About General Relativity And Missing Mass

Not new, but brought to my attention by a Physics Forums Insights article. (See also, this related Physics Form post on these articles).

[Submitted on 21 Sep 2015 (v1), last revised 24 Oct 2017 (this version, v5)]

The Missing Mass Problem as a Manifestation of GR Contextuality

W.M. Stuckey, Timothy McDevitt, A.K. Sten, Michael Silberstein

In Newtonian gravity, mass is an intrinsic property of matter while in general relativity (GR), mass is a contextual property of matter, i.e., matter can simultaneously possess two different values of mass when it is responsible for two different spatiotemporal geometries. Herein, we explore the possibility that the astrophysical missing mass attributed to non-baryonic dark matter (DM) actually obtains because we have been assuming the Newtonian view of mass rather than the GR view. Since an exact GR solution for realistic astrophysical situations is not feasible, we explore GR-motivated ansatzes relating proper mass and dynamic mass for one and the same baryonic matter, as justified by GR contextuality. We consider four GR alternatives and find that the GR ansatz motivated by metric perturbation theory works well in fitting galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (CMB, Planck 2015 data) without DM. We compare our galactic rotation curve fits to modified Newtonian dynamics (MOND), Burkett halo DM and Navarro-Frenk-White (NFW) halo DM. We compare our X-ray cluster mass profile fits to metric skew-tensor gravity (MSTG) and core-modified NFW DM. We compare our CMB angular power spectrum fit to scalar-tensor-vector gravity (STVG) and ΛCDM. Overall, we find our fits to be comparable to those of MOND, MSTG, STVG, ΛCDM, Burkett, and NFW. We present and discuss correlations and trends for the best fit values of our fitting parameters. For the most part, the correlations are consistent with well-established results at all scales, which is perhaps surprising given the simple functional form of the GR ansatz.

Comments:	18 pages text. Twice revised per referee/reviewer comments. Fit of CMB angular power spectrum and dark matter halo fits added
Subjects:	General Physics (physics.gen-ph)
Journal reference:	International Journal of Modern Physics D 27, No. 14, 1847018 (2018)
DOI:	10.1142/S0218271818470181
Cite as:	arXiv:1509.09288 [physics.gen-ph]
	(or arXiv:1509.09288v5 [physics.gen-ph] for this version)

There is another overlapping version:

[Submitted on 26 May 2016 (v1), last revised 27 Jul 2016 (this version, v3)]

End of a Dark Age?

W.M. Stuckey, Timothy McDevitt, A.K. Sten, Michael Silberstein

We argue that dark matter and dark energy phenomena associated with galactic rotation curves, X-ray cluster mass profiles, and type Ia supernova data can be accounted for via small corrections to idealized general relativistic spacetime geometries due to disordered locality. Accordingly, we fit THINGS rotation curve data rivaling modified Newtonian dynamics, ROSAT/ASCA X-ray cluster mass profile data rivaling metric-skew-tensor gravity, and SCP Union2.1 SN Ia data rivaling ΛCDM without non-baryonic dark matter or a cosmological constant. In the case of dark matter, we geometrically modify proper mass interior to the Schwarzschild solution. In the case of dark energy, we modify proper distance in Einstein-deSitter cosmology. Therefore, the phenomena of dark matter and dark energy may be chimeras created by an errant belief that spacetime is a differentiable manifold rather than a disordered graph.

Comments:	This version was accepted for publication in the International Journal of Modern Physics D; revised version of an essay that won Honorable Mention in the Gravity Research Foundation 2016 Awards for Essays on Gravitation. 10 pages, 3 figures. arXiv admin note: text overlap with arXiv:1509.09288
Subjects:	General Physics (physics.gen-ph)
Journal reference:	International Journal of Modern Physics D 25(12), 1644004 (2016)
DOI:	10.1142/S0218271816440041
Cite as:	arXiv:1605.09229 [physics.gen-ph]
	(or arXiv:1605.09229v3 [physics.gen-ph] for this version)

Chromium Steel In Persia Ca. Y1K

Southern Persia ca. 1000 CE was ahead of its time by more than eight hundred years in producing chromium steel, now commonly used in tools, a find documented with manuscripts and physical evidence from that era.

Chromium steel -- similar to what we know today as tool steel -- was first made in Persia, nearly a millennium earlier than experts previously thought, according to a new study led by UCL researchers. The discovery, published in the Journal of Archaeological Science, was made with the aid of a number of medieval Persian manuscripts, which led the researchers to an archaeological site in Chahak, southern Iran. The findings are significant given that material scientists, historians and archaeologists have long considered that chromium steel was a 20th century innovation. Dr Rahil Alipour (UCL Archaeology), lead author on the study, said: "Our research provides the first evidence of the deliberate addition of a chromium mineral within steel production. We believe this was a Persian phenomenon.

