 σ 60 100 40 50 127I(γ, n) 20 127I(γ, 2n) 0 0 8 10 12 14 16 18 20 22 16 18 20 22 24 26 28 Eγ (MeV) Eγ (MeV) 350 Berman, 1969 Berman, 1969 140 Lepretre, 1974 Lepretre, 1974 CHIPS, g4.9.6 300 CHIPS, g4.9.6 Cascade, g4.10.2 Cascade, g4.10.2 120 PEN 13 fit PEN 13 fit PEN 13 fit 250 PEN 13 fit PEN avg fit PEN avg fit 100

200 80 (mb) (mb) σ σ 150 60

100 40

20 133 50 133Cs(γ, n) Cs(γ, 2n) 0 0 16 17 18 19 20 21 22 23 24 10 12 14 16 18 20 Eγ (MeV) Eγ (MeV)

D. Poˇcani´c(UVa) Rare π decays: Method 7 Nov ’19/INT 18 / 34 Radiative electronic (πe2γ) decay: + + π → e νeγ

−7 BRnon-IB ∼ 10 (Unavoidable part of π → eν decay)

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 19 / 34 Physics of π+ → e+νγ (RPD): QED IB terms:

SM and SD V , A terms:

A tensor interaction, Exchange of S=0 leptoquarks too? P Herczeg, PRD 49 (1994) 247

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 20 / 34 The π → eνγ amplitude and FF’s TheIB amplitude (QED uninteresting!):

ν eGF Vud µ∗ kµ pµ σµνq MIB = −i √ fπme e¯ − + × (1 − γ5) ν . 2 kq pq 2kq The structure-dependent amplitude (interesting!):

eGF Vud ν∗ µ σ τ MSD = √ e¯γ (1 − γ5)ν × [FV µνστ p q + iF A(gµνpq − pνqµ)] . mπ 2

The SM branching ratio (with x = 2Eγ/mπ ; y = 2Ee /mπ ),

2 2 dΓπe2γ α n mπ = Γπe2 IB (x, y) + dx dy 2π 2fπme 2 + 2 − × (FV + FA) SD (x, y) + (FV − FA) SD (x, y) mπ + − o + (FV + FA) Sint (x, y) + (FV − FA) Sint (x, y) . fπ

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 21 / 34 Pion radiative decay regions

1.0 1.0 5 0.9 10 0.9 10 0.8 0.8 4 y 10 y 0.7 0.7 ≡ ≡ 0.6 0.6 π 103 π 1 0.5 0.5 m m / /

e 0.4 2 e 0.4

E 10 E

2 0.3 IB 2 0.3 INT 10-1 0.2 10 0.2 0.1 0.1 0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2Eγ /mπ ≡ x 2Eγ /mπ ≡ x 1.0 10 1.0 0.9 0.9 1 0.8 0.8 y y 0.7 0.7 1 ≡ ≡ 0.6 0.6 -1

π π 10 m m 0.5 0.5 / / e e 0.4 0.4 E E + − 10-1 2 2 0.3 SD 0.3 SD 10-2 0.2 0.2 0.1 0.1 0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2Eγ /mπ ≡ x 2Eγ /mπ ≡ x

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 22 / 34 Best sensitivity for SD terms

1.0 1.0 0.08 0.9 0.9 0.9 0.07 0.8 0.8 0.8 0.7 0.7 0.7 0.06 0.6 0.6 0.6 0.05

0.5 0.5 0.5 0.04 0.4 0.4 0.4 0.03 0.3 0.3 0.3 0.02 0.2 SD+ Contribution 0.2 0.2 SD− Contribution 0.1 0.1 0.1 0.01 0.0 0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

SD+ region favors high energy e+ and γ’s.

High energy track pairs occur with large opening angles.

Large solid angle coverage required ⇒ good match to PEN!

SD− is notoriously hard to measure directly.

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 23 / 34 PIBETA results for π → eνγ (2009)

Pion FF values and precision improvement factors (pif) over previous work:

150 Observable (pif) χ2 Contours 140 FV = 0.0258(17) (8×) exp 4 130 F = 0.0119(1) (16×) A (FCVC) 4σ V 120 ∗ 2σ a = 0.10(6) (∞)

110 1σ 4

Form Factor x 10 −5.2 < 10 · FT < 4.0 90 % c.l. A F −8 † 100 B = 73.86(54) × 10 (17×) CVC -4 πe2γ FV = 255(3) x 10 ∗ 2 90 a ... q dependence of FV † ◦ for (Eγ > 10 MeV, and θeγ > 40 ) 80 220 230 240 250 260 270 280 290 [Bychkov et al., PRL 103, 051802 (2009)] 4 FV Form Factor x 10

Tight constraint on SD+; not so tight on SD−!

