Mu2e , or the Muon -to- Electron Conversion Experiment , is a particle physics experiment at Fermilab in the US. The goal of the experiment is to identify physics beyond the Standard Model , namely, the conversion of muons to electrons without the emission of neutrinos , which occurs in a number of theoretical models. Former project co-spokesperson Jim Miller likens this process to neutrino oscillation , but for charged leptons . The rate for this process in the Standard Model of particle physics is unobservably small, so any observation of this process would constitute a major discovery and indicate new physics beyond the standard model. The experiment will be 10,000 times more sensitive than previous muon to electron conversion experiments, and probe effective energy scales up to 10,000 TeV .
80-770: Physicists have been searching for flavor violation since the 1940s. Flavor violation among neutrinos was proven in 1998 at the Super-Kamiokande experiment in Japan. In 1989, Russian physicists Vladimir Lobashev and Rashid Djilkibaev proposed an experiment to search for lepton flavor violation. The experiment, called MELC, operated from 1992 to 1995 at the Moscow Meson Factory at the Institute for Nuclear Research in Russia, before being shut down due to
160-402: A n t . {\displaystyle m_{A}v_{A}+m_{B}v_{B}+m_{C}v_{C}+...=constant.} This conservation law applies to all interactions, including collisions (both elastic and inelastic ) and separations caused by explosive forces. It can also be generalized to situations where Newton's laws do not hold, for example in the theory of relativity and in electrodynamics . Momentum
240-418: A Galilean transformation . If a particle is moving at speed d x / d t = v in the first frame of reference, in the second, it is moving at speed v ′ = d x ′ d t = v − u . {\displaystyle v'={\frac {{\text{d}}x'}{{\text{d}}t}}=v-u\,.} Since u does not change,
320-516: A momentum density can be defined as momentum per volume (a volume-specific quantity ). A continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. Momentum is a vector quantity : it has both magnitude and direction. Since momentum has a direction, it can be used to predict
400-752: A 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg⋅m/s due north measured with reference to the ground. The momentum of a system of particles is the vector sum of their momenta. If two particles have respective masses m 1 and m 2 , and velocities v 1 and v 2 , the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2 . {\displaystyle {\begin{aligned}p&=p_{1}+p_{2}\\&=m_{1}v_{1}+m_{2}v_{2}\,.\end{aligned}}} The momenta of more than two particles can be added more generally with
480-427: A charged meson has the same sign as its charge. Quarks have the following flavour quantum numbers: These five quantum numbers, together with baryon number (which is not a flavour quantum number), completely specify numbers of all 6 quark flavours separately (as n q − n q̅ , i.e. an antiquark is counted with the minus sign). They are conserved by both the electromagnetic and strong interactions (but not
560-402: A collision. For example, suppose there are two bodies of equal mass m , one stationary and one approaching the other at a speed v (as in the figure). The center of mass is moving at speed v / 2 and both bodies are moving towards it at speed v / 2 . Because of the symmetry, after the collision both must be moving away from the center of mass at
640-416: A decay involving a charmed quark or antiquark either as the incident particle or as a decay byproduct, Δ C = ±1 ; likewise, for a decay involving a bottom quark or antiquark Δ B′ = ±1 . Since first-order processes are more common than second-order processes (involving two quark decays), this can be used as an approximate " selection rule " for weak decays. A special mixture of quark flavours
720-405: A production solenoid will direct some of the particles produced into an S-shaped 2-Tesla evacuated transport solenoid, consisting of 50 separate superconducting electromagnets, which will select muons by charge and momentum, and carry the desired slow muons to the detector after some time delay. On entering the detector solenoid, the muons will hit (and stop within) an aluminum target that
800-549: A signal if as few as one in 100 quadrillion muons transforms into an electron. As of October 2018, the Mu2e collaboration included 240 people from 40 institutions in six countries. The collaboration is led by co-spokespersons Bob Bernstein (Fermilab) and Stefano Miscetti (INFN Frascati). The project manager for Mu2e is Julie Whitmore; the deputy project managers are Karen Byrum and Paul Derwent. Flavour (particle physics) In particle physics , flavour or flavor refers to
