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Higgs mass ~115 GeV and/or ~140 GeV? Dr Marko B Popovic Adjunct Assistant Professor Department of Physics Worcester Polytechnic Institute Physics Department Colloquium December 1, 2010 Lecture on High Energy Physics

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Large Hadron Collider (LHC) Investment: $9 billion Number of countries: over 100 Number of researchers: over scientists and engineers Built from 2001 to 2010 Became continuously operational on 30 March 2010 Tunnel, constructed between 1983 and 1988, is 27 kilometres (17 mi) long Located 1/3 in Switzerland and 2/3 in France Beam content: proton-proton collisions Collision Energy: 7 teraelectronvolts (TeV) (~35 larger than its predecessor LEP, or times larger than nuclear scale) Design luminosity is 10^34 cm−2s−1, providing a bunch collision rate of 40 MHz Data collection immediate, data analysis after months or (more realistic) years! Investment: $9 billion Number of countries: over 100 Number of researchers: over scientists and engineers Built from 2001 to 2010 Became continuously operational on 30 March 2010 Tunnel, constructed between 1983 and 1988, is 27 kilometres (17 mi) long Located 1/3 in Switzerland and 2/3 in France Beam content: proton-proton collisions Collision Energy: 7 teraelectronvolts (TeV) (~35 larger than its predecessor LEP, or times larger than nuclear scale) Design luminosity is 10^34 cm−2s−1, providing a bunch collision rate of 40 MHz Data collection immediate, data analysis after months or (more realistic) years! Show movie CERN-MOVIE

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LHC Fashion Statement

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Also unpleasant effective potential wells? Late Sidney Coleman, my professor of the Quantum Field Theory at Harvard University, worried about those…

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What I learned from Wikipedia The experiments at the Large Hadron Collider sparked fears among the public that the particle collisions might produce doomsday phenomena, involving the production of stable microscopic black holes or the creation of hypothetical particles called strangelets. Two CERN-commissioned safety reviews examined these concerns and concluded that the experiments at the LHC present no danger and that there is no reason for concern, a conclusion expressly endorsed by the American Physical Society. We don’t know if there is reason for concern. No one knows that. Stating that there is absolutely no reason for concern is a bit inappropriate. (my reaction)

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Planetary safety and Ultra High Energy Cosmic Rays? CERN document signed by number of eminent physicists including Nobel Prize laureates gives arguments for why the LHC will not blow up our planet. One of the main arguments are ultra high energy cosmic rays that haven’t damaged Earth. Unfortunately, the ultra high energy cosmic rays are everything but well understood. Their origin and fundamental properties are not known, their energy may be shockingly high* and their decay kinematics**, in particular decay products’ planarity, is still completely unexplained physical phenomenon. * While cosmic rays typically have energy in range 10 MeV to 10 GeV recorded were events with energies up to 3·10^8 TeV, i.e. with energy of a baseball (142 g or 5 ounces) traveling at 96 km/h (60 mph) [University of Utah Fly’s Eye detector]. ** Also, almost perfect planarity of 4 decay byproducts were observed for UHECR energies of couple TeV’s in more than 10% of collected UHECR data in an experiment at Pamir Mountains agreeing well with previous observations [London ‘60]. The Ultra High Energy Cosmic Rays are still mystery. They are shaky argument in support of the planetary safety!

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Reasons to worry and resolution -Mini black holes that do not just evaporate… -“New” type of stable mater (strangelets) -“New” energetically preferred Higgs ground states -“New” type of chain reactions -Something 5 th, 6 th, etc. ….probably the most responsible thing would be to have a list with all doomsday high energy collision theoretical scenarios, corresponding experimental signatures and finally an automatic real time data analysis and experiment shut down system. That would require couple of $ billions for computation. But maybe it is worth it!