"This research not only delivers the earliest known evidence for the production of chromium steel dating back as early as the 11th century CE, but also provides a chemical tracer that could aid the identification of crucible steel artefacts in museums or archaeological collections back to their origin in Chahak, or the Chahak tradition."

Chahak is described in a number of historical manuscripts dating from the 12th to 19th century as a once famous steel production centre, and is the only known archaeological site within Iran's borders with evidence of crucible steel making. While Chahak is registered as a site of archaeological importance, the exact location of crucible steel production in Iran remained a mystery and difficult to locate today, given numerous villages in Iran are named Chahak.

The manuscript 'al-Jamahir fi Marifah al-Jawahir' ('A Compendium to Know the Gems', 10th-11th c. CE) written by the Persian polymath Abu-Rayhan Biruni, was of particular importance to the researchers given it provided the only known crucible steel making recipe. This recipe recorded a mysterious ingredient that they identified as chromite mineral for the production of chromium crucible steel.

The team used radiocarbon dating of a number of charcoal pieces retrieved from within a crucible slag and a smithing slag (by-products left over after the metal has been separated) to date the industry to the 11th to 12th century CE. Crucially, analyses using Scanning Electron Microscopy enabled them to identify remains of the ore mineral chromite, which was described in Biruni's manuscript as an essential additive to the process. They also detected 1-2 weight percent of chromium in steel particles preserved in the crucible slags, demonstrating that the chromite ore did form chromium steel alloy -- a process that we do not see used again until the late 19th and early 20th century.

The paper is:

Rahil Alipour, Thilo Rehren, Marcos Martinón-Torres. "Chromium crucible steel was first made in Persia." Journal of Archaeological Science (2020); 105224 DOI: 10.1016/j.jas.2020.105224

Was The Earthquake That Destroyed A Canaanite Palace Related To The Santorini Volcano?

The Thera eruption of the volcano in what is now called the island of Santorini in Greece (sometimes pitched as a location of Plato's City of Atlantis) took place around 3600 years ago (possibly as early as 1642 BCE). 

This earthquake could have been the same seismic event that caused a Canaanite palace in what is now Israel to collapse around 3700 years ago - but with a date that the new article does not establish in a particularly precise or well documented manner and doesn't even attempt to assign a margin of error to the date used. 

A review of the primary source for the 1700 BCE date in the new article (quoted below) notes that this date has been assigned as 1650 BCE and 1590 BCE by most recent scholars, and that their review establishes a 50-100 year earlier date that could still be as late as 1640 BCE consistent with the Carbon-14 dating.

A team of Israeli and American researchers funded by grants from the National Geographic Society and the Israel Science Foundation has uncovered new evidence that an earthquake may have caused the destruction and abandonment of a flourishing Canaanite palatial site about 3,700 years ago.

The group made the discovery at the 75-acre site of Tel Kabri in Israel, which contains the ruins of a Canaanite palace and city that dates back to approximately 1900-1700 B.C. The excavations, located on land belonging to Kibbutz Kabri in the western Galilee region, are co-directed by Assaf Yasur-Landau, a professor of Mediterranean archaeology at the University of Haifa, and Eric Cline, a professor of classics and anthropology at the George Washington University.

"We wondered for several years what had caused the sudden destruction and abandonment of the palace and the site, after centuries of flourishing occupation," Yasur-Landau said. "A few seasons ago, we began to uncover a trench which runs through part of the palace, but initial indications suggested that it was modern, perhaps dug within the past few decades or a century or two at most. But then, in 2019, we opened up a new area and found that the trench continued for at least 30 meters, with an entire section of a wall that had fallen into it in antiquity, and with other walls and floors tipping into it on either side."

According to Michael Lazar, the lead author of the study, recognizing past earthquakes can be extremely challenging in the archaeological record, especially at sites where there isn't much stone masonry and where degradable construction materials like sun-dried mud bricks and wattle-and-daub were used instead. At Tel Kabri, however, the team found both stone foundations for the bottom part of the walls and mud-brick superstructures above.

From Science Daily.

The paper is:

Michael Lazar, Eric H. Cline, Roey Nickelsberg, Ruth Shahack-Gross, Assaf Yasur-Landau. Earthquake damage as a catalyst to abandonment of a Middle Bronze Age settlement: Tel Kabri, Israel. PLOS ONE, 2020; 15 (9): e0239079 DOI: 10.1371/journal.pone.0239079

The body text regarding the dating states:

Tel Kabri flourished during the Middle Bronze Age (hereafter MB) and was the third largest site in the Levant at the time (after Hazor and Ashkelon). It was a fortified center of a regional polity and housed the largest MB palace found to date in the southern Levant, with an estimated area of 6000 m2. The palace is known from its modest beginning in the MB I (Kabri Area D-West, stratigraphic Phase VI) to its zenith in the MB II (Kabri Area D-West, stratigraphic Phase III) [31–33], dated ca. 1900–1700 BCE (high middle chronology [34]; cf. [35]).

