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# High Energy Physics - Science topic

Explore the latest questions and answers in High Energy Physics, and find High Energy Physics experts.

Questions related to High Energy Physics

There are many types of detectors in high energy physics experiments. For photon detection, there can be PMTs and solid-state detectors employed but what are the typical wavelength ranges measured in these experiments? This may also be inline with Cherenkov detection.

This transition phenomena of Globular to spray mode as voltage , and especially current is raised, is very commonly known to Manual Metal Arc Welding (MMAW) and Gas-Metal Arc Welding (GMAW) practitioners, but physics behind it is invoked rarely. See for example

- (https://www.aedmotorsport.com/news/mig-welding-transfer-methods#:~:text=In%20MIG%20welding%2C%20there%20are,Spray%20Arc%20and%20Pulsed%20MIG.) Short circuit is the coldest form of MIG welding and uses low voltage. In the Short Circuit transfer method, the consumable electrode wire arcs and touches the base material and shorts. This creates a small, quickly solidifying, weld metal puddle that drips into the weld joint fusing the materials together sometimes referred to as “fast freezing.” Short Circuit method is great for thinner materials but you risk “cold lapping” on thicker materials. This method also creates an increased amount of spatter. ...

Globular transfer method is very similar to the short circuit transfer method, which the consumable electrode wire arcs and touches the base material and shorts. The difference comes in how long the consumable electrode melts. In Globular method, the wire is heated longer and creates a large volume of weld metal that drips into the weld joint. It uses a high heat input and also risks less fusion because of large amounts of spatter disrupting the weld puddle. You are limited to flat and horizontal fillet welds with this method.

**Globular Transfer**In the globular transfer mode, the weld metal transfers across the arc in a gravity feed. The droplets across the arc are usually larger than the diameter of the electrode. Globular transfer does not produce a very smooth weld bead appearance and some spatter can occur. The use of a globular transfer is usually limited to heavier plate thicknesses and limited to the flat and horizontal positions. Globular transfers are typically found in solid MIG wires, gas shielded metal cored wires and gas shielded flux cored wires when 100% CO2 shielding gas is applied.

**Spray Transfer**The spray transfer is named for the spray of tiny molten droplets across the arc, not unlike the spray coming out of a garden hose when the opening is restricted. A spray transfer is usually smaller than the diameter of the wire and uses relatively high voltage and wire feed speeds or amperage. Unlike the short circuit transfer, once the arc is established, the arc is "on" at all times. There is very little spatter with the spray transfer mode and it is usually used on thicker metals in the flat and horizontal positions. The spray transfer is normally found in solid MIG wires and metal cored wires with a high ratio of Argon in the shielding gas, usually above 90%. A partial or semi spray transfer is found in gas shielded flux cored wires when an Argon CO2 shielding gas is used.

**Globular Transfer Mode**

The globular transfer method is in effect an uncontrolled short circuit which occurs when the voltage and wire are above the dip range but too low for spray. Large irregular globules of metal are transferred between the torch and work piece under the force of gravity.

The disadvantages of this method of transfer are that it produces a large amount of spatter as well as high heat input. In addition, globular transfer is limited to flat and horizontal fillet welds above 3mm. Lack of fusion is often common because the spatter disrupts the weld puddle. Also, because globular transfer uses more wire it is generally considered less efficient.

The advantages of globular transfer are that it runs at high wire feed speeds and amperages for good penetration on thick metals. Also, when weld appearance is not critical it can be used with inexpensive, CO2 shielding gas.

**Spray Arc Mode**

The Spray arc mode is used with high voltage and current. Metal is projected in the form of a fine spray of molten droplets of the electrode, propelled across the arc to the work piece by an electromagnetic force without the wire touching the weld pool. Its advantages include high deposition rates, good penetration, strong fusion, excellent weld appearance with little spatter as no short circuits are occurring. The disadvantages of the spray arc mode are mainly due to the high heat input which can cause problems on thinner material and the limited range of welding positions where the mode can be used. Generally, the minimum thickness to be welded will be around 6mm.

Some research papers on this very common welding phenomena include

- https://www.sciencedirect.com/science/article/pii/S0924013612000490
- http://files.aws.org/wj/supplement/WJ_1992_10_s381.pdf
- https://app.aws.org/wj/supplement/WJ_1993_06_s269.pdf

............................................................................................................

Now my questions are

How high voltage and current Applied to GMAW makes the liquid metal droplets generated at electrode tip to be detached faster and in form of small droplets? Why large metallic melt droplets are not preferred at high V or I?