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Why is Higgs so important? Higgs is anticipated to acquire a non-zero vacuum expectation value (VEV) in the early Universe when the average collision center of mass energies reach certain energy scale called the Electro-Weak Symmetry Breaking (EWSB) scale. This VEV then “breaks” the original electroweak symmetry mediated by four types of lights, one associated with the “hypercharge” gauge symmetry and another three associated with the “weak” gauge symmetries. As the Universe cools down photon remains massless while W and Z gauge bosons acquire masses. The Higgs scalar particle is the last Standard Model (SM), very unique ingredient that has still not been experimentally confirmed. Top reason why LHC was built!

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Higgs and particles’ masses The Higgs’s non-zero vacuum expectation value (VEV) is responsible for all particles’ mass generation, i.e. particle mass terms are couplings with Higgs “ether”. For fermions they are equal to Yukawa couplings times VEV, for gauge bosons they are equal to combination of gauge couplings times VEV. Finally, Higgs mass is equal to second derivative of effective potential at its minimum. A global fit to the precision electroweak data, accumulated in the last decade at LEP, SLC, Tevatron and elsewhere, limits Higgs mass to GeV, or GeV is taken into account, an upper limit of <182 GeV at 95% C.L. is obtained. [Particle Data Book]

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Are we sure that there is “new physics”? Hierarchy problem: - How to connect EWSB (assumed 10^3 GeV) and Planck (10^19 GeV) scales? - The scale-renormalized Higgs mass in 4D grows quadratically with scale. - If Higgs mass in the vicinity of each of the two scales is expected to be on the order of that energy scale the parameters of the theory might need to be fine-tuned. - A slight change of the parameters at one scale causes large changes at the other scale. Vacuum energy problem is among other caused by the non-zero VEV of the Higgs field traditionally expected to span the entire 4D space-time. This, however, implies a huge energy density everywhere and, hence, an enormously large space-time curvature. Similarly, if the Universe is described by an effective local quantum field theory down to the Planck scale, then one would expect a cosmological constant of the order of Mpl^4. The measured cosmological constant is smaller than this by a factor of 10^(-120). This discrepancy is termed "the worst theoretical prediction in the history of physics!" Well, Higgs is still missing and there are two well known serious theoretical problems.

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Motivation for Higgs and order 1 TeV “new physics” The hierarchy problem becomes quadratically more acute above the 1TeV scale. common wisdom

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Energy scales and plan for the rest of this lecture 1 GeV 200 MeV Nuclear QCD scale Proton mass 80 GeV 91 GeV W mass Z mass Top quark mass EWSB VEV 173 GeV 246 GeV 1 TeV EWSB Transition 7 TeV LHC collisions Planck mass TeV I will introduce one more, i.e. third SM problem. A I will provide resolution for all three problems. B I will argue that EWSB scale is roughly 1 TeV. C I will predict both Higgs and top quark masses. D I will explain why Higgs may have two distinct, 2D and 4D like experimental manifestations. E

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Higgs Propagator Definition of ordinary particle mass Time like x t Definition of tachyon particle mass Space like x t In units Higgs Effective Mass effective mass in the propagator at scale

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Tachyon – bad! Typically signaling perturbative expansion of scalar field about the incorrect ground state. Example SM Mexican Hat Potential

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Third problem in the Standard Model La la land Based on the Standard Model (SM) Renormalization Group Equations (RGE) the Effective Higgs mass ^2 changes sign at ~1 TeV. Higgs appears tachyonic! 10 TeV 7 TeV 5 TeV 2 TeV 1 TeV 200 GeV 100 GeV SM RGE LHC LEP Large Hadron Collider (2010-) Large Electron Positron (-2000) (Popovic 2001; 2002; 2010) A Same result obtained with both MS bar and hard cutoff regularization!

