A new bound state. A theory developed by Holger Bech Nielsen and Don Bennett, Colin Froggatt, Larisa Laperashvili, et al.

Transcription

1 A new bound state A theory developed by Holger Bech Nielsen and Don Bennett, Colin Froggatt, Larisa Laperashvili, et al. Presented at Basic16, January 2016, by Astri Kleppe

2 MPP Extensive and intensive parameters. MPP as fine tuner. Bound states come about from the interaction between the Higgs boson and 12 top quarks, with a mass 12 M t. Such bound states, called T fireballs or T balls ( ) or just S, proposed long time ago by Holger B. N. as DM candidates. Proposal that the Tunguska event in 1908 vas due to a cm large ball of a condensate of such states. Creating Bose Einstein condensate by putting more and more t and together, the total binding energy might compensate for the quark and antiquark masses, so the whole bunch of such pairs eventually constitutes a tachyonic bound state. A tachyonic state per se does not really exist instead it constitutes an instability a tachyonic condensate. A Bose Einstein condensate of such bound states can thus be expected, corresponding to a new phase. Corrections from the new bound state vacuum to the Higgs mass ensure the stability of our MPP

3 MPP The basic assumption of the Multiple Point Principle (MPP) scenario is that the vacuum exists in several phases, and that Nature seeks out a point in the action parameter space where a maximal number of phases come together. At this multiple point the vacuum is maximally degenerate and the running gauge coupling constants assume "multiple point critical values" at Planck scale. In this way the MPP scheme supplies an explanation for the fine tuning of parameter values. Within this scenario, Holger Bech Nielsen and Colin Froggatt some years ago suggested the existence of a bound state formed by 6 top quarks and 6 anti top quarks, held together mainly by Higgs particle exchange, and so strongly bound that it can become tachyonic and condense in one of several degenerate vacua. 6t 6 If we live in this vacuum, such a bound state would be seen via its mixing with the Higgs particle. It would have essentially the same decay branching ratios as a Higgs particle of the same mass, but the total lifetime and production rate would deviate from those of a genuine Higgs particle. The Multiple Point Principle (MPP) postulates that there are many vacuum states with approximately the same energy density ( zero cosmological constant). The vacuum is assumed to exist in several phases corresponding to different physical behaviors that can be distinguished on the basis of the physics as viewed at a particular scale. Nature seeks out a "multiple point" in the action parameter space where a maximal number of vacuum phases come together. At this multiple point the vacuum is maximally degenerate and the running gauge coupling constants assume "multiple point critical values" at Planck scale. This allows the MPP scheme to account for the fine tuning of parameter values.

4 Analogy: an equilibrium system enclosed in an insulated container containing water in its three phases. This system has fixed extensive parameter values, i.e. the volume, the energy and the mole number of water. The system is very stable, since there is a whole range of parameter values at which the average energy and the average volume per molecule for which the three phases continue to coexist. The triple point of water spanned by the intensive parameters temperature and pressure is analogous to a MPP multiple point. The point is that at a multiple point, a point of phase transitions, the extensive parameters have values within certain ranges. In this sense, the extensive parameters span a volume in extensive parameter space, which corresponds to a point in intensive parameter space. This is fine tuning! MPP as fine tuner

5 MPP as fine tuner The MPP scheme supplies a unification of different fine tuning problems, like the problem of the hierarchy between the Planck scale and the electroweak scale. Λ Planck / Λ EW In order to "solve" the hierarchy problem, need a device that is sensitive to physics at the electroweak scale. In MPP this is obtained by having different vacuum phases such that the physics only deviate EW scale. to "solve" the large scale ratio problem using MPP we need a model with different vacuum phases that only deviate by the physics at the electroweak scale. The Bose Einstein condensate Different phases most easily obtained by having different expectation values of some scalar field, which really means different amounts of some Bose Einstein condensate. We want a condensate that only involves physics at a certain low energy scale the electroweak scale: a condensate of bound states made of Standard Model particles like top quarks and anti top quarks in bound states. A condensate with energy density not so far from the electroweak scale. Suggestion: Strongly bound states made out of top quarks bound by Higgs fields or other particles, such that the energy scale of a condensate formed from them is by dimensional arguments connected to the scale of the Standard Model Higgs field vacuum v.e.v. (i.e. the electroweak scale). t The 6 +6 bound state With several degenerate vacua in the pure SM, one of the vacua is due to the condensation of an exotic meson consisting of 6 t and 6 quarks. Its binding is based on the collective effect of attraction between several quarks due to Higgs exchange. Assumed that 6 top quarks and 6 anti top quarks can bind by Higgs exchange so strongly as to become tachyonic and form a condensate. The 12 quarks bound state

