This is just a thought but if what if the Byakugou is actually an incomplete form of Slug Sage Mode? As we are all aware the seal is a high concentration of chakra that is positioned on an individual's forehead. Well this presumption alleges that perhaps the chakra utilized in the formation of the seal may have in fact been natural energy intermixed with physical stamina and spiritiual essence to create sage chakra. Furthermore, the auto-regenerative abilities of Byakugou's activation would correlate to Hashirama's injuries being suddenly healed after entering SM.
The second quality which Byakugou and Hashirama's SM appear to have in common are the markings on the foreheads of the respective users. Both have a stark resemblance to the Urna, the propitious pineal eye of Buddha that is capable of looking past the mortal universe into the divinity. Is this just a coincidence? You could argue that it is but bear in mind that Madara commented on the similarities between Tsunade's technique and Hashirama's ability to self-heal (http://i.imgur.com/xiw1wbK.jpg). Is it really just a fortuitous resemblance to her grandfather's medical practices which she inherited? Or do they both originate from the same natural source? You have to admit that the markings do look quite similar, especially since they're on the foreheads of their respective users.
Something else I would like to bring up is that both Orochimaru and Jiraiya strove to become sages in native habitats of the creatures they created a pact with. With the recent chapter's confirmation of Shikkotsu Forest being the habitat of the slug summonings there is now the probable existence of a Slug Sage Mode. Why would Tsunade not develop an interest in senjutsu as well? It's a very lucrative field of study; one which the medical techniques and practices that she knows would greatly benefit from. It would also correspond to the equilibrium aspect of the three Sannin which Kishi has emphasized all throughout the manga. She may also desire to follow in her grandfather's footsteps by acquiring senjutsu.
This may sound odd to some of you but I believe that perhaps all of the Sannin are in a state of being where they are constantly gathering natural energy. Think back to the physical attributes of the snake sage. Does the shading around Orochimaru's eyes not resemble those markings? Now as it was stated in the manga he traveled to Ryuchi Cave to try and master Sage Mode but he couldn't because he lacked an adequate body that could sustain himself through the trials of the learning process. However, would that prevent him from being able to gather some quantity of natural energy? Orochimaru was the creator of the Curse Seal and as we all know it gathers natural energy from the world around, granting a sort of quasi-SM which would account for Sasuke's ninjutsu being more powerful whenever he entered the state, his resistance to being flung into the hard surface wall of the Valley of the End, as well as the enhanced reaction and agility which he displayed when fighting Zaku.
If Orochimaru could liberally distribute natural energy gathering seals to children whom he happened to encounter then why would he be unable to gather that energy himself? Not only that, if Orochimaru is to eventually return as an antagonist when what could possibly make him strong enough to battle against Sasuke or Naruto? A perfected SM is the most likely tool and with Zetsu's Senju DNA he may be capable of mastering the form now. Unless he left the Kage group to go to Ryuchi Cave in order to recommence with his training then he should already the process for how to create sage chakra.
The shaded encirclement around Orochimaru's eyes which spans down the sides of his nose bridge in a ridged pattern, the tear-like markings that run downward from Jiraiya's eyes, and finally the diamond shaped concentration of chakra on Tsunade's forehead. All of them are potential indicators of natural energy accumulation, are they not? Well for Orochimaru there is a sufficient amount of evidence to reinforce his aptitude for passive acquirement of nature's force. But then with Jiraiya during his battle against Nagato there's a certain anomaly which challenges the validity of this theory. As he is preparing himself to summon Fukasaku and Shima he bites his fingers to draw blood and then marks his face (http://i.imgur.com/wKnPsoU.png) as a contract of sorts which the 3rd Databook references (http://i.imgur.com/BvvEXbF.jpg)
This would lead us to believe that the markings are intentionally preserved on Jiraiya's features as a precautionary measure should he ever be placed into a combat situation where he feels compelled to summon the two frog sages. If this is true, however, why did the design and amount of blood strokes on his face vary during earlier periods of his life?