880-419: A straw tracker to measure the momentum of outgoing particles; and an electromagnetic calorimeter to identify which particle interactions to record for further study, identify what type of particle passed through the tracker, and to confirm the measurements of the tracker. An electron with energy of around 105 MeV will indicate that the electron originated in a neutrinoless muon conversion. In order to disturb
SECTION 10
#1732772922239960-553: A subgroup. The larger symmetry was named the Eightfold Way by Murray Gell-Mann , and was promptly recognized to correspond to the adjoint representation of SU(3) . To better understand the origin of this symmetry, Gell-Mann proposed the existence of up, down and strange quarks which would belong to the fundamental representation of the SU(3) flavor symmetry. To explain the observed absence of flavor-changing neutral currents ,
1040-486: A unit determinant . Such matrices form a Lie group called SU(2) (see special unitary group ). This is an example of flavour symmetry. In quantum chromodynamics , flavour is a conserved global symmetry . In the electroweak theory , on the other hand, this symmetry is broken, and flavour changing processes exist, such as quark decay or neutrino oscillations . All leptons carry a lepton number L = 1 . In addition, leptons carry weak isospin , T 3 , which
1120-512: Is a form of explicit symmetry breaking . The strength of explicit symmetry breaking is controlled by the current quark masses in QCD. Even if quarks are massless, chiral flavour symmetry can be spontaneously broken if the vacuum of the theory contains a chiral condensate (as it does in low-energy QCD). This gives rise to an effective mass for the quarks, often identified with the valence quark mass in QCD. Analysis of experiments indicate that
1200-413: Is a good example of an almost totally elastic collision, due to their high rigidity , but when bodies come in contact there is always some dissipation . A head-on elastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are v A1 and v B1 before the collision and v A2 and v B2 after,
1280-603: Is a measurable quantity, and the measurement depends on the frame of reference . For example: if an aircraft of mass 1000 kg is flying through the air at a speed of 50 m/s its momentum can be calculated to be 50,000 kg.m/s. If the aircraft is flying into a headwind of 5 m/s its speed relative to the surface of the Earth is only 45 m/s and its momentum can be calculated to be 45,000 kg.m/s. Both calculations are equally correct. In both frames of reference, any change in momentum will be found to be consistent with
1360-402: Is about 0.2 mm thick, entering orbitals around nuclei within the target. Any muons which convert into electrons without emitting neutrinos will escape these orbitals and enter the detector with a characteristic energy of 104.97 MeV (which is the muon mass minus the binding energy of about 0.5 MeV and nuclear recoil energy of about 0.2 MeV). The detector itself consists of two main components:
1440-466: Is an inelastic collision . An elastic collision is one in which no kinetic energy is transformed into heat or some other form of energy. Perfectly elastic collisions can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps the objects apart. A slingshot maneuver of a satellite around a planet can also be viewed as a perfectly elastic collision. A collision between two pool balls
1520-566: Is an eigenstate of the weak interaction part of the Hamiltonian , so will interact in a particularly simple way with the W bosons (charged weak interactions violate flavour). On the other hand, a fermion of a fixed mass (an eigenstate of the kinetic and strong interaction parts of the Hamiltonian) is an eigenstate of flavour. The transformation from the former basis to the flavour-eigenstate/mass-eigenstate basis for quarks underlies
1600-605: Is equal to the instantaneous force F acting on it, F = d p d t . {\displaystyle F={\frac {{\text{d}}p}{{\text{d}}t}}.} If the net force experienced by a particle changes as a function of time, F ( t ) , the change in momentum (or impulse J ) between times t 1 and t 2 is Δ p = J = ∫ t 1 t 2 F ( t ) d t . {\displaystyle \Delta p=J=\int _{t_{1}}^{t_{2}}F(t)\,{\text{d}}t\,.} Impulse
1680-407: Is known as Euler's first law . If the net force F applied to a particle is constant, and is applied for a time interval Δ t , the momentum of the particle changes by an amount Δ p = F Δ t . {\displaystyle \Delta p=F\Delta t\,.} In differential form, this is Newton's second law ; the rate of change of the momentum of a particle
SECTION 20