One might point out to the elevated melting rate at high V,I that causes the spray transfer, but how would higher liquid flow rate be related to disintegration into droplets? Is the scenario similar to liquid atomization at high flow rate (High Weber number scenario, lower pressure head due to high velocity head aspires surrounding gas and atomize fluid), even when phase transformation is involved here?

Liquid metal contains both +ve charged ionic core and -ve charged delocalized electrons in charge-balancing amount, so would there be any role of electrostatic/electrodynamic attraction on the molten droplet? I do not think so.

Smaller droplets' easily forming means lowering surface energy. Through which mechanisms some inert/active gases can affect surface tension of liquid metal? (excessive surface oxidation to molten liquid excluded?)

Bonjour,

S'il vous plais, pouvez vous me donner les noms des livres qui explique la théorie quantique des champs et les interactions(Niveau Licence/Master et plus), d'une manière simple et claire ?

s'il sont en Français ce serait parfait.

(Je rappelle que je suis un étudiant en master physique des hautes énergies)

Merci

Just attended some very interesting lectures as part of the "Higgs Fest" here at Uppsala (http://www.kalendarium.uu.se/en?eventId=4251), but while I think I understood how protons and neutrons gather mass from the Higgs field, I failed to comprehend how the electron gets its mass. - Would be grateful for any enlightenment for a physicist.

I have built a detector for the detection of the cosmic-ray muon. Till now, I was using point particle gun for shooting high energy muons into the detector. Now I want to create a rectangular plane above the detector to throw thousands on particles in a single event by covering the whole detector plane. It is easy to do in a macro file. But I want to implement it in src file so that I can visualize the entire process. Kindly answer.

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## I have just finished writing the paper on the measurement of the neutrino's magnetic monopole charge, ready to upload at arXiv. ##

Gamma-ray in range of 10-200 keV usually is good candida for therapy. I knew also we can use this kind of gamma in industry. However, in these applications the power of gamma-ray is normally less than 500 MW.

I am looking for powerful gamma ray (maximum power can be higher than 1 GW).

the spin of Δ(1232) is 3/2 ,but its decay product,like nuclear is 1/2,pion is 0, so the spin isn't consistent before and after decay reaction .Is some of the spin angular momentun translate to orbital angular momentum?So what is the trajectory of a free particle that carries orbital angular momentum?

Planetary interiors have pressure and temperature far different from surface, and both physics and chemistry takes unexpected turns on this region. Is there any good textbook or overview article on this topic, so that I can work on High-energy environment ceramics and hypothetical forms of biochemistry?

How many symmetry operators are required to understand Qunantum Mechanics ?

In my view only one .I feel only C -symmetry , whose physical meaning is not yet clear . In non- relativistic case what is C ? Do not say that it is like charge in high energy physics. Give some other explanation .

Supersymmetry theory proposes that the super partners of the existing bosons and fermions are extinguished through some symmetry breaking mechanism… though there are some articles that offers few or no exotic particles other than the SM particles, but it would also be the case (in the theoretical model) that the symmetry breaking may cause polarization either only towards bosons or fermions… if not, why/how nature would choose which fermions and bosons among the super particles are to survive? Further, is it at least theoretically possible that the existing bosons and fermions have their super partners within the observed fermions and bosons? I do understand that in the second proposal the constraint of equal mass will be violated.

It is considered that gravity separates from other three interactions after plank epoch i.e. before GUT epoch; why it is not after electroweak epoch i.e. where is the technical mismatch?

I'm doing a particle physics analysis (jet energy regression) by means deep neural network (in keras with tensorflow backend). I have several features (mostly kinematic variables). I trained my model on the HH->bbbb samples (Di-Higgs decaying to 2 pairs of b and anti-b quarks). I normalized this dataset to zero-mean unit variance (z-score normalization). Now, I want to predict using a different sample (HH->2b2g, di-Higgs decaying to a pair of b quarks and two photons). When predicting this dataset, should I normalize it based on the HH->bbbb statistics? When I try to do it, it doesn't predict well, even giving me negative values of pT (transverse momentum (pT) should be > 0). Should I normalize HH->2b2g samples based on its own statistics instead?

I have to discharge some kiloamps from a capacitor through an inductor by using two SCRs or thyristors in triac configuration, but I should need to be sure maximum dv/dt and di/dt current is not reached, so what of following configurations are better?

Can the electron spin reverse? What implications would this bring in terms of defining matter?

