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Today, the League remains one of the best. Beneath the great gushing growth of modern American culture, hidden and forgotten, lie the true roots of freedom, democracy and peaceful co-existence. Let us hope modern civilization will pause its arrogant, headlong rush to catastrophe long enough to look and take note. For if we follow the White Roots of Peace back to their source, we find men and women of the Iroquois Nations gathered around a hole into which Peacemaker cast the weapons of war.
There we find the spiritual inheritance of all humanity: One Peaceful World, the United. Among Indian tribes in America, Iroquois are special in that they remain autonomous, independent nations. Yes, nations, not "reservations" as many Americans mistakenly believe. Under international law Iroquois reservations aren't U. Rather, they are foreign nations within the United States and Canada, who exercise their own self government on their own national soil.
They're a distinct culture and race with their own language, religion, history, families, communities, and government. To Iroquois traditionalists the Great Law of Peace isn't merely a form of government, but religious practice of an ancient spiritual legacy. Peacemaker wasn't a military hero or social leader, but a messenger of the Creator.
Following The Great Law is a spiritual practice, and those who follow the Longhouse tradition are "faithkeepers. Nations of the human family. From Hiawatha to by Thomas R. Henry- Native of Economic Democracy the position of the Iroquois overwhelming majority of men today, an enormous gulf present proletarian and peasant.
Basest interestsmean greed, brutal appetite, sordid avarice, selfish robberymark the new class society. By vilest meanstheft, violence, fraud, treason the old gentile class society is undermined and overthrown. The new society during all the two-and-a-half thousand years has been but the development of a small minority at the expense of the great exploited, oppressed majority.
However, there is often public confusion and many overlook the year. There are many self-styled orders. Since at least the 18th century the Freemasons have incorporated some Templar symbols and rituals, most of which being found within a Masonic body referred to as the United Religious, Military and Masonic Orders of the Temple and of St John of Jerusalem, Palestine, Rhodes and Malta, or simply the Knights Templar. This organization exists either independently or as a part of the York Rite throughout much of the world. Inquisition in , the Knights Templar were accused of 'having idols, namely heads, that they adored these idols, At an said they could save them, and that the heads could create riches, make trees, flower and land germinate'.
It was believed the sculpted heads were inspired by the dark-skinned Egyptian Goddess, Isis, consort of Osiris, the dying-andresurrecting vegetational god, and mother of Horus, who was the reborn Osiris and identifiable with the Egyptian Pharaohs. This involved taking the first letter of the alphabet, and substituting for it the last letter - taking the second letter, and using the second last, and. The story of the secretive yet powerful medieval. In , after many delays, he.
Templars, especially their persecution and sudden dissolution, has been a tempting source for many other groups which have used alleged connections with the Templars as a way of enhancing their own image and mystery. Many of the Templar legends are connected with the Order's early occupation of the Temple. Mount in Jerusalem and speculation about what relics the Templars may have found there, such as the Holy Grail or the Ark of the Covenant. Their political and ecclesiastical. Sinclair was known as Glooscap by the Micmac Indians, and while there is no written record, their legend talked about Sinclair arriving and wintering in Nova Scotia, and then travelling south to Massachusetts.
He taught them the. So they accused the brave brotherhood of heretical religious observances, including the worship of enchanted human heads. It is currently the Roman Catholic Church position that the medieval persecution of the Knights Templar was unjust; that there was nothing inherently wrong with the Order or its Rule; and that Pope Clement was pressured into his actions by the magnitude of the public scandal and the dominating influence of King Philip IV.
By papal decree, the property of the Templars was transferred to the Order of Hospitallers, which also absorbed many of the Templars' members. In effect, the dissolution of the Templars could be seen as the merger of the two rival orders. From there, they traveled across the Atlantic to Nova Scotia and Massachusetts and left their marks there. And all this long before. Columbus discovered the West Indies.www.cogumelo.uevora.pt/includes/2977.php
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The eagle, bear, wolf and buffalo will be scarce because. The sky will become black and the trees and plants will die. The beautiful rainbow will disappear because people will not remember to keep the Mother Earth sacred and will destroy its beauty. Children of the Rainbow Warriors will come before all destroyed and they will love the trees and the animals. They will love and respect each other and they will help people to live in peace with all creation. The rainbow in the sky will return as a sign of the Creator's grace. She typed the Free Trade Agreement. Find out what happened to the woman who faced down the government to expose this treason in our House!
Find out just what was on the table that Mulroney gave away, and what that means for Canadians right now! Flood info Starts here and the core Haarp proof!! As we Fire the Grid throughout the day, we blaze our own unique vibration to blend with the frequencies of all Children of the Sun and the combined harmony of our hearts love can move mountains, part the sea and open stargate portals to a glorious New World! Year in Babylon. She was worshipped via the rising moon, and was often depicted as being pregnant. From this union:Nabak also known as Tashmetum.
Descendants of The AN. They rewrote the books and changed the hieroglyphs and statues. Send us your women and children and we will put them into covenant. Their marriage was celebrated annually at New. Get over it! And The Time Will Come When You See Were All One - "Prophecy tells us that at the very end the number of men with ambitious minds will decrease, while the people of good hearts, those who live in harmony with the earth, will increase until the earth is at last rid of evil.
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If the Hopi are right, this will be accomplished, and the earth will bloom again. The spiritual door remains open. Why not join the righteous people who are moving toward it? The Father spoke to me and said, "The only color I see on the nation of Canada at this moment is red for the redemptive blood, red for the cleansing fire! My glory will spread forth to the nations but first must come the fire.
The fire shall spread forth throughout the land from sea to shining sea. From the south to the north My fire will burn; a fire of purification a fire that will melt the cold, stony hearts. A fire will burn as My remnant bride comes forth out of the wilderness arrayed in glorious splendor. As My bride marches forward the fire shall burn and the golden oil shall be spread forth. I delight in you O Canada. I delight in you as you rise forth to do My will in this final hour. The very hosts of darkness will tremble and flee at the sound of this glorious army.
The shackles shall be broken; they will be removed. Truly Canada shall be free and shall rise above the nations of the earth singing a jubilant song of victory unto Me in this last of the final hour. Canada come forth! Arise to your destiny! I extend My scepter to you O Canada! I call you forth now to take your place Arise now mighty nation, arise and let the lion roar. Come forth my chosen and beloved I pour out my favor and I bestow unto you My glory. Wealth and abundance is coming for you O glorious Canada. For truly Canada is a nation of destiny, a nation of purpose.
Canada the day of intimacy is upon you. Canada My. I see the nation of Canada laid out before me. I see smoke arising across the land. I hear the voice of the Lord saying, "Arise O army of worshippers! For My bride is coming forth into a new level of intimacy and liberty in dance, in movement. She is rejoicing and praising her way to destiny. I saw a large, vibrant heart spread out across the nation of Canada. I heard the voice of the Father say, "That is My heart. My heart beats for the nation of Canada. For this nation is the heart of My global body. As I looked into the kaleidoscope and it turned, I saw only one color.
