The last ice age peaked at 20,000 years ago. The people who survived in pockets of survivable territory started to repopulate Europe in the period from 14,000 to 7,000 years ago, called the Mesolithic era. Several ancient genomes are now available from that era. They suggest that the effective male population size prior to the repopulation of Europe was just 30 men.

Thus, modern humans only barely hung on through the Ice Age in Europe, and ultimately, their ancestry makes up a fairly modest share of modern European ancestry.

# Dispatches From Turtle Island

Observations That Transcend Law and Politics

## Sunday, March 29, 2015

## Friday, March 27, 2015

### The Latest Combined Higgs Boson Mass Measurement From The LHC

The most up to date available measurement of the Higgs boson mass combining ATLAS and CMS experiment data in two different channels each at the end of the first LHC run to get a single number is:

125.09 +/- 0.237 GeV/c^2.

The two sigma range for the Higgs boson mass is now: 124.61 GeV to 125.56 GeV.

This is a material improvement in the margin of error, which had previously hovered around 0.4 GeV. Some further improvement in the margin of error should come from the second run of the LHC.

This value disfavors the 2H=2W+Z mass formula by 3.7 standard deviations.

There is an argument that the "tree-level" mass of the Higgs boson is 123.114 GeV (half the Higgs vev) but that it is increased by higher order loop corrections that bring it to its experimental value. The "tree-level" estimate of the mass of the W boson is 78.9 GeV. If the percentage increase in mass due to higher order loop corrections for the Higgs boson from the tree level value is the same as the higher order loop corrections of the W boson to the experimental value, then the implied Higgs boson mass value would be 125.43 GeV which is consistent at a 1.4 sigma level with the latest combined mass measurement. No published source actually calculates these higher order loop adjustments, however. While the actual higher order loop calculation is probably of that order of magnitude, it could easily be higher or lower. The claim is plausible, but requires further investigation. If the higher order loop corrections produced a value consistent with 124.65 GeV, that would be remarkable indeed as discussed below.

The hypothesis that the sum of the squares of the Higgs boson mass, W boson mass and Z boson mass equals half of the Higgs vev (using a global fit value of 80.376 GeV for the W boson mass) implies a Higgs boson mass of 124.65 GeV, which is within two sigma of the current measurement.

Using the 80.385 GeV PDG value of the W boson mass and assuming that the sum of squares of boson mass equals one half of the square of the Higgs vev implies a Higgs boson mass of 124.65 GeV as well, so the difference created by that assumption is too small to matter.

This suggests that the quantum corrections to the Higgs boson mass may indeed be very highly fine tuned making supersymmetry unnecessary to address that seemingly unlikely reality.

As discussed below, there is some tension between the best fit Higgs boson mass measurement and the best fit top quark measurement (under the assumption that the sum of the square of all fundamental particle masses equals to the square of the Higgs vev), with the Higgs boson measurement implying a higher than measured top quark measurement. But, these tensions are within the margins of error in the measurements. The latest combined best fit value of the top quark mass (i.e. 173.34 GeV) would imply a Higgs boson mass of 125.60 GeV, which is just outside the two sigma band of Higgs boson masses based upon the most recent measurement.

This also significantly tightens the expected value of the top mass from the formula that the sum of the square of each of the fundamental particle masses equals the square of the Higgs vaccum expectation value. The uncertainty in the Higgs boson mass had been the second greatest source of uncertainty in that calculation. The best fit for the top quark mass on that basis (using a global fit value of 80.376 GeV for the W boson rather than the PDG value) is 173.73 GeV (173.39 to 174.07 GeV within the plus or minus one sigma band of the current Higgs boson measurement). If the the sum of the square of the boson masses equals the sum of the square of the fermion masses the implied top quark mass is 174.03 GeV if pole masses of the quarks are used, and 174.05 GeV if MS masses at typical scales are used.

That compares to the latest top quark mass estimate from ATLAS of 172.99 +/- 0.91 GeV. The latest combined mass estimate of the top quark (excluding the latest top quark mass measurement estimate from ATLAS) is 173.34 +/- 0.76 GeV.

But, particles in this mass range would greatly distort the expected cross-sections of Higgs boson decays in ways that would probably already be detectable. Any such particle has been ruled out by W and Z boson decays to the extent that it can be produced by decays of these particles, and if they were present in Higgs boson decays would dramatically reduce, for example, the expected cross-section of bottom quark pairs from Higgs boson decays (which is the largest single cross-section from Higgs boson decays, making up about two-thirds of them, although this cross-section is hard to measure due to significant backgrounds that also produce bottom quark pairs). Particles with masses of 10 MeV or less, in contrast, would have only a modest impact on the decay patterns observed in Higgs bosons decays, but would still have to be sterile as to W and Z boson interactions.