In two Higgs doublet model (2HDM), how the W and Z bosons get mass? I am specifically looking for Type II 2HDM case.

Does anyone know of any work in theoretical condensed matter physics or nuclear physics where the notion of para-particles in the sense of Green* are utilised? Along side this, are there any experimental works hoping to realise para-particles?

It is not obvious that nature cannot realise such things, though the spin-statistics theorem seems to rule them out as fundamental particles, but as quasi-particles they could be allowed. There is also an interesting result in string theory by Ardalan and Mansouri, but I was thinking of a more `down to Earth' appearance of these ideas.

* H.S. Green, A Generalized Method of Field Quantization. Phys. Rev. 90, 270–273 (1953)

Some of the flavor calculations put very stringent bounds on the masses of the additional scalars. I just want to confirm the lowest bounds on them.

If we see the standard model particles, total decay width is 10% or much lower than its mass. One example, for 125 GeV standard model Higgs boson, its total decay width is 4.07*10

^{-3 }GeV. It's almost .0032%. Suppose we have a particle of mass 3 TeV. Can its total decay width be 1 TeV or say 2 TeV. Is there any constraints ? If so, please explain.L= r x p is a 3 dimensional relation. In 4 dimensions r and p are 4 vectors and L is a 4x4 matrix. We want to discuss conservation laws related to angular momentum in 4 space time dimensions. Then discuss the issue of angular momentum of a Black Hole.

What is the physical meaning of Vacuum expectation value. If we have a 2D plot for potential V(\phi) for the scalar field for negative mass square, then which distance is vev in that plot?

What is that Charge conjugate in Majorana mass term. Is that a matrix or it works as an operator. Please someone explain me.

Everybody knows that the wave function in momentum space is the Fourier transform of the wave function in the coordinate space and vice versa. So if we have the wave function in one of these spaces, we can derive the wave function in the other space. Now suppose instead of the wave function we have the absolute square of the wave function for example in momentum space, how can we obtain the wave function in coordinate space?.

The surface area is well known and the entropy is A/4 in Planck units. But what is the volume occupied by the static Black hole in space? I don't find this discussed anywhere.

Pair production via Schwinger mechanism depends on spatial length scale of the order of Compton scale. But we have seen that it strongly depends on EM field spatial inhomogeneity over the length scale variation of the order of radiation wavelength. Why does such kind of phenomenon occur?

Dear all,

I am trying to define a new element in GPT. After creating a myelem.c file, I am attempting to "make" on Mac OS Yosemite.

**Version of my compiler is:**

*Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr --with-gxx-include-dir=/usr/include/c++/4.2.1*

*Apple LLVM version 6.0 (clang-600.0.54) (based on LLVM 3.5svn)*

*Target: x86_64-apple-darwin14.0.0*

*Thread model: posix*

**I am receiving the following error messages:**

*clang: warning: treating 'c' input as 'c++' when in C++ mode, this behavior is deprecated*

*clang: warning: argument unused during compilation: '-fopenmp'*

*make: *** No rule to make target `meshscat.c.o', needed by `gpt'. Stop.*

Any ideas would be appreciated.

Many thanks,

Oznur

High Energy Physics and Mechanical Engineering are worlds apart. Can there be an area that belongs to HEP but has implications in Mechanical Engineering?

Determination of CP phase in neutrino sector.

I have been spending some time learning about quantum groups and their representations and am interested in applications to high energy physics.

Doing a literature search I found that in the last 20 or so years people have already looked into quantum groups and the Standard Model and have used quantum groups to calculate corrections to, for example, the Gell-

Mann-Okubo mass formulas. The deformation parameter q has also been related to Cabibbo mixing.

I am wondering if anyone is aware of any as of yet unexplored applications of quantum groups to high energy physics. Perhaps with the recent experimental data that has come out over the last few years (for example Higgs data), new calculation might be possible.

In particular I would be interested at looking at some aspect where a theoretical value differs from the observed experimental value and finding out if a quantum correction could account for the difference. I am not however aware of such particular instances.

Best regards,

Niels

Cauchy-Riemann equations give the conditions that for which complex functions are differentiable in a complex mathematical space.

each real-valued function could be imagined as a complex function of imaginary part equal to zero, so the same conditions should be satisfied for them too; but it seems that these equations have no sense according to real-valued function.

the question is that should these conditions be satisfied for real-valued functions? if yes, how? ; if not, why?

why x and gamma rays are overlapping from the bottom of the wave length range?