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 24 / 34 Identifying hard radiative decays in PEN

100

90 Measurement 80 PEN indirectly measures pν in π → eνγ ) 70 c / 60 p~e + p~γ = −p~ν ≡ p~obs; with: 50 (MeV 40 Ee + Eγ ≡ Eobs CsI

p 30 2 Eobs + pobsc = mπc 20

10 0 20 40 60 80 100 120 140 ECsI (MeV) 100 100

90 π → eν 90 π → eνγ

80 Simulation 80 Simulation

70 ) 70 c / 60 60

50 50 (MeV) (MeV 40 40

CsI “split clumps” CsI

p 30 p 30

20 20

10 10 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 ECsI (MeV) ECsI (MeV)

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 25 / 34 Data regions (PIBETA measurements and PEN)

70 C SD+ A 60

50 post-2004 data D subdivision: 40

(MeV) B − 1 2 3 4 SD 0.9

CsI 8

e 30 E π 0.7 /m 5 20 e 0.5 6 y=2E 10 7 0.3

0 0.5 1 0 10 20 30 40 50 60 70 x=2Eγ /mπ CsI Eγ (MeV) PIBETA (1999-01, 2004): regions A, B, and C. [B was problematic in 1999-01 ⇒ resolved with 2004 data].

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 26 / 34 PEN Run 3 data

250 90 80 Measurement 200 Measurement 70 Simulation Simulation 60 150 50 Region A Region B

40 100 counts counts 30

20 50 10 0 0 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 λ λ

2500 600 Measurement Measurement 2000 500 Simulation Simulation 400 1500 Region C Region D 300 1000 counts counts 200 500 100

0 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 λ 2 λ λ = 2Ee/mπ sin (θeγ )

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 27 / 34 Timing for radiative decays

70 300 1000 60 Measurement Measurement Measurement 250 800 50 Simulation Simulation Simulation 200 40 Region A Region B 600 Region C 30 150

counts counts counts 400 20 100 200 10 50

0 0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 decay time (ns) decay time (ns) decay time (ns)

1800 180 800 P/B = 121 P/B = 1.7 1600 P/B = 4.4 160 Measurement 700 Measurement Measurement (2004) (99-01) 1400 (99-01) 140 600 Simulation Simulation 1200 Simulation 120 P/B ∼ 100 500 P/B = 10 P/B = 30 1000 100 Region A Region B Region C Current 400 (2004) (2004) 80 800

counts counts 300 counts 60 P/B ∼ 40 600 P/B ∼ 28 200 40 Current 400 Current 20 100 200 0 0 0 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 te − tγ (ns) te − tγ (ns) te − tγ (ns) Measured spectra inﬂuenced by instrumental response and event statistics.

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 28 / 34 Region D: only in PEN

120 160 1400 Measurement 140 100 1200 120 P/B ∼ 70 Simulation 80 1000 100 800 60 80

Counts Measurement Counts Counts 600 60 40 400 Simulation 40 Measurement 20 20 Simulation 200 0 0 0 15 20 25 30 35 40 45 50 55 15 20 25 30 35 40 45 50 55 -20 -15 -10 -5 0 5 10 15 20 Eγ (MeV) Ee (MeV) te − tγ (ns)

350 300 Measurement Measurement 300 250 Simulation 250 Simulation 200 200 150 150 Counts Counts 100 100

50 50

0 0 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 50 100 150 200 2 λ = 2Ee/mπ sin (θeγ ) decay time (ns)

D. Poˇcani´c(UVa) Rare π decays: The πe2γ decay 7 Nov ’19/INT 29 / 34 Table of uncertainties

peak π Nπ→eν Aπ-µ-e (Eµ→eνν¯)MWPC fπ-µ-e(Te) Re/µ = (1 + tail) Nπ→µν Aπ-µ-e (Eπ→eν)MWPC fπ-µ-e(Te)

rA r rf

π π Systematics Value ∆Re/µ/Re/µ

−4 tail 0.032 3.5 × 10 −6 rf 0.04292034 5 × 10 ∗ −4 rAr ' 0.98 ∼ 3 × 10 Statistical: −4 † ∆Nπ→eν/Nπ→eν 5.15 × 10 (Runs 2 &3) Goal5 × 10−4

∗ Blinded † incomplete

D. Poˇcani´c(UVa) Rare π decays: Uncertainties 7 Nov ’19/INT 30 / 34 Summary

I PEN is on track to evaluate the experimental ratio + + π Γ(π →e νe (γ)) −3 R = + + with sub-10 relative precision. e/µ Γ(π →µ νµ(γ))

I Comprehensive systematics studies have been completed; all relevant contributions are understood.