http://i.imgur.com/DlKG8Ue.png - Does anyone here notice the variances in length of Jiraiya's markings? When he was a child (presumably 6 years of age if he began the bell test immediately after graduation from the academy) they extended halfway down his cheeks before coming to a halt. It's odd that he would already have a small portion of the markings already drawn on himself when he has only just graduated from the academy. Unless he decided to mark himself for some other undisclosed reason for this to be rationalized Jiraiya would have had to have started senjutsu training when he was 6 years of age or younger. The toad sages did refer to him with a few puerile nicknames which would indicate that he's either being treated as someone of a lower status (the context of the Japanese honorific "kun" would be applicable here) or they're expressing a form of endearment because they have known him for so many years. Personally, I believe that the latter explanation is more logical.
When he is summoned to the Great Toad Sage years later as what appears to be a teenage Jiraiya the markings have apparently shortened but since the art style has changed so dramatically over the course of the manga you could attribute the discrepancies to his redesign in P2. Now for the militarily outfitted Jiraiya (who resembles someone in their twenties) it would seem that once again the markings have lengthened to frame half of his face. Naturally as one progresses they hone their abilities and become more powerful. His ability to gather natural energy and the amount that he can store should have improved as he matured into an adult.
Lastly, we come to the Jiraiya we all know and cherish. By this time the markings have extended down to the lower margins of his face and have widened to form a geometric pattern. Could this be an indication that he has fully mastered the natural energy gathering process similar to Orochimaru? It would seem that Jiraiya may have been abiding by a training routine that's comparable to Sakura's. Instead of being able to quickly access large reserves of natural energy like Naruto he was forced to gradually acquire it over the course of his childhood as he was an imperfect sage much like Sakura was inexperienced with developing the Byakugou seal and required three years before she could complete it.
It's the most logical explanation that I can create to account for the markings. If they were only segments of a necessary pattern to formulate a unique contract on his face then why did Jiraiya wait so long to continue drawing blood for this process? Does the contractual formation require large periods of time to complete? For what reason would it take so long though? I understand that Jiraiya chooses not to maintain the full blood contract because he finds it to be visually unappealing but why could he have not drawn the geometrically shaped markings when he was a child? He goes about his business with those markings on his face every single day and the fact that it only appeared to lengthen as he grew older with no acknowledgement of repugnance implies that he didn't really mind it.
Whilst we're on the subtopic of Jiraiya's markings there's something else I would like to present as evidence. It appears that with the greater amounts of sage chakra he acquires his appearance and personality become more animalistic, which inadvertently causes the shaded encirclements around his eyes, one of the primary indicators of senjutsu usage, to overlap with his blood markings. Thus causing all of his face except for the mouth region and his nose to become overspread with these peculiar cosmetic shadings.
Here, let me arrange a development chart of the growth of Jiraiya's markings:
http://i.imgur.com/VL2i2PS.png - As it was addressed above the shaded areas around Jiraiya's eyes overlap with the markings darken the majority of his features. It appears that it may have even thickened the markings slightly in the third stage. How does this demonstrate that the markings are directly related to sage chakra?
http://img.mangastre...to_379_pg10.png, http://img.mangastream.to/manga/naruto/379/Naruto_379_pg12.png - Well as the fight with Pain continued after the other realms unexpectedly appeared behind Jiraiya to remove one of his arms the shading which coated most of his face in the 4th stage was removed and it regressed back to the appearance of the 3rd stage. Not only that, the serrated teeth are missing as well. How could that be though? All Jiraiya did was lose one of his appendages. Unless the amount of sage chakra in that arm helped to provide him with that facial colouring then I fail to see why this regression would occur since Fukasaku and Shima should still be gathering natural energy for him.