*The LHC experiment is the most grandiose experiment of history.*

*In 2008 it was shown that if c is a global constant of nature (as demonstrated for the Schwarzschild metric for the first time), there is no Hawking radiation and hence the most cogent safety argument of the LHC experiment is gone.*

*The question is important because the LHC experiment is producing the hottest resident spot anywhere in the universe, down on earth. CERN used the term "Big Bang Experiment" for this reason. The original hope to thereby produce micro black holes on earth may very well have been sound. In the absence of Hawking radiation, one of these if slow enough may grow exponentially inside matter.*

I know most of the answers will say infinity, but still this needs deeper look about its physical meaning and does it consider a practical logic?

Infinity usually used for something we could not measure, however the reality may be different!

The top and Higgs mass determination arose the old discussion about electroweak vacuum metastablity. There is an interesting fact that with available data or universe place in the edge of stable and meta-stable zone tends to be inside the meta-stable region. This conclusion confirms up to 3-loop renormalization group and even shows convergence. I know that changing the electroweak vacuum propertionally changes the top and higgs masses. But what I cant realize is that how the stability and meta-stability boundaries move. So to speak, can the universe become stable by new high energy physics emergence as <h>=246Gev replacement?

Is the anisotropic pressure can destroy the spherical symmetry of

the space-time? Can we use Anisotropic pressure for a spherically symmetric star?

By the 1950s, when Yang–Mills theory, also known as non-abelian gauge

theory, was discovered, it was already known that Quantum Electrodynamics (QED) gives an extremely accurate account of electromagnetic fields and forces. So it was natural to inquire whether non-abelian gauge theory described other forces in nature, notably the weak force and the strong or nuclear force. The massless nature of classical Yang–Mills waves was a

serious obstacle to applying Yang–Mills theory to the other forces, for the weak and nuclear forces are short range and many of the particles are massive. Hence these phenomena did not appear to be associated with long-range fields describing massless particles. In the 1960s and 1970s, physicists overcame these obstacles to the physical interpretation of non-abelian gauge theory. In the case of the weak force, this was accomplished by the Glashow–Salam– Weinberg electroweak theory. By elaborating the theory with an additional “Higgs field,” one avoided the massless nature of classical Yang–Mills waves. The solution to the problem of massless Yang–Mills fields for the strong interactions has a completely different nature. That

solution did not come from adding fields to Yang–Mills theory, but by discovering a remarkable property of the quantum Yang–Mills theory itself, called “asymptotic freedom”.Asymptotic freedom, together with other experimental and theoretical discoveries made in the 1960s and 1970s involving the symmetries and high-energy behaviour of the strong

interactions, made it possible to describe the nuclear force by a non-abelian gauge theory in which the gauge group is G = SU(3). The non-abelian gauge theory of the strong force is called Quantum Chromodynamics (QCD). But classical non-abelian gauge theory is very different from the observed world of strong interactions; for QCD to describe the strong force successfully, it must have at the quantum level the mass-gap and related color confinement

properties. Both experiment—since QCD has numerous successes in confrontation with experiment—and computer simulations carried out since the late 1970s, have given strong encouragement that QCD does have the properties of mass-gap and color confinement cited above. But they are not fully understood theoretically. In the attached link, http://dx.doi.org/10.13140/RG.2.1.1637.3205 the theoretical understanding of mass-gap and related color confinement property have been provided during mathematical calculation of the gluon emission cross section for QCD process by taking over the corresponding results from closely related aforesaid QED process under the assumption that color interactions in perturbative sector are “a copy of electromagnetic interactions.

As such, the direct mathematical calculation for QCD process has been

avoided because the presence of point-like Dirac particles inside hadrons through Bjorken scaling and the carriage of a substantial portion of proton’s momentum by neutral partons, as revealed by the ‘asymptotic freedom’ based analysis of the data on deep inelastic scattering of leptons by nucleons, do not constitute direct evidence that the aforesaid Dirac particles and neutral partons can be identified with quarks and gluons respectively for making QCD the correct physical theory.

I have some results about the fermion spectral function. In which I find there is a peak at \omega=0 for some momentum k. However, this peak is broad and the height is low. Can I still interpret this peak is a quasiparticle peak around a Fermi surface? So my question is if we find some broad peak in the fermion spectral function, is there any criterion to help us to determine the validness of quasiparticle picture and existence of a Fermi surface?