#17327729222391760-449: Is known as a flavour change, or flavour transmutation. Due to their quantum description, flavour states may also undergo quantum superposition . In atomic physics the principal quantum number of an electron specifies the electron shell in which it resides, which determines the energy level of the whole atom. Analogously, the five flavour quantum numbers ( isospin , strangeness , charm , bottomness or topness ) can characterize
1840-468: Is measured in the derived units of the newton second (1 N⋅s = 1 kg⋅m/s) or dyne second (1 dyne⋅s = 1 g⋅cm/s) Under the assumption of constant mass m , it is equivalent to write F = d ( m v ) d t = m d v d t = m a , {\displaystyle F={\frac {{\text{d}}(mv)}{{\text{d}}t}}=m{\frac {{\text{d}}v}{{\text{d}}t}}=ma,} hence
1920-414: Is more useful: electronic lepton number (+1 for electrons and electron neutrinos), muonic lepton number (+1 for muons and muon neutrinos), and tauonic lepton number (+1 for tau leptons and tau neutrinos). However, even these numbers are not absolutely conserved, as neutrinos of different generations can mix ; that is, a neutrino of one flavour can transform into another flavour . The strength of such mixings
2000-560: Is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics , quantum mechanics , quantum field theory , and general relativity . It is an expression of one of the fundamental symmetries of space and time: translational symmetry . Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics , allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems
2080-466: Is numerically equivalent to 3 newtons. In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum remains constant. This fact, known as the law of conservation of momentum , is implied by Newton's laws of motion . Suppose, for example, that two particles interact. As explained by the third law, the forces between them are equal in magnitude but opposite in direction. If
2160-547: Is specified by a matrix called the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix). All quarks carry a baryon number B = + + 1 / 3 , and all anti-quarks have B = − + 1 / 3 . They also all carry weak isospin , T 3 = ± + 1 / 2 . The positively charged quarks (up, charm, and top quarks) are called up-type quarks and have T 3 = + + 1 / 2 ;
2240-422: Is the center of mass frame – one that is moving with the center of mass. In this frame, the total momentum is zero. If two particles, each of known momentum, collide and coalesce, the law of conservation of momentum can be used to determine the momentum of the coalesced body. If the outcome of the collision is that the two particles separate, the law is not sufficient to determine the momentum of each particle. If
2320-499: Is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum p (from Latin pellere "push, drive") is: p = m v . {\displaystyle \mathbf {p} =m\mathbf {v} .} In the International System of Units (SI),
2400-516: Is the basis of the classification in the quark model . The relations between the hypercharge, electric charge and other flavour quantum numbers hold for hadrons as well as quarks. The flavour problem (also known as the flavour puzzle) is the inability of current Standard Model flavour physics to explain why the free parameters of particles in the Standard Model have the values they have, and why there are specified values for mixing angles in
2480-409: Is the product of the units of mass and velocity. In SI units , if the mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meters per second (kg⋅m/s). In cgs units , if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters per second (g⋅cm/s). Being a vector, momentum has magnitude and direction. For example,
Mu2e - Misplaced Pages Continue
2560-455: Is unchanged. Forces such as Newtonian gravity, which depend only on the scalar distance between objects, satisfy this criterion. This independence of reference frame is called Newtonian relativity or Galilean invariance . A change of reference frame, can, often, simplify calculations of motion. For example, in a collision of two particles, a reference frame can be chosen, where, one particle begins at rest. Another, commonly used reference frame,
2640-478: Is − 1 / 2 for the three charged leptons (i.e. electron , muon and tau ) and + 1 / 2 for the three associated neutrinos . Each doublet of a charged lepton and a neutrino consisting of opposite T 3 are said to constitute one generation of leptons. In addition, one defines a quantum number called weak hypercharge , Y W , which is −1 for all left-handed leptons. Weak isospin and weak hypercharge are gauged in
