Measurement of the Higgs boson mass and width using the four-lepton final state in proton-proton collisions at √s = 13 TeV

 

A measurement of the Higgs boson mass and width via its decay to two Z bosons is presented. Proton-proton collision data collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb^−1 at a center-of-mass energy of 13 TeV, is used. The invariant mass distribution of four leptons in the on-shell Higgs boson decay is used to measure its mass and constrain its width. This yields the most precise single measurement of the Higgs boson mass to date, 125.04 ± 0.12 GeV, and an upper limit on the width Γ H < 330 MeV at 95% confidence level. A combination of the on-and off-shell Higgs boson production decaying to four leptons is used to determine the Higgs boson width, assuming that no new virtual particles affect the production, a premise that is tested by adding new heavy particles in the gluon fusion loop model. This result is combined with a previous CMS analysis of the off-shell Higgs boson production with decay to two leptons and two neutrinos, giving a measured Higgs boson width of 3.0 +2.0, −1.5 MeV, in agreement with the standard model prediction of 4.1 MeV. The strength of the off-shell Higgs boson production is also reported. The scenario of no off-shell Higgs boson production is excluded at a confidence level corresponding to 3.8 standard deviations.

Higgs boson mass and width measurements with on-shell production

The Higgs boson mass and width are measured, using on-shell production, by fitting the m4ℓ distribution in the mass range 105 < m4ℓ < 140 GeV. The results have been determined using the CMS statistical analysis tool COMBINE, which is based on the ROOFIT and ROOSTATS frameworks. Table 1 shows the mass measurements obtained from the 1D approach, where no further assumptions have been made. In comparison to the 1D model, the 1D′BS model reduces the uncertainty by about 15%. Implementing the δm4ℓ/m4ℓ categorization then gives the N –1D′BS model, which leads to an additional 10% improvement. Finally, using the D kin, bkg discriminant to reduce the background produces the N –2D′BS model with another 4% improvement. Table 5 shows the resulting m4ℓ measurements using this last model. All the measured m4ℓ values from the different fits are statistically compatible, given their uncertainties and correlations. Figure 1 displays the observed 1D likelihood scans as functions of mH, from the fits for the different 4ℓ categories and combined. Combining all the m4ℓ final states and data-taking years, our final result is mH = 125.04 ± 0.11 (stat) ± 0.05 (syst) = 125.04 ± 0.12 GeV. The largest systematic uncertainty is from the lepton momentum scale and equals 0.03 and 0.04 GeV for final states with muons and electrons, respectively. 

Table 1: Best fit values for the mass of the Higgs boson measured in the inclusive 4ℓ final state and separately for different flavor categories using the 1D approach. Uncertainties are separated into statistical and systematic uncertainties. Expected uncertainties are also given assuming mH = 125.38 GeV 

Table 2: Best fit values for the mass of the Higgs boson measured in the inclusive 4ℓ final state and separately for different flavor categories, using the final fit configuration (N –2D’BS). Uncertainties are separated into statistical and systematic uncertainties. Expected uncertainties are also given assuming mH = 125.38 GeV.

As a check on the analysis technique and the systematic uncertainty from this method, the 1D′BS model is applied to Z → 4ℓ events in the m4ℓ range 70–105 GeV. The signal shape is obtained using a convolution of a Breit–Wigner function and a double-sided Crystal Ball function. The fitted values of mZ in different subchannels are m4µ Z = 91.02 ± 0.14 GeV, m4e Z = 91.18 ± 0.45 GeV, m2e2µ Z = 91.40 ± 0.29 GeV, and m2e2µ Z = 91.40 ± 0.37 GeV, leading to a combined value of mZ = 91.17 ± 0.12 GeV, consistent with the world-average Z boson mass and with the uncertainty in agreement with the expected value of ± 0.12 GeV from simulation. The results from this analysis are combined with those extracted using data recorded with the CMS detector during Run 1 at √ s = 7 and 8 TeV. Since this analysis uses an improved method to extract the systematic uncertainties affecting lepton momentum, the lepton energy scales and resolution uncertainties are considered uncorrelated between the two runs. The combined observed result from both data-taking periods is mH = 125.08 ± 0.12 GeV = 125.08 ± 0.10 (stat)±0.05 (syst) GeV. The corresponding expected statistical and systematic uncertainties are ±0.10 and ±0.05 GeV, respectively. Figure 2 presents a summary of the Higgs boson mass measurements by the CMS Collaboration in the four-lepton decay channel.