It was the color red. We are a Friendship Group. If you are attached and seek fellowhip with others, you are welcome here. Just behave yourself. Build lasting friendships based oncommon interests. Let's network, plan events, meetings, suggest activities. Let's get connected again. We are hiding Moon was also male divinity in ancient Semitic religion, and the Arabic word for the moon qamar is of the masculine gender, on the other hand, the Arabic word for sun shams is feminine gender.
Essenes: The roots of the Christianity and the Devil- writings are the real roots of Christianity, thus, it is the essence of the concept of Beast Number in Johns Revelation. And second, it integrates a Devil of absolute evil into Judeo-Christian ideology and directly uses the name and image of a Babylonian god in this concept. The Essenes, a male-only sect in Qumran, imported the Zoroastroanist absolute evil and considered it as the eternal enemy of the Lord God.
Not surprisingly for us, they named this entity as Belial, a synonim for the Canaanite God Baal or Bel. This was nothing but the Canaanite version of Babylonian god Marduk. I believe that all these monotheistic religions have more or less similar origins. This idea of monotheistic religion was not a brand new invention. Differences were, these kings demanded that they themselves were the God whom everybody should worship. What rules you? At the moment the Star dies,.
The same is the heart and Soul of a person. True beauty results from cultivating a pure soul. Ever been around people who look physically attractive and after spending a few minutes around them, their beauty seems to fade in from of your eyes? Then you have people in time, just looks prettier the more you know them? The world bombards us to focus on the external. Women are driven to anorexia in efforts to achieve model-like thinness and make-up companies earn a fortune from our efforts to look more "perfect.
Fitness clubs have become temples of the body, where men try to sculpt themselves into the image of a perfect man--bursting biceps, six pack abs, and chiseled pecks. All of this in efforts to look more beautiful; to be more attractive. The problem is, real beauty can't be achieved through diets and make up. A truly attractive person isn't born in a gym.
Soul deep, last-a-lifetime beauty comes from a pure soul. You can see these in the eyes the window of everyone's soul. Our societies have purposely destroyed everything that is sacred. All relationships have turned into commodity and market place, a trade. People don't commit to working on the content of their character, their sacredness and their purity. People get things they want, not based on need. They don't know the difference.
They just accumulate There is a compulsive andimpulsive "shopping" behavior. They don't know their Purpose in life. They don't have deep meaning for their existence. They just roll wherever they please. This is not a religious "preaching". I am pointing out how our world is. I do not believe that as human beings, we are to behave lower than animals. For what? What is the purpose? What is the purpose of killing another race? I think we all need to be alarmed. I am calling Humanity to BE pro-active and compassionate human beings. Being a human being means you have a Soul.
Whatever you feed, it grows. Do you feed your Ego or your Soul? Are you a Black hole or a Star? Humanity delves into much depravity and debauchery. The saddest thing, is the parents are passing this on to their babies, exposing them on television where sex, lies and violence and all sorts of mind-control programming takes place.
Impurity is a grimy film that coats the soul, a shadow that blocks light and darkens our countenance. Mesopotamian Shamashplays an important role during the Bronze Age, and "my Sun" is eventually used as an address to royalty. Similarly, South American cultures have emphatic Sun worship, see Inti. Svarog is the Slavic god sun and spirit of fire. Would you drink filthy water to quench your thirst? The heaviness of external corruption that bombards our daily lives can be overwhelming.
Many walk around this world unconsciously "awake". This passivity andapathy to. Sun worship was exceptionally prevalent in ancient Egyptian religion. The earliest deities associated with. We put up with the assault by the Corporatists who manipulate everyone to consumerism. First Hathor, and then Isis, give birth to and nurse Horus and Ra.
Hathor the horned-cow is one of the 12 daughters of Ra, gifted with joy and is a wet-nurse to Horus. Toci "Our grandmother" in Nahuatl is a deity figuring prominently in the religion and mythology of the pre-Columbian Aztec civilization of Mesoamerica. Sun's movement across the sky represents a struggle between the Pharaoh's soul and an avatar of Osiris.
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Ra travels across the sky in his solar-boat; at dawn he drives away the demon Apep of darkness. Akhenaten changed the polytheistic religion of Egypt to a monotheistic one, Akhenaten changed the polytheistic religion of Egypt to a monotheistic one, Atenism of the solar-disk and is the first recorded state monotheism. All other deities were replaced by the Aten, including Amun-Ra, the reigning sun god of Akhenaten's own region. Unlike other deities, the Aten did not have multiple forms.
His only image was a disk a symbol of the sun. Can appear as a jaguar. A sinister rival to Quetzalcoatl. Tezcatlipoca is the Smoking Mirror, god of time and the Lord of the North, the embodiment of change through conflict. Tezcatlipoca is the ruler of day Acatl. He is Lord of the Day for days with number 10 "mahtlactli" in Nahuatl. He was also god of beauty and war, the lord of heroes and lovely girls. He once seduced the goddess of flowers, Xochiquetzal, wife of the god Xochipilli, because such a lovely goddess was a good match for him, being a handsome war-like god.
Yet he appeared most frequently as a magician, a shape shifter and a god of mysterious powers. Quetzalcoatl was related to gods of the wind, of Venus, of the dawn, of merchants and of arts, crafts and knowledge. He was also the patron god of theAztec priesthood, of learning and knowledge. Serpent has the human face of the young maize god, further suggesting a connection to fertility and vegetational renewal, the Mayan Young Maize god was also connected to Venus. Quetzalcoatl was one of several important gods in the Aztec pantheon along with the gods Tlaloc, Tezcatlipoca and Huitzilopochtli.
Quetzalcoatl is the Aztec creator god. He was one of the eight gods viewed as serpents. He was also known as White Tezcatlipoca to oppose from his twin Tezcatlipoca known as Black Tezcatlipoca. They wereopposites. Together, they created the world and during the process Tezcatlipoca lost a foot. There is also speculation that he created the world by himself because one of.
Marduk killed the gods of them previous generation and became the new king. His symbol was also twin serpents and he was also known as the builder of pyramids, which were formed to venerate mountains. According to the Mesopotamian Creation text Enuma Elish our solar system once housed a planet called Tiamat, which was struck by a rogue planet called Nibiru later renamed Marduk in Babylonian text. This event happened when the solar system was very young and still forming. This collision was so severe it caused the splitting of Tiamat.
One portion of Tiamat spun off and became the Earth, while the other portion of the planet broke up into small pieces and became the asteroid belt that the Sumerians referred to as. Thus just like any otherparasite - the Demiurge must harness energy degradation across a gradient flow in order to maintain his own structure. In other words, even the creator god of the Bible has to eat or die. That in itself is hardly remarkable the world is filled with polytheistic cultures, and gods both malevolent and benevolent who feed on blood and worship. What makes the Demuirge so uniquely insane and dysfunctional is this: Unlike the sacrifical gods of polytheistic cultures theDemiurge recognizes no other source above himself he thinks that he himself is the Supreme Being.
