Regeneration (biology)

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https://en.wikipedia.org/wiki/Regeneration_(biology) 

 

Sunflower sea star regenerates its arms.

 

Dwarf yellow-headed gecko with regenerating tail

In biology, regeneration is the process of renewal, restoration, and tissue growth that makes genomes, cells, organisms, and ecosystems resilient to natural fluctuations or events that cause disturbance or damage. Every species is capable of regeneration, from bacteria to humans. Regeneration can either be complete where the new tissue is the same as the lost tissue, or incomplete where after the necrotic tissue comes fibrosis.

At its most elementary level, regeneration is mediated by the molecular processes of gene regulation and involves the cellular processes of cell proliferation, morphogenesis and cell differentiation. Regeneration in biology, however, mainly refers to the morphogenic processes that characterize the phenotypic plasticity of traits allowing multi-cellular organisms to repair and maintain the integrity of their physiological and morphological states. Above the genetic level, regeneration is fundamentally regulated by asexual cellular processes. Regeneration is different from reproduction. For example, hydra perform regeneration but reproduce by the method of budding.

The hydra and the planarian flatworm have long served as model organisms for their highly adaptive regenerative capabilities. Once wounded, their cells become activated and restore the organs back to their pre-existing state. The Caudata ("urodeles"; salamanders and newts), an order of tailed amphibians, is possibly the most adept vertebrate group at regeneration, given their capability of regenerating limbs, tails, jaws, eyes and a variety of internal structures. The regeneration of organs is a common and widespread adaptive capability among metazoan creatures. In a related context, some animals are able to reproduce asexually through fragmentation, budding, or fission. A planarian parent, for example, will constrict, split in the middle, and each half generates a new end to form two clones of the original.

Echinoderms (such as the sea star), crayfish, many reptiles, and amphibians exhibit remarkable examples of tissue regeneration. The case of autotomy, for example, serves as a defensive function as the animal detaches a limb or tail to avoid capture. After the limb or tail has been autotomized, cells move into action and the tissues will regenerate. In some cases a shed limb can itself regenerate a new individual. Limited regeneration of limbs occurs in most fishes and salamanders, and tail regeneration takes place in larval frogs and toads (but not adults). The whole limb of a salamander or a triton will grow again and again after amputation. In reptiles, chelonians, crocodilians and snakes are unable to regenerate lost parts, but many (not all) kinds of lizards, geckos and iguanas possess regeneration capacity in a high degree. Usually, it involves dropping a section of their tail and regenerating it as part of a defense mechanism. While escaping a predator, if the predator catches the tail, it will disconnect.

Ecosystems

Main article: Regeneration (ecology)

Ecosystems can be regenerative. Following a disturbance, such as a fire or pest outbreak in a forest, pioneering species will occupy, compete for space, and establish themselves in the newly opened habitat. The new growth of seedlings and community assembly process is known as regeneration in ecology.

Cellular molecular fundamentals

Pattern formation in the morphogenesis of an animal is regulated by genetic induction factors that put cells to work after damage has occurred. Neural cells, for example, express growth-associated proteins, such as GAP-43, tubulin, actin, an array of novel neuropeptides, and cytokines that induce a cellular physiological response to regenerate from the damage. Many of the genes that are involved in the original development of tissues are reinitialized during the regenerative process. Cells in the primordia of zebrafish fins, for example, express four genes from the homeobox msx family during development and regeneration.

Tissues

"Strategies include the rearrangement of pre-existing tissue, the use of adult somatic stem cells and the dedifferentiation and/or transdifferentiation of cells, and more than one mode can operate in different tissues of the same animal. All these strategies result in the re-establishment of appropriate tissue polarity, structure and form." During the developmental process, genes are activated that serve to modify the properties of cell as they differentiate into different tissues. Development and regeneration involves the coordination and organization of populations cells into a blastema, which is "a mound of stem cells from which regeneration begins". Dedifferentiation of cells means that they lose their tissue-specific characteristics as tissues remodel during the regeneration process. This should not be confused with the transdifferentiation of cells which is when they lose their tissue-specific characteristics during the regeneration process, and then re-differentiate to a different kind of cell.

In animals

Arthropods

Limb regeneration

Many arthropods can regenerate limbs and other appendages following either injury or autotomy. Regeneration capacity is constrained by the developmental stage and ability to molt.

Crustaceans, which continually molt, can regenerate throughout their lifetimes. While molting cycles are generally hormonally regulated, limb amputation induces premature molting.

Hemimetabolous insects such as crickets can regenerate limbs as nymphs, before their final molt.

Holometabolous insects can regenerate appendages as larvae prior to the final molt and metamorphosis. Beetle larvae, for example, can regenerate amputated limbs. Fruit fly larvae do not have limbs but can regenerate their appendage primordia, imaginal discs. In both systems, the regrowth of the new tissue delays pupation.

Mechanisms underlying appendage limb regeneration in insects and crustaceans are highly conserved. During limb regeneration species in both taxa form a blastema that proliferates and grows to repattern the missing tissue.

Venom regeneration

Arachnids, including scorpions, are known to regenerate their venom, although the content of the regenerated venom is different from the original venom during its regeneration, as the venom volume is replaced before the active proteins are all replenished.

Fruit fly model

The fruit fly Drosophila melanogaster is a useful model organism to understand the molecular mechanisms that control regeneration, especially gut and germline regeneration. In these tissues, resident stem cells continually renew lost cells. The Hippo signaling pathway was discovered in flies and was found to be required for midgut regeneration. Later, this conserved signaling pathway was also found to be essential for regeneration of many mammalian tissues, including heart, liver, skin, and lung, and intestine.