Figure 1: The profile likelihood from the mH fit using the N –2D′BS model for each of the 4ℓ categories and combined. The change in likelihood corresponding to 68 and 95% CLs are shown by the dashed horizontal lines. Both statistical and systematic uncertainties are included in the fits.

Figure 2: Summary of the CMS Higgs boson mass measurements using the four-lepton final state. The red vertical line and the gray column represent the best fit value and the total uncertainty, respectively, as measured by combining the Runs 1 and 2 data. The yellow band and horizontal black bars show the statistical and total uncertainties in each measurement, respectively. The value of each measurement is given, along with the total and statistical only (in parentheses) uncertainties.

 Higgs boson width measurement with off-shell production

Table 3: Summary of the total Higgs boson width ΓH measurement, showing the 68% CL (central values with uncertainties) and 95% CL (in square brackets) intervals for the H → ZZ → 4ℓ channel alone and in combination with the off-shell H → ZZ → 2ℓ2ν channel.

Figure 3: Observed (solid) and expected (dashed) profile likelihood projections from the Higgs boson width fit using on- and off-shell production from this analysis. The analysis of the offshell H → ZZ → 4ℓ channel combined with the on-shell H → ZZ → 4ℓ channel is shown in black. The full combination of H → ZZ → 4ℓ with the off-shell H → ZZ → 2ℓ2ν is given in red. The black horizontal dashed lines show the 68 and 95% CL values. 

The observed limits on ΓH are stronger than the average expected values from simulation. This is supported by the upper left, where the number of observed events in the sensitive region of m4ℓ > 340 GeV and Dbkg > 0.6 in the Untagged category is below the expected value, but still consistent with it. The smaller number of events in this region favors the hypothesis of negative interference between the signal and background contributions, which dominates over the pure signal contributions for ΓH values near the SM value. Therefore, large and very small values of ΓH are disfavored. 

A measurement of the Higgs boson mass (mH) and width (ΓH) using the decays to two Z bosons is presented. The data sample comes from proton-proton collisions at the LHC recorded by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb−1 . On-shell Higgs boson production with the H → 4ℓ decay (ℓ = e, µ) is used to measure its mass and constrain its width. The mass measurement yields mH = 125.04± 25.

 Table 4: Measured values of the signal strengths µ off-shell , µ off-shell, F , and µ off-shell, V , and their 68% and 95% (in square brackets) CL intervals from the combined fit to the off-shell H → ZZ → 4ℓ and 2ℓ2ν channels.

Figure 4: Observed 2D profile likelihood projection of the off-shell signal strength parameters (µ off-shell, F , and µ off-shell, V  ) from the fit to the combined off-shell H → ZZ → 4ℓ and 2ℓ2ν channels. The best fit value is shown by the black cross and the SM prediction by the red x. The 68 and 95% CL contours are given by the dashed and solid curves, respectively. The color scale to the right of the plot relates the quantitative values. 

0.11 (stat) ± 0.05 (syst) GeV = 125.04 ± 0.12 GeV, in agreement with the expected precision of ±0.12 GeV. From on-shell production events, an upper limit of ΓH < 330 MeV is set at 95% confidence level. The mass measurement is further improved by combining data from Runs 1 and 2, leading to the most precise single measurement of the mass to date in this channel, mH = 125.08 ± 0.10 (stat) ± 0.05 (syst) GeV = 125.08 ± 0.12 GeV. Using on- and off-shell Higgs boson production with the decay to four leptons, and combining them with a separate analysis with Higgs boson decay to two leptons plus two neutrinos, we measure ΓH = 3.0+2.0, −1.5 MeV, consistent with the standard model prediction of 4.1 MeV. These results are summarized in Table 5. The strength of the off-shell Higgs boson production is also reported, and the scenario of no off-shell Higgs boson production is excluded at a confidence level corresponding to 3.8 standard deviations. Results of the measurements are tabulated in the HEPData record for this analysis.

Table 5: Summary of the Higgs boson mass and total width ΓH measurements, showing the allowed 68% CL (central values with uncertainties) and 95% CL (in square brackets) intervals. Uncertainties are reported as a combination of statistical and systematic uncertainties. The first two rows display the outcomes of the analysis conducted within the on-shell H → ZZ → 4ℓ region, where the width is restricted to be positive. The third row incorporates results from the off-shell H → ZZ → 4ℓ region combined with the on-shell H → ZZ → 4ℓ and off-shell H → ZZ → 2ℓ2ν.