Tecciztecatl "old moon god"; also Tecuciztecal, Tecuciztecatl was a lunar deity, representing the old "man-onthe-moon". He could have been the sun god, but he feared the sun's fire, so Nanahuatzin became the sun god and Tecciztecatl in the form of a rabbit was promptly thrown into the moon. In some depictions he carried a large, white seashell on his back, representing the moon itself; in others he had butterfly wings. He was a son of Tlaloc and Chalchiuhtlicue.
In the Gnostic tradition, the planets were actually Archons, the servants of the Demiurge, also known as Ialdaboth. TheDemiurge was the false god the terrible, egotistic god of the Old Testament, who seems to take great relish in smiting those who do not agree with him. The Demiurge was a mistake Sophia, the divine wisdom, birthed Ialdaboth through becoming curious about the lower emanations of the Divine Source, the true God. Each one is simultaneously the gate barring the way and the key to.
Their functional role is to keep living creatures humans, animals, the material world in general in their place. This means that they regulate our will through their motions, and living things, while unawakened to the Source beyond the Demiurges influence, dance to their tune. This serves the Demiurge just fine it is a jealous and possessive creature, and likes to watch over its little ant farm. But it means that we are condemned to suffering.
Humans move in apparently erratic fashion, triggering human-made catastrophes, wars and murder and other unpleasantries, always asking why?. Why do we do these things? We feel ourselves to be innately greater than we apparently are, but we cannot discern how to free that potential. The Archons of the planets and the Demiurge condemn us to rote living. And what about death? In Gnosticism, there is no such thing as heaven or hell.
The Archons are barriers to our rejoining the Pleroma, the Source. We merely reincarnate to do it all over again. In Gnosticism the Demiurge,creator of the material world, was not God but the Archon, or chief of the lowest order of spirits or aeons. According to the Gnostics, the Demiurge was able to endow man only with psyche sensuous soul the pneuma rational soul having been added by God. The Gnostics identified the Demiurge with theJehovah of the Hebrews.
In philosophy the term is used to denote a divinity who is the builder of the universe rather than its creator. Creator deity- The idea that human kind is the product of genetic engineering carried out by extraterrestrials from outside our tiny planet challenges both Darwinian evolution and creationism. Have the dogmas of science and religion blinded us to the truth of our origins? Church promotes the doctrine that they are saved by Grace regardless of the manner in which they live their lives, Peter not only states that this doctrine is in grave error, but correctly states that: "It would have been better for them not to have known the way of righteousness, than to have known it and then to turn their backs on the sacred command that was passed on to them.
Saturn is associated both with Sophia, the Divine Wisdom, and Ialdaboth, the grasping and largely unpleasant Demiurge. Saturn is both the ultimate in limitation a jealous and destructive creature who inflicts plagues and wars and genocide but also embodies the heights of human intellectual understanding of God, the source, and of Creation beyond the base material. One of Saturns other names is Pronoia, meaning Forethought. Venus is the planet of beauty, art, the loveliness of the world and of creation, but also binds us to it.
Mercury rules both magicians and thieves. Mars, fraternity and war b. Hyperborea "Beyond the North Wind" , where people lived in complete happiness and had extraordinarily long lifespans. Greeks thought that Boreas, the North Wind, lived in Thrace, and that therefore Hyperborea was an unspecified region in the northern lands that lay beyond the north wind. Their land, called Hyperborea or Hyperboria "beyond the Boreas" was perfect, with the sun. Jupiter, temperance and excess. There is a paradoxical element in the traditional scheme.
So does one claim free will? By consciously embracing the higher qualities of those planets, and seizing the keys. How one does this is a very individual exercise this is the goal of Buddhism, as well asHermeticism and Gnostic Christianity. It is the goal of all of the non-Demiurge lack-based spiritual paths. One does not need to apply oneself to -isms to find this, either many people who are agnostic or non-religious can find ways of transcending the limitations of fate.
For example, when one is not ruled by the motions of Venus, her rulerships no longer effect us compulsively we can be moved by beauty, stirred by our lovers, enjoy good company, but we do not feel compulsively attached to such things. That Venus-Saturn square that might have, in other circumstances, threatened your relationship through provoking your insecurities can do nothing if you are free of insecurity in the first place. It is Metatron, the Guardian at the Gate, and in Gnostic associations, represents Sophia, the feminine wisdom, as well asIaldoboth, the demiurge the highest and lowest.
A body of dual associations, he is the beginning and the end, and was regarded as the greatest of the planets in classic times. Saturn, lord of time and the rise and fall of cities, countries and peoples simply conti nues his operations underground with grand patience. We can defer our suffering to other countries, wreak war, employ cheap labour so that we do not have to do it, and yet Saturnine principles remain. A quick glance at the child mortality statistics of Bangladesh or the toll from the latest round of earthquakes, tsunamis and famines around the world confirms that we do not, in fact, live in a cotton-wool shrouded world in which Saturn has been reduced to the stern but paternal CEO of the solar system.
The world is still a deeply harsh place for half the worlds population, and unfortunately, out of sight is not out of mind. Saturn is in many ways the testing angel, the angel of Job and the guardian of Eden in biblical literature. He is Ammit, the eater of unworthy hearts, and Ereshkigal, the Sumerian goddess of the underworld to whom we all must, eventually, submit to to move beyond what we already are.
Saturn has been associated with the sixpointed star, the Star of David or the Hexagram interesting, considering that the ancients had no idea about the storm raging at its pole. The Golden Dawn associated it with Binah, the second divine emanation of the Tetragrammaton and the steadying, divisive and settling principles of Creation. It is the highest of the emanations save for Kether, the crown, but also represents the greatest tragedy the split from the Monad, the singularity, in which all things were united with the Source.
Friday, Thank Venus its Vendredi! Saturn is referred to as a taskmaster, or as a father figure steering individuals to their long term destiny. Not the sort of father I would want, I must admit Saturn classically rules death, chronic disease, depression, famine, infertility, dark places, underground settings, crypts, locks. Aten, Akhenaten himself as "the enemy"which is sometimes described as monotheistic solar deity a status above mere gods. All the religions have the same source! The entity worshipped as Lakshmi in Ancient India is said to be the same as Innana, Astarte, Aphrodite and Venus, but insights from Tantriks will reveal that 64 emanations of the Divine Feminine exist across dimensions.
Kaali is the dark polarity, Parvati is the light Polarity for instance. For Kaali herself 9 existances are known, including "Smashan Tara". Siva has many emanataions including Rudra, Hanuman, Mahakal etc. Such insights are found in this book: KundaliniAghora 2 by Robert Svoboda. Also, many Alien Systems have contributed to the myths. Narasimha is a. Well, almost. Inanna had a twin brother who was called Utu.
He revealed to them that although the Fallen Lords had greatly tampered with their mortal bodies through eons of genetic manipulation, human kind were still angels unaware. Job "Canst thou bind the sweet influences of Pleiades, or loose the bands of Orion? This becomes the word Ptah, in Egypt who some Heli os for example believe is identical with the person Ale ph Hyperion. It took a fair amount of trickery to get such radically self replicating DNA droids installed on the mining planet, without arousing too much suspicion on the home star. He was the pride of the DNAs droids of Enkis fleet.