2720-600: The Cabibbo–Kobayashi–Maskawa matrix (CKM matrix). This matrix is analogous to the PMNS matrix for neutrinos, and quantifies flavour changes under charged weak interactions of quarks. The CKM matrix allows for CP violation if there are at least three generations. Flavour quantum numbers are additive. Hence antiparticles have flavour equal in magnitude to the particle but opposite in sign. Hadrons inherit their flavour quantum number from their valence quarks : this
2800-459: The Franck–Hertz experiment ); and particle accelerators in which the kinetic energy is converted into mass in the form of new particles. In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If
2880-880: The GIM mechanism was proposed in 1970, which introduced the charm quark and predicted the J/psi meson . The J/psi meson was indeed found in 1974, which confirmed the existence of charm quarks. This discovery is known as the November Revolution . The flavor quantum number associated with the charm quark became known as charm . The bottom and top quarks were predicted in 1973 in order to explain CP violation , which also implied two new flavor quantum numbers: bottomness and topness . Momentum In Newtonian mechanics , momentum ( pl. : momenta or momentums ; more specifically linear momentum or translational momentum )
2960-519: The PMNS and CKM matrices. These free parameters - the fermion masses and their mixing angles - appear to be specifically tuned. Understanding the reason for such tuning would be the solution to the flavor puzzle. There are very fundamental questions involved in this puzzle such as why there are three generations of quarks (up-down, charm-strange, and top-bottom quarks) and leptons (electron, muon and tau neutrino), as well as how and why
3040-496: The Standard Model . Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos ( electron neutrino , muon neutrino and tau neutrino ). These are conserved in strong and electromagnetic interactions, but violated by weak interactions. Therefore, such flavour quantum numbers are not of great use. A separate quantum number for each generation
3120-454: The doublet (the spin- 1 ⁄ 2 , 2 , or fundamental representation ) of SU(2), with the proton and neutron being then associated with different isospin projections I 3 = + + 1 ⁄ 2 and − + 1 ⁄ 2 respectively. The pions are assigned to the triplet (the spin-1, 3 , or adjoint representation ) of SU(2). Though there is a difference from the theory of spin: The group action does not preserve flavor (in fact,
3200-455: The kaon led to a new quantum number that was conserved by the strong interaction: strangeness (or equivalently hypercharge). The Gell-Mann–Nishijima formula was identified in 1953, which relates strangeness and hypercharge with isospin and electric charge. Once the kaons and their property of strangeness became better understood, it started to become clear that these, too, seemed to be a part of an enlarged symmetry that contained isospin as
3280-446: The particle 's dynamical state, i.e., its momentum , angular momentum, etc. Quantum field theory , however, allows interactions that can alter other facets of a particle's nature described by non dynamical, discrete quantum numbers. In particular, the action of the weak force is such that it allows the conversion of quantum numbers describing mass and electric charge of both quarks and leptons from one discrete type to another. This
Mu2e - Misplaced Pages Continue
3360-435: The species of an elementary particle . The Standard Model counts six flavours of quarks and six flavours of leptons . They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles . They can also be described by some of the family symmetries proposed for the quark-lepton generations. In classical mechanics, a force acting on a point-like particle can only alter
3440-405: The unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second . Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference , but in any inertial frame it is a conserved quantity, meaning that if a closed system
3520-463: The Mu2e experiment began in 2009, with the conceptual design complete in mid-2011. In July 2012, Mu2e received Critical Decision 1 approval (the second of five critical decision levels) from the Department of Energy , about one month after initial review. Project Manager Ron Ray asserted, "I know of no other project that has received sign-off that quickly after review." Funding of the Mu2e experiment
3600-502: The conserved quantity is generalized momentum , and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function . The momentum and position operators are related by the Heisenberg uncertainty principle . In continuous systems such as electromagnetic fields , fluid dynamics and deformable bodies ,