During its final phase, the palace underwent massive renovation, reaching its greatest size. This involved the addition of a two-room complex lined with carved stone blocks known as “orthostats” (the “Orthostat Building”), probably used for banqueting, and a wing for the accommodation of hundreds of large storage jars (pithoi) containing spiced wine—the “Southern and Northern Storage Complexes” [26, 31–33, 36].

At the end of this phase, ca. 1700 BCE, the palace and its surrounding areas were abandoned [34], for reasons that are still unclear. The site then lay uninhabited for almost a millennium, after which only minimal human activity is recorded from the Iron Age and later (e.g. [31] and references therein). This study examines the possibility that the demise of this palace and settlement, during a period of flourishing and expansion, may be attributed to an earthquake. , , , 

In terms of historic earthquakes, the Dead Sea basin, one of the pull-apart basins located along the length of the DSF, preserves in its sediments the largest and most comprehensive near-continuous record of earthquakes in the southeastern Levant going back at least 70,000 years (e.g. [39–41]). Examination of these records for a possible large earthquake at the time of the damage of the Tel Kabri palace indicates the occurrence of an earthquake around 3700 BP (i.e., 1700 BCE). However, there is little evidence to connect this event with the destruction at Tel Kabri. . . .

A comprehensive examination of the Tel Kabri MB II palace was carried out in order to shed light on the reason(s) for its demise during what appears to be a very prosperous period in its history. These are discussed below, in light of additional factors that could have led to the abandonment of the site.

Pollen records from the southern Levant indicate a relatively wet period between 1750–1550 BCE [53, 54], correlated to a period of high lake levels in the Dead Sea [55]. This agrees with climatic conditions in central Europe during this time (e.g. [56]). Therefore, it seems that there was no extreme environmental crisis, or vast fluctuations in the climate during the MB II, at the time of abandonment.

Economic decline also seems not to have been a factor. On the contrary, a significant renovation program was implemented in the palace during its last constructional phase (site stratigraphic Phase III), just a short time before its end, showing that considerable means were still available at the time [32, 51].

Another indicator of wealth towards the palace’s end was uncovered in the large storage rooms, which contained pithoi that were filled with at least 4000 liters of wine when the palace was destroyed [33]. That quantity of wine would have had an estimated value of 625 silver shekels, a very high sum in a society where a worker’s salary was one shekel per month and a sheep cost 1.5 shekels [33].

Furthermore, the palace seems to have had several traits that strengthened its environmental resilience: zooarchaeological finds are consistent with a diverse and non-specializing animal economy using different ecological niches within the nearby territories without creating excessive environmental stress ([57] and references therein). The use of fuel for commodities consumed by the palace was also evaluated. A study of the plaster floors [58] concluded that most of their volume was prepared from pulverized chalk, while only a few localities included very thin (less than 1 cm) superimposed lime plaster surfaces. Similarly, the pithoi used in the wine storage rooms were shown to be fired at low temperatures not exceeding 600°C, in contrast to findings from other Bronze Age palatial workshops [59]. Taken together, both studies indicate that demands on local wood fuel supplies were not excessive, as pyrotechnology was conducted on a rather fuel-conservative scale. Kabri seems to have been maintaining a sustainable relationship with its environment.

Finally, it seems to us that the destruction of Kabri is unlikely to have been caused by violent human activity. There are no visible signs of conflagration, no weapons such as arrows like those uncovered in the destruction layer of Ugarit (ca. 1190 BCE–[60, 61]) that would indicate a battle, nor any unburied bodies related to combat. No hoards that would indicate preparation for a siege or an organized abandonment have been found, nor mass graves that indicate pandemic fatalities. Additionally, the MB II is a peaceful period in terms of Egyptian military activity. The demise of Kabri occurs during the Second Intermediate Period in Egypt and thus postdates the earlier Middle Kingdom incursions into Canaan, such as that of Khu-Sebek, which took place during the days of Senusret III in the 19th century BCE. At the same time, the abandonment of the site predates the renewals of Egyptian campaigns during the 18th dynasty, beginning with Ahmose, ca. 1540–1530 BCE [62]. Furthermore, there seems to be an overall decrease in the level of intra- and inter-group violence in Canaanite society, which is reflected in a dramatic decrease in the number of warrior tombs as well as weapons in burials from MB I to MB II [63]. 