Annelids

Many annelids (segmented worms) are capable of regeneration. For example, Chaetopterus variopedatus and Branchiomma nigromaculata can regenerate both anterior and posterior body parts after latitudinal bisection. The relationship between somatic and germline stem cell regeneration has been studied at the molecular level in the annelid Capitella teleta. Leeches, however, appear incapable of segmental regeneration. Furthermore, their close relatives, the branchiobdellids, are also incapable of segmental regeneration. However, certain individuals, like the lumbriculids, can regenerate from only a few segments. Segmental regeneration in these animals is epimorphic and occurs through blastema formation. Segmental regeneration has been gained and lost during annelid evolution, as seen in oligochaetes, where head regeneration has been lost three separate times.

Along with epimorphosis, some polychaetes like Sabella pavonina experience morphallactic regeneration. Morphallaxis involves the de-differentiation, transformation, and re-differentation of cells to regenerate tissues. How prominent morphallactic regeneration is in oligochaetes is currently not well understood. Although relatively under-reported, it is possible that morphallaxis is a common mode of inter-segment regeneration in annelids. Following regeneration in L. variegatus, past posterior segments sometimes become anterior in the new body orientation, consistent with morphallaxis.

Following amputation, most annelids are capable of sealing their body via rapid muscular contraction. Constriction of body muscle can lead to infection prevention. In certain species, such as Limnodrilus, autolysis can be seen within hours after amputation in the ectoderm and mesoderm. Amputation is also thought to cause a large migration of cells to the injury site, and these form a wound plug.

Echinoderms

Tissue regeneration is widespread among echinoderms and has been well documented in starfish (Asteroidea), sea cucumbers (Holothuroidea), and sea urchins (Echinoidea). Appendage regeneration in echinoderms has been studied since at least the 19th century. In addition to appendages, some species can regenerate internal organs and parts of their central nervous system. In response to injury starfish can autotomize damaged appendages. Autotomy is the self-amputation of a body part, usually an appendage.  Depending on severity, starfish will then go through a four-week process where the appendage will be regenerated. Some species must retain mouth cells to regenerate an appendage, due to the need for energy. The first organs to regenerate, in all species documented to date, are associated with the digestive tract. Thus, most knowledge about visceral regeneration in holothurians concerns this system.

Planaria (Platyhelminthes)

Regeneration research using Planarians began in the late 1800s and was popularized by T.H. Morgan at the beginning of the 20th century. Alejandro Sanchez-Alvarado and Philip Newmark transformed planarians into a model genetic organism in the beginning of the 20th century to study the molecular mechanisms underlying regeneration in these animals. Planarians exhibit an extraordinary ability to regenerate lost body parts. For example, a planarian split lengthwise or crosswise will regenerate into two separate individuals. In one experiment, T.H. Morgan found that a piece corresponding to 1/279th of a planarian or a fragment with as few as 10,000 cells can successfully regenerate into a new worm within one to two weeks. After amputation, stump cells form a blastema formed from neoblasts, pluripotent cells found throughout the planarian body. New tissue grows from neoblasts with neoblasts comprising between 20 and 30% of all planarian cells. Recent work has confirmed that neoblasts are totipotent since one single neoblast can regenerate an entire irradiated animal that has been rendered incapable of regeneration. In order to prevent starvation a planarian will use their own cells for energy, this phenomenon is known as de-growth.

Amphibians

Limb regeneration in the axolotl and newt has been extensively studied and researched. The nineteenth century studies of this subject are reviewed in Holland (2021). Urodele amphibians, such as salamanders and newts, display the highest regenerative ability among tetrapods. As such, they can fully regenerate their limbs, tail, jaws, and retina via epimorphic regeneration leading to functional replacement with new tissue. Salamander limb regeneration occurs in two main steps. First, the local cells dedifferentiate at the wound site into progenitor to form a blastema. Second, the blastemal cells will undergo cell proliferation, patterning, cell differentiation and tissue growth using similar genetic mechanisms that deployed during embryonic development. Ultimately, blastemal cells will generate all the cells for the new structure.

Axolotls can regenerate a variety of structures, including their limbs.

After amputation, the epidermis migrates to cover the stump in 1–2 hours, forming a structure called the wound epithelium (WE). Epidermal cells continue to migrate over the WE, resulting in a thickened, specialized signaling center called the apical epithelial cap (AEC). Over the next several days there are changes in the underlying stump tissues that result in the formation of a blastema (a mass of dedifferentiated proliferating cells). As the blastema forms, pattern formation genes – such as HoxA and HoxD – are activated as they were when the limb was formed in the embryo. The positional identity of the distal tip of the limb (i.e. the autopod, which is the hand or foot) is formed first in the blastema. Intermediate positional identities between the stump and the distal tip are then filled in through a process called intercalation. Motor neurons, muscle, and blood vessels grow with the regenerated limb, and reestablish the connections that were present prior to amputation. The time that this entire process takes varies according to the age of the animal, ranging from about a month to around three months in the adult and then the limb becomes fully functional. Researchers at Australian Regenerative Medicine Institute at Monash University have published that when macrophages, which eat up material debris, were removed, salamanders lost their ability to regenerate and formed scarred tissue instead.

