The Current Status of the Fermilab Muon g–2 Experiment^†

Round 1

Reviewer 1 Report

The paper is solid and deserves publication

Author Response

Thank you very much for your kind consideration. 

Based on the comments of other reviewers I have uploaded the first round of corrections.

Author Response File: Author Response.pdf

Reviewer 2 Report

Thanks for the nice paper. Some comments:

L3: ...found a discrepancy from the SM predicted value of about three standard deviation.

L5: 540 parts per billion

L7: attained the same level of statistics as E821

L8: I will compare the statistics of this run with E821 and discuss the future outlook.

L26: This could indicate several new physics models.

L29: a muon mass is *corrected* by radiative effects.

L30: Some new physics models may include Z', W', universal extra dimensions and littlest Higgs which assume a typical weak-interaction coupling.

L31: Other possibilities can represent unparticles...

L33: "in the 10 - 100 MeV mass range", mass range of what? photon? light particles?  "extremely small coupling", coupling between what?

L35: continue to *further* constrain...

L36: This can be achieved by acquiring 21 times more statistics...

L45: missing a reference for the below formula, e.g. E821 PRD.

L50/53: The right/left plot of *Figure* 3

L55: The details of each of these components are described in the subsequent sections.

L56: A positron/electron calorimeter is placed at a position indicated by the number in green (1,2,...24).

L57: The decayed positrons are detected by the 24 calorimeters shown in Fig. 3.

L60: due to pile-up, gain instabilities, beam losses and other systematic effects.

L63: an improved collection rate

L66: (after several turns)

L67: This helps to...

L68: which provide better spatial separation between pions and background protons

L69: eliminates *most* background

L72: ...with other software, a month of the first...

L73: The first physics run (Run 1) from the end of March to July 7th 2018 took place and collected almost twice the raw positron data compared to the E821 experiment.

L75: The next physics run (Run 2) is scheduled to run from December 2018 to July 15th 2019, which is expected to collect ?? times more data than Run 1.

L84: onto the *ideal* orbit

L88: focusing

L94: Further improvements and checks in Run 1

L95: a few detectors were installed...

L98: are both *used* to 

L98: In Run 1 a single fiber harp was used...

L100: an electric field at 180 near calorimeter 12? where does this 180 electric field come from? you meant vertical electric field maybe?

L101: respectively in Run 1 as shown in Fig. 3.

L103: Fiber Harps – Checking the beam in Run 1

L107: Two of such harps were used... ---> this conflicts with L98 where it says that a single harp was used, which one is true??

L108: and the other places the fibers horizontally

L110: The right plot of Figure 4 shows the horizontal measurements in y...

L119: A forward extrapolation...

L120: (Figure 5 right).

L121: produces a good imaging of the calorimeters (Figure 5 center).

L122: show a good particle discrimination

L123: (Figure 5 left)

L129: missing a reference to omega_a systematics improvement, e.g. TDR (maybe it should be added to omega_p reference as well).

L134: Table 1 shows...

Figure 6: The left plot shows the customized pulse shape fitting of all 54 crystals of a calorimeter. The right plot shows the time resolution measurements fitted with a Gaussian function form for each calorimeter

L142: We reconstruct the pulses read by each crystal with a customized pulse shape fitting (called template fitting) to the actual pulses (shown in the left plot of Figure 6).

L143: The time resolution of the crystals is 25 ps at 3 GeV providing a pile-up separation of 4.5 ns.

L146: to keep gain fluctuations at the sub-per mil level --> uncertainties are much smaller than sub-per mil!

L150: divided with a ratio

Figure 8: after applying temperature corrections.

L162: Remove (Timing and gain calibrations at the subpermil level requires the system to be very stable). It is redundant and obvious.

L163: both the SM and the LM show gain fluctuations in the order of 10^-4 in a time scale of hours, as shown in Fig. 8.

L166: Remove (the most important criteria for)

L174: in Run 1 further increased the uniformity of the magnetic field to be within +-25ppm of nominal value.

L177: trolley measurements of Bo ? --> Bo undefined, the magnetic field?

L178: We used plunging probes to cross calibrate off-central probes with a better position accuracy.

L180: to improve the field mapping.

L181: the *improved* stability

L182: in Fig. 9. Remove (The brown shows...), redundant of Figure 9 caption.

