CPT Symmetry Searches in the Neutral Meson System
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe author present a comprehensive review of CPT symmetry tests, examining the potential for subtle CPT violations by analyzing their consequences on the quantum-mechanical propagation, mixing, and quantum numbers of the neutral-meson system. Pertinent theories and various experiments are discussed.
The manuscript is well written and I believe it will be of interest to the readers of this journal.
Before publication I would ask the author to address these points:
1) Line 131: "String theory offered the possibility of extended
particles, some quantum gravity scenarios allow for non-local interactions."
I think that here it would be appropriate to cite some relevant works, e.g. D. A. Eliezer and R. P. Woodard, The problem of nonlocality in string theory, Nucl. Phys. B
325, 389 (1989). W. Taylor and B. Zwiebach, D-branes, tachyons, and string field theory in Strings, Branes and Extra Dimensions: TASI 2001: Proceedings pp. 641–759 (2003).
I would also highlight that, more generally, nonlocality seems to emerge a general property of all theories preserving Lorentz invariance while accounting for "spacetime discreteness" at some minimal scale. Relevant examples in the quantum gravity (QG) literature include causal set theory [see R. D. Sorkin, Approaches to Quantum Gravity: Towards a New Understanding of Space and Time, edited by D. Oriti (Cambridge University Press, 2006)] and J. High Energy Phys. 03, 036 (2015), noncommutative geometry [ Phys. Rept. 378, 207 (2003)] and loop quantum gravity [Int. J. Mod. Phys. D 23, 1442023 (2014)]. These nonlocal interactions could give rise to nonlocal modifications of quantum mechanics at non-relativistic energies [see Phys. Rev.Lett. 116, 161303 (2016)], where they could be detected or constrained by high-precision quantum experiments [see Phys. Rev. D 95, 026012 (2017) and Class. Quant. Grav. 36, 155006 (2019)].
2) There is a typo at Line 161: "unitariy" --> unitarity.
3) Line 181: "There is, however, a significant scenario, where the nontrivial spacetime is a fluctuating spacetime at the Planck scale."
I think that here the author is referring to the Wheelerʼs concept of quantum foam, i.e., the non-smooth texture of spacetime on length scales of the Planck order [ J. Wheeler, "Geometrodynamics 1962 (New Jork:Academic)].
4) Line 190: NM should be defined.
5) Line 197: "It can also cause modification to the Lorentz invariant dispersion relation leading to nontrivial "optics" of spacetime.
This sentence should be clarified. Does the author refer here to modified dispersion relations including higher-order momentum or energy-dependent terms? Please explain and add relevant references.
6) Line 214: ... an effective theory where the spacetime foam background is replaced by a fixed(classical) background but the interaction of low-energy fields in nonlocal.
I think this partially relates with what said in point 1).
7) Line 372: xi --> \xi
8) The conclusions seem overly short considering the extensive review provided. I think that apart from summarizing the main points raised in the paper, it would be beneficial for the reader to offer a perspective on the possible future of the field, mentioning new directions (if any) and possible experimental tests.
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsThe main goal of this review paper is to search for the CPT in the neutral meson system using several theory approaches. The review is fascinating to the readers interested in this topic. However, I have several comments as follows:
1. Please add more keywords in line 12
2. Please change discrete symmetries ---> CPT discrete symmetries in line 18
3. Please add "and" between continuous, infinitesimal ...----> continues and infinitesimal ... in line 19
4. Please add "comma" before vector and spinor...---> vector, and spinor... in line 26
5. Please add "comma" before it describes...in line 27
6. Please give space after (CPTV) in line 44
7. To be consistent, please replace CP violation ---> CPV because it was defined in previous sentences in line 45
8. Again, please replace CP violation ---> CPV in line 49 to be consistent
9. Again, please replace CP violation ---> CPV in line 64 to be consistent
10. Please replace General Relativity ---> GR in line 83 to be consistent with the previous word
11. Please replace Standard Model and General Relativity ---> SM and GR in line 92
12. Please replace CP violation ---> CPV in line 99
13. Please replace CP violation ---> CPV in line 101
14. Please replace CPT-violation ---> CPTV in line 101
15. Please replace CPT-violation ---> CPTV in line 103
16. Please replace Lorentz violation ---> LV in line 103
17. Please replace CP violation ---> CPV in line 106
18. Please replace CP violation ---> CPV in line 110
19. Please replace beyond the Standard Model ---> BSM in line 121
20. Please replace CPT violation ---> CPTV in line 122
21. Please replace Standard Model Extention ---> SME in lines 123 and 124
