# Search for lepton-flavor-violating decays of the tau lepton at a future muon collider

### Submission summary

 As Contributors: Gholamhossein Haghighat Preprint link: scipost_202111_00031v1 Date submitted: 2021-11-18 08:56 Submitted by: Haghighat, Gholamhossein Submitted to: SciPost Physics Proceedings Proceedings issue: 16th International Workshop on Tau Lepton Physics (TAU2021) Academic field: Physics Specialties: High-Energy Physics - Phenomenology Approach: Phenomenological

### Abstract

Tau leptons can have lepton-flavor-violating (LFV) couplings to a muon or an electron and an Axion-Like Particle (ALP). ALPs are pseudo Nambu-Goldstone bosons associated with the spontaneously broken global U(1)$_{PQ}$ symmetry. LFV ALPs have been of a great interest in the last several decades as they can address some of the SM long-lasting problems. Assuming a future muon collider proposed by the Muon Accelerator Program (MAP), we search for LFV decays $\tau\rightarrow\ell a$ ($\ell=e,\mu$) of one of the tau leptons produced in the muon-anti muon annihilation. The ALP mass is assumed to be in the range 100 eV to 1 MeV and three different chiral structures are considered for the LFV coupling. Using a multivariate technique and performing a realistic detector simulation, we obtain expected 95$\%$ confidence level upper limits on the LFV couplings tau-electron-ALP and tau-muon-ALP. Limits are computed assuming the center-of-mass energies of 126, 350 and 1500 GeV which the future muon collider is supposed to operate at. We study the two cases of unpolarized and polarized muon beams independently and show that taking advantage of tau polarization-induced effects in the polarized muon beams case, the main SM background $\tau\rightarrow e/\mu + \nu\bar{\nu}$ can be significantly reduced. Results indicate that current experimental limits on the studied LFV couplings can be improved by roughly one order of magnitude with the help of the present analysis.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 2204.04433v1 on 12 April 2022

Submission scipost_202111_00031v1 on 18 November 2021

## Reports on this Submission

### Report

The authors study the reach for lepton-flavour-violating decays of tau leptons at a future muon collider using a multivariate approach. They propose an analysis strategy based on boosted decision trees and several kinematic inputs from the reconstructed event. The results are presented for a collider configuration at √s = 350 GeV. They find that the lepton flavour violating couplings c_taue/fa and c_taumu/fa could be probed at the 10^-4 TeV-1 level or better.
I found the document well written and interesting.
Nevertheless, I have a few questions that I hope will help in making this proceeding contribution stronger.

- Does the event generation include VBF processes? These can become quite important especially in the highest centre-of-mass energy scenarios.
- The current plans for a muon collider start with a “low energy” stage with a centre-of-mass energy of 3 TeV, and plan to go higher. I believe it would be important to state/or show how the sensitivity to the LFV couplings is expected to change in these scenarios (for example comparing the 350 GeV results with those obtained at 1.5 TeV).
- The abstract mentions the use of a realistic detector simulation. I suggest to rephrase this to something like “a parameterized simulation based on the ideal target performance”
- If possible, I think that giving a minimal description of (or reference for) the event selection criteria would be needed to eventually reproduce this study.
- Section 3 mentions c_taue and c_taumu, while the results are presented in as the ratio of these couplings with fa. It would be good to harmonise the discussion and explicitly state which value of fa was assumed in the generation/interpretation.
- The concluding statement is somewhat strong, given that obtaining polarized muon beams would be highly unlikely. The authors might want to rephrase their closing statements to make them softer.

### Requested changes

1) Does the event generation include VBF processes? These can become quite important especially in the highest centre-of-mass energy scenarios.
2) The current plans for a muon collider start with a “low energy” stage with a centre-of-mass energy of 3 TeV, and plan to go higher. I believe it would be important to state/or show how the sensitivity to the LFV couplings is expected to change in these scenarios (for example comparing the 350 GeV results with those obtained at 1.5 TeV).
3) The abstract mentions the use of a realistic detector simulation. I suggest to rephrase this to something like “a parameterized simulation based on the ideal target performance”
4) If possible, I think that giving a minimal description of (or reference for) the event selection criteria would be needed to eventually reproduce this study.
5) Section 3 mentions c_taue and c_taumu, while the results are presented in as the ratio of these couplings with fa. It would be good to harmonise the discussion and explicitly state which value of fa was assumed in the generation/interpretation.
6) The concluding statement is somewhat strong, given that obtaining polarized muon beams would be highly unlikely. The authors might want to rephrase their closing statements to make them softer.

• validity: -
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### Author:  Gholamhossein Haghighat  on 2022-04-12  [id 2377]

(in reply to Report 2 on 2022-03-21)

We would like to thank the referee for reviewing our manuscript. We are especially grateful for his/her insightful comments and suggestions. We have revised our manuscript in response to the comments and hope that this improved manuscript is acceptable for publication. Below is our response to the issues raised in the review.