http://i.imgur.com/P83KDx1.png - Following Shima's departure from the fight SM has apparently been deactivated as Jiraiya's pupils are seen in their normal state and he no longer has the physical imperfections associated with his SM. Interestingly enough his facial markings have returned to stage one of the above chart. Fukasaku should still be channeling natural energy to Jiraiya so why would he be unable to maintain SM? And what about the markings? Perhaps they were washed off as he was swimming underwater. However, why would those additional symbols be removed and not the ones trailing beneath Jiraiya's eyes to the frame of his cheeks? Could they be irremovable? Perhaps they're similar to Orochimaru's acuminated marks lengthening down the sides of his nose and Tsunade's Yin Seal?
http://i.imgur.com/9eN2XFk.png - The colouration is off by a few shades but the general redness of Naruto and Jiraiya's respective features is there. These variations could be the product of Naruto being in a perfected state of SM whilst the lines are just indicators of untapped natural energy or "faulty" sage chakra made. Also, can you see the wart on Jiraiya's nose? That wasn't there when he was a child. The wart is common characteristic of an imperfect Frog Sage. Could his experimentation into senjutsu at a young age have caused that? He didn't seem to have it when he was a child but as he became a teenager it appeared on his face; and yes, the wart was there in P1 as well so it's not a trait that Kishi provided during P2.
This may just be an over analysis of a simple aesthetic feature which Kishi decided to give to Jiraiya. The contract he made with his blood may not even be related to the markings. All of this is just hypothesis. However, there is one thing that I do know and it's that the second stage of the chart I made above does have some sort of relation to being to SM as Jiraiya seemed to need it for the summoning of the two sages.
http://i.imgur.com/IGCNxtc.png - Notice something oddly similar to a certain panel of Hashirama's? Humourously enough the markings on both of their faces somewhat resemble one another. Why would Jiraiya require sage chakra to summon Fukasaku and Shima when he has conjured up so many frogs before with just his ordinary reserves? This random theory only deepens the mystery behind certain aspects of the Narutoverse. Or does it? I may be overlooking certain statements or panels that already addressed this.
Now as for Orochimaru we understand that he has been experimenting with his body for some time. The final product of his research, as Sasuke put it, was the assemblage of white snakes to form a single creature that holds Orochimaru's consciousness. But is the hue of his eyes really just a snakelike quality that he acquired through the experiments? To me, it's highly unlikely since he was depicted as a kid with those marks and animal-esque slits for pupils (http://i.imgur.com/Ml5nk5A.png). Unless he was already modifying himself at the tender age of 6 when his heart was still dedicated to seeing his parents once again then there must be another cause for these peculiar traits.
http://i.imgur.com/qaG8kXt.png - There really isn't too much variation in Orochimaru's markings that can be seen. In P2 the hue may have become more pronounced and it seems like that there was some lengthening and widening down the sides of his nose but nothing as drastic as the tear-like symbols that Jiraiya had.adorning his face. The most valuable information acquired from this is the three tomoe on Orochimaru's clothing resembling the Cursed Seal of Heaven. Could it be foreshadowing of its eventual role in the story as one of Sasuke's weapons? Or is it a reference to the natural energy gathering properties of the form?
Interestingly enough despite Orochimaru's *former* inability to learn SM his markings look quite a bit like the pattern on Jiraiya's eyes as he is using Toad/Frog Sage Mode (http://i.imgur.com/KGKB7uE.png).
We finally come to the person who is perhaps the most significant and interesting character of this conversation, Tsunade. I already presented my theories concerning Byakugou at the beginning of this post but I would just like to add that unlike Jiraiya and Ororchimaru her seal never took form until she was an adult.
http://i.imgur.com/MIg58d1.png - All throughout her life Tsunade was never drawn with the Yin Seal in existence on her forehead until after the 2nd Ninja War. If anyone has any panels or information that refutes this claim then please offer it as counter evidence.