In spite of the historically few researchers studying limb regeneration, remarkable progress has been made recently in establishing the neotenous amphibian the axolotl (Ambystoma mexicanum) as a model genetic organism. This progress has been facilitated by advances in genomics, bioinformatics, and somatic cell transgenesis in other fields, that have created the opportunity to investigate the mechanisms of important biological properties, such as limb regeneration, in the axolotl. The Ambystoma Genetic Stock Center (AGSC) is a self-sustaining, breeding colony of the axolotl supported by the National Science Foundation as a Living Stock Collection. Located at the University of Kentucky, the AGSC is dedicated to supplying genetically well-characterized axolotl embryos, larvae, and adults to laboratories throughout the United States and abroad. An NIH-funded NCRR grant has led to the establishment of the Ambystoma EST database, the Salamander Genome Project (SGP) that has led to the creation of the first amphibian gene map and several annotated molecular data bases, and the creation of the research community web portal.

Frog model

Anurans (frogs) can only regenerate their limbs during embryonic development. Reactive oxygen species (ROS) appear to be required for a regeneration response in the anuran larvae. ROS production is essential to activate the Wnt signaling pathway, which has been associated with regeneration in other systems.

Once the limb skeleton has developed in frogs, regeneration does not occur (Xenopus can grow a cartilaginous spike after amputation). The adult Xenopus laevis is used as a model organism for regenerative medicine. In 2022, a cocktail of drugs and hormones (1,4-DPCA, BDNF, growth hormone, resolvin D5, and retinoic acid), in a single dose lasting 24 hours, was shown to trigger long-term leg regenration in adult X. laevis. Instead of a single spike, a paddle-shaped growth is obtained at the end of the limb by 18 months.

Hydra

Hydra is a genus of freshwater polyp in the phylum Cnidaria with highly proliferative stem cells that gives them the ability to regenerate their entire body. Any fragment larger than a few hundred epithelial cells that is isolated from the body has the ability to regenerate into a smaller version of itself. The high proportion of stem cells in the hydra supports its efficient regenerative ability.

Regeneration among hydra occurs as foot regeneration arising from the basal part of the body, and head regeneration, arising from the apical region. Regeneration tissues that are cut from the gastric region contain polarity, which allows them to distinguish between regenerating a head in the apical end and a foot in the basal end so that both regions are present in the newly regenerated organism. Head regeneration requires complex reconstruction of the area, while foot regeneration is much simpler, similar to tissue repair. In both foot and head regeneration, however, there are two distinct molecular cascades that occur once the tissue is wounded: early injury response and a subsequent, signal-driven pathway of the regenerating tissue that leads to cellular differentiation. This early-injury response includes epithelial cell stretching for wound closure, the migration of interstitial progenitors towards the wound, cell death, phagocytosis of cell debris, and reconstruction of the extracellular matrix.

Regeneration in hydra has been defined as morphallaxis, the process where regeneration results from remodeling of existing material without cellular proliferation. If a hydra is cut into two pieces, the remaining severed sections form two fully functional and independent hydra, approximately the same size as the two smaller severed sections. This occurs through the exchange and rearrangement of soft tissues without the formation of new material.

Aves (birds)

Owing to a limited literature on the subject, birds are believed to have very limited regenerative abilities as adults. Some studies on roosters have suggested that birds can adequately regenerate some parts of the limbs and depending on the conditions in which regeneration takes place, such as age of the animal, the inter-relationship of the injured tissue with other muscles, and the type of operation, can involve complete regeneration of some musculoskeletal structure. Werber and Goldschmidt (1909) found that the goose and duck were capable of regenerating their beaks after partial amputation and Sidorova (1962) observed liver regeneration via hypertrophy in roosters. Birds are also capable of regenerating the hair cells in their cochlea following noise damage or ototoxic drug damage. Despite this evidence, contemporary studies suggest reparative regeneration in avian species is limited to periods during embryonic development. An array of molecular biology techniques have been successful in manipulating cellular pathways known to contribute to spontaneous regeneration in chick embryos. For instance, removing a portion of the elbow joint in a chick embryo via window excision or slice excision and comparing joint tissue specific markers and cartilage markers showed that window excision allowed 10 out of 20 limbs to regenerate and expressed joint genes similarly to a developing embryo. In contrast, slice excision did not allow the joint to regenerate due to the fusion of the skeletal elements seen by an expression of cartilage markers.

Similar to the physiological regeneration of hair in mammals, birds can regenerate their feathers in order to repair damaged feathers or to attract mates with their plumage. Typically, seasonal changes that are associated with breeding seasons will prompt a hormonal signal for birds to begin regenerating feathers. This has been experimentally induced using thyroid hormones in the Rhode Island Red Fowls.

Mammals

Spiny mice (Acomys cahirinus pictured here) can regenerate skin, cartilage, nerves and muscle.

Mammals are capable of cellular and physiological regeneration, but have generally poor reparative regenerative ability across the group. Examples of physiological regeneration in mammals include epithelial renewal (e.g., skin and intestinal tract), red blood cell replacement, antler regeneration and hair cycling. Male deer lose their antlers annually during the months of January to April then through regeneration are able to regrow them as an example of physiological regeneration. A deer antler is the only appendage of a mammal that can be regrown every year. While reparative regeneration is a rare phenomenon in mammals, it does occur. A well-documented example is regeneration of the digit tip distal to the nail bed. Reparative regeneration has also been observed in rabbits, pikas and African spiny mice. In 2012, researchers discovered that two species of African Spiny Mice, Acomys kempi and Acomys percivali, were capable of completely regenerating the autotomically released or otherwise damaged tissue. These species can regrow hair follicles, skin, sweat glands, fur and cartilage. In addition to these two species, subsequent studies demonstrated that Acomys cahirinus could regenerate skin and excised tissue in the ear pinna.

Despite these examples, it is generally accepted that adult mammals have limited regenerative capacity compared to most vertebrate embryos/larvae, adult salamanders and fish. But the regeneration therapy approach of Robert O. Becker, using electrical stimulation, has shown promising results for rats and mammals in general.