I Radiative component of the decay is well accounted for, and will enhance the existing PIBETA data set.

I Work is under way to improve the statistical uncertainty of ∆N/N ∼ 5.1 × 10−4.

I Unblinding will be performed once the MC acceptances and eﬃciencies for all beam subperiods are optimized.

I Analysis is ongoing; special recognition to Charlie Glaser.

D. Poˇcani´c(UVa) Rare π decays: Status and prospects 7 Nov ’19/INT 31 / 34 Pion beta decay (πe3): + 0 + π → π e νe

BR ∼ 10−8

PIBETA result:

π −8 B.R. ≡ Re3 = 1.038 (6) × 10 [Poˇcani´cet al., PRL 93 (2004) 181803] π (updated for current Re/µ)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 32 / 34 PIBETA results (2004)

π + → π0 e+ ν 2000 e τ = 26.23 ± 0.12 ns

1000 Number of events

0 0 20 40 60 80 100 120 140 t( π 0 ) − t(AD) (ns)

7000 + 0 + π → π e ν 40000 simulation π → e ν 6000 • measurement → γ +γ 5000 1 2 30000

4000 simulation 20000 3000 • measurement

2000 Number of events Number of Events 10000 1000

0 0 160 165 170 175 180 45 50 55 60 65 70 75 Positron Energy (MeV) Opening angle θγ1γ2 (deg)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 33 / 34 40000 simulation π → e ν • measurement

30000

20000

Number of Events 10000

0 45 50 55 60 65 70 75 Positron Energy (MeV)

PIBETA results (2004)

π + → π0 e+ ν 2000 e τ = 26.23 ± 0.12 ns

1000 Number of events

0 0 20 40 60 80 100 120 140 t( π 0 ) − t(AD) (ns)

Pion beta decay observables

7000 + π → π0e+ν 6000 → γ +γ 5000 1 2

4000 simulation

3000 • measurement

2000 Number of events

1000

0 160 165 170 175 180

Opening angle θγ1γ2 (deg)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 33 / 34 π + → π0 e+ ν 2000 e τ = 26.23 ± 0.12 ns

1000 Number of events

0 0 20 40 60 80 100 120 140 t( π 0 ) − t(AD) (ns)

7000 + π → π0e+ν 6000 → γ +γ 5000 1 2

4000 simulation

3000 • measurement

2000 Number of events

1000

0 160 165 170 175 180

Opening angle θγ1γ2 (deg)

PIBETA results (2004)

Electronic π → eν decay observables

40000 simulation π → e ν • measurement

30000

20000

Number of Events 10000

0 45 50 55 60 65 70 75 Positron Energy (MeV) D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 33 / 34 A possible setup:

separable I stopped pion beam in active target halves with central tracking,

I main detector: liquid Xe, π 6 −1 I hrstopi ∼ 1.5 × 10 s , active tgt live 7 I running for T ∼ 3 × 10 s LXe run (> 2 years of calendar time): LXe 9 fast I Nπ+→e+ν(γ) > 5 × 10 , i.e., tracker π π −5 ∆Re/µ/Re/µ < 2 × 10 ; stat

5 I Nπ+→π0e+ν ≥ 4 × 10 , i.e., π π −3 (∆Re3/Re3)stat < 2 × 10 .

Concept for an improved PEN/PIBETA experiment π −4 Goals: (a) (∆R/R)e/µ < 10 (to match theoretical precision), and π −3 (b) (∆R/R)e3 ∼ 2 − 3 × 10 (per W. Marciano’s talk).