26. Yasur-Landau A, Cline EH, Goshen N, Marom N, Samet I. An MB II Orthostat building at Tel Kabri, Israel. Bull Am Schools Orient Res. 2012;367: 1–29.

27. Sneh A. Geological Maps of Israel (1:50,000) Sheet 1-IV: Nahariyya. Jerusalem: Geological Survey of Israel; 2004. 

28. Singer A. The Soils of Israel. Berlin: Springer-Verlag; 2007. 

29. Tsuk T. Chapter 3: The springs of Kabri in Tel Kabri: The 1986–1993 Excavations Seasons. In: Kempinski A, editor. Tel Aviv: Emery and Claire Yass Publications in Archaeology; 2002. pp 15–18. 

30. Horowitz A. Chapter 2: The natural environment in Tel Kabri: The 1986–1993 Excavations Seasons. In: Kempinski A, editor. Tel Aviv: Emery and Claire Yass Publications in Archaeology; 2002. pp. 7–14. 

31. Yasur-Landau A, Cline EH, Goshen N. Initial results of the stratigraphy and chronology of the Tel Kabri Middle Bronze Age palace. Äg Lev. 2014;24: 355–364.

32. Yasur-Landau A, Cline EH, Koh AJ, Ben-Shlomo D, Marom N, Ratzlaff A, et al. Rethinking Canaanite palaces? The palatial economy of Tel Kabri during the Middle Bronze Age. J Field Archaeol. 2015;40: 607–625.

33. Yasur-Landau A, Cline EH, Koh AJ, Ratzlaff A, Goshen N, Susnow M, et al. The wine storage complexes at the Middle Bronze II palace of Tel Kabri: Results of the 2013 and 2015 seasons. Am J Archaeol. 2018;122: 309–338.

34. Höflmayer F, Yasur-Landau A, Cline EH, Dee MW, Lorentzen B, Riehl S. New radiocarbon dates from Tel Kabri support a high Middle Bronze Age chronology. Radiocarbon. 2016;58: 599–613.

35. Bietak M. Relative and absolute chronology of the Middle Bronze Age: comments on the present state of research. In: Bietak M, editor. The Middle Bronze Age in the Levant. Proceedings of an International Conference on MB IIA Ceramic Material, Vienna: Osterreichischen Akademie der Wissenschaften; 2002. pp. 29–42. 

36. Koh AJ, Yasur-Landau A, Cline EH. Characterizing a Middle Bronze palatial wine cellar from Tel Kabri, Israel. PLoS One. 2014;9 e106406.

37. Ben-Menahem A. Variation of slip and creep along the Levant rift over the past 4500 years. Tectonophysics. 1981;80: 183–197.

38. Salamon A, Zviely D, Na’aman I. Zones of required investigation for liquefaction hazard in the western Zevulun Plain, Israel. Isr J Earth Sci. 2007;55: 141–157.

39. Kagan E, Stein M, Marco S. Integrated paleoseismic chronology of the last glacial Lake Lisan: from lake margin seismites to deep-lake mass transport deposits. J Geophys Res. 2018;123. https://doi.org/10.1002/2017JB014117

40. Migowski C, Agnon A, Bookman R, Negendank JFW, Stein M. Recurrence pattern of Holocene earthquakes along the Dead Sea Transform revealed by varve-counting and radiocarbon dating of lacustrine sediments. Earth Planet Sci Lett. 2004;222: 301–314.

41. Kagan E, Stein M, Agnon A, Neumann F. Intrabasin paleoearthquake and quiescence correlation of the late Holocene Dead Sea. J Geophys Res. 2011; 116: B04311, 10.1029/2010JB007452.

42. Ben-Menahem A. Four thousand years of seismicity along the Dead Sea rift. J Geophys Res. 2011;96: 20,195–20,216.

43. Ambraseys N. Chapter 3: Catalogue of earthquakes. In Ambraseys N. editor. Earthquakes in the Mediterranean and Middle East: A Multidisciplinary Study of Seismicity up to 1900. Cambridge: Cambridge University Press. 2009. pp. 60–814. 

44. Frumkin A, Barzilai O, Hershkovitz I, Ullman M, Marder O. Karst terrain in the western upper Galilee, Israel: Speleogenesis, hydrogeology and human preference of Manot Cave. J Hum Evol. 2019; https://doi.org/10.1016/j.jhevol.2019.05.006. 

45. Matmon A, Wdowinski S, Hall JK. Morphological and structural relations in the Galilee extensional domain, northern Israel. Tectonophysics. 2003;371: 223–241.

46. Kafri U. The Cenomanian-Turonian calcareous aquifer of central and western Galilee, Israel. Hydrol Sci J. 1970;15: 77–91. 