Some researchers have also claimed that the MRL mouse strain exhibits enhanced regenerative abilities. Work comparing the differential gene expression of scarless healing MRL mice and a poorly-healing C57BL/6 mouse strain, identified 36 genes differentiating the healing process between MRL mice and other mice. Study of the regenerative process in these animals is aimed at discovering how to duplicate them in humans, such as deactivation of the p21 gene. However, recent work has shown that MRL mice actually close small ear holes with scar tissue, rather than regeneration as originally claimed.

MRL mice are not protected against myocardial infarction; heart regeneration in adult mammals (neocardiogenesis) is limited, because heart muscle cells are nearly all terminally differentiated. MRL mice show the same amount of cardiac injury and scar formation as normal mice after a heart attack. However, recent studies provide evidence that this may not always be the case, and that MRL mice can regenerate after heart damage.

Humans

Main article: Regeneration in humans

The regrowth of lost tissues or organs in the human body is being researched. Some tissues such as skin regrow quite readily; others have been thought to have little or no capacity for regeneration, but ongoing research suggests that there is some hope for a variety of tissues and organs. Human organs that have been regenerated include the bladder, vagina and the penis.

As are all metazoans, humans are capable of physiological regeneration (i.e. the replacement of cells during homeostatic maintenance that does not necessitate injury). For example, the regeneration of red blood cells via erythropoiesis occurs through the maturation of erythrocytes from hematopoietic stem cells in the bone marrow, their subsequent circulation for around 90 days in the blood stream, and their eventual cell-death in the spleen. Another example of physiological regeneration is the sloughing and rebuilding of a functional endometrium during each menstrual cycle in females in response to varying levels of circulating estrogen and progesterone.

However, humans are limited in their capacity for reparative regeneration, which occurs in response to injury. One of the most studied regenerative responses in humans is the hypertrophy of the liver following liver injury. For example, the original mass of the liver is re-established in direct proportion to the amount of liver removed following partial hepatectomy, which indicates that signals from the body regulate liver mass precisely, both positively and negatively, until the desired mass is reached. This response is considered cellular regeneration (a form of compensatory hypertrophy) where the function and mass of the liver is regenerated through the proliferation of existing mature hepatic cells (mainly hepatocytes), but the exact morphology of the liver is not regained. This process is driven by growth factor and cytokine regulated pathways. The normal sequence of inflammation and regeneration does not function accurately in cancer. Specifically, cytokine stimulation of cells leads to expression of genes that change cellular functions and suppress the immune response.

Adult neurogenesis is also a form of cellular regeneration. For example, hippocampal neuron renewal occurs in normal adult humans at an annual turnover rate of 1.75% of neurons. Cardiac myocyte renewal has been found to occur in normal adult humans, and at a higher rate in adults following acute heart injury such as infarction. Even in adult myocardium following infarction, proliferation is only found in around 1% of myocytes around the area of injury, which is not enough to restore function of cardiac muscle. However, this may be an important target for regenerative medicine as it implies that regeneration of cardiomyocytes, and consequently of myocardium, can be induced.

Another example of reparative regeneration in humans is fingertip regeneration, which occurs after phalange amputation distal to the nail bed (especially in children) and rib regeneration, which occurs following osteotomy for scoliosis treatment (though usually regeneration is only partial and may take up to one year).

Yet another example of regeneration in humans is vas deferens regeneration, which occurs after a vasectomy and which results in vasectomy failure.

Reptiles

The ability and degree of regeneration in reptiles differs among the various species, but the most notable and well-studied occurrence is tail-regeneration in lizards. In addition to lizards, regeneration has been observed in the tails and maxillary bone of crocodiles and adult neurogenesis has also been noted. Tail regeneration has never been observed in snakes. Lizards possess the highest regenerative capacity as a group. Following autotomous tail loss, epimorphic regeneration of a new tail proceeds through a blastema-mediated process that results in a functionally and morphologically similar structure.

Chondrichthyes

It has been estimated that the average shark loses about 30,000 to 40,000 teeth in a lifetime. Leopard sharks routinely replace their teeth every 9–12 days and this is an example of physiological regeneration. This can occur because shark teeth are not attached to a bone, but instead are developed within a bony cavity.

Rhodopsin regeneration has been studied in skates and rays. After complete photo-bleaching, rhodopsin can completely regenerate within 2 hours in the retina.

White bamboo sharks can regenerate at least two-thirds of their liver and this has been linked to three micro RNAs, xtr-miR-125b, fru-miR-204, and has-miR-142-3p_R-. In one study, two-thirds of the liver was removed and within 24 hours more than half of the liver had undergone hypertrophy.

Some sharks can regenerate scales and even skin following damage. Within two weeks of skin wounding, mucus is secreted into the wound and this initiates the healing process. One study showed that the majority of the wounded area was regenerated within 4 months, but the regenerated area also showed a high degree of variability.

Quantum chromodynamics

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Quantum_chromodynamics 

In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.

QCD exhibits three salient properties:

• Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although analytically unproven, color confinement is well established from lattice QCD calculations and decades of experiments.
• Asymptotic freedom, a steady reduction in the strength of interactions between quarks and gluons as the energy scale of those interactions increases (and the corresponding length scale decreases). The asymptotic freedom of QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the same year. For this work, all three shared the 2004 Nobel Prize in Physics.
• Chiral symmetry breaking, the spontaneous symmetry breaking of an important global symmetry of quarks, detailed below, with the result of generating masses for hadrons far above the masses of the quarks, and making pseudoscalar mesons exceptionally light. Yoichiro Nambu was awarded the 2008 Nobel Prize in Physics for elucidating the phenomenon, a dozen years before the advent of QCD. Lattice simulations have confirmed all his generic predictions.