Another interesting possibility is that baryons could contribute to the fermion side, and that mesons could contribute to the boson side, rather than just the fundamental particles. My intuition is that this would not work, but I haven't run the numbers. Light baryons wouldn't add much, but the heaviest baryons with B quarks would make a significant contribution. Still, order of magnitude, it isn't impossible.

Another issue is which masses we should be using: pole masses or masses at a single consistent mass scale. Quark and lepton masses get slightly lower at higher energy scales. The Higgs boson mass declines more rapidly with higher energy scales. I think, but don't know, that the W and Z boson masses also decrease faster the quark and lepton masses at higher energy scales.

Since the top quark is the predominant contribution to the fermion side of the equation, only the decline from the top pole mass to some energy scale above the top pole mass is relevant. But, since the fermion side is already "light" relative to the 50-50 expectation, any decline in the top mass hurts the balance (and would probably be less than 1% in addition to being less than the boson side reduction). On the boson side, a reduction of 0.185% from the current best fit values would bring the sum of the square of the masses to one half of the Higgs vev. This may understate the amount of actual renormalization reduction at plausible targets like the top quark mass and the Higgs vev.

The Higgs boson mass runs from 125 GeV at 125 GeV to zero at about 10^15 GeV, on a curve that is concave with respect to a log-linear relationship (i.e. masses are lower at every point except the end points relative to a log-linear relationship of Higgs boson mass and energy scale). This seems to suggest that the Higgs boson mass at 246 GeV should be more than 13% lower than the pole mass (i.e. about 108.8 GeV), which is far too much of a reduction to fit the formula and would favor using pole masses across the board, as would the Higgs boson mass at 173.35 GeV which should be more than 11% lower than the pole mass of the Higgs boson, if I have the calculations right. The 0.185% shift required would imply an energy scale of something less than 133.34 GeV (but more than 125.09 GeV), which doesn't make much sense under any theory.

Given how close the experimental masses are to the preferred values using pole masses, however, it isn't obvious that renormalized values are necessary.

But, if the apparent relationship does involve pole masses, then there is very little wiggle room indeed in the predicted values of the Higgs boson mass and top quark mass, although this can be relaxed a little if the sum of the square of the fundamental fermion masses need not be exactly equal to the sum of the square of the fundamental boson masses.

125.09 +/- 0.237 GeV/c^2.

*Analysis*The two sigma range for the Higgs boson mass is now: 124.61 GeV to 125.56 GeV.

This is a material improvement in the margin of error, which had previously hovered around 0.4 GeV. Some further improvement in the margin of error should come from the second run of the LHC.

This value disfavors the 2H=2W+Z mass formula by 3.7 standard deviations.

There is an argument that the "tree-level" mass of the Higgs boson is 123.114 GeV (half the Higgs vev) but that it is increased by higher order loop corrections that bring it to its experimental value. The "tree-level" estimate of the mass of the W boson is 78.9 GeV. If the percentage increase in mass due to higher order loop corrections for the Higgs boson from the tree level value is the same as the higher order loop corrections of the W boson to the experimental value, then the implied Higgs boson mass value would be 125.43 GeV which is consistent at a 1.4 sigma level with the latest combined mass measurement. No published source actually calculates these higher order loop adjustments, however. While the actual higher order loop calculation is probably of that order of magnitude, it could easily be higher or lower. The claim is plausible, but requires further investigation. If the higher order loop corrections produced a value consistent with 124.65 GeV, that would be remarkable indeed as discussed below.

The hypothesis that the sum of the squares of the Higgs boson mass, W boson mass and Z boson mass equals half of the Higgs vev (using a global fit value of 80.376 GeV for the W boson mass) implies a Higgs boson mass of 124.65 GeV, which is within two sigma of the current measurement.

Using the 80.385 GeV PDG value of the W boson mass and assuming that the sum of squares of boson mass equals one half of the square of the Higgs vev implies a Higgs boson mass of 124.65 GeV as well, so the difference created by that assumption is too small to matter.

This suggests that the quantum corrections to the Higgs boson mass may indeed be very highly fine tuned making supersymmetry unnecessary to address that seemingly unlikely reality.