22. Please replace CPT violation ---> CPTV in line 135
23. Please change Lorentz violation (LV) with only LV in line 135 because it has been defined in the previous sentences/paragraph
24. Please replace Standard Model Extention (SME) ---> SME in line 137
25. Please replace Lorentz violation ---> LV in lines 159 and 168
26. What is NM? It was never defined before in line 190. Once you defined please use NM in the next sentences/paragraph to be consistent
27. Please replace CPT violation ---> CPTV in line 211
28. Similar to NM, what is NMS? in line 232. It was never defined before
29. Please replace CP violation ---> CPV in line 243
30. Please add a full stop "." before matter quantum... in line 316
31. Please add a comma "," after BaBar in line 344
32. Please add "." at the end of the equation in Eq. (10)
33. Please add "." at the end of the equation in Eq.(12)
34. Please replace CP violation ---> CPV in line 359
35. In line 372, I think it is a typo, please replace xi ---> \xi based on Eq.(14)
36. Please give a space before the word "They" in line 395
37. Please replace CPT violation ---> CPTV in line 418
38. Please add "." at the end of the equation in Eq.(23)
39. Please add a comma "," at the end of the equation in Eq.(24)
40. Please add "." at the end of the equation in Eq.(26)
41. Please add "." at the end of the sentence in line 470
42. Please change let ---> Let in line 478
43. Please add "." at the end of the equation in Eq.(29)
44. Please add "." before "Note ..." in the line 496
45. Please drop "." in line 497
46. Please add a comma "," at the end of the equation in Eq.(30)
47. Please drop "." in line 503
48. What is SCCEF? in line 522. It was never defined before
49. Please add "," at the end of the equation in Eqs. (33) and (34)
50. Please add "," at the end of the equation in Eq. (36)
51. Please replace CPT violation ---> CPTV in line 579
52. what is the parameter om? It was never defined before in line 584. Please clarify
53. Please add "." at the end of the equation in Eq. (39)
54. Please replace id---> is in line 678. I think it is a typo
55. Please add "," at the end of the first and second lines in Eq.(40)
56. Please add "," at the end of the first and second lines in Eq. (41)
57. Please drop "." in line 687
58. Please add "," at the end of the first and second lines of Eq. (43)
59. Please add "." at the end of a sentence in line 704
60. What is it? Please clarify in line 731
61. Please add "." at the end of the equation in Eq. (46)
62. Please add "." at the end of the equation in Eq. (47)
63. Please add "." at the end of the equation in Eq. (48)
64. Please drop "." in line 771
65. Please add "." in Eq. (50)
66. Please put the reference [110] before Eq. (50), not after
67. What is it?? in line 701 please clarify
68. Please add "." after CPTV in line 788
69. Please drop "." in line 793
70. Please add "." at the end of Eq. (53)
71. What is Dexi? in line 818. Please clarify
72. Please add "." at the end of Eq. (56)
73. Please add "." at the end of Eq. (57)
74. Please add respectively "," and "." at the first and second lines of Eq. (58)
75. Please write "GeV" using the latex \mathrm{GeV} in line 880
76. Please give space before KTeV in line 884
77. Please add "." at the end of Eq. (59)
78. Please change \phi 00 ---> \phi^{00} based on \phi^{+-}. Also please add "," after phi^{+-} in the line 896
79. Please add "." before For ... in line 897
80. Please replace CP and CPV violations ---> CPV and CPTV in line 926
81. Please add "," in the first line of Eq. (62)
82. Please add "." at the end of Eq. (63)
83. Please replace CPT violation ---> CPTV in line 943
84. Please add "and" between CPV and CPTV and expression ---> expressions in line 944
85. Please add "." at the end of Eq. (65)
86. Please add respectively "," and "." at the first and second lines of Eq.(66)
87. Please change GeV---> \mathrm{GeV} in Eq. (67) and please replace "," ---> "." at the last line equations of Eq. (67)
88. Please replace D^0-s --- D_s^0 in line 957
89. Please clarify what kind of D^0 can decay to K^- \pi^+? I expect it must be D^0_s ---> K^- \pi^+
90. Please add "." at the end of Eq. (70)
91. Please add respectively ",", "," , and "." at the end of the first, second, and last line of Eq. (71)
92. Please also clarify type of D^0 --> K^- \pi^+ in line 977
93. Please add "." at the end of a sentence in line 980
94. Please put the reference [109] before the equation and add "." at the end of the equation in line 984
95. I think the conclusion is too short. It is better to summarize what has been reviewed in this paper and what are the results obtained for the studies in this review paper.
Also, it is more interesting to give the outlook to be done in the future, which is relevant to what has been done in this review paper. I think it would be a useful and good clue for the readers who have an interest in this topic.
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe author has satisfactorily addressed all points raised in my previous report and I have no further comment. I therefore recommend publication.
