Moller.MollerPhysics History
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Where Q^e_W = 1 - 4\sin^2\theta_W .
The MOLLER experiment will measure the parity violating asymmetry in the number of polarized electrons scattering off unpolarized electrons in a liquid hydrogen target:
The MOLLER experiment will measure the parity violating asymmetry in the number of polarized electrons scattered off unpolarized electrons in a liquid hydrogen target:
provides a clean window to study weak neutral current interactions.
Polarized electron scattering off unpolarized targets provides a clean window to study weak neutral current interactions. These experiments measure an asymmetry defined by
where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak and electromagnetic amplitudes.
The MOLLER experiment will measure the parity violating asymmetry in the number of polarized electrons scattering off unpolarized electrons in a liquid hydrogen target:
Where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak and electromagnetic amplitudes.
provides a clean window to study weak neutral current interactions.
{$A_{PV} = mE{G_F\over\sqrt{2}\pi\alpha}{4\sin^2\theta\over(3+\cos^2\theta)^2}Q^e_W = mE{G_F\over\sqrt{2}\pi\alpha}\frac{2y(1-y)}{1+y^4+(1-y)^4}Q^e_W$}
The parity-violating asymmetry A_{PV} , due to the interference between the photon and Z_0 boson exchange diagrams above is given by
{$A_{PV} = mE{G_F\over\sqrt{2}\pi\alpha}{4\sin^2\theta\over(3+\cos^2\theta)^2}Q^e_W = mE{G_F\over\sqrt{2}\pi\alpha}\frac{2y(1-y)}{1+y^4+(1-y)^4}Q^e_W$}
$${d\sigma\over d\Omega} = {\alpha^2\over 2mE}{(3+\cos^2\theta)^2\over\sin^4\theta} = {\alpha^2\over 4mE}{\frac{1+y^4+(1-y)^4}{y^2(1-y)^2}}$$
{$$d\sigma\over d\Omega} = {\alpha^2\over 2mE} {(3+\cos^2\theta)^2\over\sin^4\theta} = {\alpha^2\over 4mE}{\frac{1+y^4+(1-y)^4}{y^2(1-y)^2}$$}
$${d\sigma\over d\Omega} = {\alpha^2\over 2mE}{(3+\cos^2\theta)^2\over\sin^4\theta} = {\alpha^2\over 4mE}{\frac{1+y^4+(1-y)^4}{y^2(1-y)^2}}$$
{$$d\sigma\over d\Omega} = {\alpha^2\over 2mE} {(3+\cos^2\theta)^2\over\sin^4\theta} = {\alpha^2\over 4mE}{\frac{1+y^4+(1-y)^4}{y^2(1-y)^2}$$}
where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak and electromagnetic amplitudes.
where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak and electromagnetic amplitudes.
The leading order Feynman diagrams relevant for Møller scattering, involving both direct and exchange diagrams that interfere with each other, are
QPweak uses its eight main detectors to measure the difference in the number of electrons scattered from protons in a liquid hydrogen target, as a function of the electron polarization. The electrons are accelerated to near the speed of light, before they collide with the protons. The electrons must be this fast (among other reasons) in order to resolve ("see") the individual protons (rather than the hydrogen molecule as a whole). The normalized difference in the number of scattered electrons is referred to as an asymmetry (or sometimes as the analyzing power of the target):
Where Y_{L,R} are the experimentally measured signal yields in the main detectors, for left (L) and right (R) handed electron helicity (polarization), which is produced with circularly polarized laser light at the electron source (cathode) before the electrons are accelerated. A right-handed electron has its magnetic moment (think of a compass needle) aligned with its direction of motion, while a left-handed electron has its magnetic moment anti-aligned with its direction of motion.
The measured signal yield depends on many things, including physical parameters, such as scattering angle (w.r.t the incoming electron direction) and electron energy, as well as experimental effects, such as detector gain and efficiency, spectrometer performance and target performance.
A high precision measurement of this asymmetry is a challenging undertaking and requires years of careful design and development of the experimental components.
The above expression for the asymmetry is entirely experimental (e.g. Y_{L,R} are measured quantities), but the ultimate goal (as in any scientific endeavor) is to compare the measured results to a theoretical model that claims to, or is proven to have predictive power in some physical context. In other words, we want to use experimental results to test our scientific theories. In order to do so consistently, we must have a mathematical expression (i.e. a model) and equate it with the measured asymmetry above. For subatomic physics, the currently accepted model is referred to as the "Standard Model" of the electro-weak and strong interactions, combining three of the four currently known forces of nature. Within this model (leaving out all of the real computational detail, but see, for example: AIP 1 and references within) the asymmetry can be expressed as a combination of two main parts:
The first part arises as a result of the so called weak charge of the proton (like the electromagnetic charge sets the strength of the electromagnetic interaction, the weak charge of a particle sets the strength with which it interacts via the weak interaction with other particles):
The so called weak mixing angle \theta_{W} is a fundamental parameter of the Standard Model, which means that it does not depend on other parameters and that it must have a single specific value for all interactions that are described by the Standard Model. The quantity given by sin^2{\theta_{W}} is therefore also fixed in the Standard Model, but this is only true under very simple assumptions.