He was the one submitted back to the Orion council when they demanded a specimen of the result of the genetic experiments on Earth, after they learned that the Anunnaki had crossed in their OWN DNA! This was all part of the Enki-Thoth subterfuge against Enlil and later Marduk. Individuation vs. Pics of reptiles eating humans in monument valley at www. With me, I brought the Enochian Table Toth-Mus-Zurud was known in Atlantis as the. Another possible hint to his identity with the Jesus myth.
The resulting squabble lead to Ras booting Thoth out of Egypt precipitating his Mes oAmeri can life as. Quetzlcoatel etc. Sword of Orion. He tells me that this denotes the dime. He was given credit for inventing hieroglyphic writing. He was known as the "Sc ribe of the Gods," and as such, was ther ecorder of all human deeds.
It has also bnsion of his realm, which is the eighth. In that dimension he contains the genetics of the Light Races of Orion with the sun of his creation being Rigel. The ancient Egyptians often depicted Thoth as Ibis-headed, although he was also portrayed at times with the head of a baboon. Thoth was the architect of the Great Pyramid of Giza. Thoth served to enlighten humans in that age that they were not the spawn of the Nephilim, thefallen angels of Lucifer. Hiburu is a harmonic language, mimicking the waveform properties of light.
The "keys" Enoch speaks of, turn out to be sound keys, keys to be vibratory matrix of reality itself, the mythic "Power of the World". The Enochian knowledge describes sonic equations, encoded within the ancient mantras and god names, capable of directly affect the nervous system and producing profound effect of healing and higher consciousness states.
As the ancient texts declare, "If you would. His pyramid is the Pyramid of the Sun in Teotihuacan, Mexico. It's measurements are in the same proportion as the Great Pyramid in Egypt. He was fathered by EN. KI, the "Lord of the Earth," an extraterrestrial master-geneticist and one of the Creator Gods of the homo sapien species. DA, the "Lord of the Tree of Life," and the master architect andbuilder of the Sumerian stepped-pyramid, -On a lonely mission far from their home planet of Nibura, the gods under Enlil began to take the daughters of the humans as wives and began to have hybrid children.
Enlil saw this as an abomination of his race and wanted the human race destroyed. Enlil tried on many occasions, by floods and plagues, but Enki had thwarted Enlil at every attempt. Leading to further divisions between the god's, Enki's first born son Marduk-Ra, believed that he was destined to rule the Earth from theEnlilian city of Babylon, the "Gateway of the Gods," rather than Enlil's first born son Ninurta.
The following millennia would be a time of war between the competing extraterrestrial gods and their armies in the Middle East. Wherever the winged serpent god went, great civilizations sprung forth. True teachings were taught humankind evolved. By our continued blindness, ignorance, and participation in the Enlilian war god religions, we are fulfilling Enlil's systematic destruction of the human species by onrushing toward Enlil's ultimate deception Armageddon. When Quetzalcoatl was driven out of the land of Mexico by the Enlilian war god Huitzilopochtli, who later demanded war and human sacrifice, Quetzalcoatl promised to return.
If Quetzalcoatl returned on the day of 1 Reed, of the Year 1 Reed, it would signal the fact that mankind had evolved and a new era of peace upon earth was at hand.
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If the false Quetzalcoatl returned, it would signal that the war gods had prevailed and a period of nine 52 year "hell cycles" would begin. It was predestined that Quetzalcoatl couldn't return until the time of the sixth sun - This was the Tiger Sun, the Sun of Quetzalcoatl, the total eclipse of July 11th, He would be there to usher in the last katun approximately 20 years of the Great 26, year Mayan cycle, whichends at the time of the winter solstice, December 21, on the Gregorian calendar. This last katun would be a time of great change, both in human consciousness and in physical Earth Changes.
It is a time when our Earth Mother returns to her. Marduk-Ra escaped back into space, but now, the Enlilian gods were able to begin their plan for the ultimate destruction and crippling of the human species. The Earth and her resources were theirs to use and abuse as they saw fit and a united human race would be a threat to their overlordship. However, they needed to change their previous apocalyptic plans. It was now too difficult to wipe out humanity with a military mission or a natural disaster.
Enlil decided to direct humanities own destruction by creating a religious division among all people. There would never be a unified Earth. In the name of god, neighbor would fight neighbors, nations would rise against other nations. Immediately, Enlil himself came to the biblical Abraham, demanded to be worshipped as the one and only true god and declared the serpent gods as evil incarnate. The earlier Sumerian and Babylonian Creation and Great Flood stories, embracing the serpent god as mankind's patron defender, were now plagiarized into the Enlilian spin-doctored biblical accounts of the good El-god and the rebellious evil serpent.
Over the millennia, the Enlilian war. Our original prehistoric ancestors lived in an area of our world that was subtropical at one time. Today those landmasses are in the Arctic and Antarctic regions. The Adams and Eves are descendents of theseHyperborean ancestors as were all of us. Yes, there really were E. Are you ready for some real wisdom? OK - Good. And yes, the ancient Israelites, are actually descendants of the Elohiym royal family. This race was black skinned with coarse black hair, large features, and type O Rh-positive blood.
Descendants of the Adam's inhabited all continents and islands of the world. The Adams and the Eves all naturally have Rhpositive blood, connecting them to the Earth. MBA Deadlines List. Deadlines by School. Deadlines Chronological. Placement and Salary Trends. All School Discussions. MBA Success Stories. Submit a Free Profile Evaluation Request. See All. Veritas Prep. Avanti Prep.
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Claim it now. Attend this free webinar to learn how to pre-think assumptions and solve the most challenging questions in less than 2 minutes. Registration is Open! Ends July 26th. The key point is that if a sterile neutrino was responsible, one should observe the same deficit for all neutrinos from the reactor fuel, independent of nuclear species origin, but this was observed to not be the case.
Because the situation with the above anomalies is unclear, and there are challenges to explaining them with oscillations, this review will focus on neutrino mass models that feature just the three known light active neutrinos. If any of the above anomalies is eventually shown to be due to oscillations, then all neutrino mass models will need to be extended to incorporate light sterile neutrinos, including the radiative models that are our subject in this review. The rest of this review is structured as follows: section 2 provides a general discussion of schemes for neutrino mass generation and attempts a classification.
The structure of radiative neutrino mass models is then described in section 3. Section 4 covers phenomenological constraints and search strategies, including for cosmological observables. Detailed descriptions of specific models are then given in section 5, with the examples chosen so as to exemplify some of the different possibilities that the radiative mechanisms permit.
We conclude in section 6, where we discuss some research directions for the future. Appendix gives further details on the relative contributions of the different operators to neutrino masses. In this section, we survey the many different general ways that neutrinos can gain mass, and attempt a classification of at least most of the proposed schemes.