Terminology

Physicist Murray Gell-Mann coined the word quark in its present sense. It originally comes from the phrase "Three quarks for Muster Mark" in Finnegans Wake by James Joyce. On June 27, 1978, Gell-Mann wrote a private letter to the editor of the Oxford English Dictionary, in which he related that he had been influenced by Joyce's words: "The allusion to three quarks seemed perfect." (Originally, only three quarks had been discovered.)

The three kinds of charge in QCD (as opposed to one in quantum electrodynamics or QED) are usually referred to as "color charge" by loose analogy to the three kinds of color (red, green and blue) perceived by humans. Other than this nomenclature, the quantum parameter "color" is completely unrelated to the everyday, familiar phenomenon of color.

The force between quarks is known as the colour force (or color force) or strong interaction, and is responsible for the nuclear force.

Since the theory of electric charge is dubbed "electrodynamics", the Greek word χρῶμα chroma "color" is applied to the theory of color charge, "chromodynamics".

History

Main articles: History of quantum mechanics and History of quantum field theory

With the invention of bubble chambers and spark chambers in the 1950s, experimental particle physics discovered a large and ever-growing number of particles called hadrons. It seemed that such a large number of particles could not all be fundamental. First, the particles were classified by charge and isospin by Eugene Wigner and Werner Heisenberg; then, in 1953–56, according to strangeness by Murray Gell-Mann and Kazuhiko Nishijima (see Gell-Mann–Nishijima formula). To gain greater insight, the hadrons were sorted into groups having similar properties and masses using the eightfold way, invented in 1961 by Gell-Mann and Yuval Ne'eman. Gell-Mann and George Zweig, correcting an earlier approach of Shoichi Sakata, went on to propose in 1963 that the structure of the groups could be explained by the existence of three flavors of smaller particles inside the hadrons: the quarks. Gell-Mann also briefly discussed a field theory model in which quarks interact with gluons.

Perhaps the first remark that quarks should possess an additional quantum number was made as a short footnote in the preprint of Boris Struminsky in connection with the Ω⁻ hyperon being composed of three strange quarks with parallel spins (this situation was peculiar, because since quarks are fermions, such a combination is forbidden by the Pauli exclusion principle):

Three identical quarks cannot form an antisymmetric S-state. In order to realize an antisymmetric orbital S-state, it is necessary for the quark to have an additional quantum number.

— B. V. Struminsky, Magnetic moments of barions in the quark model, JINR-Preprint P-1939, Dubna, Submitted on January 7, 1965

Boris Struminsky was a PhD student of Nikolay Bogolyubov. The problem considered in this preprint was suggested by Nikolay Bogolyubov, who advised Boris Struminsky in this research. In the beginning of 1965, Nikolay Bogolyubov, Boris Struminsky and Albert Tavkhelidze wrote a preprint with a more detailed discussion of the additional quark quantum degree of freedom. This work was also presented by Albert Tavkhelidze without obtaining consent of his collaborators for doing so at an international conference in Trieste (Italy), in May 1965.

A similar mysterious situation was with the Δ⁺⁺ baryon; in the quark model, it is composed of three up quarks with parallel spins. In 1964–65, Greenberg and Han–Nambu independently resolved the problem by proposing that quarks possess an additional SU(3) gauge degree of freedom, later called color charge. Han and Nambu noted that quarks might interact via an octet of vector gauge bosons: the gluons.

Since free quark searches consistently failed to turn up any evidence for the new particles, and because an elementary particle back then was defined as a particle that could be separated and isolated, Gell-Mann often said that quarks were merely convenient mathematical constructs, not real particles. The meaning of this statement was usually clear in context: He meant quarks are confined, but he also was implying that the strong interactions could probably not be fully described by quantum field theory.

Richard Feynman argued that high energy experiments showed quarks are real particles: he called them partons (since they were parts of hadrons). By particles, Feynman meant objects that travel along paths, elementary particles in a field theory.

The difference between Feynman's and Gell-Mann's approaches reflected a deep split in the theoretical physics community. Feynman thought the quarks have a distribution of position or momentum, like any other particle, and he (correctly) believed that the diffusion of parton momentum explained diffractive scattering. Although Gell-Mann believed that certain quark charges could be localized, he was open to the possibility that the quarks themselves could not be localized because space and time break down. This was the more radical approach of S-matrix theory.

James Bjorken proposed that pointlike partons would imply certain relations in deep inelastic scattering of electrons and protons, which were verified in experiments at SLAC in 1969. This led physicists to abandon the S-matrix approach for the strong interactions.

In 1973 the concept of color as the source of a "strong field" was developed into the theory of QCD by physicists Harald Fritzsch and Heinrich Leutwyler, together with physicist Murray Gell-Mann. In particular, they employed the general field theory developed in 1954 by Chen Ning Yang and Robert Mills (see Yang–Mills theory), in which the carrier particles of a force can themselves radiate further carrier particles. (This is different from QED, where the photons that carry the electromagnetic force do not radiate further photons.)

The discovery of asymptotic freedom in the strong interactions by David Gross, David Politzer and Frank Wilczek allowed physicists to make precise predictions of the results of many high energy experiments using the quantum field theory technique of perturbation theory. Evidence of gluons was discovered in three-jet events at PETRA in 1979. These experiments became more and more precise, culminating in the verification of perturbative QCD at the level of a few percent at LEP, at CERN.