L183: Run 1 analysis status

L184: Several analysis techniques are developed and performed with the Run 1 dataset.

L185-192: (**There are many more methods than T and Q, e.g. R method and possibly new ones are being developed, so let's try not to be conclusive.**)

All analysis methods utilize the event time and/or energy information reconstructed by the calorimeters with additional information from other detectors. One analysis method builds the events vs. time-in-fill histogram (so-called T-method) and then parameterizes the distributions with Equation 5 plus various systematic effects to extract omega_a. T method selects events with reconstructed energy above a threshold energy (1.86 GeV) with the same weight. Pile-up correction is important for this method. From the previous simulation study [8] with T-method, a >95% polarization of the muon beam, an asymmetry of A = 0.38 and the number of events in the fit No = 1.6 X10^11 yield a 100 ppb statistical uncertainty.  A T-method fit to the positron time distribution is shown on the left of Figure 10. The fit residual together with its Fourier transform is shown on the right of Figure 10. The Fourier transform on the fit residual shows structures from CBO effects ( fCBO), vertical oscillations ( fvw) and muon losses (with other effects).

Figure 10: A fit to the modulated positron distribution with time (left). A plot of the fit residual (top right) and a Fourier transform of the fit residual (bottom right).

L193-201: Another analysis method called Q(charge)-method digitizes the detector current vs. time distribution, which is proportional to the energy deposited in the calorimeters vs. time from the decayed positrons. All events are weighted inherently with energy and have a close to zero energy threshold (to reject background noises). The Q-method then parameterizes the energy distribution to extract omega_a. One advantage of this approach is that it does not require pile-up correction. There are also other analysis methods besides T- and Q-methods optimized in various ways and with different treatments of systematics and corrections. All the methods serve as a cross check of each other and will be later combined to produce the final result.

We perform a blind analysis with both hardware offset (in clock frequency) and software offset (for each analysis method) to ensure that there is no bias on the final result.

L203: In Run 1 we were able to achieve performance improvements in beam transportation, beam injection and detector systems.

L204: as discussed above.

L205: but the current rate of positrons per fill is still below the expectation by a factor of two (compared to TDR Goal [8], as shown on the left of Figure 11).

Figure 11: ...with future projections...in red for Run 1.

L208: In Run 1 we accumulated the *raw* statistics of ~2 times the BNL experiment

L209: After applying data quality cuts on reconstructed data, the accumulated statistics is about the same as the BNL experiment.

L210-213: A complete analysis of this data is expected to be done by the second half of 2019. The Run 1 result is expected to be at the same level of precision with the BNL experiment. In a few years we expect to measure the anomalous magnetic moment of the muon with the precision of 140 ppb. If the previously measured value of alpha_mu is confirmed, we will have a 7 sigma discrepancy from SM, which will be a firm indication of new physics beyond the Standard Model.

Author Response

Thank you very much for the comments. I tried my best to apply most of the changes you suggested. 

I have listed below a few changes that require an explanation of what I rephrased or rewrote (note that the line number may have changed since I applied your suggestions):

L33: "in the 10 - 100 MeV mass range", mass range of what? photon? light particles?  "extremely small coupling", coupling between what? 

Mass range is of the light particles and Coupling b/w muon and the dark photon. I changed the language to “The existence of dark photons or dark Z [9] from very weakly interacting (due to extremely small coupling of the muon with the dark photon) and very light particles corresponding to a narrow mass range from 10 - 100 MeV,  can also be possible.” 

L75: The next physics run (Run 2) is scheduled to run from December 2018 to July 15th 2019, which is expected to collect ?? times more data than Run 1. 

L80: 5 to 10 times 

L98: In Run 1 a single fiber harp was used...

Changed to “two fiber harps were used” – I confirmed the information from our run logs. Sorry for being wrong.

L100: an electric field at 180 near calorimeter 12? where does this 180 electric field come from? you meant vertical electric field maybe? 

Yes, I meant a vertical electric field in general (not just at 180). Rephrased to “In Run 1 two fiber harps were used to study behaviour of the muon beam flux and the horizontal and vertical oscillatory effects of the beam due to an electric field. These harps were installed at 180^o and 270^o near calorimeters 12 and 18 respectively as shown in Fig. 3.”  Also changed figure 3 accordingly.