As part of this, we place both the tree-level and radiative models in an overarching context—a systematic approach, if you will, or at least as systematic as we can make it. In the minimal standard model, there is no way to generate non-zero neutrino masses and mixings at the renormalizable level. Dirac masses are impossible because of the absence of RH neutrinos,. The discovery of neutrino oscillations means that the family-lepton number symmetries must be broken.
If total lepton number is also broken, then the neutrinos are either fully Majorana fermions or pseudo-Dirac 5. The question of whether neutrinos are Dirac or Majorana or possibly pseudo-Dirac is one of the great unknowns. The answer is vital for model building, as well as for some aspects of phenomenology.
In fact, many of the radiative models we shall review below do not feature them. But another logical possibility, motivated by quark-lepton symmetry and SO 10 grand unification, is that RH neutrinos exist but have large SM gauge invariant Majorana masses, leading to the extremely well-known type-I seesaw model [ 47 — 51 ].
On the other hand, if neutrinos are Dirac, then RH neutrinos that are singlets under the SM gauge group, as per Equation 8 , are mandatory and they must not have Majorana masses even though such terms are SM gauge invariant and renormalizable. Thus, at the SM level, something like total lepton-number conservation must be imposed by hand.
Most of the radiative models we shall discuss lead to Majorana neutrinos, though we shall also briefly review the few radiative Dirac models that have been proposed. The choice of Dirac or Majorana is thus a really important step in model building. It is perhaps fair to say that theoretical prejudice, as judged by number of papers, favors the Majorana possibility. There are a couple of reasons for this. Recall that a Dirac fermion is equivalent to two CP-conjugate, degenerate Majorana fermions.
Another was already discussed above: even if RH neutrinos exist, at the SM level they can have gauge-invariant Majorana masses, leading to Majorana mass eigenstates overall. Yet another reason is a connection between Majorana masses and an approach to understanding electric charge quantization using classical constraints and gauge anomaly cancellation [ 52 , 53 ]. Nevertheless, theoretical prejudice or popularity in the literature is not necessarily a reliable guide to how nature actually is, so the Dirac possibility should be given due consideration.
The simplest way to obtain Dirac neutrinos is by copying the way the charged-fermions gain mass. Right-handed neutrinos are added to the SM particle content, producing the gauge-invariant, renormalizable Yukawa term. The Dirac neutrino mass matrix is then. To accommodate the O 0. Nevertheless, it seems unsatisfactory to most people. The really tiny neutrino masses strongly suggest that the generation of neutrino mass proceeds in some different, less obvious manner, one that provides a rationale for why the masses are so small.
As well as the Dirac vs. Majorana question, the explanation of the tiny masses has dominated model-building efforts in the literature. So, how may one produce very light Dirac neutrinos? We highlight three possibilities, but there may be others: i a Dirac seesaw mechanism, ii radiative models, and iii extra-dimensional theories.
With these imposed symmetries, the most general Yukawa and fermion bare mass terms are. The light neutrino mass eigenvalue is thus. The above structure is the minimal one necessary to illustrate the Dirac seesaw mechanism and has a cosmological domain wall problem because of the spontaneously broken Z 2 , but the most elegant implementation is in the left—right symmetric model [ 55 ].
The usual scalar bidoublet is not introduced. The absence of the bidoublet ensures the zero in the top-left entry of the mass matrix 7. Alternatively a neutrinophilic two Higgs doublet model [ 57 , 58 ] is an attractive possibility to obtain small Dirac neutrino masses. A generalization of the symmetry structure of the Z 2 Dirac seesaw model discussed above provides us with one perspective on the construction of radiative Dirac neutrino mass models.
A basic structural issue with such models is the prevention of the tree-level term generated by the renormalizable Yukawa interaction of Equation In the case of radiative models, this must be made to happen at loop order. The effective operator. It generates a neutrino Dirac mass of order.
See Ma and Popov [ 56 ] for a recent systematic study of 1-loop models based on this kind of idea. If one wishes to avoid this long range force, one could find a way to make the new U 1 anomaly-free and then gauge it so that the NGB gets eaten, or one may use a discrete subgroup of the U 1 to forbid Equation See Wang and Han [ 60 ] for a discussion of the Z 2 case for 1-loop models that also include a dark matter candidate. The above is simply an example of the kind of thinking that has to go into the development of a radiative Dirac neutrino model—we are not claiming it is the preferred option.
To our knowledge, a thorough analysis of symmetries that can prevent a tree-level Dirac mass and thus guide the construction of complete theories has not yet been undertaken in the literature. That is one of the reasons this review will discuss Majorana models at greater length than Dirac models. In warped or Randall-Sundrum extra-dimensional theories [ 61 , 62 ], the geometry of fermion localization in the bulk [ 63 , 64 ] can lead to the suppression of Dirac neutrino masses through having a tiny overlap integral between the profile functions for the neutrino chiral components and the Higgs boson [ 63 , 65 — 68 ].
The phenomenological implications of Dirac neutrinos in extra-dimensional set-ups have been studied in De Gouvea et al. In the same way, it is also useful to have low-scale seesaw [ 72 ]. This mechanism can be implemented with a discrete number of new fields or via an extra spatial dimension [ 73 ]. We now come to our main subject: radiative Majorana neutrino mass generation. We also briefly review tree-level seesaw schemes, both for completeness and for the purposes of comparison and contrast to the loop-level scenarios. In the course of the discussion below, an attempt will be made to classify the different kinds of radiative models.
This is a multidimensional problem: no single criterion can be singled out as definitely the most useful discriminator between models. The main distinctive feature of Majorana neutrino mass is, of course, that it violates lepton-number conservation by two units. This approach permits the tree-level seesaw [ 47 — 51 , 74 — 80 ] and radiative models to be seen from a unified perspective. Taking the particle content of the minimal SM, it is interesting that the simplest and lowest mass-dimension effective operator one can produce is directly related to Majorana neutrino mass generation.
This is the famous Weinberg operator [ 81 ]. Replacing the Higgs doublets with their vacuum expectation values VEVs , one immediately obtains the familiar Majorana seesaw formula,. One obtains ever more powerful seesaw suppression,. The task now is to derive, from an underlying renormalizable or UV complete theory, one of the Weinberg-type operators as the leading contribution to neutrino mass. Here are some possible choices:. Open up O 1 at tree-level using only exotic massive fermions and scalars as the new physics.
Open up O 1 at j -loop level using heavy exotics only. Open up O 1 at j -loop level using both light SM particles and heavy exotics. Option 1 leads, in its simplest form, precisely to the familiar type-I [ 47 — 51 ], type-II [ 74 — 79 ] and type-III [ 80 ] seesaw mechanisms, as we review in the next subsection. Option 2 leads to a certain kind of radiative model, to be contrasted with that arising from option 3. Opening up the non-Weinberg operators at tree-level then provides a systematic method of constructing a large class of theories that generate neutrino masses at loop order.
