1. ¹ N ! e N Physics Backgrounds
Decay in Orbit, Radiative Muon Capture, Normalization and other Effects
A.Norman
University of Virginia

2. Overview Introduction Lifetimes and Capture fractions Decay in Orbit
Tails and endpoints
Modeling & Approximations
Radiative Muon Capture
Approximations and projected backgrounds

3. Normalization Intro. Reminders:
To measure ¹ N ! e N we normalize to the total number of muons that stop in a target and cascade down to a 1S orbital
This process determines our single event sensitivity
BUT, we report a branching ratio relative to ordinary muon capture
The total capture rate for us will have 3 components of interest
¹ ! e coherent conversion (we hope)
Ordinary Nuclear capture ¹ + N ! º N*
Decay in orbit ¹ + N ! e º º N
This is not kinematicly the same as decay in flight because of the nuclear recoil term
The challenge is to get the relative and absolute normalizations of these terms correct, specifically in the neighborhood of the ¹ ! e signal region.
For simulation, these normalizations will depend on a combination of measured parameters (mostly old muon data) and approximations for the long tails

4. ¹ Total Capture Rates Updated ¹- mean ¿
Relative fraction of nuclear capture to decay in orbit has strong a Z dependence
We rely on comparison of ¹+ lifetime to ¹- lifetime on a given target to determine the relative fractions of capture and decay in orbit processes.
Data for the ¹- lifetime on some nuclear targets varies enough to be a problem
for Z=13 the best measurement was assumed 880§10 ns (MECO)
But more modern measurement yield 864§1ns [Bergbusch 1999]
Difference leads to ¼ 2% changes in fractions and absolute normalization
But also affects the resulting beam time structures and time window acceptance
Small difference on AL, but significant enough that the proper number must be used in simulations
Updated mean lifetimes and capture rates exist for: O, Al, Si, Ca, Ti, Zr and Ag
Nucleus
Capture Fraction
Lifetime (ns) O §
§ 2.0 Al §
864.0 § 1.0 Si §
756.0 § 1.0 Ca §
332.7 § 1.5 Ti §
329.3 § 1.3 Zr §
110.0 § 1.0 Ag §
87.0 § 1.5
Updated ¹- mean ¿
The most recent measurements of ¹- lifetimes and capture rates come from TRIUMP [Bergbusch 1999 PRC ]

5. Aside: ¹ lifetime and beam windows
Knowing the bound ¹- life time well is required to get the acceptances right for the live window.
Small variations in the actual lifetime affect the optimal start of the first live window
The first live window dominates the variation in the total acceptance
Match of the muonic atomic lifetime to the readout window to maximize acceptance vs prompt background. Places requirements on the beam structure
Strong Dependence of first readout ¿ 864

6. Heavy Nuclei
For heavy nuclei, to correctly calculate the total capture rate, we need to include a correction factor for the binding energy of the ¹- to the decay in orbit rate
This is done with a “Huff factor” Q which suppresses the DIO contribution
The Huff factor for AL is only but again shifts the absolute normalization
On heavier nuclei this effect accounts for 2% (Ti) up to a 15% (Au) suppression of the decay fraction
Capture to DIO rates have been calculated and corrected in this talk. Mostly we verified or updated the Al, Ti and Au numbers.
What this leads to is a trade off in stopping target choice between:
Higher DIO rates (background) with endpoint near 105MeV or
Large nuclear capture rate (short lifetime , beam window acceptance, lower endpoint energy)

7. Capture to DIO Fractions
Decay Fraction
Light nuclei (Z < 25)

8. High energy tail from recoil
DIO Spectrum
The reason DIO is so important is that the normal decay in flight spectrum is modified to include a high energy tail (> 57MeV) coming from the nuclear target absorbing the recoil momentum and shifting the possible electron energy up a maximum Emax
Emax depends on the available muon energy E¹ which depends on the binding energy of the target nucleus
High energy tail from recoil

9. ¹ Conversion/Decay Endpoints (light nuclei)

10. ¹ Conversion/Decay Endpoints (heavy nuclei)
Note: for high Z stopping targets, lower Z materials near the beam (support structure) can contribute background well into the signal region from stopped muons
Difference is due to nuclear screening
when the 1S muonic oribital overlaps
Or is effectively within the nuclear radius
In the high Z region near Gold the difference is not well known except where explicitly measured. (need to mention isotopic differences etc…)

11. DIO Tail
However……
High end recoil tail falls sharply above the Michel edge.
Near the end point this distribution changes slope rapidly. (at Emax)

12. Above 100MeV…
The normalized electron energy spectrum is calculated for 27Al. Calculation includes the high side tail from MeV in 5MeV steps. [Watanabe 1993]
The full form of the spectrum isn’t calculated above 100MeV
Instead approximations for the endpoint spectrum assume a rapid slope falling like (Emax – E)5 where the normalizations and corrections to this form make assumptions about the interaction [Shanker 1982, Shanker 1997]
Need to reconcile the full (normalized) spectrum w/ endpoint approximations to obtain the correct probability functions for estimating the background contribution from DIO.
Or extend the full calculation past 100MeV (and in finer bins) on the targets of interest