                                                       ====== Physics =======

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References :

S. L. Glashow, “Partial-symmetries of weak interactions”, Nucl. Phys. 22 (1961) 579, doi:10.1016/0029-5582(61)90469-2. 

F. Englert and R. Brout, “Broken symmetry and the mass of gauge vector mesons”, Phys. Rev. Lett. 13 (1964) 321, doi:10.1103/PhysRevLett.13.321. 

CMS Collaboration, “The CMS statistical analysis and combination tool: COMBINE”, Comput. Softw. Big Sci. 8 (2024) 19, doi:10.1007/s41781-024-00121-4, arXiv:2404.06614. 

W. Verkerke and D. P. Kirkby, “The RooFit toolkit for data modeling”, in Proceedings of the 13th International Conference for Computing in High-Energy and Nuclear Physics (CHEP03). 2003. arXiv:physics/0306116. 

L. Moneta et al., “The RooStats project”, PoS ACAT2010 (2010) 057, doi:10.22323/1.093.0057, arXiv:1009.1003. 

CMS Collaboration, “A measurement of the Higgs boson mass in the diphoton decay channel”, Phys. Lett. B 805 (2020) 135425, doi:10.1016/j.physletb.2020.135425, arXiv:2002.06398. 

Particle Data Group, K. A. Olive et al., “Review of Particle Physics”, Chin. Phys. C 38 (2014) 090001, doi:10.1088/1674-1137/38/9/090001. 

CMS Collaboration, “Measurement of the properties of a Higgs boson in the four-lepton final state”, Phys. Rev. D 89 (2014) 092007, doi:10.1103/PhysRevD.89.092007, arXiv:1312.5353.

“HEPData record for this analysis”, 2024. doi:10.17182/hepdata.153670.

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Neuromorphic Spintronics - Neuromorphic Computing with Spin Torque Nano-oscillators

 

Neuromorphic computing uses basic principles inspired by the brain to design circuits that perform artificial intelligence tasks with superior energy efficiency. Traditional approaches have been limited by the energy area of artificial neurons and synapses realized with conventional electronic devices.

In recent years, multiple groups have demonstrated that spintronic nanodevices, which exploit the magnetic as well as electrical properties of electrons, can increase the energy efficiency and decrease the area of these circuits. Among the variety of spintronic devices that have been used, magnetic tunnel junctions play a prominent role because of their established compatibility with standard integrated circuits and their multifunctionality.

Magnetic tunnel junctions can serve as synapses, storing connection weights, functioning as local, nonvolatile digital memory or as continuously varying resistances. As nano-oscillators, they can serve as neurons, emulating the oscillatory behavior of sets of biological neurons. As superparamagnets, they can do so by emulating the random spiking of biological neurons. Magnetic textures like domain walls or skyrmions can be configured to function as neurons through their non-linear dynamics.

Several implementations of neuromorphic computing with spintronic devices demonstrate their promise in this context. Used as variable resistance synapses, magnetic tunnel junctions perform pattern recognition in an associative memory. As oscillators, they perform spoken digit recognition in reservoir computing and when coupled together, classification of signals. As superparamagnets, they perform population coding and probabilistic computing.

Simulations demonstrate that arrays of nanomagnets and films of skyrmions can operate as components of neuromorphic computers. While these examples show the unique promise of spintronics in this field, there are several challenges to scaling up, including the efficiency of coupling between devices and the relatively low ratio of maximum to minimum resistances in the individual devices.

figure 1.

(a) Magnetic tunnel junctions for memory applications. A magnetic junction consists of two ferromagnetic layers (gray) separated by an insulating layer (blue) with the magnetization of one layer fixed and that of the other either parallel (low resistance) or antiparallel (high resistance) to it.

(b) Cross-bar array of magnetic tunnel junctions for high density storage (Magnetic Random Access Memory). The resistance of a particular tunnel junction is measured by activating the appropriate word line (red) allowing conduction between the bottom bit line and the top sense line (both blue). The alignment of the magnetization can be switched by passing sufficient currents through the device.

(c) Associative memory. (i) Handwritten digits from the MNIST dataset used for training the associative memory. (ii) Sample test input after training. (iii) Output of trained network from the test input showing successful association.

Figure 2. Neuromorphic computing with Spin Torque nano-oscillators. 