47. Gvirtzman Z, Zaslavsky Y. Map of zones with potentially high ground motion amplification. Geophysical Institute of Israel Report GSI/15/2009; 2009 [cited 2020 May 10]. http://www.gsi.gov.il/eng/?CategoryID=290&ArticleID=732

48. Stoops G. Guidelines for Analysis and Description of Soil and Regolith Thin Sections. Madison Wisconsin: Soil Science Society of America; 2003.

49. Berna F, Behar A, Shahack-Gross R, Berg J, Boaretto E, Gilboa A, et al. Sediments exposed to high temperatures: reconstructing pyrotechnological processes in Late Bronze and Iron Age strata at Tel Dor (Israel). J Archaeol Sci. 2007;34: 358–373.

50. Regev L, Poduska KM, Addadi L, Weiner S, Boaretto E. Distinguishing between calcites formed by different mechanisms using infrared spectrometry: archaeological applications. J Archaeol Sci. 2010;37: 3022–3029.

51. Yasur-Landau A, Cline EH. Activity areas within the last palace of Kabri. In: Bietak M, Matthiae P, Prell S, editors. Ancient Egyptian and Ancient Near Eastern Palaces Volume 2. Vienna: Austrian Academy of Sciences Press; 2019. pp. 181–191. 

52. Forget M, Regev L, Friesem D, Shahack-Gross R. Physical and mineralogical properties of experimentally heated sun-dried mud bricks: implications for reconstruction of environmental factors influencing the appearance of mud bricks in archaeological conflagration events. J Archaeol Sci Rep. 2015;2: 80–93.

53. Finkelstein I, Langgut D. Dry climate in the Middle Bronze I and its impact on settlement patterns in the Levant and beyond: new pollen evidence. J Near East Stud. 2014;73: 219–234.

54. Langgut D, Finkelstein I, Litt T, Neumann FH, Stein M. Vegetation and climate changes during the Bronze and Iron Ages (~3600–600 BCE) in the southern Levant based on palynological records. Radiocarbon. 2015;57: 217–235.

55. Kagan EJ, Langgut D, Boaretto E, Neumann FH, Stein M. Dead Sea levels during the Bronze and Iron Ages. Radiocarbon. 2015;57: 237–252.

56. Demény A, Kern , Czuppon G, Németh A, Schöll-Barna G, Siklósy Z, et al. Middle Bronze Age humidity and temperature variations, and societal changes in East-Central Europe. Quat Int. 2019;504: 80–95.

57. Marom N, Yasur-Landau A, Cline EH. The silent coast: Zooarchaeological evidence to the development trajectory of a second millennium palace at Tel Kabri. J Anthropol Archaeol. 2015;39: 181–192.

58. Goshen N, Yasur-Landau A, Cline EH, Shahack-Gross R. Palatial architecture under the microscope: production, maintenance, and spatiotemporal changes gleaned from plastered surfaces at a Canaanite palace complex, Tel Kabri, Israel. J Archaeol Sci Rep. 2017;11: 189–199.

59. Waiman-Barak P, Susnow M, Nickelsberg R, Cline EH, Yasur-Landau A, Shahack-Gross R. Technological aspects of Middle Bronze Age II production of pithoi at Tel Kabri, Israel: specialized pottery production in a palatial system. Levant. 2018;50: 32–51.

60. Singer I. A political history of Ugarit. In: Watson WGE, Wyatt N, editors. Handbook of Ugaritic Studies. Leiden, The Netherlands: Brill Publishing; 1999. pp. 603–733. 

61. Yon M. The City of Ugarit at Tell Ras Shamra. Pennsylvania: Eisenbrauns; 2006.  

62. Rainey AF, Notley RS. The Sacred Bridge: Carta’s Atlas of the Biblical World. Jerusalem: Carta; the Israel Map & Publishing Company Limited; 2006.

63. Yasur-Landau A. The Canaanite city as a domesticating apparatus. In: Yasur-Landau A, Cline EH, Rowan YM, editors. The Social Archaeology of the Levant from Prehistory to the Present. Cambridge: Cambridge University Press; 2019. pp. 224–244.

The paper mostly relies for the date on reference 34 which states:

We note again that the end of Phase III has already been dated by ceramic material to the late Middle Bronze II period and that there is no direct evidence for Middle Bronze III pottery from the palatial phases (see above). If Model A is correct and the end of Phase III at Kabri dates to around Figure 4 Modeled probability range for the transition from Phase IV to Phase III of the Middle Bronze Age palace of Tel Kabri based on Model A. Figure 5 Modeled probability range for the end of Phase III of the Middle Bronze Age palace of Tel Kabri based on Model A at 1700 BC, this will also give a result for the end of Middle Bronze II that is approximately 50 yr higher than the traditional chronology date of ~1650 BC for the transition from Middle Bronze II to Middle Bronze III (e.g. Dever 1992, 1997). 