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 34 / 34 Concept for an improved PEN/PIBETA experiment π −4 Goals: (a) (∆R/R)e/µ < 10 (to match theoretical precision), and π −3 (b) (∆R/R)e3 ∼ 2 − 3 × 10 (per W. Marciano’s talk). A possible setup:

separable I stopped pion beam in active target halves with central tracking,

5 I Nπ+→π0e+ν ≥ 4 × 10 , i.e., π π −3 (∆Re3/Re3)stat < 2 × 10 .

D. Poˇcanić(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 34 / 34 Current and former PIBETA and PEN collaborators L. P. Alonzia, K. Assamagana, V. A. Baranovb, W. Bertlc, C. Broennimannc, S. Brucha, M. Bychkova, Yu.M. Bystritskyb, M. Daumc, T. Flügelc, E. Frleˇza, R. Froschc, C. Glasera, K. Keetera, V.A. Kalinnikovb, N.V. Khomutovb, J. Koglina, A.S. Korenchenkob, S.M. Korenchenkob, M. Korolijad, T. Kozlowskie, N.P. Kravchukb, N.A. Kuchinskyb, D. Lawrenceh, W. Lia, J. S. McCarthya, R. C. Mineharta, D. Mzhaviab,f, E. Munyangabea, A. Palladinoa,c, D. Poˇcanića∗, B. Ritchieh, S. Ritta,c, P. Robmanng, O.A. Rondon-Aramayoa, A.M. Rozhdestvenskyb, T. Sakhelashvilif, P.L. Slocuma, L.C. Smitha, R.T. Smitha, N. Soićd, U. Straumanng, I. Supekd, P. Truölg, Z. Tsamalaidzef, A. van der Schaafg∗, E.P. Velichevab, V.P. Volnykhb, Y. Wanga, C. Wiggerc, H.-P. Wirtzc, K. Ziocka. aUniv. of Virginia, USA bJINR, Dubna, Russia cPSI, Switzerland dIRB, Zagreb, Croatia eSwierk, Poland fIHEP, Tbilisi, Georgia gUniv. Zürich, Switzerland hArizona State Univ., USA Home pages: http://pibeta.phys.virginia.edu http://pen.phys.virginia.edu Additional slides

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 36 / 34 where m 2 1 ∆ = m − m = 4.5936(5) MeV and = e ' + 0 ∆ 81 while √ √ 9 2 1 − 1 − f (, ∆) = 1 − 1 − − 42 + ln √ 2 4 3 ∆2 − 2 ' 0.941 7 (m+ + m0)

and δπ ∼ 0.035 is the sum of radiative/loop corrections with ∼ 0.03% relative uncertainty. Prior to 2004, Γ and B measured with about 4 % precision.

− − πe3 decay rate in the SM (a pure vector 0 → 0 decay)

2 2 5 3 GF |Vud | ∆ ∆ Γ = Γ0(1 + δπ) = 3 f (, ∆) 1 − (1 + δπ) , 30π 2m+

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 37 / 34 Prior to 2004, Γ and B measured with about 4 % precision.

− − πe3 decay rate in the SM (a pure vector 0 → 0 decay)

2 2 5 3 GF |Vud | ∆ ∆ Γ = Γ0(1 + δπ) = 3 f (, ∆) 1 − (1 + δπ) , 30π 2m+ where m 2 1 ∆ = m − m = 4.5936(5) MeV and = e ' + 0 ∆ 81 while √ √ 9 2 1 − 1 − f (, ∆) = 1 − 1 − − 42 + ln √ 2 4 3 ∆2 − 2 ' 0.941 7 (m+ + m0)

and δπ ∼ 0.035 is the sum of radiative/loop corrections with ∼ 0.03% relative uncertainty.

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 37 / 34 − − πe3 decay rate in the SM (a pure vector 0 → 0 decay)

and δπ ∼ 0.035 is the sum of radiative/loop corrections with ∼ 0.03% relative uncertainty. Prior to 2004, Γ and B measured with about 4 % precision.

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 37 / 34 PiENu experiment at TRIUMF

Csl ring

x I Goal:∆ B/B ' 0.001 V3 Excellent E resolution y I V2 WC3 I Very precise tracking WC1 V1 with Si-strip detectors π+ Nal (TI) and MWPCs V1 WC2 T2 I Data taking completed V2 in 2012 B1 S1S1 S3 V3 7 I O(10 ) πe2 events collected Csl ring I analysis is ongoing.

B2 Tg T1

−4 First result: 1.2344(23)stat(19)syst × 10 [Aguilar-Arevalo et al, PRL 115 (2015) 071801].