The other side of asymptotic freedom is confinement. Since the force between color charges does not decrease with distance, it is believed that quarks and gluons can never be liberated from hadrons. This aspect of the theory is verified within lattice QCD computations, but is not mathematically proven. One of the Millennium Prize Problems announced by the Clay Mathematics Institute requires a claimant to produce such a proof. Other aspects of non-perturbative QCD are the exploration of phases of quark matter, including the quark–gluon plasma.

The relation between the short-distance particle limit and the confining long-distance limit is one of the topics recently explored using string theory, the modern form of S-matrix theory.

Theory

Some definitions

Unsolved problem in physics:

QCD in the non-perturbative regime:

• Confinement: the equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei and nuclear constituents?
• Quark matter: the equations of QCD predict that a plasma (or soup) of quarks and gluons should be formed at high temperature and density. What are the properties of this phase of matter?

Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations. These can be

• local symmetries, which are the symmetries that act independently at each point in spacetime. Each such symmetry is the basis of a gauge theory and requires the introduction of its own gauge bosons.
• global symmetries, which are symmetries whose operations must be simultaneously applied to all points of spacetime.

QCD is a non-abelian gauge theory (or Yang–Mills theory) of the SU(3) gauge group obtained by taking the color charge to define a local symmetry.

Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate flavor symmetry, which is broken by the differing masses of the quarks.

There are additional global symmetries whose definitions require the notion of chirality, discrimination between left and right-handed. If the spin of a particle has a positive projection on its direction of motion then it is called right-handed; otherwise, it is left-handed. Chirality and handedness are not the same, but become approximately equivalent at high energies.

• Chiral symmetries involve independent transformations of these two types of particle.
• Vector symmetries (also called diagonal symmetries) mean the same transformation is applied on the two chiralities.
• Axial symmetries are those in which one transformation is applied on left-handed particles and the inverse on the right-handed particles.

Additional remarks: duality

As mentioned, asymptotic freedom means that at large energy – this corresponds also to short distances – there is practically no interaction between the particles. This is in contrast – more precisely one would say dual– to what one is used to, since usually one connects the absence of interactions with large distances. However, as already mentioned in the original paper of Franz Wegner, a solid state theorist who introduced 1971 simple gauge invariant lattice models, the high-temperature behaviour of the original model, e.g. the strong decay of correlations at large distances, corresponds to the low-temperature behaviour of the (usually ordered!) dual model, namely the asymptotic decay of non-trivial correlations, e.g. short-range deviations from almost perfect arrangements, for short distances. Here, in contrast to Wegner, we have only the dual model, which is that one described in this article.

Symmetry groups

The color group SU(3) corresponds to the local symmetry whose gauging gives rise to QCD. The electric charge labels a representation of the local symmetry group U(1), which is gauged to give QED: this is an abelian group. If one considers a version of QCD with N_f flavors of massless quarks, then there is a global (chiral) flavor symmetry group SU_L(N_f) × SU_R(N_f) × U_B(1) × U_A(1). The chiral symmetry is spontaneously broken by the QCD vacuum to the vector (L+R) SU_V(N_f) with the formation of a chiral condensate. The vector symmetry, U_B(1) corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry U_A(1) is exact in the classical theory, but broken in the quantum theory, an occurrence called an anomaly. Gluon field configurations called instantons are closely related to this anomaly.

There are two different types of SU(3) symmetry: there is the symmetry that acts on the different colors of quarks, and this is an exact gauge symmetry mediated by the gluons, and there is also a flavor symmetry that rotates different flavors of quarks to each other, or flavor SU(3). Flavor SU(3) is an approximate symmetry of the vacuum of QCD, and is not a fundamental symmetry at all. It is an accidental consequence of the small mass of the three lightest quarks.

In the QCD vacuum there are vacuum condensates of all the quarks whose mass is less than the QCD scale. This includes the up and down quarks, and to a lesser extent the strange quark, but not any of the others. The vacuum is symmetric under SU(2) isospin rotations of up and down, and to a lesser extent under rotations of up, down, and strange, or full flavor group SU(3), and the observed particles make isospin and SU(3) multiplets.

The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate string description of QCD.

Lagrangian

The dynamics of the quarks and gluons are controlled by the quantum chromodynamics Lagrangian. The gauge invariant QCD Lagrangian is

${\displaystyle {\mathcal{L}}_{\mathrm{Q}\mathrm{C}\mathrm{D}}={\overline{\psi }}_i\left(i{\gamma }^{\mu }(D_{\mu }{)}_{ij}-m{\delta }_{ij}\right){\psi }_j-\frac{1}{4}{G}_{\mu \nu }^a{G}_a^{\mu \nu }}$

where ${\displaystyle {\psi }_i(x)}$ is the quark field, a dynamical function of spacetime, in the fundamental representation of the SU(3) gauge group, indexed by ${\displaystyle i}$ and ${\displaystyle j}$ running from ${\displaystyle 1}$ to ${\displaystyle 3}$; ${\displaystyle D_{\mu }}$ is the gauge covariant derivative; the γ^μ are Dirac matrices connecting the spinor representation to the vector representation of the Lorentz group.

Herein, the gauge covariant derivative ${\displaystyle {\left(D_{\mu }\right)}_{ij}={\mathrm{\partial }}_{\mu }{\delta }_{ij}-ig{\left(T_a\right)}_{ij}{\mathcal{A}}_{\mu }^a}$couples the quark field with a coupling strength ${\displaystyle g}$to the gluon fields via the infinitesimal SU(3) generators ${\displaystyle T_a}$in the fundamental representation. An explicit representation of these generators is given by ${\displaystyle T_a={\lambda }_a/2}$, wherein the ${\displaystyle {\lambda }_a(a=1\dots 8)}$are the Gell-Mann matrices.