L119: A forward extrapolation...

L125-127 (after updating).  I tried rewriting as "A forward extrapolation of the track to map with the front face of the calorimeter from the point of tangency of the muon track allows the determination of the beam profile distribution (Fig. 5 right). This, in turn, produces a good image of the positron distribution on the crystal grid of the calorimeters (Fig. 5 center)." 

L146: to keep gain fluctuations at the sub-per mil level --> uncertainties are much smaller than sub-per mil!

No, I think we should achieve a statistical uncertainty of 0.04% and a systematic one at 0.1% within the time of the fill (700 us) regarding the gain corrections, so the statement is correct. 

L185-201: (**There are many more methods than T and Q, e.g. R method and possibly new ones are being developed, so let's try not to be conclusive.**)

L192-212(new line # after updating): Thank you for the clarification. I just changed exactly as you suggested. 

Thank you very much!

Author Response File: Author Response.pdf

Reviewer 3 Report

see report attached

Comments for author File: Comments.pdf

Author Response

Thank you very much for point out these errors!

Just for your reference I have listed the responses below and submitted/attached the new version of the proceeding.

1) I think Eq. (5) should read

N(t,E₀) = N₀(E₀) e−t/γτ (1 + A(E₀) cos(ω _at + φ(E₀)))

with E0 a chosen cut energy on the positron spectrum. The phase and the time dilatation Lorentz factor are missing. The experiments performs a 5 parameter fit, I guess; the formula given has only 4 parameters.

I fixed the equation as you suggested. The fit parameters are N_0, A, ω _a, φ and muon lifetime (tau). Although the γτ can be fixed to 64.4 us but it is one of the fit parameters in the analysis.

 

2) Fig. 7 has problems with overlays and deserves appropriate improvements.

I moved the labels to avoid the overlays, changed some font sizes etc. Hope it looks better now.

 

3) Ref. 5 Stockinger −− ! St¨ockinger

I fixed it.

 

4) Ref. 10 the given link is not available to the public and should be replaced

or dropped.

This is an internal note and so I dropped it.

 

Thank you once again!

Author Response File: Author Response.pdf

Reviewer 4 Report

This paper reports the status of the Fermilab Muon g-2 experiment. Experimental techniques and preliminary results for the first run were described.

The comments below are intended to make the paper more approachable to readers interested in the progress of the Muon g-2 measurement. 

L5: The BNL precision should read 540 parts per billion instead of million

L13: of mass m and charge q" is not needed

L15-16: quantum electrodynamics (QED), electroweak (EW), and quantum chromodynamics (QCD), as shown in Fig. 1. (space between Fig. and 1)

Figure 1: Title should read "The SM contribution to a_{\mu} ...." to be precise

Figure 1: The Feynman diagrams are not consistent with each other (some are with the symbol B and some are not). The first diagram is the tree-level diagram of the magnetic moment (where g=2), the subsequent three diagrams are examples of the SM corrections from QED, EW and QCD. Sub-labels (a,b,c) are missing.

L17-18: of a virtual photon in Fig. 1(a), i.e. the "Schwinger term" (when the first diagram is omitted)

L21: Fig. 2 (space)

L21: The yellow band is the prediction plus uncertainty from the KNT18 calculation

L24: Diagram reads 3.7 sigma but 3.6 sigma is written in text

L38: muon anomalous magnetic moment, "magnetic" is missing

L41-42: "including the Larmor and Thomas precession" should follow \omega_{s} instead of \omega_{c}

Equation (4): \omega_{p}, \mu_{\mu}/\mu_{p} are not explained. 

L48: "These positrons modulate with a frequency of \omega_{a}" should read "Number of these positrons modulate"

L50: For consistency use Fig. 3 instead of figure 3

L51: "muonic hyperfine experiment" -> "muonium hyperfine splitting experiment" to be precise

L54: The collimators (C) and the NMR trolley garage are not shown in Fig. 3.

L62: the BNL to Fermilab improvement in statistical uncertainty should be from 460 ppb to 100 ppb

L63: The separation is mainly done on proton vs muon while the pion flux is reduced due to its shorter lifetime

L65-67: This is incorrect. A rewrite is needed. Muons are produced from pions decay in the long decay channel before the beam (a mixture of protons, pions, muons, etc) is injected into the delivery ring

L71-73: "To test all hardware .... " This sentence is broken. 

