Or is it another instance of crying wolf? Hopefully not. Next date on your calendar: Dec. 13th.

http://blog.vixra.org/2011/12/02/higgs- ... o-125-gev/

An article in the Guardian, with several prominent physicists commenting on the rumour:

http://www.guardian.co.uk/science/blog/ ... boson-real

Exciting, in an unconfirmed sort of way

It looks like the rumour was confirmed, a Higgs boson at 125 GeV, with a 2.8 sigma/ Here's the best graph that includes Atlas+CMS+Tevatron (from Phil Gibbs)

Yes, but still needs more evidence. This is simply a hint, not a certainty.

Darkchilde wrote:Yes, but still needs more evidence. This is simply a hint, not a certainty.

yes, the truth is hard to deCern in this instance

Looks pretty good - 2.8 sigma would be good enough in medicine and biosciences.

3 sigma gives us a 95% confidence limit : confident that a real signal is present above background noise levels.

If ever the time 5 sigma is attained, we'd look back through the arxivs to find the 4wards looking physicists who have, by now, already calculated the remainder of MSSM (minimal supersymmetric extension to the standard model) and relaxed into thinking about measures and dimensions beyond. My bet is that those like twistor59, Darkchilde &c... have this covered.

newolder wrote:3 sigma gives us a 95% confidence limit : confident that a real signal is present above background noise levels.

If ever the time 5 sigma is attained, we'd look back through the arxivs to find the 4wards looking physicists who have, by now, already calculated the remainder of MSSM (minimal supersymmetric extension to the standard model) and relaxed into thinking about measures and dimensions beyond. My bet is that those like twistor59, Darkchilde &c... have this covered.

I don't really have a feel for these confidence levels. 2 sigma signals have come and gone in the past. I vaguely remember that Tevatron had some 2 point something hint of Higgs at 140 ish a while ago, but it disappered. Maybe the really significant thing is the correlation between the two experiments, but I don't know how you figure this into the confidence level.

twistor59 wrote:...snip...
I don't really have a feel for these confidence levels. 2 sigma signals have come and gone in the past. I vaguely remember that Tevatron had some 2 point something hint of Higgs at 140 ish a while ago, but it disappered. Maybe the really significant thing is the correlation between the two experiments, but I don't know how you figure this into the confidence level.

I think there is increased confidence that the 3 signals/hints of signals from fermilab, ATLAS & CMS are pointers to at least 1, 2 and/or maybe 3 or more extension(s) to SM. I'm also confident that the methods to combine the current measurements are chuntering(?) through wolfram-alpha as we write.

Arxived pdf seems to show that the simplest, Standard Model extension to relate to early hominids is probably that of minimal supersymmetry, but i cud eezilee b rong. Perhaps twistors achieve similar results with increased parsimony and I've missed an obvious step somewhere, again?

newolder wrote:3 sigma gives us a 95% confidence limit : confident that a real signal is present above background noise levels.

2 sigma ~ 95%, 3 sigma ~ 99.7%.

I have a question, if mass is due to higgs field, then gravity too should be due to the attraction between bodies in this field.

Made of Stars wrote:

newolder wrote:3 sigma gives us a 95% confidence limit : confident that a real signal is present above background noise levels.

2 sigma ~ 95%, 3 sigma ~ 99.7%.

5 sigma - ?

newolder wrote:

Made of Stars wrote:

newolder wrote:3 sigma gives us a 95% confidence limit : confident that a real signal is present above background noise levels.

2 sigma ~ 95%, 3 sigma ~ 99.7%.

5 sigma - ?

Moar!

(1 potato, 2 potato... Never mind...)

Albert Ross, Pessimist, b. 1958
heyho...

cavarka9 wrote:I have a question, if mass is due to higgs field, then gravity too should be due to the attraction between bodies in this field.

Nah, source of gravity is energy/momentum. Photons source gravity for example, but the Higgs field doesn't give them any mass.

twistor59 wrote:

cavarka9 wrote:I have a question, if mass is due to higgs field, then gravity too should be due to the attraction between bodies in this field.

Nah, source of gravity is energy/momentum. Photons source gravity for example, but the Higgs field doesn't give them any mass.

thanks for the reply a lot. One more question, how exactly is it that higgs field is supposed to be responsible for mass.

Also, (Gm1m2)/r^2 . Does it hold very well when relativistic correction is taken?.

cavarka9 wrote:

twistor59 wrote:

cavarka9 wrote:I have a question, if mass is due to higgs field, then gravity too should be due to the attraction between bodies in this field.

Nah, source of gravity is energy/momentum. Photons source gravity for example, but the Higgs field doesn't give them any mass.

thanks for the reply a lot. One more question, how exactly is it that higgs field is supposed to be responsible for mass.