13. Endpoint Approximations
The most basic endpoint approximation assumes the shape of the distribution falls as ±5 where ± is the distance between the Emax and the decay electron energy.
This must be normalized (see MECO-004)
This neglects recoil, need to correct
Including recoil [Shanker 1982] :
Need to pay attention to normalization
Peg the distribution probabilities at 100MeV
Shape differences alone contribute and extra integrated probability for DIO above 100MeV ¼ 4.3£10-15
Still neglects nuclear corrections
Neglecting recoil
Underestimates the end point contribution ¼ 8% at 104 MeV
Norm determined by Watanabe calc at 100MeV

14. Shanker Corrected
The endpoint shape requires further corrections based on the nuclear target.
Coefficients are calculated on limited nuclei, not directly available for Al and Ti
Resulting corrections are supposedly accurate near the endpoint but deviate in slope below 100MeV
Constants D, E, F determined from interpolation
Still requires overall normalization determined by match to probability and slope of Watanabe calculations near 100MeV
Mu2E & MECO both have considered this, absolute normalization is still uncertain.
Depends to highly on accuracy of theory spectrum.

15. Watanabe/Shanker Match 100MeV

16. Watanabe/Shankar Slope Match

17. Effect of DIO Modeling
Inclusion of the nuclear corrections reduces the DIO probability near the end point
The effect results in a factor of 7 suppression of the DIO tail above MeV (3.3 above MeV)
Suppression is greatest in the ¹ ! e signal region

18. Estimated Background
The primary physics background for ¹ N ! e N conversion is the high energy tail of the DIO spectrum.
The endpoint of the DIO spectrum is the same as the coherent conversion electron energy
The sensitivity of the experiment can be characterized by the signal over fluctuation in background
In the case of Mu2E the Figure of Merit (FoM) in the signal region for a signal to nominal background (DIO dominated) is 5.5 from simulation

19. Radiative Muon Capture
Spectrum and Background

20. Radiative Muon Capture (RMC)
Process is:
Measurements on light nuclei dominated by background of brem off DIO, leads to large uncertainties
Physics interest is access to gp (induced pseduoscalar coupling)
gp extracted from shape of high side tail on ° spectrum
Recent data exists on some nuclear targets (O,Al,Si,Ti,Zr,Au)
Possible background for ¹ N ! e N coming from high energy conversion of °
Process is rare. Branching fraction for E° > 57 MeV » 1.4 £ 10-5
But the tails are not well known
RMC measurements typically use a “closure approximation” which neglects higher nuclear states resulting in a truncation of the RMC ° energy spectrum
For 27Al the truncated endpoint is at MeV
These approximations (Fearing and welsh models) are known to be poor for (A<40)

21. RMC Background
For ¹ ! e conversion the RMC background contribution comes from conversion of ° near the signal region (>90 MeV)
This corresponds to the region that is excluded from closure approximations for the RMC spectrum
We can estimate the RMC rate in an adhoc manner by looking at the integrated rate at the endpoint

22. RMC Tail Spec
It is possible to compute the branching ratio of RMC to OMC in the tail region
We integrate from a lower limit to the endpoint
Need to then compute conversion probability, etc…
Elower Al Ti 85
4.53£ 10-7
2.64£ 10-7 86
2.41£ 10-7
1.19£ 10-7 87
1.07£ 10-7
3.99£ 10-8 88
3.41£ 10-8
6.64£ 10-9 89
5.03£ 10-9
3.15£ 10-11 90
3.87£ 10-12

23. RMC Summary We don’t know the true background contribution from RMC
Requires knowledge of the tail past the truncation point
We can determine an upper limit on the contribution from current data, but this most likely a poor estimate.
Need to still compute the conversion probability and acceptances of resulting e in the spectrometer

24. Understanding Sig/Background
In the real detector all the base distributions are convoluted with both:
Detector Resolution
Energy Loss (dE/dx)
The dE/dx results in roughly a 1 MeV downward shift in the spectra
The detector resolution is primarily a low side (long tail)
All the backgrounds (DIO & RMC) model’s real contributions depend highly on detector resolution and the amount of material in the particle trajectory
These have not been fully modeled yet
DIO Tail + dE/dx Shift
Signal Peak
Shifted (dE/dx)
Endpoint
Detector Resolution Tail + dE/dx
Peak Sensitivity 103.5MeV

25. Summary DIO background model needs to be verified
Suffers from normalization and shape uncertainties in the signal region
RMC background needs data that includes higher nuclear states to model tail
Other muon properties which affect real acceptances or the global normalization need to be verified or updated

26. Backup Slides
DIO and RMC Backgrounds