The symbol ${\displaystyle G_{\mu \nu }^a}$ represents the gauge invariant gluon field strength tensor, analogous to the electromagnetic field strength tensor, F^μν, in quantum electrodynamics. It is given by:

${\displaystyle G_{\mu \nu }^a={\mathrm{\partial }}_{\mu }{\mathcal{A}}_{\nu }^a-{\mathrm{\partial }}_{\nu }{\mathcal{A}}_{\mu }^a+g{f}^{abc}{\mathcal{A}}_{\mu }^b{\mathcal{A}}_{\nu }^c,}$

where ${\displaystyle {\mathcal{A}}_{\mu }^a(x)}$ are the gluon fields, dynamical functions of spacetime, in the adjoint representation of the SU(3) gauge group, indexed by a, b and c running from ${\displaystyle 1}$ to ${\displaystyle 8}$; and f_abc are the structure constants of SU(3). Note that the rules to move-up or pull-down the a, b, or c indices are trivial, (+, ..., +), so that f^abc = f_abc = f^a_bc whereas for the μ or ν indices one has the non-trivial relativistic rules corresponding to the metric signature (+ − − −).

The variables m and g correspond to the quark mass and coupling of the theory, respectively, which are subject to renormalization.

An important theoretical concept is the Wilson loop (named after Kenneth G. Wilson). In lattice QCD, the final term of the above Lagrangian is discretized via Wilson loops, and more generally the behavior of Wilson loops can distinguish confined and deconfined phases.

Fields

The pattern of strong charges for the three colors of quark, three antiquarks, and eight gluons (with two of zero charge overlapping).

Quarks are massive spin-1⁄2 fermions that carry a color charge whose gauging is the content of QCD. Quarks are represented by Dirac fields in the fundamental representation 3 of the gauge group SU(3). They also carry electric charge (either −1⁄3 or +2⁄3) and participate in weak interactions as part of weak isospin doublets. They carry global quantum numbers including the baryon number, which is 1⁄3 for each quark, hypercharge and one of the flavor quantum numbers.

Gluons are spin-1 bosons that also carry color charges, since they lie in the adjoint representation 8 of SU(3). They have no electric charge, do not participate in the weak interactions, and have no flavor. They lie in the singlet representation 1 of all these symmetry groups.

Each type of quark has a corresponding antiquark, of which the charge is exactly opposite. They transform in the conjugate representation to quarks, denoted ${\displaystyle \overline{\mathbf{3}}}$.

Dynamics

According to the rules of quantum field theory, and the associated Feynman diagrams, the above theory gives rise to three basic interactions: a quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact. This contrasts with QED, in which only the first kind of interaction occurs, since photons have no charge. Diagrams involving Faddeev–Popov ghosts must be considered too (except in the unitarity gauge).

Area law and confinement

Detailed computations with the above-mentioned Lagrangian show that the effective potential between a quark and its anti-quark in a meson contains a term that increases in proportion to the distance between the quark and anti-quark (${\displaystyle \propto r}$), which represents some kind of "stiffness" of the interaction between the particle and its anti-particle at large distances, similar to the entropic elasticity of a rubber band (see below). This leads to confinement  of the quarks to the interior of hadrons, i.e. mesons and nucleons, with typical radii R_c, corresponding to former "Bag models" of the hadrons The order of magnitude of the "bag radius" is 1 fm (= 10⁻¹⁵ m). Moreover, the above-mentioned stiffness is quantitatively related to the so-called "area law" behavior of the expectation value of the Wilson loop product P_W of the ordered coupling constants around a closed loop W; i.e. ${\displaystyle ⟨P_W⟩}$ is proportional to the area enclosed by the loop. For this behavior the non-abelian behavior of the gauge group is essential.

Methods

Further analysis of the content of the theory is complicated. Various techniques have been developed to work with QCD. Some of them are discussed briefly below.

Perturbative QCD

Main article: Perturbative QCD

This approach is based on asymptotic freedom, which allows perturbation theory to be used accurately in experiments performed at very high energies. Although limited in scope, this approach has resulted in the most precise tests of QCD to date.

Lattice QCD

Main article: Lattice QCD

 

⟨E²⟩ plot for static quark–antiquark system held at a fixed separation, where blue is zero and red is the highest value (result of a lattice QCD simulation by M. Cardoso et al.)

Among non-perturbative approaches to QCD, the most well established is lattice QCD. This approach uses a discrete set of spacetime points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation that is then carried out on supercomputers like the QCDOC, which was constructed for precisely this purpose. While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means, in particular into the explicit forces acting between quarks and antiquarks in a meson. However, the numerical sign problem makes it difficult to use lattice methods to study QCD at high density and low temperature (e.g. nuclear matter or the interior of neutron stars).

1/N expansion

Main article: 1/N expansion

A well-known approximation scheme, the 1⁄N expansion, starts from the idea that the number of colors is infinite, and makes a series of corrections to account for the fact that it is not. Until now, it has been the source of qualitative insight rather than a method for quantitative predictions. Modern variants include the AdS/CFT approach.

Effective theories

For specific problems, effective theories may be written down that give qualitatively correct results in certain limits. In the best of cases, these may then be obtained as systematic expansions in some parameters of the QCD Lagrangian. One such effective field theory is chiral perturbation theory or ChiPT, which is the QCD effective theory at low energies. More precisely, it is a low energy expansion based on the spontaneous chiral symmetry breaking of QCD, which is an exact symmetry when quark masses are equal to zero, but for the u, d and s quark, which have small mass, it is still a good approximate symmetry. Depending on the number of quarks that are treated as light, one uses either SU(2) ChiPT or SU(3) ChiPT. Other effective theories are heavy quark effective theory (which expands around heavy quark mass near infinity), and soft-collinear effective theory (which expands around large ratios of energy scales). In addition to effective theories, models like the Nambu–Jona-Lasinio model and the chiral model are often used when discussing general features.