These results are also considerably higher—by about a century—than the low Middle Bronze Age chronology, in which the transition from Middle Bronze II to Middle Bronze III is dated to ~1590 BC (Bietak 2013), even when the most recent range of the 95.4% probability distribution in our model is considered. Our end date for Phase III is thus 50–100 yr higher (older) than expected, at least according to current chronological frameworks. 

Therefore, we wanted to test how low (i.e. how young) the end date for Phase III theoretically could be. 

For Model B (Exponential Model), we considered the samples only from archaeological Phase III and assumed that their dates are distributed exponentially towards the end of the use of the building, using a Tau_Boundary paired with a Boundary in OxCal. This essentially tests how recent the end of the Middle Bronze Age palace of Kabri could possibly be, given the 14C data. 

For Model C (Uniform Phase), we eliminated all samples with potential inbuilt age (i.e. wood charcoal samples) and only considered short-lived samples from archaeological Phase III and assumed that their dates are uniformly (rather than exponentially) distributed throughout the Phase. 

According to Model B (exponential), the end date for Phase III still falls around 1700 BC, but with a slightly larger error margin that now also includes the first half of the 17th century BC, between 1712 and 1670 BC at 68.2% probability, or between 1731 and 1640 BC at 95.4% probability. Model C (uniform) also places the end date for archaeological Phase III around 1700 BC, again with a slightly larger error margin compared to Model A (stratigraphical). 

According to Model C (uniform), archaeological Phase III ends between 1732 and 1676 BC at 68.2% probability, or between 1742 and 1640 BC at 95.4% probability. 

However, we note that Models B and C disregard the site’s stratigraphic evidence (using samples of earlier stratigraphical phases as termini post quos) and were only created to test how low (young) the end of Phase III could technically be, given the 14C data. We regard Model A as representative for the site and conclude that the palace (and Phase III) at Kabri ended around 1700 BC, thus 50–100 yr earlier than expected based on current chronological models for the Middle Bronze Age Levant.

New Muon g-2 Measurement Coming Soon

One of the most important discrepancies between theory and experiment in the Standard Model is the muon g-2 anomaly, a roughly 3 sigma tension. The last precision measurement of muon g-2 was done by the E821 Muon g-2 Experiment at Brookhaven National Laboratory which finished collecting data in 2001 and issued its final report analyzing that data in 2006. 

Two more experiments are underway to make a new more precise measurement. The first to produce results will be the E989 Muon g-2 Experiment at Fermilab which is projected to obtain ∼20 times more data and a ∼3-fold reduction of systematic errors compared to E821. The relative error in the new measurement of muon g-2 at E989 will be about 150 parts per billion and will make the experimental error smaller than the uncertainty in theoretical prediction.

Like all major government projects, it is behind schedule. But a Conference paper released today at arXiv discussing the technical details of one part of the E989 experimental setup also included a hint about how far along E989 is on data collection and when the first results will be announced. According to this paper:

The Muon g-2 Experiment (E989) at Fermilab has a goal of measuring the muon anomaly (a(μ)) with unprecedented precision . . . the experiment has recently commenced Run-3, and the release of Run-1 physics results is planned for 2020.

So, the nearly two decades long wait for new experimental data related to this issue is almost over. Another experiment (the J-PARC E34 experiment see also here) measuring Muon g-2 will be releasing its new measurement result a year or two or so after the E989 results are released, providing a quick replication or non-replication of whatever measurement emerges from the E989 experiment.

More background is available in a June 11, 2020 post at this blog. In a real nutshell, the theoretical side is summed up in this chart from a Fermilab website article:

The theoretical value of the anomalous magnetic moment of the muon is:

a = (g-2)/2 (theory) = 116 591 810(43) x 10-11

The most precise experimental result available so far is:

a = (g-2)/2 (experiment) = 116 592 089(63) x 10-11

The experimental value exceeds the theoretical value by:

279(76) x 10-11

This discrepancy is about 2 parts per million, which is a 3.7 sigma tension.

If the experimental measurement from E989 is 1.6 parts per million lower than it was in the E821 experiment, the new measurement would be considered to be "consistent" with the theoretical prediction. 

The muon g-2 measurement is of great interest to scientists because almost all components of the Standard Model contribute to it to some extent.