Comment 1 – At the center-of-mass (c.m.) energies assumed in this study, the cross section of the standard model VBF processes is so small that their contribution to the background can be safely neglected. arXiv:2005.10289 provides a thorough study of vector boson fusion processes and their cross sections at a muon collider (see section 4, for example).

Comment 2 – Results indicate that the limits obtained at the c.m. energy of 350 GeV are stronger than the limits at \sqrt(s)=1.5 TeV. Cross sections of both the signal and background processes get smaller as the c.m. energy increases from 350 GeV to 1.5 TeV with the overall result that the limits get weaker. Assuming that the change in the event selection efficiency is small, it can be seen based on the signal cross section and the integrated luminosities (assumed for scenarios with higher energies) that the number of signal events gets lower at higher energies. Furthermore, as the energy grows, additional sources of background (VBF processes) become important and degrade the limits. It is, therefore, expected that at c.m. energies higher than 1.5 TeV, the limits get worse.

Comment 3 – We are thankful to the reviewer for this suggestion. The requested change has been made to the text.

Comment 4 – As requested, a minimal description of the event selection criteria has been added to the manuscript.

Comment 5 – As the reviewer has correctly pointed out, the ratio of c_taue (or c_taumu) to f_a has been constrained. We have modified the manuscript to avoid any misunderstandings. The f_a value used for the event generation is 10 TeV.

Comment 6 – As requested, we modified the concluding statements and made them softer.

### Report

Axion-like particles (ALPs) can have Lepton Flavour Violating (LFV) couplings, e.g. a $\tau$-$\mu$-axion coupling. As a result, they might induce LFV decays of $\tau$ leptons, which in the SM are highly suppressed by neutrino masses.
Assuming the axion mass to be $<1$ MeV, the main decay channel of the axion is to two photons, and the width is such that the axion typically escapes the detector, and manifests itself as missing energy. The main SM background for the $\tau \to \mu(e) a$ process is therefore the SM process $\tau \to \mu(e) \nu \bar\nu$. The latter, however, being a three-body decay, has a different spectrum of the energy of the outgoing lepton, which depends on the angle. This doesn't happen for $\tau\to\mu(e) a$, and can therefore be used to distinguish between the two processes.
The authors explore the possibility of probing such a coupling at a future muon collider, operating at 126, 350 and 1500 GeV centre-of-mass energy, for different configurations of the muon beam (polarised or unpolarised), and chiral structures of the axion coupling.
Their results show that especially in the case of the polarised muon beam, the exclusion limits coming from a muon collider can improve the expected limits of current experiments.

I believe that the content of the proceeding by G. Haghighat and M. M. Najafabadi is summarised in the paragraph above. The proceeding is well-written, with clear and simple argumentations that are easy to follow. I think it meets the criteria to be published, but there are a few minor things that I would like to point out (and the authors to address):

1- In the abstract and in the main text the authors claim that their analysis shows an improvement of the sensitivity of an order of magnitude w.r.t. current experimental bounds (coming from the ARGUS experiment). Technically, this cannot be seen in the plots of Figure 2, as the scale on the y-axis contains only one point. A few more values on the scale would help reading the plots.

2- Regarding the projected limits from Belle-II in comparison to the hypothetical muon collider, I believe that the statement by the authors is a bit too strong, and should be phrased in a clearer way. Indeed the plots show that, especially for unpolarised muon beams, the expected sensitivity from Belle-II is the same, if not better, while the muon collider seems to be doing only slightly better with polarised beams, and only in the case of V+A couplings.

### Requested changes

1- In the abstract and in the main text the authors claim that their analysis shows an improvement of the sensitivity of an order of magnitude w.r.t. current experimental bounds (coming from the ARGUS experiment). Technically, this cannot be seen in the plots of Figure 2, as the scale on the y-axis contains only one point. A few more values on the scale would help reading the plots.

2- Regarding the projected limits from Belle-II in comparison to the hypothetical muon collider, I believe that the statement by the authors is a bit too strong, and should be phrased in a clearer way. Indeed the plots show that, especially for unpolarised muon beams, the expected sensitivity from Belle-II is the same, if not better, while the muon collider seems to be doing only slightly better with polarised beams, and only in the case of V+A couplings.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Author:  Gholamhossein Haghighat  on 2022-04-12  [id 2378]

(in reply to Report 1 on 2022-03-15)

We would like to thank the referee for reviewing our manuscript. We are especially grateful for his/her insightful comments and suggestions. We have revised our manuscript in response to the comments and hope that this improved manuscript is acceptable for publication. Below is our response to the issues raised in the review.

Comment 1 – We are thankful to the reviewer for this suggestion. As requested, we have modified the plots of Figure 2.

Comment 2 – We have modified the concluding statements and made them softer, as requested.