L74: "... took place were we collected ..." should read "... took place where we collected ..."

L75: July 15th (without superscript for "th" for consistency)

L83: ... is displaced radially "outward" by 77 mm ...  (for clarity)

L84: omit "the help of"

L86-87: self-contradicting statement of "enhances the radial focusing" ... "but defocuses horizontally" 

L93: [10]. (period after citation)

L97: T0 and IBMS are outside the storage ring and should not be able to monitor the beam during kicking and scrapping process. 

L100: Two straw tracker stations to be exact

Figure 4: A period before the text should be removed

Figure 4: Vertical BO is not explained

Figure 4 right: It is not referenced in the text

L111: It is not clear by the sentence "Maximum oscillations are in the center of the beam". Maximum oscillation of what? The beam intensity or the beam motion or? 

L119-123: This paragraph is a bit confusing. A rewrite is needed. First sentence should be about the forward extrapolation of the track to the front face of a calorimeter. The role of the ideal muon orbit is not clear here. What does "a good imaging of the calorimeters" mean here? 

Table 1: It is not clear how the Laser system is a key element in helping with pileup

Table 1: It is not clear how the Calo + Laser system is a key element in helping with Lost muons

L139: PbF_{2}, Symbols for elements in the periodic table should be roman instead of italic

Figure 6 right: It is not clear what kind of time distributions are being plotted here.

L142:  ... by each crystal "by" fitting a customized pulse shape ...

L146: All the 1296 "channels" of the calorimeters .... (technically it is the crystal+SiPM+electronics that is being calibrated)

L150: ... each laser is divided "at" a ratio

L152: ... to "four of the calorimeters" ...

Figure 7: It is not referenced in the text

L154: PbF_{2}, Symbols for elements in the periodic table should be roman instead of italic

L164: ... as shown in Fig. 8. (Fig. is omitted)

L170: .... to quadrupoles and "to" eliminate fringe field ...

L177: B_{0} is not explained

L189: What does "pile up protection" mean here? From L144, the pile up separation is 4.5 ns. How do you deal with pile up below 4.5 ns?

L191: Is this N_{0} related to the N_{0} in Equation (5)? If the total count in the histogram is 1.6 x 10^{11}, then N_{0} from the fit (Eq. 5) should be smaller than 1.6 x 10^{11} as 1.6 x 10^{11} is the total count of the histogram.

L193: How about the T-method? Is the positron reconstructed without digitizing the detector signal? 

L197: Again, what is a "pile-up protection"? Use "pile up" instead of "pile-up" (or pileup) for consistency. 

L199: Fig. 10. (use of Fig. and a missing period after 10)

L200-201: While the top right plot shows very flat residual, the bottom right plots several peaks in the Fourier power spectrum. What is the explanation for that? How are these additional frequencies affecting the measurement?

L203-207: Only \omega_{a} is mentioned here. How about \omega_{p}? Is there a plan to achieve the TDR rate of positrons/fill?

L208-209: It seems that after the data quality cut, the amount of data is reduced by half. This seems to be contradicting L203 where the performance of the experiment was improved when compared to BNL E821. What is the main reason for this reduction? 

Author Response

Thank you very much for the valuable suggestions. Please note that the line numbers have changed since I updated. Responses to a few of your questions and changes I made are as follows:

Figure 1: The Feynman diagrams are not consistent with each other (some are with the symbol B and some are not). The first diagram is the tree-level diagram of the magnetic moment (where g=2), the subsequent three diagrams are examples of the SM corrections from QED, EW and QCD. Sub-labels (a,b,c) are missing.

I have changed the labels of each figure to a, b, c and d and labeled them accordingly.

L65-67: This is incorrect. A rewrite is needed. Muons are produced from pions decay in the long decay channel before the beam (a mixture of protons, pions, muons, etc) is injected into the delivery ring.

L69-71(line # changed since I updated) Rewrote as: Pions with an energy of 3.11 GeV are selected which decay to mouns in a long decay channel before the beam (a mixture of protons, pions, muons, etc.) is injected into the delivery ring.

L71-73: "To test all hardware .... " This sentence is broken.  

L76-77 - Changed to - ...with other software, a month of the first...