If the new measurement is consistent with the theoretical prediction, this would be strong evidence that the Standard Model is globally consistent with reality at the electroweak scale plus or minus several orders of magnitude, and that the Standard Model is a complete low energy effective description of the laws of Nature (although, it is not inconceivable that there could be more than one kind of beyond the Standard Model physics and that these new physics contributions offset each other in their contribution to muon g-2). In the event that the results were consistent, the discrepancy would be less than or equal to:

93 x 10-11

On the other hand, if the discrepancy between theory and prediction increased to 5 sigma, this would be considered a scientific discovery of unknown new physics at the same energy scale, but an incomplete one, because the discrepancy tells us only the magnitude of the undiscovered new physics and not its source. A 5 sigma discrepancy would be equal to or more than:

233 x 10-11

For discrepancies between those values, we would be left in more or less the same place where we are now, with a tension between theory and experiment, but not a big enough tension to constitute a definitive scientific discovery of new physics.

But, the reduced magnitude of the absolute size of the discrepancy between theory and experiment in a significantly more accurate measurement of muon g-2 would still probably tend to favor the conventional wisdom that the muon g-2 anomaly is due to some combination of theoretical and experimental error, and not due to new physics.

How Big Are The Lepton Universality Violation Tensions With The Standard Model?

A "tension" with the Standard Model that isn't definitive proof of new physics, is normally defined as more than two sigma (less than that is "consistent" with the Standard Model prediction) and less than five sigma (which is considered a discovery of new physics if replicated and other conditions regarding vetting of the results are met). 

One of the most notable tensions with the Standard Model involves violations of its assumption of lepton universality (i.e. that the electron, muon and tau lepton have identical properties apart from fundamental rest mass). So far, this is see only in in certain decays of mesons that contain valence bottom quarks (a meson is a short lived compound particle with integer spin made up of a valence quark and a valence antiquark, in addition to a sea of virtual quark and antiquarks, bound together by the strong force as mediated by gluons). 

The abstract from the new preprint below sums up how strong those tensions are (which arguably approach a new physics level of treated as independent manifestations of the same new physics phenomena and multiplied). But it does not, however, list of myriad null results in different decays, nor does it fully take into account look elsewhere effects or consider issues like correlated errors, so it is somewhat overstated.

Lepton universality violations are not seen in W boson decays at the LHC, are not found in tau lepton decays or pion decays (also here), and are not found in anti-B meson and D* meson decays or in Z boson decays. There were still tensions in the data from B meson decays, but the deviations were smaller as of 2019 than they were in 2015 (also here).

Angular analysis of Bs→f′2(1525)(→K+K−)μ+μ− decays as a probe to lepton flavor universality violation

N Rajeev, Niladribihari Sahoo, Rupak Dutta

The flavor anomalies reported in RK, RK∗, P′5 and (Bs→ϕμ+μ−) indicate lepton flavor universality violation in b→sl+l− quark level transition decays. The deviation from the SM prediction reported in the underlying flavor observables currently stand at the level of 2.5σ, 2.4σ, 3.3σ and 3.7σ, respectively. 

In this context, we perform an angular analysis of the four-body differential decay of Bs→f′2(1525)(→K+K−)μ+μ− in a model independent effective field theory framework. The decay mode Bs→f′2(1525)l+l− undergoes similar b→s neutral current quark level transition and, in principle, can provide complementary information regarding lepton flavor universality violation in b→sl+l− quark level transition decays. We give predictions of various physical observables such as the branching ratio, the longitudinal polarization fraction, the forward-backward asymmetry, the angular observables P1, P2, P′4, P′5 and also the lepton flavor sensitive observables such as the ratio of branching ratio Rf′2, QFL, QAFB, Q1, Q2, Q′4, Q′5 for Bs→f′2(1525)(→K+K−)μ+μ− decays in the standard model and in the presence of several 1D and 2D new physics scenarios.

Comments:	25 pages, 7 figures
Subjects:	High Energy Physics - Phenomenology (hep-ph)
Cite as:	arXiv:2009.06213 [hep-ph]
	(or arXiv:2009.06213v1 [hep-ph] for this version)

From the introduction in the body text:

Exploring and identifying the Lorentz structure of possible new physics (NP) that lies beyond the standard model (SM) is of great importance particularly in semileptonic B meson decays mediated via b → s l+ l− neutral current and b → c l ν charged current interactions. It is well known that the flavor sector could be an ideal platform to explore NP since it can provide possible indirect evidence of NP in the form of new interactions that can, in principle, be very sensitive to the existing experiments. It is also well known that, apart from the flavor sector, existence of NP is also evident from several other phenomena such as the matter antimatter asymmetry of the universe, neutrino mass, dark matter, dark energy and so on. 