3680-535: The current quark masses of the lighter flavours of quarks are much smaller than the QCD scale , Λ QCD , hence chiral flavour symmetry is a good approximation to QCD for the up, down and strange quarks. The success of chiral perturbation theory and the even more naive chiral models spring from this fact. The valence quark masses extracted from the quark model are much larger than the current quark mass. This indicates that QCD has spontaneous chiral symmetry breaking with
3760-520: The detector hall, where final assembly will be completed. The Mu2e apparatus will be 92 feet (28 m) in length, and will consist of three sections. The total cost of the experiment is $ 271 million. Repurposed elements from the Tevatron collider will be used to generate and deliver an 8 GeV proton beam . The protons will be extracted from Fermilab's Delivery Ring through a non-linear third-integer resonance extraction process and sent in pulses to
3840-425: The difference between them ( B − L ) is conserved (see Chiral anomaly ). Strong interactions conserve all flavours, but all flavour quantum numbers are violated (changed, non-conserved) by electroweak interactions . If there are two or more particles which have identical interactions, then they may be interchanged without affecting the physics. All (complex) linear combinations of these two particles give
3920-914: The equations expressing conservation of momentum and kinetic energy are: m A v A 1 + m B v B 1 = m A v A 2 + m B v B 2 1 2 m A v A 1 2 + 1 2 m B v B 1 2 = 1 2 m A v A 2 2 + 1 2 m B v B 2 2 . {\displaystyle {\begin{aligned}m_{A}v_{A1}+m_{B}v_{B1}&=m_{A}v_{A2}+m_{B}v_{B2}\\{\tfrac {1}{2}}m_{A}v_{A1}^{2}+{\tfrac {1}{2}}m_{B}v_{B1}^{2}&={\tfrac {1}{2}}m_{A}v_{A2}^{2}+{\tfrac {1}{2}}m_{B}v_{B2}^{2}\,.\end{aligned}}} A change of reference frame can simplify analysis of
4000-765: The following: p = ∑ i m i v i . {\displaystyle p=\sum _{i}m_{i}v_{i}.} A system of particles has a center of mass , a point determined by the weighted sum of their positions: r cm = m 1 r 1 + m 2 r 2 + ⋯ m 1 + m 2 + ⋯ = ∑ i m i r i ∑ i m i . {\displaystyle r_{\text{cm}}={\frac {m_{1}r_{1}+m_{2}r_{2}+\cdots }{m_{1}+m_{2}+\cdots }}={\frac {\sum _{i}m_{i}r_{i}}{\sum _{i}m_{i}}}.} If one or more of
4080-456: The force is between particles. Similarly, if there are several particles, the momentum exchanged between each pair of particles adds to zero, so the total change in momentum is zero. The conservation of the total momentum of a number of interacting particles can be expressed as m A v A + m B v B + m C v C + . . . = c o n s t
SECTION 50
#17327729222394160-453: The formation of a chiral condensate . Other phases of QCD may break the chiral flavour symmetries in other ways. Isospin, strangeness and hypercharge predate the quark model. The first of those quantum numbers, Isospin, was introduced as a concept in 1932 by Werner Heisenberg , to explain symmetries of the then newly discovered neutron (symbol n): Protons and neutrons were grouped together as nucleons and treated as different states of
4240-679: The gas in the straw, allowing the trajectory of the electrons to be reconstructed. The rate of neutrinoless conversion of muons to electrons was previously constrained by the MEG experiment to less than 2.4×10, and further constrained to 7×10 by the SINDRUM II experiment at the Paul Scherrer Institute in Switzerland. Mu2e has an expected sensitivity of 5×10, four orders of magnitude beyond SINDRUM II, meaning that it will see
4320-463: The group action is specifically an exchange of flavour). When constructing a physical theory of nuclear forces , one could simply assume that it does not depend on isospin, although the total isospin should be conserved. The concept of isospin proved useful in classifying hadrons discovered in the 1950s and 1960s (see particle zoo ), where particles with similar mass are assigned an SU(2) isospin multiplet . The discovery of strange particles like
4400-1047: The initial velocities are known, the final velocities are given by v A 2 = ( m A − m B m A + m B ) v A 1 + ( 2 m B m A + m B ) v B 1 v B 2 = ( m B − m A m A + m B ) v B 1 + ( 2 m A m A + m B ) v A 1 . {\displaystyle {\begin{aligned}v_{A2}&=\left({\frac {m_{A}-m_{B}}{m_{A}+m_{B}}}\right)v_{A1}+\left({\frac {2m_{B}}{m_{A}+m_{B}}}\right)v_{B1}\\v_{B2}&=\left({\frac {m_{B}-m_{A}}{m_{A}+m_{B}}}\right)v_{B1}+\left({\frac {2m_{A}}{m_{A}+m_{B}}}\right)v_{A1}\,.\end{aligned}}} If one body has much greater mass than
4480-435: The left- and right-handed parts of each quark field. This approximate description of the flavour symmetry is described by a chiral group SU L ( N f ) × SU R ( N f ) . If all quarks had non-zero but equal masses, then this chiral symmetry is broken to the vector symmetry of the "diagonal flavour group" SU( N f ) , which applies the same transformation to both helicities of the quarks. This reduction of symmetry