As discussed below, there is some tension between the best fit Higgs boson mass measurement and the best fit top quark measurement (under the assumption that the sum of the square of all fundamental particle masses equals to the square of the Higgs vev), with the Higgs boson measurement implying a higher than measured top quark measurement. But, these tensions are within the margins of error in the measurements. The latest combined best fit value of the top quark mass (i.e. 173.34 GeV) would imply a Higgs boson mass of 125.60 GeV, which is just outside the two sigma band of Higgs boson masses based upon the most recent measurement.

*Implications for Top Quark Mass*This also significantly tightens the expected value of the top mass from the formula that the sum of the square of each of the fundamental particle masses equals the square of the Higgs vaccum expectation value. The uncertainty in the Higgs boson mass had been the second greatest source of uncertainty in that calculation. The best fit for the top quark mass on that basis (using a global fit value of 80.376 GeV for the W boson rather than the PDG value) is 173.73 GeV (173.39 to 174.07 GeV within the plus or minus one sigma band of the current Higgs boson measurement). If the the sum of the square of the boson masses equals the sum of the square of the fermion masses the implied top quark mass is 174.03 GeV if pole masses of the quarks are used, and 174.05 GeV if MS masses at typical scales are used.

That compares to the latest top quark mass estimate from ATLAS of 172.99 +/- 0.91 GeV. The latest combined mass estimate of the top quark (excluding the latest top quark mass measurement estimate from ATLAS) is 173.34 +/- 0.76 GeV.

*How big are the gaps?**The fermion side of the balance sheet could fit a particle as massive as 19 GeV if the fermion sides and boson sides must be equal, and about 16 GeV if they need not be equal, consistent with current particle mass data alone.*

But, particles in this mass range would greatly distort the expected cross-sections of Higgs boson decays in ways that would probably already be detectable. Any such particle has been ruled out by W and Z boson decays to the extent that it can be produced by decays of these particles, and if they were present in Higgs boson decays would dramatically reduce, for example, the expected cross-section of bottom quark pairs from Higgs boson decays (which is the largest single cross-section from Higgs boson decays, making up about two-thirds of them, although this cross-section is hard to measure due to significant backgrounds that also produce bottom quark pairs). Particles with masses of 10 MeV or less, in contrast, would have only a modest impact on the decay patterns observed in Higgs bosons decays, but would still have to be sterile as to W and Z boson interactions.

Another interesting possibility is that baryons could contribute to the fermion side, and that mesons could contribute to the boson side, rather than just the fundamental particles. My intuition is that this would not work, but I haven't run the numbers. Light baryons wouldn't add much, but the heaviest baryons with B quarks would make a significant contribution. Still, order of magnitude, it isn't impossible.

Another issue is which masses we should be using: pole masses or masses at a single consistent mass scale. Quark and lepton masses get slightly lower at higher energy scales. The Higgs boson mass declines more rapidly with higher energy scales. I think, but don't know, that the W and Z boson masses also decrease faster the quark and lepton masses at higher energy scales.

Since the top quark is the predominant contribution to the fermion side of the equation, only the decline from the top pole mass to some energy scale above the top pole mass is relevant. But, since the fermion side is already "light" relative to the 50-50 expectation, any decline in the top mass hurts the balance (and would probably be less than 1% in addition to being less than the boson side reduction). On the boson side, a reduction of 0.185% from the current best fit values would bring the sum of the square of the masses to one half of the Higgs vev. This may understate the amount of actual renormalization reduction at plausible targets like the top quark mass and the Higgs vev.

The Higgs boson mass runs from 125 GeV at 125 GeV to zero at about 10^15 GeV, on a curve that is concave with respect to a log-linear relationship (i.e. masses are lower at every point except the end points relative to a log-linear relationship of Higgs boson mass and energy scale). This seems to suggest that the Higgs boson mass at 246 GeV should be more than 13% lower than the pole mass (i.e. about 108.8 GeV), which is far too much of a reduction to fit the formula and would favor using pole masses across the board, as would the Higgs boson mass at 173.35 GeV which should be more than 11% lower than the pole mass of the Higgs boson, if I have the calculations right. The 0.185% shift required would imply an energy scale of something less than 133.34 GeV (but more than 125.09 GeV), which doesn't make much sense under any theory.

Given how close the experimental masses are to the preferred values using pole masses, however, it isn't obvious that renormalized values are necessary.

But, if the apparent relationship does involve pole masses, then there is very little wiggle room indeed in the predicted values of the Higgs boson mass and top quark mass, although this can be relaxed a little if the sum of the square of the fundamental fermion masses need not be exactly equal to the sum of the square of the fundamental boson masses.

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