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 38 / 34 + 0 + PIBETA result for π → π e ν (πβ) decay [PRL 93, 181803 (2004)]

Pion beta decay yield normalized to measured π → eν events:

exp-t −8 Bπβ = [1.040 ± 0.004 (stat) ± 0.004 (syst)] × 10 ,

exp-e −8 Bπβ = [1.036 ± 0.004 (stat) ± 0.004 (syst) ± 0.003 (πe2)] × 10 ,

McFarlane et al. [PRD 1985]: B = (1.026 ± 0.039) × 10−8

SM Prediction (PDG): B = 1.038 − 1.041 × 10−8 (90% C.L.) (1.005 − 1.007 × 10−8 excl. rad. corr.) ⇒ Most sensitive test of CVC/radiative corr. in a meson to date!

PDG 2018: Vud = 0.97420(21) PIBETA: Vud =0 .9748(25) or Vud =0 .9728(30).

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 39 / 34 + 0 + PIBETA result for π → π e ν (πβ) decay [PRL 93, 181803 (2004)]

Pion beta decay yield normalized to measured π → eν events:

exp-t −8 Bπβ = [1.040 ± 0.004 (stat) ± 0.004 (syst)] × 10 ,

exp-e −8 Bπβ = [1.036 ± 0.004 (stat) ± 0.004 (syst) ± 0.003 (πe2)] × 10 ,

McFarlane et al. [PRD 1985]: B = (1.026 ± 0.039) × 10−8

SM Prediction (PDG): B = 1.038 − 1.041 × 10−8 (90% C.L.) (1.005 − 1.007 × 10−8 excl. rad. corr.) ⇒ Most sensitive test of CVC/radiative corr. in a meson to date!

PDG 2018: Vud = 0.97420(21) PIBETA: Vud =0 .9748(25) or Vud =0 .9728(30).

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 39 / 34 + 0 + PIBETA result for π → π e ν (πβ) decay [PRL 93, 181803 (2004)]

Pion beta decay yield normalized to measured π → eν events:

exp-t −8 Bπβ = [1.040 ± 0.004 (stat) ± 0.004 (syst)] × 10 ,

exp-e −8 Bπβ = [1.036 ± 0.004 (stat) ± 0.004 (syst) ± 0.003 (πe2)] × 10 ,

McFarlane et al. [PRD 1985]: B = (1.026 ± 0.039) × 10−8

SM Prediction (PDG): B = 1.038 − 1.041 × 10−8 (90% C.L.) (1.005 − 1.007 × 10−8 excl. rad. corr.) ⇒ Most sensitive test of CVC/radiative corr. in a meson to date!

PDG 2018: Vud = 0.97420(21) PIBETA: Vud =0 .9748(25) or Vud =0 .9728(30).

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 39 / 34 + 0 + PIBETA result for π → π e ν (πβ) decay [PRL 93, 181803 (2004)]

Pion beta decay yield normalized to measured π → eν events:

exp-t −8 Bπβ = [1.040 ± 0.004 (stat) ± 0.004 (syst)] × 10 ,

exp-e −8 Bπβ = [1.036 ± 0.004 (stat) ± 0.004 (syst) ± 0.003 (πe2)] × 10 ,

McFarlane et al. [PRD 1985]: B = (1.026 ± 0.039) × 10−8

SM Prediction (PDG): B = 1.038 − 1.041 × 10−8 (90% C.L.) (1.005 − 1.007 × 10−8 excl. rad. corr.) ⇒ Most sensitive test of CVC/radiative corr. in a meson to date!

PDG 2018: Vud = 0.97420(21) PIBETA: Vud =0 .9748(25) or Vud =0 .9728(30).

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 39 / 34 Reach of πe2 decay beyond the SM (New Physics)

π π α LNP = ± 2 u¯γαd ± 2 u¯γαγ5d e¯γ (1 − γ5)ν 2ΛV 2ΛA π π (Λ . . . scale ofNP) + ± 2 ud¯ ± 2 u¯γ5d e¯(1 − γ5)ν , i 2ΛS 2ΛP CKM unitarity and superallowed Fermi nuclear decays currently limit:

ΛV ≥ 20 TeV, andΛ S ≥ 10 TeV .

π π −3 At∆ Re/µ/Re/µ = 10 , πe2 decay is directly sensitive to:

ΛP ≤ 1000 TeV andΛ A ≤ 20 TeV ,

and indirectly, through loop eﬀects toΛ S ≤ 60 TeV . In general multi-Higgs models with charged-Higgs couplings π λeν ≈ λµν ≈ λτν, at 0.1 % precision, Reµ probes mH± ≤ 400 GeV .