Here’s a general rundown of the theory:

(1) in QM: x → operator
But to satisfy Relativity, in which time is on an equal footing with space, in QFT: x → parameter, and Φ(x) → operator. Now Φ(x), a function of x, is called the “field”.

(2) L = T – V. The Lagrangian plays an important role. From Noether’s theorem, we know that if the Lagragian is invariant under a symmetry, this symmetry points to a conservation law.

Corresponding to L there is a Hamiltonian, H = T + V. The Hamiltonian is known to measure the energy of a system.

(3)In classical mechanics, let v = dx/dt, then L = ½ mv2 – V(x). The corresponding Hamiltonian is, H = ½ mv2 + V(x). Quantizing this, (ℏ =1),we get the Schroedinger equation:

i∂Ψ(x)/∂t =( -½m∆ 2 + V(x)) Ψ(x).

(4) In Relativity, the energy equation is:

E2= p2c2 + m2c4.

Quantizing this, (c =1) yields the K-G equation:

½(∂μΦ)(∂μΦ) + ½mΦ2 = 0.

From this, the Lagrangian can be deduced as: L = ½ (∂μΦ) 2 – ½mΦ2.


(5) In QFT, the general Lagrangian is taken to be:

L = ½ (∂μΦ) 2 – V(Φ).

(6) Comparing (5) and (4), if V(Φ) contains any terms with Φ 2, its coefficient is taken to be the mass of the field quanta (particles).

Gauge theory:

From electromagnetism, it was known that Maxwell’s equations were gauge invariant. In QM, gauge invariance of the Lagragian involves three important steps:

(7) the wave function is transformed as Φ → eiqXΦ
(8) the operator ∂μ → ∂μ + iqAμ
(9) the electromagnetic field Aμ → Aμ - ∂μX

(10) In QED, in equation (5), V(Φ) → - ¼ Fμν Fμν, where Fμν = ∂μAν - ∂νAμ

If you apply, 7,8,9,10 to equation (5), you get the invariance of the Lagrangian under gauge transformation, in which the photon mediates the electromagnetic force. Note that the photon has no mass.

In the weak force, the bosons involved in the exchange have mass, and one had to figure out how to include a mass term, keeping the Lagrangian gauge invariant.

There is where number (6) comes into play under the notion of SPONTANEOUS SYMMETRY BREAKING.



Higgs Mechanism:

Basically, I will only look at U(1) symmetry. Electroweak interactions need a U(1) x SU(2) symmetry, but SU(2) requires 2 by 2 matrices, and the software on this forum is inadequate to deal with matrices. But you can get the flavor just by doing U(1) symmetry and how mass is introduced in the Lagrangian of equation (5).

I will rewrite this equation as:

(11) L = ∂μΦ† ∂μΦ - ¼ Fμν Fμν – V(Φ†Φ).

(12) where V(Φ†Φ) = (m2)/(2φ2) [Φ†Φ - φ2 ] 2

Three important things to note:

(13) The field Φ is now a complex number, denoted by (Φ1, Φ2) or Φ = Φ1 + iΦ2 ( i being the imaginary number, square root of – 1), and Φ† = Φ1 – iΦ2.

(14) the minimum field energy is obtained when Φ†Φ = φ2.

(15) The number of possible vacuum states is infinite. We break this symmetry by requiring that Φ is real, we take the vacuum state to be (φ,0), and expand:

Φ = φ + (½ ½)h

Substituting 7,8,9, 12, and 15 into 11, we get

(17) L = {(∂μ - iqAμ)( φ + (½ ½)h)}{( ∂μ + iqAμ)( φ + (½ ½)h} - ¼ Fμν Fμν - (m2)/(2φ2) [2½φh + ½h2 ]2

After calculating the Lagrangian, we separate it into two parts:

(18) L = Lfree + Lint

where

(19) Lfree = ½∂μh∂μh - m2h2 - ¼ Fμν Fμν + q2φ2AμAμ

All the remaining terms are lumped into Lint, which offer no interest.

So, we can see that by breaking the symmetry, we end up with two massive particles. In equation 19, the second term refers to a scalar particle with mass equal to 2½m, associated with h (the higgs field) and the fourth term, a vector boson with mass 2½qφ, associated with Aμ( the electromagnetic field).

NOTE: in the Weinberg electroweak theory with SU(2), equation 19 would have three extra terms for the vector boson instead of a single term, each one was identified with the W+, W -, and Z bosons. This prediction, which was confirmed subsequently in the following years, earned Weinberg, Salam and Glashow the Nobel prize.

zaybu wrote:

cavarka9 wrote:

twistor59 wrote:

Nah, source of gravity is energy/momentum. Photons source gravity for example, but the Higgs field doesn't give them any mass.

thanks for the reply a lot. One more question, how exactly is it that higgs field is supposed to be responsible for mass.