We do not know whether the neutrino is a Dirac particle or a Majorana particle. If neutrino turns out to be a Majorana particle then two additional phases are to be introduced in the 3x3 lepton flavor mixing matrix. Why these phases cannot be removed by field redefinitions. In the two generation case, we know that in the CKM matrix there is no CP violating Dirac phase. Similarly, will the Majorana phases disappear in the two generation case, or, will they continue to be non-zero even in the 2x2 mixing case. In which experiments will they show up.

References:

- J. Schechter and J. W. F. Valle, Phys. Rev. D 23, 1666 (1981)
- J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980)

high energy physics + particles physics +applied Mathematics

I am using Co-steel M35 as a pole piece for hybrid undulator.

Ageing of materials in particle detectors due to high energy particles and waves affect all the set up of the detectors, from trajectory detection to luminosity detection. Indeed, this ageing happens in all kind of materials: semiconductors, metals and amorphous materials. So, the higher the energy of the particles and waves, the smallest the duration of experiment without errors.

Does the Meissner effect incorporate the dimensions of the superconductor? If so, what is the limit to the length of the superconductor (perpendicular to the magnetic field)? How much is the curvature of the field lines WRT the levitating object?

I have recently upgraded to GEANT4.10.01 and I realised that the Coulomb scattering is completely ignored even if I include it in my custom physics list. I double-checked the environmental variables are set as they should be. I tried the built in list QBBC as well. It is running with e- ionisation, MSC but still no sign of Coulomb scattering. I would appreciate it if anyone can throw me a few ideas.

Many thanks, Oznur

I want to know whether Lorentz symmetry is conserved for all the velocity ranges or not?

Is the Lorentz invariance completely related to Lorentz symmetry; i.e. if Lorentz symmetry conserved then Lorentz invariance is also conserved or there are certain conditions where the Lorentz invariance conserved while Lorentz symmetry is not? what are they if there are such conditions.

with the second one has a zero intensity?! So the first order of diffraction would be bright and the weak light from far stars could be analyzed

I am especially working on Top Quark Decay within SM and BSM, through the technique of Effective Lagrangian. Please help me.

Does a mass (assumed point-like m), that follows its geodesic, emit gravitational radiation?

This could be looked at from the point of view of volume compression. That is, as pressure is applied through continuous volume compression, the band gap of NiO widens. I would like an explanation.

Thanks.

In Bohmian quantum mechanics we can derive Bohmian quantum potential by using conformal transformation on a metric. I think since a conformal transformation changes the metric globally, this can induce a simultaneous effect on dynamics of a particle and give it quantum mechanical behavior. Who can help me?

Hi all,

I wanted a detailed explanation of why Rho meson is so very important in marking a Gamma gamma event.Or it would be great if someone could suggest me some papers related to this topic.

I found from literature that threshold energies for the reactions

^{123}Sb(γ,n)^{122m}Sb and^{123}Sb(γ,n)^{122g}Sb are 9.103 and 8.933 MeV respectively, using the Q-value calculation formula threshold energy of the reaction which leads to ground state can be calculated. But how to calculate the threshold energy when the product reaches to metastable state?There exists a subtle difference between hermitian and self-adjoint operator ? Is momentum operator self-adjoint here ?

Which place use both, explain briefly. Is there any connection with compact stars?

Is anyone familiar with any sort of theoretical explanation of the number of chiral families? Any model or idea in this direction would be very interesting and useful.

It is known that hadrons can be divided in baryons (fermions of three quarks) and mesons (bosons of two quarks). The sum of their electric charge is always an integer number, e.g. the proton is one and the neutron is zero. What is the reason that we have not found one particle with, say, five or seven quarks?

In the Newtonian approach gravitational force can be written as the

gradient of a scalar field. It is sufficient to know the gravitational

scalar potential at each point. Then gravitational field can be obtained

by taking the gradient of a scalar.

How these concept is extended in Einstein's gravity ? In this case how

to obtain gravitational potential ? We know that Einstein described

gravitational effects in terms of a geometric phenomenon by introducing

a metric tensor field. Is it possible to obtain the metric tensor field from

a potential ? In this case will that be a vector potential or a scalar

potential ? Are there underlying symmetries such as gauge symmetries

in this field theory ?

When delta T/T is plotted against angular separations between points we see several peaks in the plot. The first one is most prominent one is between l value 200-300, or in terms of angular scales at about 1 degrees. How to explain the existence of these

peaks. We know that CMBR anisotropies provide a snapshot of the surface of last scattering. How does acoustic oscillations deform that surface? What are acoustic oscillations in primordial universe?