Figure 4 right: It is not referenced in the text  -

Fixed this in line 116 replaced with "The right plot of Fig. 4 shows the horizontal measure in y of the beam profile."

L119-123: This paragraph is a bit confusing. A rewrite is needed. First sentence should be about the forward extrapolation of the track to the front face of a calorimeter. The role of the ideal muon orbit is not clear here. What does "a good imaging of the calorimeters" mean here?

L125-128(new line #): I tried rewriting as: A forward extrapolation of the track to map with the front face of the calorimeter from the point of tangency of the muon track allows the determination of the beam profile distribution (Fig. 5 right). This in turn produces a good image of the positron distribution on the crystal grid of the calorimeters (Fig. 5 center).

Figure 6 right: It is not clear what kind of time distributions are being plotted here.

Rephrased to “time resolution measurements”

L142:  ... by each crystal "by" fitting a customized pulse shape ...

L149: Rephrased to "We reconstruct the pulses read by each crystal with a customized pulse shape fitting (called template fitting) to the actual pulses (shown in the left plot of Fig. 6)" as suggested by another reviewer.

L189: What does "pile up protection" mean here? From L144, the pile up separation is 4.5 ns. How do you deal with pile up below 4.5 ns?

For pile up below 4.5 ns will not be separable in time (as it is below the resolution) and should probably automatically considered as pile up (the TDR mentions an artificial dead time of 5 ns). We consider two pulses to be pile up even if they can be resolved as separate to a pile up below this time. Is it required to mention this detail?

Since I used pile up several times I defined it in its first usage in line 62 as - refers to overlapping events that originate from separate muon decays which are too close to each other in time and space to be resolved into individual pulses.

L191: Is this N_{0} related to the N_{0} in Equation (5)? If the total count in the histogram is 1.6 x 10^{11}, then N_{0} from the fit (Eq. 5) should be smaller than 1.6 x 10^{11} as 1.6 x 10^{11} is the total count of the histogram.

I think that is right.

L200-201: While the top right plot shows very flat residual, the bottom right plots several peaks in the Fourier power spectrum. What is the explanation for that? How are these additional frequencies affecting the measurement?

The top plot in fig. 10 show the residues (data - fit function after fitting) in the time domain. I think we expect that the frequency dependent structure arising from the betatron oscillations or other factors will not be evident here. But a Fourier transform to the frequency domain will show us the frequency dependent structures like the effect of the muon beam motion due to resonances from  the frequncy of the coherent radial beam - "coherent betatron oscillations", f_cbo (which is max) and certain beat frequencies wrt to the anamolous freqeuncy f_a itself at f_cbo+/-f_a. The vertical component The very initial peak is well taken care of (I have seen it in some presentations) if muon losses, pile up correction etc. is applied well. Yes, there will be a very small effect in our measurements for these structures in general and so we need to minimize them. Thus proper gain correction, muon loss, pile up are a few things I can think of that would reduce these generally. To minimize the f_cbo, I think the phase space mapping is very important and I think the closer the f_cbo is to f_a the better the systematic error. This is my understanding but am not sure if I should have all the detail in this proceeding.

BTW, I have changed the text based on the review of another referer. Could you please go through this specific portion again and suggest if I need to explain more?

L203-207: Only \omega_{a} is mentioned here. How about \omega_{p}? Is there a plan to achieve the TDR rate of positrons/fill?

I could mention \omega_{p}, but I am thinking if it would be redundant or not as I mentioned in L175 in the field uniformity section and probably \omega_{a} is more important. But if you insist I could add it in this section too. Kindly suggest what you think.

We do plan to achieve the TDR rate of positrons/fill.

L208-209: It seems that after the data quality cut, the amount of data is reduced by half. This seems to be contradicting L203 where the performance of the experiment was improved when compared to BNL E821. What is the main reason for this reduction?

I think this is partly due to a careful reconstruction of data which gives very good quality data. It involves several cuts for muon losses, pileup, reducing CBO effects, mapping phase space are a few I can think of. The runtime is much lower and positron fill rate is low too. These are anticipated to improve which will surely help. We hope to collect 5 to 10 times more data this current run and that will help achieve our goal.

I mentioned this in L80-81.

I submitted/attached the new version.

Thank you very much! I really appreciate the time and effort you put for your great insight!

Author Response File: Author Response.pdf