Here’s a general rundown of the theory:

(1) in QM: x → operator
But to satisfy Relativity, in which time is on an equal footing with space, in QFT: x → parameter, and Φ(x) → operator. Now Φ(x), a function of x, is called the “field”.

(2) L = T – V. The Lagrangian plays an important role. From Noether’s theorem, we know that if the Lagragian is invariant under a symmetry, this symmetry points to a conservation law.

Corresponding to L there is a Hamiltonian, H = T + V. The Hamiltonian is known to measure the energy of a system.

(3)In classical mechanics, let v = dx/dt, then L = ½ mv2 – V(x). The corresponding Hamiltonian is, H = ½ mv2 + V(x). Quantizing this, (ℏ =1),we get the Schroedinger equation:

i∂Ψ(x)/∂t =( -½m∆ 2 + V(x)) Ψ(x).

(4) In Relativity, the energy equation is:

E2= p2c2 + m2c4.

Quantizing this, (c =1) yields the K-G equation:

½(∂μΦ)(∂μΦ) + ½mΦ2 = 0.

From this, the Lagrangian can be deduced as: L = ½ (∂μΦ) 2 – ½mΦ2.


(5) In QFT, the general Lagrangian is taken to be:

L = ½ (∂μΦ) 2 – V(Φ).

(6) Comparing (5) and (4), if V(Φ) contains any terms with Φ 2, its coefficient is taken to be the mass of the field quanta (particles).

Gauge theory:

From electromagnetism, it was known that Maxwell’s equations were gauge invariant. In QM, gauge invariance of the Lagragian involves three important steps:

(7) the wave function is transformed as Φ → eiqXΦ
(8) the operator ∂μ → ∂μ + iqAμ
(9) the electromagnetic field Aμ → Aμ - ∂μX

(10) In QED, in equation (5), V(Φ) → - ¼ Fμν Fμν, where Fμν = ∂μAν - ∂νAμ

If you apply, 7,8,9,10 to equation (5), you get the invariance of the Lagrangian under gauge transformation, in which the photon mediates the electromagnetic force. Note that the photon has no mass.

In the weak force, the bosons involved in the exchange have mass, and one had to figure out how to include a mass term, keeping the Lagrangian gauge invariant.

There is where number (6) comes into play under the notion of SPONTANEOUS SYMMETRY BREAKING.



Higgs Mechanism:

Basically, I will only look at U(1) symmetry. Electroweak interactions need a U(1) x SU(2) symmetry, but SU(2) requires 2 by 2 matrices, and the software on this forum is inadequate to deal with matrices. But you can get the flavor just by doing U(1) symmetry and how mass is introduced in the Lagrangian of equation (5).

I will rewrite this equation as:

(11) L = ∂μΦ† ∂μΦ - ¼ Fμν Fμν – V(Φ†Φ).

(12) where V(Φ†Φ) = (m2)/(2φ2) [Φ†Φ - φ2 ] 2

Three important things to note:

(13) The field Φ is now a complex number, denoted by (Φ1, Φ2) or Φ = Φ1 + iΦ2 ( i being the imaginary number, square root of – 1), and Φ† = Φ1 – iΦ2.

(14) the minimum field energy is obtained when Φ†Φ = φ2.

(15) The number of possible vacuum states is infinite. We break this symmetry by requiring that Φ is real, we take the vacuum state to be (φ,0), and expand:

Φ = φ + (½ ½)h

Substituting 7,8,9, 12, and 15 into 11, we get

(17) L = {(∂μ - iqAμ)( φ + (½ ½)h)}{( ∂μ + iqAμ)( φ + (½ ½)h} - ¼ Fμν Fμν - (m2)/(2φ2) [2½φh + ½h2 ]2

After calculating the Lagrangian, we separate it into two parts:

(18) L = Lfree + Lint

where

(19) Lfree = ½∂μh∂μh - m2h2 - ¼ Fμν Fμν + q2φ2AμAμ

All the remaining terms are lumped into Lint, which offer no interest.

So, we can see that by breaking the symmetry, we end up with two massive particles. In equation 19, the second term refers to a scalar particle with mass equal to 2½m, associated with h (the higgs field) and the fourth term, a vector boson with mass 2½qφ, associated with Aμ( the electromagnetic field).

NOTE: in the Weinberg electroweak theory with SU(2), equation 19 would have three extra terms for the vector boson instead of a single term, each one was identified with the W+, W -, and Z bosons. This prediction, which was confirmed subsequently in the following years, earned Weinberg, Salam and Glashow the Nobel prize.

wow, thanks a lot. quarter way down and all of MSc was done, why dont they actually say things down instead of jumping to nitty gritty, too many details without a line of thought spoils many days. Thanks!