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 40 / 34 Lepton universality (and neutrinos)

From: 2 2 2 2 2 Γ(π → eν¯(γ)) ge me (1 − me /mµ) Re/µ = = 2 2 2 2 2 1 + δRe/µ Γ(π → µν¯(γ)) gµ mµ (1 − mµ/mπ) 2 3 2 2 2 Γ(τ → eν¯(γ)) gτ mτ (1 − mπ/mτ ) Rτ/π = = 2 2 2 2 2 1 + δRτ/π Γ(π → µν¯(γ)) gµ 2mµmπ (1 − mµ/mπ) one can evaluate: g g e = 0.9996 ± 0.0012 and τ = 1.0030 ± 0.0034 . gµ π gµ πτ For comparison, g g e = 0.999 ± 0.011 and τ = 1.029 ± 0.014 . gµ W ge W

I signiﬁcant consequences in the neutrino sector;

I interesting limits on MSSM extension observables.

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 41 / 34 MSSM calculations (R parity cons.) [Ramsey-Musolf et al., PR D76 (2007) 095017]

0.005 0.005 CURRENT UL (90% c.l.) CURRENT UL (90% c.l.)

0.002 0.002

Μ µ e e R minimal R 0.001 lowest 0.001

selectron, Μ µ SUSY e SUSY PEN GOAL mass e 0.0005 PEN GOAL R smuon 0.0005 R chargino: masses: 0.0002 0.0002

100 150 200 300 500 700 1000 100 150 200 300 500 700 1000 Min m , m GeV m GeV eL µL χ1 0.005 CURRENT UL (90% c.l.)

0.002

µ e

R Higgsino slepton 0.001 mass µ SUSY mass de- e PEN GOAL PEN GOAL R 0.0005 param’s. generacy: µ, mu˜L : 0.0002

0.1 1 10 m m eL µL (R parity violating scenario constraints also discussed.)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 42 / 34 Loinaz et al., PRD 70 (2004) 113004

∆``0 = g 2 ` − 1 g`0

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 43 / 34 PIBETA detector assembly

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 44 / 34 PIBETA detector on platform

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 45 / 34 GEANT4 Monte Carlo Canonical Geant gives energies, timings, and positions Requires additional physics input to simulate full detector response In the Experiment:

I digitized energies and timings of detector elements

I mTPC, beam counters, and target waveforms

I photoelectron statistics smear signal

0.040 Crystal 24 0.025 0.035 Measurement Measurement 0.030 0.020 Simulation No PE Simulation No PE Simulation W PE 0.025 Simulation W PE 0.015 0.020 yield yield

0.010 0.015

0.010 0.005 0.005

0.000 0.000 0 0.5 1 1.5 2 2.5 50 55 60 65 70 75 80 EHodoscope (MeV) ECsI (MeV)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 46 / 34 rf : δt for beam particles

1200 1000 1000 800 800

600 600

400 400

200 200

0 0 80 100 120 140 160 180 200 220 240 260 280 100 120 140 160 180 200 220 240 260 280 300 bin (in B0 beam counter) bin (in DEG counter) 260 zoomed ⇓ 1000 240

220 800

200 600

bin 180 RF= 50.63 MHz 400 160

140 ∆tRF= 19.75 ns 200 120 δt = 57ps 0 0 1 2 3 4 5 6 7 204 206 208 210 212 214 216 218 220 peak point (in DEG) bin

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 47 / 34 Chamber eﬃciencies 1.00 1.00

0.95 0.95

0.90 0.90 0.85 Eﬃciency Eﬃciency 0.85 Outer Chamber 0.80 Outer Chamber Inner Chamber Inner Chamber 0.80 Total 0.75 Total

0.75 0.70 0 10 20 30 40 50 60 70 50 60 70 80 90 100 110 120 130 CsI Ee (MeV) θ 1 140 140 0.9 0.9 0.8 0.8 120 120 ne Eﬃciency Inner Eﬃciency Outer 0.7 0.7

100 0.6 100 0.6 0.5 0.5 θ θ 80 0.4 80 0.4 0.3 0.3 60 60 0.2 0.2 0.1 0.1 40 40 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 φ φ D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 48 / 34 Chamber eﬃciencies: simulation

1.00 1.00 1.00 + Inner Chamber + Inner Chamber + Inner Chamber - Outer Chamber - Outer Chamber - Outer Chamber 0.95 Inner Chamber Simulation 0.95 Inner Chamber Simulation 0.95 Inner Chamber Simulation Outer Chamber Simulation Outer Chamber Simulation Outer Chamber Simulation 0.90 0.90 0.90