(a) Schematic spin torque nano-oscillator. When designed appropriately, the free layer magnetization of a tunnel junction precesses when a dc current is passed through it. Because of the oscillating magnetoresistance, a fixed input current gives an oscillating voltage across the junction. 

(b) Reservoir computing with a spin torque nano-oscillator. Using time multiplexing in pre- and post-processing, a single spin torque nano-oscillator gives state of the art performance as a reservoir in a reservoir computing scheme. 

(c) Schematic use of coupled nano-oscillators for vowel recognition. The input is represented by the frequencies of two microwaves applied through a stripline to the oscillators. The natural frequencies of the oscillators are tuned by dc bias currents through the devise. These can be tuned so that the synchronization pattern between the oscillators corresponds to the desired output.

Figure 3

(a) Schematic skyrmion structure. The magnetization direction of a single skyrmion is schematically given both by the directions of the arrows and the color coding, ranging from blue for magnetization up, through white for in-plane magnetization directions, to red for magnetization down. (b) Simulated skyrmion assembly. A reservoir computing scheme based on skyrmions in a random potential makes use of the distortions of the assembly due to current flow to provide the necessary non-linearity and memory.

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References :

1. Big data needs a hardware revolution. Nature (2018). doi:10.1038/d41586-018-01683-1 

2. Furber S Large-scale neuromorphic computing systems. J. Neural Eng 13, 051001 (2016). [PubMed: 27529195] 

3. Indiveri G et al. Neuromorphic silicon neuron circuits. Neuromorphic Eng 5, 73 (2011). 

4. Locatelli N, Cros V & Grollier J Spin-torque building blocks. Nat. Mater 13, 11–20 (2014). [PubMed: 24343514] 

5. Grollier J, Querlioz D & Stiles MD Spintronic Nanodevices for Bioinspired Computing. Proc. IEEE 104, 2024–2039 (2016).

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The Fundamental Conundrum About The Basic Reality in Quantum Physics By Management Practicalintroduction

What is quantum physics? Put simply, it’s the physics that explains how everything works: the best description we have of the nature of the particles that make up matter and the forces with which they interact.

Quantum physics underlies how atoms work, and so why chemistry and biology work as they do. You, me and the gatepost – at some level at least, we’re all dancing to the quantum tune. If you want to explain how electrons move through a computer chip, how photons of light get turned to electrical current in a solar panel or amplify themselves in a laser, or even just how the sun keeps burning, you’ll need to use quantum physics.

The difficulty – and, for physicists, the fun – starts here. To begin with, there’s no single quantum theory. There’s quantum mechanics, the basic mathematical framework that underpins it all, which was first developed in the 1920s by Niels Bohr, Werner Heisenberg, Erwin Schrödinger and others. It characterises simple things such as how the position or momentum of a single particle or group of few particles changes over time.

But to understand how things work in the real world, quantum mechanics must be combined with other elements of physics – principally, Albert Einstein’s special theory of relativity, which explains what happens when things move very fast – to create what are known as quantum field theories.

Three different quantum field theories deal with three of the four fundamental forces by which matter interacts: electromagnetism, which explains how atoms hold together; the strong nuclear force, which explains the stability of the nucleus at the heart of the atom; and the weak nuclear force, which explains why some atoms undergo radioactive decay.

Over the past five decades or so these three theories have been brought together in a ramshackle coalition known as the “standard model” of particle physics. For all the impression that this model is slightly held together with sticky tape, it is the most accurately tested picture of matter’s basic working that’s ever been devised. Its crowning glory came in 2012 with the discovery of the Higgs boson, the particle that gives all other fundamental particles their mass, whose existence was predicted on the basis of quantum field theories as far back as 1964.

Conventional quantum field theories work well in describing the results of experiments at high-energy particle smashers such as CERN’s Large Hadron Collider, where the Higgs was discovered, which probe matter at its smallest scales. But if you want to understand how things work in many less esoteric situations – how electrons move or don’t move through a solid material and so make a material a metal, an insulator or a semiconductor, for example – things get even more complex.

The billions upon billions of interactions in these crowded environments require the development of “effective field theories” that gloss over some of the gory details. The difficulty in constructing such theories is why many important questions in solid-state physics remain unresolved – for instance why at low temperatures some materials are superconductors that allow current without electrical resistance, and why we can’t get this trick to work at room temperature.