After looking over some of the flashback panels of the Sannin when they were children and taking into consideration the above theory I am going to stay that they may have first been introduced to senjutsu when they were 6 years old. Each of them could have been designated a specific summoning class to centre their studies on or they may have chosen the animal which they felt they had an affinity towards. Oh, but that begs the question of why Hiruzen or any Konoha teacher for that matter would allow their infantile students who just graduated from the academy to partake in an activity as dangerous as senjutsu training. Would they even have the chakra reserves necessary to attempt it? Well that's where the gradual natural energy accumulation theory comes into play. As for the ethics behind it all well you have to keep in mind that this a world where children from a young age are instructed on how to think and act like a military force would; essentially they're child soldiers who must suppress their emotions even during the most traumatic of situations lest it interfere with their duties and they are killed by their enemies. Yes, even Naruto and his generation, despite what they may argue, have to do this in some capacity otherwise their apprehension or uncertainty would cloud their judgement.
Teachers like Guy and Kakashi taught their students incredibly hazardous techniques that could very well have killed them. To believe that Hiruzen would permit his squad to train at the sage locations isn't entirely unrealistic although I couldn't fathom a guess as to why he would allow Orochimaru to join the snakes when their customs and practices are considered to be "evil" by the standards of the Narutoverse.
Jiraiya, Tsunade, and Orochimaru should be capable of acquiring a basic understanding of natural energy and sage chakra. For the boys the markings of senjutsu practice would have already appeared on their persons with Orochimaru appearing to have greater success as he was capable of attaining the ocular characteristics of the snakes. On the other hand, Tsunade's natural energy gathering indicator comes in the form of a seal that will only materialize after enough chakra has been gathered. Since it would require several years for her natural reserves to increase and with the necessity of her medical expertise in a world war Tsunade may not have quite as much chakra to allocate to the seal as she would be capable of without those hindrances.
Yet another aspect that can attest to the SM and Sannin trinity are the focal points of the individual animals that they are taking after.
Frog - Emphasis on strength, offensive ability, and physicality in general
Snake - Emphasis on sensory perception of the world around and the instilling of life into the lifeless
Slug - Emphasis on the implementation of the mind and imagination to a person's abilities that allows them self-preservation
The Slug Sage Mode basis is assumption and probably contains some errors relating to the source material or inspiration for its emphasis.
So in conclusion how exactly does this correlate to Sakura's seal or the possibility of her acquiring SSM? Well the single most important aspect of her new abilities is that her seal was provided an entirely different name compared to Tsunade's mitosis jutsu; as opposed to what Narutopedia would lead someone to believe. Is their article about the White Strength Seal accurate? I noticed that they're no longer differentiating between it and the Yin Seal?
Anyways, a second significant condition to factor in is that Sakura has yet to release her seal. Will it create the markings on her body that are associated with Byakugou jutsu? Or will it be something else entirely?
http://i.imgur.com/Fxw5Lwd.png - This probably has absolutely no relevance to the matter but has anyone noticed that Tsunade's nail colouring is the same as her seals? It's probably just a coincidence though I think Sakura's fingernails/toenails were coloured a sea foam green at some point in one of P1's cover pages. Could it be foreshadowing what her seal's intended colour will resemble? But even if the colouring of the seals could vary due to trivial details like the shade of person's nails how would that individualize their abilities? At best it's only an indication of what Tsunade and Sakura's chakra colours are.
That's it for over analysis. Much of this is just presumptuous speculation over abilities and ideas that have yet to even be confirmed. It wouldn't be a surprise to learn that several informative panels from the manga completely debunk these theories. I just really want there to be an explanation that affirms our suspicions of the Sannin counterbalancing each other not just through their summonings but through their own respective Sage Modes as well. Perhaps it could somehow verify the possibility of Sakura's personal SM.
http://i.imgur.com/dtPd53C.png - One other random comparison of panels image was of Tsunade in Byakugou and Jiraiya in SM. The markings are similar in placement and proportions but Tsunade's lacks the shading around her eyes.
If there are any errors then I apologize.