Efficiency 0.85 Efficiency 0.85 Efficiency 0.85

0.80 0.80 0.80

0.75 0.75 0.75 0 5 10 15 20 25 30 35 40 45 50 40 50 60 70 80 90 100 110 120 130 140 0 50 100 150 200 250 300 350 E CsI (MeV) θ φ

1.005 1.005 1.005 1.004 Inner Chamber 1.004 Inner Chamber 1.004 Inner Chamber 1.003 Outer Chamber 1.003 Outer Chamber 1.003 Outer Chamber 1.002 Unity 1.002 Unity 1.002 Unity 1.001 1.001 1.001 1.000 1.000 1.000

Data/Sim 0.999 0.999Data/Sim Data/Sim 0.999 0.998 0.998 0.998 0.997 0.997 0.997 0.996 0.996 0.996 0.995 0.995 0.995 0 5 10 15 20 25 30 35 40 45 50 40 50 60 70 80 90 100 110 120 130 140 0 50 100 150 200 250 300 350 E CsI (MeV) θ φ + dE/dx = g(E) in chamber gas π → e νe 70 MeV monoenergetic µ → eνν¯ 0 − 52.5 MeV spectrum Monte Carlo is weighted to simulate chamber eﬃciencies Absorbed into acceptances (blinded)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 49 / 34 Observables to aid discrimination

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 50 / 34 rN : number of π → µ → e (“Michel”)3 events ××10310 107 2500

6 10 2000 Before subtraction 105 1500 After subtraction

Counts 104 Counts Event Selection 1000 103 50 ns window Pileup 500

102 Window 0 20 40 60 80 100 120 140 160 0 50 100 150 200 Invariant Mass (MeV) Decaytime (ns) 5 Nπ-µ-e, Run 2 = (5203.57 ± 0.32) × 10 5 Nπ-µ-e, Run 3 = (9545.50 ± 0.44) × 10 −5 δNπ-µ-e, Run 2/Nπ-µ-e, Run 2 = 6.2 × 10 −5 δNπ-µ-e, Run 3/Nπ-µ-e, Run 3 = 4.6 × 10

π π contribution to ∆Re/µ/Re/µ . . . not signiﬁcant

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 51 / 34 rN : number of πe2(γ) events 107 106 Event Selection 6 10 105 Mass> 125 MeV 105 104 Mass> 125 MeV, ∆χ2 > 0 3 counts 104 counts 10 τﬁt = 26.02 ± 0.02 ns 102 3 Event Selection 10 τ = 26.033 ± 0.0005 ns −5 < decay time < 85 ns π ∆χ2 > 0 10 2 10 −5 < decay time < 85 ns, ∆χ2 > 0 1 0 20 40 60 80 100 120 140 160 0 50 100 150 200 inv. mass (MeV) decay time (ns)

40000 −5 < decay time < 85 ns, 35000 Waveform cut is needed, ∼ 97% ∆χ2 > 0 30000 Nπe2(γ), Run 2 = 1387431 ± 1179.91 25000 Michel Simulation Nπe2(γ), Run 2 = 2383805 ± 1545.93 20000 Subtraction counts 15000 δNπe2(γ), Rn 2&3 10000 ' 5.1 × 10−4 5000 Nπe2(γ), Rn 2&3 0 80 90 100 110 120 130 140 150 160 inv. mass (MeV) D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 52 / 34 πe2 tail including photoneutron corrections 0.044

0.042 σ δ σ mean,Varl + Varl σ 0.040 mean,Varl σ δ σ mean,Varl - Varl 0.038 ∈ 0.036

0.034

0.032

0.030

114 114.5 115 115.5 116 116.5 117 117.5 118 118.5 invariant mass (MeV)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 53 / 34 MC simulated vs. experimental πe2 tail

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 54 / 34 note

(FT = −56 ± 17)