4560-453: The mass and mixing hierarchy arises among different flavours of these fermions. Quantum chromodynamics (QCD) contains six flavours of quarks . However, their masses differ and as a result they are not strictly interchangeable with each other. The up and down flavours are close to having equal masses, and the theory of these two quarks possesses an approximate SU(2) symmetry ( isospin symmetry). Under some circumstances (for instance when
4640-411: The momentum of one particle after the collision is known, the law can be used to determine the momentum of the other particle. Alternatively if the combined kinetic energy after the collision is known, the law can be used to determine the momentum of each particle after the collision. Kinetic energy is usually not conserved. If it is conserved, the collision is called an elastic collision ; if not, it
4720-742: The negative sign indicating that the forces oppose. Equivalently, d d t ( p 1 + p 2 ) = 0. {\displaystyle {\frac {\text{d}}{{\text{d}}t}}\left(p_{1}+p_{2}\right)=0.} If the velocities of the particles are v A1 and v B1 before the interaction, and afterwards they are v A2 and v B2 , then m A v A 1 + m B v B 1 = m A v A 2 + m B v B 2 . {\displaystyle m_{A}v_{A1}+m_{B}v_{B1}=m_{A}v_{A2}+m_{B}v_{B2}.} This law holds no matter how complicated
4800-421: The negatively charged quarks (down, strange, and bottom quarks) are called down-type quarks and have T 3 = − + 1 / 2 . Each doublet of up and down type quarks constitutes one generation of quarks. For all the quark flavour quantum numbers listed below, the convention is that the flavour charge and the electric charge of a quark have the same sign . Thus any flavour carried by
4880-400: The net force is equal to the mass of the particle times its acceleration . Example : A model airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The net force required to produce this acceleration is 3 newtons due north. The change in momentum is 6 kg⋅m/s due north. The rate of change of momentum is 3 (kg⋅m/s)/s due north which
SECTION 60
#17327729222394960-447: The other, its velocity will be little affected by a collision while the other body will experience a large change. In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as heat or sound ). Examples include traffic collisions , in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in
5040-456: The particles are numbered 1 and 2, the second law states that F 1 = d p 1 / d t and F 2 = d p 2 / d t . Therefore, d p 1 d t = − d p 2 d t , {\displaystyle {\frac {{\text{d}}p_{1}}{{\text{d}}t}}=-{\frac {{\text{d}}p_{2}}{{\text{d}}t}},} with
5120-421: The particles is moving, the center of mass of the system will generally be moving as well (unless the system is in pure rotation around it). If the total mass of the particles is m {\displaystyle m} , and the center of mass is moving at velocity v cm , the momentum of the system is: p = m v cm . {\displaystyle p=mv_{\text{cm}}.} This
5200-402: The path of the electrons as little as possible, the tracker uses as little material as possible. The wire chamber tracker consists of panels of 15- micron -thick straws of metalized mylar filled with argon and carbon dioxide , the thinnest such straws ever used in a particle physics experiment. Electronics at each end of the straws will record the signal produced when electrons interact with
5280-476: The political and economic crises of the time. In 1997, American physicist William Molzon proposed a similar experiment at Brookhaven National Laboratory . Research and development on the MECO experiment began in 2001, but funding was pulled in 2005. Mu2e is based on the MECO experiment proposed at Brookhaven, and the earlier MELC experiment at Russia's Institute for Nuclear Research. Research and development for
5360-454: The quantum state of quarks, by the degree to which it exhibits six distinct flavours (u, d, c, s, t, b). Composite particles can be created from multiple quarks, forming hadrons , such as mesons and baryons , each possessing unique aggregate characteristics, such as different masses, electric charges, and decay modes. A hadron 's overall flavour quantum numbers depend on the numbers of constituent quarks of each particular flavour. All of
5440-405: The quark masses are much smaller than the chiral symmetry breaking scale of 250 MeV), the masses of quarks do not substantially contribute to the system's behavior, and to zeroth approximation the masses of the lightest quarks can be ignored for most purposes, as if they had zero mass. The simplified behavior of flavour transformations can then be successfully modeled as acting independently on