In Newtonian notion force between to masses m1 and m2 separated

by a distance d is simply G m1 m2/d^2. This is an example of a theory

which accepts action at a distance. A second example is Coulomb's

law which states how two point charges interact with each other.

These laws do not specify when the effect of a source located

at the `source point' will be felt at a particular `field point'. The

interactions are assumed to be `instantaneous'.

Einstein's gravity however does not admit this principle.

How, then, in Einstein's gravity, gravitational attraction propagates

locally, by the local deformations of space-time.

Is there experiment where particles with opposite spin vectors are introduced precisely (vectors) head-on? And what was the outcome? My model predicts particle annihilation. If no such experiment is done can you conduct one?

Nature of dark energy is unknown. It is a form of energy causing expansion of universe. Satellite based experiments such as Planck has estimated that 68.3 % of total matter and energy is in the form of dark energy.

Concept of the equation of state perhaps originated in the study of thermodynamics, describing a relation between two or more state functions such as pressure, volume or temperature. These state functions are macroscopic variables.

How can one formulate an equation of state for dark energy? How do different theories lead to different forms of the equations of state of dark energy ? How can we experimentally test or distinguish between different forms of the equations of state? Are there proposed or ongoing experiments aiming to understand equation of state of dark energy ?

I want to know how much time it takes to accelerate the electrons to such energy. I wish an answer from one who knows the experimental details of LEP.

Currently I am using this formalism, but it is giving me incorrect values compared to available literature.

The electro-weak unification states in very simple words means that at very high energies both were actually one force. And this force must be mediated by some bosonic particle. Did this mediator get split into a massless photon, and very massive Ws and Z bosons?

The question has following implications

1) What does the term anisotropy mean ?

2) Because universe is homogeneous and isotropic in general

how does one expect anisotropies ?

3) Is it a purely quantum effect ? or is it possible to have

classical explanations of this phenomenon ?

4) Is there a definite pattern in the anisotropy ? If so

how to explain that pattern ?

5) What are theoretical implications for inflationary theories ?

6) Does anisotropies give any indications on the nature

of dark matter. For example is DM cold or warm ?

I am adding a figure; source is

Some say the standard model is stable by the Planck scale, some others claim we must have new physics at the TeV scale, and some claim we need axions (and what else?).

What is the minimum number of new discoveries that is really needed to answer these unexplained observations?

It is said that tensor perturbations in FRW metric satisfies some wave equations. And the solutions of those wave equations are called gravity waves. My confusion is why the word "gravity" comes into picture. Also scalar perturbations satisfy a wave equations. Why scalar perturbation are not called gravity waves?

Vacuum expectation value (VEV) of the Higgs scalar is responsible for fermion

masses and also masses of the W+ W- and Z gauge bosons. Does it mean

that the Higgs particle can extract energy out of vacuum and convert it to a

new form in which gauge bosons and fermions are massive ? For quarks

one can also have QCD correction to masses which are

unrelated to Higgs VEV

In a big bang cosmology there is a parameter called spectral index that measures deviation of scalar curvature perturbation from scale invariance. I want to know what is this invariance?

I am simulating an electron beam which should linearly gain kinetic energy along its path. Should I implement this in UserSteppingAction?

The relativistic equations of energy and momentum forbid the possibility that anybody with nonzero rest mass reaches the speed of light because both quantities tend to infinity. In the case of the photon and neutrino, the problem is saved annulling their masses, so that the equations lead to an indetermination, and opens thus the ability to assign the value E = pc for both quantities. But on the other hand, the measurements indicate that neutrinos have nonzero mass. The question is how this theoretical dilemma is resolved.

If I understand correctly, then any matrix can be diagonalized with real and +ve diagonal entries via a bi-unitary transformation. My question is, given a matrix, are the unitary matrices unique?? Is there any common textbook that provides a simple proof of this fact?

The next part of my question involves the quark sector of the Standard Model. In the gauge basis, the "mass matrix" of the quarks is a general complex one. We can then rotate the left and right handed fields separately to go to the mass basis. Now, my problem is that they are called "mass eigenstates" and the masses are called "eigenvalues". But, the Yukawa matrix in the original gauge basis is an arbitrary complex one which does not necessarily have "eigenvalues" in the usual sense of the term. So, is there any way to understand the meaning of the term "mass eigenstate" in this context ?

Proton lifetime is believed to be comparable to the lifetime of the

universe. What is the most recent experimental numbers of

proton lifetime ? What are the unified models which are ruled

out by the latest data of proton lifetime ?