QCD sum rules

Main article: QCD sum rules

Based on an Operator product expansion one can derive sets of relations that connect different observables with each other.

Experimental tests

The notion of quark flavors was prompted by the necessity of explaining the properties of hadrons during the development of the quark model. The notion of color was necessitated by the puzzle of the
Δ⁺⁺
. This has been dealt with in the section on the history of QCD.

The first evidence for quarks as real constituent elements of hadrons was obtained in deep inelastic scattering experiments at SLAC. The first evidence for gluons came in three-jet events at PETRA.

Several good quantitative tests of perturbative QCD exist:

• The running of the QCD coupling as deduced from many observations
• Scaling violation in polarized and unpolarized deep inelastic scattering
• Vector boson production at colliders (this includes the Drell–Yan process)
• Direct photons produced in hadronic collisions
• Jet cross sections in colliders
• Event shape observables at the LEP
• Heavy-quark production in colliders

Quantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The best is probably the running of the QCD coupling as probed through lattice computations of heavy-quarkonium spectra. There is a recent claim about the mass of the heavy meson B_c . Other non-perturbative tests are currently at the level of 5% at best. Continuing work on masses and form factors of hadrons and their weak matrix elements are promising candidates for future quantitative tests. The whole subject of quark matter and the quark–gluon plasma is a non-perturbative test bed for QCD that still remains to be properly exploited.

One qualitative prediction of QCD is that there exist composite particles made solely of gluons called glueballs that have not yet been definitively observed experimentally. A definitive observation of a glueball with the properties predicted by QCD would strongly confirm the theory. In principle, if glueballs could be definitively ruled out, this would be a serious experimental blow to QCD. But, as of 2013, scientists are unable to confirm or deny the existence of glueballs definitively, despite the fact that particle accelerators have sufficient energy to generate them.

Cross-relations to condensed matter physics

There are unexpected cross-relations to condensed matter physics. For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom ${\displaystyle s_i=\pm 1}$ for i =1,...,N, with the special fixed "random" couplings ${\displaystyle J_{i,k}={ϵ}_i{J}_0{ϵ}_k.}$ Here the ε_i and ε_k quantities can independently and "randomly" take the values ±1, which corresponds to a most-simple gauge transformation ${\displaystyle (s_i\to s_i\cdot {ϵ}_i{J}_{i,k}\to {ϵ}_i{J}_{i,k}{ϵ}_k{s}_k\to s_k\cdot {ϵ}_k).}$ This means that thermodynamic expectation values of measurable quantities, e.g. of the energy $\mathcal{H}:=-\sum s_i{J}_{i,k}{s}_k,$ are invariant.

However, here the coupling degrees of freedom ${\displaystyle J_{i,k}}$, which in the QCD correspond to the gluons, are "frozen" to fixed values (quenching). In contrast, in the QCD they "fluctuate" (annealing), and through the large number of gauge degrees of freedom the entropy plays an important role (see below).

For positive J₀ the thermodynamics of the Mattis spin glass corresponds in fact simply to a "ferromagnet in disguise", just because these systems have no "frustration" at all. This term is a basic measure in spin glass theory. Quantitatively it is identical with the loop product ${\displaystyle P_W:=J_{i,k}{J}_{k,l}...J_{n,m}{J}_{m,i}}$ along a closed loop W. However, for a Mattis spin glass – in contrast to "genuine" spin glasses – the quantity P_W never becomes negative.

The basic notion "frustration" of the spin-glass is actually similar to the Wilson loop quantity of the QCD. The only difference is again that in the QCD one is dealing with SU(3) matrices, and that one is dealing with a "fluctuating" quantity. Energetically, perfect absence of frustration should be non-favorable and atypical for a spin glass, which means that one should add the loop product to the Hamiltonian, by some kind of term representing a "punishment". In the QCD the Wilson loop is essential for the Lagrangian rightaway.

The relation between the QCD and "disordered magnetic systems" (the spin glasses belong to them) were additionally stressed in a paper by Fradkin, Huberman and Shenker, which also stresses the notion of duality.

A further analogy consists in the already mentioned similarity to polymer physics, where, analogously to Wilson loops, so-called "entangled nets" appear, which are important for the formation of the entropy-elasticity (force proportional to the length) of a rubber band. The non-abelian character of the SU(3) corresponds thereby to the non-trivial "chemical links", which glue different loop segments together, and "asymptotic freedom" means in the polymer analogy simply the fact that in the short-wave limit, i.e. for ${\displaystyle 0\leftarrow {\lambda }_w\ll R_c}$ (where R_c is a characteristic correlation length for the glued loops, corresponding to the above-mentioned "bag radius", while λ_w is the wavelength of an excitation) any non-trivial correlation vanishes totally, as if the system had crystallized.

There is also a correspondence between confinement in QCD – the fact that the color field is only different from zero in the interior of hadrons – and the behaviour of the usual magnetic field in the theory of type-II superconductors: there the magnetism is confined to the interior of the Abrikosov flux-line lattice, i.e., the London penetration depth λ of that theory is analogous to the confinement radius R_c of quantum chromodynamics. Mathematically, this correspondendence is supported by the second term, ${\displaystyle \propto g{G}_{\mu }^a{\overline{\psi }}_i{\gamma }^{\mu }{T}_{ij}^a{\psi }_j,}$ on the r.h.s. of the Lagrangian.