Figure 1. Running and matching for radiative Majorana neutrino masses. See Appendix for a discussion of the relative contribution of the different operators. The three familiar seesaw models may be derived in a unified way by opening up the Weinberg operator O 1 at tree level in the simplest possible way, using as the heavy exotics only scalars or fermions. The available renormalizable interactions are then just of Yukawa and scalar-scalar type. The opening-up process is depicted in Figure 2. The type-I and type-III seesaw models are obtained by Yukawa coupling LH with the two possible choices of 1, 1, 0 and 1, 3, 0 fermions, both of which can have gauge-invariant bare Majorana masses.
The seesaw effect is obtained in this case by requiring a positive quadratic term for the triplet in the scalar potential, that on its own would cause the triplet's VEV to vanish, but which in combination with the cubic term induces a small VEV for it. Figure 2. Minimally opening up the Weinberg operator at tree-level using either exotic massive fermions or scalars. A Type-I seesaw model. B Type-II seesaw model. It gains a small induced VEV from the latter coupling.
C Type-III seesaw model. As is clear from Figure 2 , there are two interaction vertices for all three cases, and there is only one type of exotic per case. This model is a kind of hybrid of the type-II and type-III seesaw mechanisms, because it features both a small induced VEV for the quadruplet and a seesaw suppression from mixing with the fermion quintuplet. As noted above, there are many different kinds of radiative neutrino mass models and there is probably no single classification scheme that is optimal for all purposes. We thus discuss a few different perspectives, some much more briefly than others.
This approach can be considered as stemming from the observations made about options 3 and 6 in section 2. They must be of different type, because if they were not, then the heavy exotics would produce the Weinberg operator without participation by light SM particles, leading either to a class 1 model if O 1 is produced at tree-level or a class 2 model if O 1 is produced at loop level.
Such a list was provided by Babu and Leung BL [ 85 ], based on the following assumptions: i the gauge group is that of the SM only, ii no internal global symmetries are imposed apart from baryon number, iii the external lines are SM quarks, SM leptons and a single Higgs doublet, and iv no operators of mass dimension higher than 11 were considered. We first comment on these assumptions. Clearly, if the gauge symmetry was extended beyond that of the SM, then some combination of effective operators might be restricted to having a single coefficient, and others might be forced to vanish, compared to the SM-gauge-group-only list.
Similar observations follow for imposed global symmetries. It is sensible to impose baryon number conservation, because otherwise phenomenological constraints will force the new physics to such high scales that obtaining neutrino masses of the required magnitude at least one at 0. The case of a single Higgs doublet can readily be generalized to multiple Higgs doublets, given that the gauge quantum numbers are the same. This would obviously enrich the phenomenology of the resulting models, and if additional symmetries were also admitted, then it would change the model-building options. The addition of non-doublet scalar multiplets into the external lines is a more serious complication.
Some discussion of the possible roles of additional scalars that gain non-zero VEVs that contribute to neutrino mass generation will be given in later sections. Another restriction worth noting in the BL list is the absence of the gauge-singlet RH neutrinos. In assumption iv , the point to highlight is the absence of SM gauge fields. Babu and Leung did actually write down the mass-dimension-7 operators containing gauge fields, and Bhattacharya and Wudka [ 86 ] further examined them. As far as we know, however, no complete analysis has been undertaken for the dimension-9 and cases.
Finally, it is sensible to stop at dimension 11 because at any higher order the contribution to neutrino mass will be insufficiently large. Operators meeting all of these requirements exist at all odd mass dimensions [ 85 , 88 , 89 ], starting with the Weinberg operator O 1 as the unique dimension-5 case up to family indices. The dimension-7 list is as follows:. We follow the BL numbering scheme, which was based on tracking the number of fermion fields in the operator rather than the mass dimension. The operators are separated in three groups with 2, 4, and 6 fermions.
Some comments now need to be made about the schematic notation and what features are suppressed. The field-string defining each operator above completely defines the flavor content of that operator. The color indices and the different possible Lorentz structures are suppressed. In general, there are a number of independent operators corresponding to each flavor-string. For the dimension-7 list, operators O 3 and O 4 each have two independent possibilities for the contraction of the isospin indices, as explicitly defined above, but obviously a unique color contraction.
Babu and Leung specify the independent internal-index contractions, but only make general remarks on the Lorentz structures, and we shall follow suit. To assist the reader to understand the notation, we write out the above operators more completely in standard 4-component spinor notation, but for scalar and pseudoscalar Lorentz structures only and with isospin indices suppressed:. Of course, these operators feature quark and charged-lepton fields in addition to neutrinos and Higgs bosons, so they do not by themselves produce neutrino masses.
The charged fermion fields have to be closed off in a loop or loops to produce a neutrino self-energy graph which then generates a Weinberg-type operator, as per options 3 and 6. In fact, using this procedure and naive dimensional analysis one can estimate their matching contribution to the Weinberg operator, as done in de Gouvea and Jenkins [ 87 ]. At dimension 9, there are many more operators. Six of the flavor strings feature four fermion fields and three Higgs doublets:. Another 12 are six-fermion operators:.
The large number of dimension operators can be found listed in Babu and Leung [ 85 ] and de Gouvea and Jenkins [ 87 ]. The operators. In each of these cases, one may derive an indicative upper bound on the scale of new physics from the requirement that at least one neutrino mass be at least 0.
These estimates come from an examination of the loop contribution to neutrino mass only, and do not take into account other phenomenological constraints that will exist for each complete model. In a realistic theory, many of these constants would be expected to be less than one, which would bring the scale of new physics to lower values. In any case, one can see that the required new physics, even for 1-loop models, is typically more testable than the type-I, II, and III seesaw models. Some high loop models, as the O 19 case demonstrates, have very low scales of new physics and some may even be ruled out already.
At the dimension operator level, so not explicitly discussed here, there are even examples which can at best produce a 5-loop neutrino mass contribution. Those models are definitely already excluded. Examples of full models that are associated with specific operators will be presented in later sections. Number of loops. Equations 28—30 already form the basis for such a classification for type 3 and type 6 scenarios, but a more general analysis will also capture the type 2 and type 5 possibilities. All coupling constants, and for some models also certain mass-scale ratios, are absorbed in the dimensionless coefficient C.
In order to explain the atmospheric mass splitting lower bound of 0. Constraints from flavor physics severely constrain the scale of new physics and the couplings entering in C. Thus, apart from a few 4-loop models [ 96 — 98 ] which compensate the loop suppression by a high multiplicity of particles in the loop, the vast majority of radiative neutrino mass models generate neutrino mass at 1-, 2-, or 3-loop level.
We therefore focus on these cases. The opening up of the Weinberg operator at 1-loop level has been systematically studied in Ma [ 99 ] and Bonnet et al. The authors of Bonnet et al. Among all the topologies and possible Lorentz structures, topology T2 cannot be realized in a renormalizable theory. For the other topologies, the expression for neutrino mass and the possible particle content for electroweak singlet, doublet, and triplet representations is listed in the appendix of Bonnet et al.