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The Higgs mass zero crossing (HMZC) 0.8 TeV

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The HMZC scale (enlarged) A C 0.8 TeV

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HMZC scale = EWSB scale If there is no time period when the early Universe is dominated by the effective tachyon physics then, necessary, HMZC scale is to be identified with EWSB scale. Other Option 1 Other Option 2 EWSB HMZC Dominated with tachyons during non-zero VEV phase Dominated with tachyons during zero VEV phase C VEV=0 GeV VEV=246 GeV VEV=0 GeV VEV=246 GeV B + 1/3

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Other two problems Both hierarchy and vacuum energy problems may be eradicated If EW symmetry breaking takes place in 2D which “embeds” the physical propagation in 4D. The leading divergences in 2D are only logarithmically divergent and therefore the large hierarchy can be more easily attained. Moreover, the Higgs scalar field doesn’t need to be non-zero constant in the entire 4D space hence leading to reasonable 4D space-time curvature. The non-Abelian gauge fields carry charge that causes their propagation to mimic the 1-space dimensional flux providing confinement between static charges. Actually, could EWSB be a consequence of dynamic process like top – anti-top condensation? This condensate has exactly the right quantum numbers as Higgs. B 2/3

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Top condensation consistent with gluon and Higgs scalar mediation? Theoretical prediction (Popovic 2010) Current world average

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Top quark and Higgs masses As suggested by Nambu one should expect Higgs particle like excitation on the order of 2 top quark masses ~350 GeV. Unfortunately that is way outside the current limits on Higgs! What if top quark is also composite?

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Composite Particles Model (CPM) In CMP, one expects the QCD assisted with a “new” physics to create: (1)Higgs, “meson”-like particle consisting of two “fundamental” fermions, (2)top quark, “baryon”-like particle consisting of three “fundamental” fermions and (3)top condensates breaking the electroweak symmetry at the HMZC scale. (Popovic 2002; 2010)

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Composite Movers Model or Composite Particles Model (CPM) This is artistic representation of top - anti-top condensate. This is artistic representation of Higgs scalar particle. According to Popovic (2002, 2010) one should expect Higgs like excitation on the order of ~350 GeV / 3 or ~115 GeV And what about the “more fundamental” fermion mass? 1/3 top quark mass? D

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Zero-VEV boundary condition Obtained by requiring simultaneous cancellation of leading divergences in 2D and 4D consistent with both propagating and non-propagating Higgs and correct counting of gauge boson polarization degrees of freedom in 2D and 4D in accordance with zero-VEV. leading divergences

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Zero-VEV boundary condition (continued) SAME!

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Zero-VEV boundary condition (continued) Exactly as anticipated by Composite Particles Model (CPM)!!!

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Transition D

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Transition (continued) D Radiatively generated heavy top quark mass Cancellation of leading divergences

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Transition (continued) ! D assume z=1

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From 2D to 4D D

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~115 GeV and ~140 GeV Higgs LEP observed a number of suspicious events in the vicinity of 115 GeV, at the center of mass energies a bit above 206 GeV, just before the accelerator was shut down. And there is something quite “magical” about the 140 GeV Higgs; three curves come together at almost exactly the same scale which is equal to the Planck mass scale… (!) D !

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~115 GeV and ~140 GeV Higgs Duality E I consider the 2D 115 GeV Higgs as “naked” Higgs excitation whereas the 4D 140 GeV Higgs is Higgs excitation “dressed” in the ground state. I believe that both excitations may be experimentally confirmed. However the reality may be only one or none. And that is yet to be tested.

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Conclusion Results presented here are summary of Popovic (2002; 2010). The SM tachyon problem is introduced and resolved by requiring EWSB=HMZC. The Composite Particle Model predicts the EWSB mediated by condensation of fundamental fermion like excitations in 1-space and 1-time dimensions. The “naked” 2D Higgs mass is expected to be ~115 GeV whereas the ground state “dressed” 4D Higgs mass is expected to be ~140 GeV. These predictions are in excellent agreement with cancellation of leading divergences in both 2D and 4D. The hierarchy problem is resolved both by cancellation of leading divergences and fact that this is dynamic condensation process. The vacuum energy problem may be resolved as, due to 2D nature of process, it is not necessary to assume ground state that is uniform and homogenous in entire 4D space.

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