In the recent years, several measurements have shown hints of lepton flavor universality violation (LFUV) in the semileptonic decays of B mesons involving b → s l+ l− (l ∈ e, µ) neutral current and b → c l ν (l ∈ e/µ, τ ) charged current quark level transitions. Significant deviation from the SM expectation has been reported in various flavor observables such as RK, RK∗ , P'5 in B → K(∗) l + l− decays; B(Bs → φ µ+ µ−); RD, RD∗ , P τ D∗ , F D∗ L in B → D(∗) l ν decays and RJ/Ψ in Bc → J/Ψ l ν decays. 

Here we will focus mainly on the anomalies present in B meson decays mediated via b → s l+ l− quark level transitions. The ratio of branching ratio RK and RK∗ in B → (K , K∗ )l+ l− decays are defined as: 

RK(∗) = B(B → K(∗) µ+ µ−)  / B(B → K(∗) e+ e−). (1) 

After the Rencontres de Moriond, 2019, the current status of several observables pertaining to b → s l+ l− quark level transition decays is as follows: 

the measurement of RK from the combined data of both Run 1 and Run 2 of LHCb reports RK = 0.846+0.060 −0.054 (stat) +0.016 −0.014 (syst) in the central q^2 region (1 ≤ q^2 ≤ 6 GeV2 ) where, q^2 is the invariant mass-squared of the dilepton. The deviation from the SM value of RK ∼ 1 is found to be at the level of ∼ 2.5σ. 

Similarly, the RK∗ was measured in two different q^2 bins from two different experiments where, the LHCb reports RK∗ = 0.660+0.110 −0.070 (stat) ±0.024 (syst) and Belle reports RK∗ = 0.52+0.36 −0.26 (stat) ±0.05 (syst) in the low q^2 bin (0.045 ≤ q 2 ≤ 1.1 GeV2 ) and similarly in the central q^2 bin (1.1 ≤ q 2 ≤ 6 GeV2 ), LHCb reports RK∗ = 0.685+0.113 −0.069 (stat) ±0.047 (syst) and Belle reports RK∗ = 0.96+0.45 −0.29 (stat) ±0.11 (syst). 

These measurements differ from the SM prediction of RK∗ ∼ 1 at the level of ∼ 2.4σ. 

In addition to RK and RK∗ , the deviation from the SM expectation is also found in the measurements of the angular distributions of B → K∗ µ+ µ−, particularly in P'5. The ATLAS and LHCb collaborations measured P'5 in the bin q^2 ∈ [4, 6] GeV2 and they differ by ∼ 3.3σ from the SM expectation. 

Similarly, the CMS measurement in q^2 ∈ [4.3, 6] GeV2 and the Belle measurement in q^2 ∈ [4.3, 8] GeV2 differ by 1σ and 2.1σ, respectively from the SM expectations. 

In addition, the measured value of the branching ratio B(Bs → φ µ+ µ−) is found to deviate at the level of ∼ 3.7σ from the SM expectations. 

In Table I we report the current status of RK, RK∗ and P'5 . At present, the dedicated ongoing B factory programs at Belle II and LHCb emerge as promising platforms that can either confirm or refute the existence of NP in b → s l+ l− transition decays. 

Our main aim is to study the impact of NP on Bs → f 0 2 (1525) µ+ µ− decay observables in a model independent effective theory formalism. The Bs → f 0 2 (1525) µ+ µ− decay mode has received less attention both from the theoretical and the experimental side and it has not been discussed earlier in detail. Although, in Ref. [18], the authors discussed the SM results for both the µ mode and τ mode of Bs → f 0 2 (1525)l+ l− along with the B → K∗ 2 (1430)l+ l− decays, but more emphasis was given to B → K∗ 2 rather than Bs → f 0 2 decays. Also the branching ratio of f 0 2 decaying into K+ K− was not considered in their numerical analysis. In Ref. [18], the authors also discussed the impact of NP on several observables coming from two different NP models such as the vector-like quark model and the family non-universal Z 0 model. Similarly, there are ample number of literatures discussing the B → K∗ 2 (1430)l+ l− decays mediated vis same b → s l+ l− quark level transition. 

So far we don’t have many experimental results on electroweak penguin decays involving spin 2 particles. The experimental techniques used for Bs → φ l+ l− can be adjusted to Bs → f 0 2 (1525)l+ l− decay as well because both φ and f 0 2 (1525) decay to a pair of charged kaons which are easily detected by the LHCb detector. Since the dominating structures in K+K− spectrum are the P wave φ(1020), and there are several possible resonances around 1500 MeV/c 2, it’s a natural thing to look at this regime to study. Further, the presence of D waves in this mass region yields a richer spectrum for exploring interesting angular observables. Moreover, we will show afterwards that the branching ratio of this decay mode is found to be sizable using pQCD form factors, hence we expect hundreds of signal events to be observed by analyzing the current LHCb data available