The divergent ones, Ti, Tii, Tii, T5 and T6, need counter-terms to absorb the divergences, which are indeed tree-level realizations of the Weinberg operators. Furthermore, for Tii, there is no mechanism to forbid or suppress the tree-level contribution from Weinberg operator, such as extra discrete symmetry or U 1. Therefore, there are in total six topologies which generate neutrino mass via a genuine 12 1-loop diagram: T1-i, T1-ii, T1-iii, T3, Ti, Ti, which are depicted in Figure 3. Depending on the particle content, the topologies do not rely on any additional symmetry.
However, the topologies T4-x-i require a discrete Z 2 symmetry in addition to demanding Majorana fermions in the loop with lepton-number conserving couplings.
This is difficult to achieve in a field theory, as lepton-number is necessarily broken by neutrino mass. For example, in topology Ti the scalar connected to the two Higgs doublets H is necessarily an electroweak triplet and thus its direct coupling to two lepton doublets L is unavoidable. This coupling induces a type-II seesaw tree-level contribution to neutrino mass. Similar arguments hold for the other topologies T4-x-i.
Figure 3. Dashed lines could be scalars or gauge bosons if allowed. A similar analysis has been performed for 1-loop topologies that give rise to the dimension-7 generalized Weinberg operator [ ]. Of the 48 possible topologies, only the eight displayed in Figure 4 are relevant for genuine 1-loop models. For specific cases, not all of these eight diagrams will be realized. The three-point vertices can be Yukawa, gauge or cubic scalar interactions, while the four-point vertices only contain scalar and gauge bosons. Figure 4. A systematic analysis of 2-loop openings of O 1 was performed in Aristizabal Sierra et al.
Figure 5 displays the topologies identified in this study as able to contribute to genuine 2-loop models. They remark the class II topologies may be useful for justifying why a certain vertex has an unusually small magnitude. Figure 5. Solid dots denote interaction vertices.
Crossed lines without a dot at the intersection denote a non-planar configuration. Other considerations. We now briefly survey other perspectives on classifying or discriminating between neutrino mass models. One suggested criterion is complexity [ ]. While recognizing that sometimes nature appears to favor minimal possibilities in an Occam's razor approach , and at other times not e.
Law and McDonald [ ] proposes a hierarchy based on i whether or not the model relies on the imposition of ad hoc symmetries, ii the number of exotic multiplets required, and iii the number of new parameters. Interestingly, they construct radiative models that are even simpler, on the basis of these criteria, than the 1-loop Zee-Wolfenstein model [ , ].
However, like the Zee-Wolfenstein model, while these models generate non-zero neutrino masses, they fail phenomenologically. Thus, we must conclude that if nature utilizes the radiative mechanism, it will be non-minimal. That would point to a non-minimal framework, which may be connected with radiative neutrino mass generation.
A further interesting aspect is the existence or otherwise of a deep theoretical reason for a given radiative model. At first sight, each such model looks random. However, some of them can be connected with, for example, grand unified theories GUTs. One simple point to make is that exotics, such as scalar leptoquarks, that often feature in radiative models can be components of higher-dimension multiplets of SU 5 and SO Also, by contributing to renormalization group running, some of them can assist with gauge coupling constant unification [ ].
If they are to be light enough to play these roles, while other exotics within the multiplets have, for example, GUT-scale masses, then we face a similar issue to the famous doublet-triplet splitting problem. Nevertheless, this is a starting point for investigating the possible deeper origin of some of the required exotics. For example, the dimension-7 operator O 3 a from Equation 24 does not appear as a component in any SU 5 operator of the same dimension. On the other hand, other SM operators are embedded in the same GUT operator, with only one of them being able of giving the dominant contribution to neutrino masses.
Another strategy for uncovering a deeper origin for a radiative model is by asking if a given model has some close connection with the solution of important particle physics problems beyond just the origin of neutrino mass. One that has been explored at length in the literature is a possible connection to dark matter. Examples of such models will be given in more detail in later sections.
Here, we simply mention some systematic analyses of what new symmetries can be imposed in radiative models to stabilize dark matter [ , ]. Farzan et al. Restrepo et al. The considered models are those that generate mass at 1-loop level using exotics that are at most triplets under weak isospin, and where the stabilizing symmetry is Z 2. They found 35 viable models. A similar analysis, but requiring 2-loop neutrino mass generation, can be found in Simoes and Wegman [ ].
Besides dark matter, radiative neutrino mass models may also be connected to other physics beyond the SM such as the anomalous magnetic moment of the muon, the strong CP problem, the baryon asymmetry of the Universe or B-physics anomalies, among others. Phenomenology related to radiative neutrino mass models is briefly discussed in section 4 in general and an example of a possible connection to the recent B-physics anomalies is presented in section 5.
We adopt the classification of radiative neutrino mass models according to their Feynman diagram topology 13 , but refer to the other classification schemes where appropriate. In the subsections 3. In section 3. This section is divided into several parts: i 1-loop UV completions of the Weinberg operator, ii 1-loop seesaws, iii UV completions with additional VEV insertions, iv 1-loop UV completions of the higher dimensional operators and v other 1-loop models. Notice that the first part includes models with multi-Higgs doublets, while the second part discusses external fields which transform under an extended symmetry.
Besides the genuine topologies discussed in section 2, there are models based on the non-genuine 1-loop topologies in Figure 6. We follow the general classification of UV completions of the Weinberg operator at 1-loop [ ] discussed in section 2. The six genuine topologies are shown in Figure 3.
Analytic expressions for all 1-loop topologies are listed in the appendix of Bonnet et al. Here we list the theories falling into respective categories. As the topologies stay the same while incorporating multiple Higgs doublets, theories with more than one Higgs doublet will also be listed here. Models in which the generation of neutrino mass relies on additional VEVs connected to the neutrino mass loop diagram are discussed in section 3.
We first discuss the models based on topology T3, the only one with a quartic scalar interaction, before moving on to the other topologies. Topology T3 is one of the most well-studied. It was first proposed in Ma [ 99 ] and its first realization, the scotogenic model with a second electroweak scalar doublet and sterile fermion singlets at least two both odd under a Z 2 symmetry, was later proposed in Ma [ ].
See section 5. Its appeal lies in the simultaneous explanation of dark matter, which is stabilized by a Z 2 symmetry. Finally, the authors of Megrelidze and Tavartkiladze [ ] proposed the generation of neutrino mass via lepton-number-violating soft supersymmetry-breaking terms. Another variant involves a global continuous dark symmetry [ ], Hagedorn, in prep , termed the generalized scotogenic model. Ma [ ] discusses a supersymmetrized version of the scotogenic model, which is based on topology T3 and we discuss in detail in section 5.
An embedding of this model in SU 5 is given in Ma [ ]. In a non-supersymmetric context, the same topology is discussed in Farzan [ ], which introduces one real singlet scalar, in the context of a dark left—right symmetric model [ , ], and in Budhi et al. One of the singlet scalars in the neutrino mass model can be the inflaton via a non-minimal coupling with the Ricci-scalar. Finally the authors of Lu and Gu [ ] proposed a model with electroweak singlet and triplet scalars as well as fermions and study the dark matter phenomenology and leptogenesis.