But beneath all these practical problems lies a huge quantum mystery. At a basic level, quantum physics predicts very strange things about how matter works that are completely at odds with how things seem to work in the real world. Quantum particles can behave like particles, located in a single place; or they can act like waves, distributed all over space or in several places at once. How they appear seems to depend on how we choose to measure them, and before we measure they seem to have no definite properties at all – leading us to a fundamental conundrum about the nature of basic reality.

This fuzziness leads to apparent paradoxes such as Schrödinger’s cat, in which thanks to an uncertain quantum process a cat is left dead and alive at the same time. But that’s not all. Quantum particles also seem to be able to affect each other instantaneously even when they are far away from each other. This truly bamboozling phenomenon is known as entanglement, or, in a phrase coined by Einstein (a great critic of quantum theory), “spooky action at a distance”. Such quantum powers are completely foreign to us, yet are the basis of emerging technologies such as ultra-secure quantum cryptography and ultra-powerful quantum computing.

But as to what it all means, no one knows. Some people think we must just accept that quantum physics explains the material world in terms we find impossible to square with our experience in the larger, “classical” world. Others think there must be some better, more intuitive theory out there that we’ve yet to discover.

In all this, there are several elephants in the room. For a start, there’s a fourth fundamental force of nature that so far quantum theory has been unable to explain. Gravity remains the territory of Einstein’s general theory of relativity, a firmly non-quantum theory that doesn’t even involve particles. Intensive efforts over decades to bring gravity under the quantum umbrella and so explain all of fundamental physics within one “theory of everything” have come to nothing.

Meanwhile cosmological measurements indicate that over 95 per cent of the universe consists of dark matter and dark energy, stuffs for which we currently have no explanation within the standard model, and conundrums such as the extent of the role of quantum physics in the messy workings of life remain unexplained. The world is at some level quantum – but whether quantum physics is the last word about the world remains an open question.

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How to Determine Quality Keywords for Writing Articles in Blog and Website

On this occasion, Mimin will share one way to determine quality keywords to be used as material for making articles later. But before that, let's first look at a brief explanation of keywords.

What are the keywords?

A Keyword is a word or series of words used by someone to search for information on the internet through search engines, such as Google, Yahoo, and Bing. Keywords are divided into two categories, namely short-tail keywords and long-tail keywords.

Short Tail Keyword (STK) is a keyword that only consists of one word, such as Facebook, Google, Yahoo, Twitter, Wikipedia, and others. This STK will later be connected to a blog or website along with the article, through their respective URLs.

Long Tail Keywords (LTK) are keywords that consist of several words and can be formed into a sentence, such as how to get rich, how to blog, what are keywords? cooking tutorials to be a good mother, the internet, and so on. This LTK is more directed at an article on a blog or website. In addition, LTK plays an important role in SEO because of its wider use compared to STK.

 

If you want to learn more about keywords, you can search for them directly on Google. Next, let's look at one way to determine quality keywords to be used as material for writing articles.

1. Open the Ubersuggest site or you can simply "Click Here".

2. Enter keywords either STK or LTK as you wish, such as AdSense or what is AdSense. Don't forget to change the country's location according to the location of the destination country and the language used by your blog or website. Next, click Search.

3. After that, scroll down and various keywords will appear related to the keywords you typed earlier. Here, you can see how many people found that keyword, how high the CPC (Cost Per Click) was for that keyword, and how difficult it was for you to find that keyword with other users.

4. To determine quality keywords, you can see how many publishers there are. The higher the number of publishers, the better the quality of the keyword. However, the competition will be more difficult for these keywords. Therefore, look for keywords that have a large number of publishers but little competition, to make it easier for you to be first in the search.

In addition, you can use keywords that have a small number of publishers and competitors to make it easier to enter the first page of searches. Even with keywords that have a small number of publishers, but manage to enter the first page of search results, this will increase your Alexa Global Rank, which makes your blog or website more popular.

5. After determining which keywords you will use, enter these keywords in the title of the article and also in the content of the article later.

Example:

For example, We will choose the keyword "AdSense on Blog" on the second page of the keyword data that we have entered previously, namely AdSense. Then we created a new article with the title "How to Register for AdSense on a Hosted Account Only Blog". After that, we changed the content of the article by including the keyword in the first 100 words to make it more SEO.

That's it for the article How to Determine Quality Keywords for Writing Articles This Time. Hopefully, it will be useful. Thank you all for visiting my blog and wait for the next update. 😊

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