5520-402: The relevant laws of physics. Suppose x is a position in an inertial frame of reference. From the point of view of another frame of reference, moving at a constant speed u relative to the other, the position (represented by a primed coordinate) changes with time as x ′ = x − u t . {\displaystyle x'=x-ut\,.} This is called
5600-538: The resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations (see multiple dimensions ). The momentum of a particle is conventionally represented by the letter p . It is the product of two quantities, the particle's mass (represented by the letter m ) and its velocity ( v ): p = m v . {\displaystyle p=mv.} The unit of momentum
5680-402: The same particle, because they both have nearly the same mass and interact in nearly the same way, if the (much weaker) electromagnetic interaction is neglected. Heisenberg noted that the mathematical formulation of this symmetry was in certain respects similar to the mathematical formulation of non-relativistic spin , whence the name "isospin" derives. The neutron and the proton are assigned to
5760-432: The same physics, as long as the combinations are orthogonal , or perpendicular, to each other. In other words, the theory possesses symmetry transformations such as M ( u d ) {\displaystyle M\left({u \atop d}\right)} , where u and d are the two fields (representing the various generations of leptons and quarks, see below), and M is any 2 × 2 unitary matrix with
5840-644: The same speed. Adding the speed of the center of mass to both, we find that the body that was moving is now stopped and the other is moving away at speed v . The bodies have exchanged their velocities. Regardless of the velocities of the bodies, a switch to the center of mass frame leads us to the same conclusion. Therefore, the final velocities are given by v A 2 = v B 1 v B 2 = v A 1 . {\displaystyle {\begin{aligned}v_{A2}&=v_{B1}\\v_{B2}&=v_{A1}\,.\end{aligned}}} In general, when
5920-418: The second reference frame is also an inertial frame and the accelerations are the same: a ′ = d v ′ d t = a . {\displaystyle a'={\frac {{\text{d}}v'}{{\text{d}}t}}=a\,.} Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton's second law
6000-418: The tungsten target. These protons will then collide with the tungsten production target in the production solenoid, producing a cascade of particles including pions , which decay into muons. Mu2e will produce between 200 and 500 quadrillion (2×10 to 5×10) muons per year. For every 300 protons hitting the production target, about one muon will enter the transport solenoid. The 4.5- Tesla magnetic field of
6080-512: The various charges discussed above are conserved by the fact that the corresponding charge operators can be understood as generators of symmetries that commute with the Hamiltonian. Thus, the eigenvalues of the various charge operators are conserved. Absolutely conserved quantum numbers in the Standard Model are: In some theories, such as the grand unified theory , the individual baryon and lepton number conservation can be violated, if
6160-406: The weak interaction). From them can be built the derived quantum numbers: The terms "strange" and "strangeness" predate the discovery of the quark, but continued to be used after its discovery for the sake of continuity (i.e. the strangeness of each type of hadron remained the same); strangeness of anti-particles being referred to as +1, and particles as −1 as per the original definition. Strangeness
6240-458: Was delayed, contributing to the shift in start-date. The experiment is expected to run for three years. Later improvements to the detector may increase the sensitivity of the experiment by one to two orders of magnitude, allowing a more in-depth study of any charged lepton conversion that may be discovered in the initial run. As of February 2024, two Mu2E transport solenoids had been constructed and moved from Fermilab's Heavy Assembly Building to
6320-459: Was introduced to explain the rate of decay of newly discovered particles, such as the kaon, and was used in the Eightfold Way classification of hadrons and in subsequent quark models . These quantum numbers are preserved under strong and electromagnetic interactions , but not under weak interactions . For first-order weak decays, that is processes involving only one quark decay, these quantum numbers (e.g. charm) can only vary by 1, that is, for
6400-444: Was recommended by the Department of Energy 's Particle Physics Project Prioritization Panel , in its 2014 report. Groundbreaking on the detector hall took place on April 18, 2015. Originally, commissioning was anticipated in 2019 and preliminary results were expected 2020; however, the project was significantly delayed, and, in 2022, the experiment was projected to begin in 2026. The delivery of two magnets from General Atomics
#238761