Among the models based on the topology T1-ii, there are four possible operators which models are based on. Besides models with only heavy new particles, there are models with SM charged leptons, down-type quarks, or up-type quarks in the loop, which are based on the operators O 2 and O 3 , respectively.
We first discuss the models based on operator O 2. The first radiative Majorana neutrino mass model, the Zee model [ ], is based on this operator. Several variants of the Zee model exist in the literature. The minimal Zee-Wolfenstein model [ ] with a Z 2 symmetry to forbid tree-level FCNCs has been excluded by neutrino oscillation data [ , ], while the general version with both Higgs doublets coupling to the leptons is allowed [ 91 , ].
Imposing a Z 4 symmetry [ ] allows to explain neutrino data and forbid tree-level FCNCs in the quark sector. Previously in Aranda et al. A supersymmetric version of the Zee model has been proposed in Leontaris and Tamvakis [ ], Haba et al. Its embedding into a grand unified theory has been discussed in Zee [ ], Tamvakis and Vergados [ ] and Fileviez Perez and Murgui [ ], and in models with extra dimensions in Chang and Ng [ ] and Chang et al. Other flavor symmetries beyond Z 4 have been studied in Babu and Mohapatra [ , ], Koide and Ghosal [ ], Kitabayashi and Yasue, [ ], Adhikary et al.
Babu and Mohapatra [ , ] studied large transition magnetic moments of the electron neutrino, which was an early, now excluded, explanation for the solar neutrino anomaly. General group theoretic considerations about the possible particle content in the loop are discussed in Ma [ 99 ]. Models with multiple leptoquarks, which mix among each other, also generate neutrino mass via topology T1-ii.
We discuss this possibility in more detail in section 5. They induce the operator O 3 if the leptoquark couples down-type quarks to neutrinos. Well-studied examples of leptoquarks are down-type squarks in R-parity violating SUSY models, which generate neutrino masses, as was first demonstrated in Hall and Suzuki [ ]. Specific examples with multiple leptoquarks which mix with each other were discussed in Nieves [ ], Chua et al. There are several supersymmetric models [ , — ] which generate neutrino mass via different down-type quarks or charged leptons in the loop and consequently induce the operators O 3 and O 2 , respectively.
Finally, there are models with only heavy particles in the loop such as the inert Zee model [ ] or supersymmetric models with R-parity conservation [ , ]. This topology was first proposed in Ma [ 99 ] and it naturally appears in the supersymmetrized version of the scotogenic model [ , , — ] together with topology T1-i.
The topology can be used to implement the radiative inverse seesaw [ — ], which resembles the structure of the inverse seesaw [ , ]. This model has been extended by a softly-broken non-Abelian flavor symmetry group [ — ] in order to explain the flavor structure in the lepton sector. This mechanism was first pointed out in Hirsch et al.
In the realization of Ma and Sarkar [ ], the masses of the real and imaginary parts of the sneutrinos are split by the VEV of a scalar triplet, which only couples to the sneutrinos via a soft-breaking term and thus does not induce the ordinary type-II seesaw. Similarly it has been used in a model with vector-like down-type quarks [ , ], which requires mixing of the SM quarks with the new vector-like quarks.
This model leads to the operator O 3. For completeness we also include the two possible 1-loop seesaw topologies Ti and Ti which have been identified in Bonnet et al. Topology Ti always involves a electroweak scalar triplet like in the type-II seesaw mechanism and topology Ti contains an electroweak singlet or triplet fermion like in the type-I or type-III seesaw mechanism, respectively.
Based on our knowledge, there are currently no models based on topologies Ti and Ti in the literature. Finally, although the topology Tii shown in Figure 6C has been discarded in Bonnet et al. Similar constructions may be possible for other topologies and lead to new interesting models.
The above discussed classification technically does not cover models with additional scalar fields, which contribute to neutrino mass via their vacuum expectation value in contrast to being a propagating degree of freedom in the loop. Inspired by the above classification, we similarly classify these new models according to the topologies in Figure 3 by disregarding the additional VEV insertions.
The authors of Ho et al. The models in Chang and Wong [ ], Dasgupta et al. All these models lead to the operator O 2. Foot et al. Finally, there is the inert Zee model with a flavor symmetry [ , ]. The model in Nomura et al. The topology can also be generated by new heavy lepton-like doublets and sterile fermions, which are charged under a new gauged dark U 1 in addition to a Z 2 symmetry [ ].
There are several variants of the scotogenic model with additional VEV insertions. Apart from additional symmetries, the mixing of the fermionic singlet with a fermionic triplet in the loop requires the VEV of an electroweak triplet with vanishing hypercharge [ — ]. Finally, the two models discussed in Okada and Yagyu [ , ] rely on a similar topology as the scotogenic model, but with triplet VEVs instead of electroweak doublet VEVs.
Based on our knowledge, there are currently no models based on topology Ti in the literature. These types of models contain a triplet scalar which couples to the lepton doublet as per the tree-level type-II seesaw. However, the neutral component of the triplet scalar gets an induced VEV at 1-loop and thus generates neutrino masses effectively at 1-loop.
The model in Nomura and Okada [ ] is based on topology Ti shown in Figure 6A , which is finite due to additional VEV insertions on the fermion line. The tree-level contribution is forbidden by a discrete symmetry and renormalizability of the theory. However, at loop-level neutrino mass is generated by a dimension-7 operator L L H H s 1 2 with two additional SM singlet fields s 1.
Apart from UV completions of the Weinberg operator, there are a few models which induce one of the higher dimensional operators with additional Higgs doublets at 1-loop level. It was realized using at most adjoint representations and an additional softly-broken Z 5 symmetry and an exact Z 2 symmetry and thus allows to use the topologies T12 Figure 4E and T31 Figure 7 , which would otherwise be accompanied by the dimension-5 operator O 1. Cepedello et al. Figure 7. In Law and McDonald [ ] and Baldes et al. The mass of the additional SM singlets is induced at tree-level and then first transmitted to the neutral components of new electroweak doublets via a 1-loop diagram, before it induces neutrino mass via the seesaw.
There is also a 2-loop contribution, which may dominate neutrino mass depending on the masses of the new particles. As can be seen from the discussion above, in order to generate Weinberg-like effective operators at dimension larger than five, typically extra symmetries in some cases large discrete symmetries , new large representations, a large number of fields or a combination of all the previous need to be invoked. This makes the model-building of such scenarios much more involved than for the case of the Weinberg operator.
Apart from the models in the general classification [ ], it is possible to generate neutrino mass via a radiative inverse seesaw mechanism shown in Figure 8 at 1-loop order, which has been proposed in Ahriche [ ]. Tree-level contributions are forbidden by a softly-broken Z 4 symmetry. The soft-breaking is indicated by the cross on the scalar line.
Note the cross on the fermion line in the loop denotes a Majorana mass term, while the other two denote Dirac mass terms.