In reality, especially at higher energies, the value of the weak mixing angle becomes energy dependent (\kappa(Q)sin^2{\theta_{W}}) as a result of corrections to the basic interaction (referred to as radiative corrections).
QPweak is one of a number of experiments that map out the so called running of the weak mixing angle (the term running referring to the variation of \kappa(Q)sin^2{\theta_{W}} with energy). Each experiment measures this quantity in a different system or interaction (such as the proton in this case) with a different dependence on the underlying physics. In this way the full dependence of the Standard Model on the weak mixing angle is determined.
If the measured value of \sin^2{\theta_{W}} deviates from the predicted value (given in the above figure) in a statistically significant way, then this way indicate important new physics beyond the Standard Model.
QPweak constitutes the first measurement of the weak charge of the proton.
where \sigma_R ( \sigma ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R ( \sigma ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R (\sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R ( \sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R (\sigma_L) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R (\sigma_L ) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R(\sigma_L) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R (\sigma_L) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R(\sgma_L) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where \sigma_R(\sigma_L) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where $$\sigma_R(\sgma_L)$$ is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at $$Q^2 \ll M^2_Z$$ by the interference between the weak
where \sigma_R(\sgma_L) is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at Q^2 \ll M^2_Z by the interference between the weak
where $\sigma_R(\sgma_L)$ is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at $Q^2 \ll M^2_Z$ by the interference between the weak
where $$\sigma_R(\sgma_L)$$ is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at $$Q^2 \ll M^2_Z$$ by the interference between the weak
Polarized electron scattering off unpolarized targets provides a clean window to study weak neutral current interactions. These experiments measure an asymmetry defined by
where $\sigma_R(\sgma_L)$ is the scattering cross-section using incident right (left) handed electrons. A non-zero asymmetry constitutes parity nonconservation, dominated at $Q^2 \ll M^2_Z$ by the interference between the weak and electromagnetic amplitudes.
The total unpolarized cross section, dominated by photon exchange, is given by
The QPweak Experiment Physics: \\\
The MOLLER Experiment Physics:
The QPweak Experiment Physics:
QPweak uses its eight main detectors to measure the difference in the number of electrons scattered from protons in a liquid hydrogen target, as a function of the electron polarization. The electrons are accelerated to near the speed of light, before they collide with the protons. The electrons must be this fast (among other reasons) in order to resolve ("see") the individual protons (rather than the hydrogen molecule as a whole). The normalized difference in the number of scattered electrons is referred to as an asymmetry (or sometimes as the analyzing power of the target):
Where Y_{L,R} are the experimentally measured signal yields in the main detectors, for left (L) and right (R) handed electron helicity (polarization), which is produced with circularly polarized laser light at the electron source (cathode) before the electrons are accelerated. A right-handed electron has its magnetic moment (think of a compass needle) aligned with its direction of motion, while a left-handed electron has its magnetic moment anti-aligned with its direction of motion.
The measured signal yield depends on many things, including physical parameters, such as scattering angle (w.r.t the incoming electron direction) and electron energy, as well as experimental effects, such as detector gain and efficiency, spectrometer performance and target performance.
A high precision measurement of this asymmetry is a challenging undertaking and requires years of careful design and development of the experimental components.
The above expression for the asymmetry is entirely experimental (e.g. Y_{L,R} are measured quantities), but the ultimate goal (as in any scientific endeavor) is to compare the measured results to a theoretical model that claims to, or is proven to have predictive power in some physical context. In other words, we want to use experimental results to test our scientific theories. In order to do so consistently, we must have a mathematical expression (i.e. a model) and equate it with the measured asymmetry above. For subatomic physics, the currently accepted model is referred to as the "Standard Model" of the electro-weak and strong interactions, combining three of the four currently known forces of nature. Within this model (leaving out all of the real computational detail, but see, for example: AIP 1 and references within) the asymmetry can be expressed as a combination of two main parts:
The first part arises as a result of the so called weak charge of the proton (like the electromagnetic charge sets the strength of the electromagnetic interaction, the weak charge of a particle sets the strength with which it interacts via the weak interaction with other particles):
The so called weak mixing angle \theta_{W} is a fundamental parameter of the Standard Model, which means that it does not depend on other parameters and that it must have a single specific value for all interactions that are described by the Standard Model. The quantity given by sin^2{\theta_{W}} is therefore also fixed in the Standard Model, but this is only true under very simple assumptions.
In reality, especially at higher energies, the value of the weak mixing angle becomes energy dependent (\kappa(Q)sin^2{\theta_{W}}) as a result of corrections to the basic interaction (referred to as radiative corrections).
QPweak is one of a number of experiments that map out the so called running of the weak mixing angle (the term running referring to the variation of \kappa(Q)sin^2{\theta_{W}} with energy). Each experiment measures this quantity in a different system or interaction (such as the proton in this case) with a different dependence on the underlying physics. In this way the full dependence of the Standard Model on the weak mixing angle is determined.
If the measured value of \sin^2{\theta_{W}} deviates from the predicted value (given in the above figure) in a statistically significant way, then this way indicate important new physics beyond the Standard Model.
QPweak constitutes the first measurement of the weak charge of the proton.