Pre-2004 data on pion form factors

s cvc 1 2~ |FV | = =0 .0255(3) . m α πτπ0 π

4 FA × 10 reference

106 ± 60 Bolotov et al. (1990) 135 ± 16 Bay et al. (1986) 60 ± 30 Piilonen et al. (1986) 110 ± 30 Stetz et al. (1979) 116 ± 16 world average (PDG 2004)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 55 / 34 Pre-2004 data on pion form factors

s cvc 1 2~ |FV | = =0 .0255(3) . m α πτπ0 π

4 FA × 10 reference note

106 ± 60 Bolotov et al. (1990) (FT = −56 ± 17) 135 ± 16 Bay et al. (1986) 60 ± 30 Piilonen et al. (1986) 110 ± 30 Stetz et al. (1979) 116 ± 16 world average (PDG 2004)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 55 / 34 PIBETA πe2γ 400 1 2 3 400 400 diﬀerential 300 distributions: 200 2009 analysis of 200 200 100 1999-01, 2004 0 0 0 data sets. 0 0.5 1 0.5 1 0.5 1 4 400 300 300 5 6 300 200 200 200 100 100 100 Number of events 0 0 0 0.5 0.75 1 0.5 1 0 0.5

600 1 2 3 4 7 8 8 400 π 400 )/m 5 e

200 6 200

y=2(E 7

0 0 0 0.25 0.5 0.5 1 0.5 1 2 λ=(2Ee/mπ)sin (Θeγ /2) x=2(Eγ /mπ)

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 56 / 34 RMD preliminary results, cont’d.

Preliminary result for RMD branching ratio (thesis E. Munyangabe):

−3 Bexp= 4.365 (9)stat. (42)syst. × 10 , 29× −3 ◦ BSM= 4.342 (5)stat-MC × 10 (for Eγ > 10 MeV, θeγ > 30 ) 2 χ 18 Analysis of PS subset: 16 13 MeV < Eγ < 45 MeV, and η = 0.006 ± 0.017 14 10 MeV < Ee+ < 43 MeV, yields 12 χ2/NDF = 0.8 10 η¯= 0.006 (17)stat. (18)syst., or 8

6 η¯< 0.028 (68%CL) .

4 2 ∼ 4× better than best previous -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 η experiment (Eichenberger et al, 84). NB: preliminary results!

D. Poˇcani´c(UVa) Rare π decays: The πe3 decay 7 Nov ’19/INT 57 / 34 Radiative muon decay: + + µ → e νeν¯µγ

BR ∼ 10−3 for energetic γ’s

I Sensitive to admixtures beyond V − A

I Limiting factor in µ → eγ LFV searches

D. Poˇcani´c(UVa) Rare π decays: Radiative muon decay 7 Nov ’19/INT 58 / 34 RMD: µ+ → e+ννγ¯ , [E. Munyangabe’s analysis of 2004 PIBETA data]

×103 ×106 12 Signal MC

CsI Time Coincidence xx xx xx 100 cut Misid Events 10 N0. of Events = 518813 946 σ = 0.71 ns ±

Entries/0.5 ns 80 Signal MC + Misid. events 8 DATA(measured) 60 6

40 4

2 20

0 -10 -8 -6 -4 -2 0 2 4 6 8 10 0 -1xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx -0.8xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx -0.6xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx -0.4xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx -0.2xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx 0xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx 0.2xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx 0.4xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx 0.6xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx 0.8xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx 1 xxxxxxxxxxxxxxxx ∆t = te - tγ (ns) cos θ 60000 Signal MC 40000 Signal MC cut Misid Events cut Misid Events 50000 35000 Signal MC + Misid. events Signal MC + Misid. events DATA(measured) 30000 DATA(measured) 40000 25000

30000 20000

15000 20000 10000 10000 5000

0 15 20 25 30 35 40 45 50 55 10 15 20 25 30 35 40 45 50 55 Photon Energy [MeV] Positron Energy [MeV] ”Split clumps” very well accounted for! ∼30-fold improvement in precision of the RMD BR. ∼4-fold improvement over best previous limit onη ¯ Michel parameter.

D. Poˇcani´c(UVa) Rare π decays: Radiative muon decay 7 Nov ’19/INT 59 / 34 PEN RMD plots (Run 3 data set)

1800 1000 1600

800 1400 1200 Data 600 Data 1000 Simulation 800

counts 400 Simulation counts 600

400 200 200

0 0 0 20 40 60 80 100 120 140 160 180 200 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 24000 decay time (ns) cos θeγ 22000 20000 18000 16000 Data Simple track requirement, 14000 Data selection using target cuts, 12000 Simulation 10000 Adding coverage to PiBeta data set. counts 8000 6000 Ready for new BR andη ¯ evaluations. 4000 2000 0 -20 -15 -10 -5 0 5 10 15 20 D. Poˇcani´c(UVa) tγ − te Rare π decays: Radiative muon decay 7 Nov ’19/INT 60 / 34