6 The 12 quarks bound state The exchange of virtual Higgses between two quarks, between two antiquarks, or between a quark and an antiquark is always attractive. Around the top quark, due to the Higgs there is a certain reduction of the value of the v.e.v. Therefore the quark mass and thereby the energy of the quark Higgs interaction is somewhat diminished. Higgs field a bit pushed down effective local mass of another quark shrinks in this region, which is the same as an attraction between the quarks/antiquarks. In the neighbourhood of the top quark the Higgs field is like a Coulomb (or Yukawa) field, t and attract each other by Coulomb like potentials. Allows for a rough calculation of the pair binding energy by means of the Bohr formula. Binding energies The Bohr formula for atomic energy levels gives a crude estimate of the binding energy of a collection of t and. n n(n 1)/2 The binding energy of a collection of such particles grows as, whereas the total rest mass energy nm t of these n constituents obviously grows as n. with a large enough number of constituents, we should be able to achieve a situation where the total binding energy exceeds the rest mass energy. Only a limited number of constituents can be placed in the ground state S wave, and for constituents in the P wave, the pair binding energy decreases. The quarks however have two spin states and 3 colour states, so we can stuff together 2 3 = 6 t quarks into relative S waves, and likewise 2 3 = 6 antiquarks, so all in all we can have constituents in the S wave = 12 This is the crude estimate. One could in principle put in more quarks by letting them be in higher states, roughly 2s or 2p, their binding energy would however be weaker by a factor 4, since the higher states have a binding energy. 1/n 2 Consider the binding energy E1 of one quark to the remaining 11 constituents (treated as one particle like an atomic nucleus). Assuming that the radius be relatively small, use the Bohr formula for the binding energy for an atom with one electron and atomic number 11, replacing the electric charge with the top Yukawa coupling g t / 2,

7 E n ( ) Z = g2 /2 t = 4π which for the ground state S wave with 2 M reduced ( ) t Z g 2 t /2 2n 2 n = 1 4π, gives the estimate 2 ZM t 2(Z + 1)n 2 11 /12 = M t M reduced where t is the reduced mass of the top and is the top quark Yukawa coupling constant. The non relativistic binding energy of the 12 particle system is then E1 multiplied by 12 divided by 2 to avoid double counting. This however only gives the t channel of the Higgs exchange between the twelve constituents. The u channel contribution increases the binding energy by another factor ( )2, resulting in the total non relativistic binding energy due to Higgs exchange interaction Also taking gluon exchange into consideration increases the binding energy by a factor (15/11) 2, which finally gives ( 11 ) g /2 E1 = 2 2 t 11Mt 4π 24 E binding E binding ( ) 11g = 4 t π 2 ( ) 225g = 4 t 11π 2 M t M t g t Experimental support for the existence of T balls

8 Experimental support for the existence of T balls The 6 t+6 state is a scalar particle and a colour singlet. There is also a 6 t+5 state, which has the quantum nimbers of the t quark, and could be perceived as a 4th generation quark in the up sector. Call these bound states T balls, T f 6t+6 = 6t+5 There are 2 resonances, with masses around 300 ev and 750 GeV, respectively. The mass iss estimated to be. < /2 M f GeV If M s M H, M H = the Higgs mass, we would be able to observe decays of the type H 2Ts T f Such decays have not been observed. What nonetheless has been observed are 10 jets, which can be explained by T ball gluon interactions. Another observation that points towards the existence of two gammas, states is the decay of the Higgs into H γγ which has been observed in LHC. Data indicate that for this process the width, which can be interpreted as due to the presence of T balls. Γ (Observed) > Γ (StandardModel) The presence of the New Bound State

9 The presence of the New Bound State If the bound state of the 6 top + 6 anti top really exists, it can be treated as effectively a new fundamental particle to be included into diagrams, the most important diagram being which gives the main contribution to the Higgs self coupling, and thus modifies the Higgs selfinteraction so the Higgs mass gets somewhat changed compared to the "naive Standard Model", i.e. the Standard Model + MPP. Vacuum stability

10 Vacuum stability M H = 125 ± 0.5GeV The experimental value of the Higgs mass,, is intriguingly close to the minimum Higgs mass value that ensures absolute vacuum stability within the Standard Model. This on the other hand implies a vanishing Higgs quartic coupling ( λ) around the Planck scale. In the MPP approach, two vacua will have the same cosmological constant provided the top Yukawa coupling is about 1.1 ± 0.2 at the weak scale, in good correspondence with the experimental value A hierarchical scale ratio between the fundamental and weak scales of order. The vacuum stability condition The condition for absolute stability up to Planck scale is (G. Degrassi et al, [hepph] v2) M t (GeV ) M H 0.7 (GeV ) > ( ) 0.5( ) ± where is the estimated overall error. Combining in quadrature the theoretical uncertainty with experimental errors on and, we get M H C th M t α s > ± 1.8GeV M H α s ( M Z ) vacuum stability of the Standard Model up to Planck scale is excluded at 2 σ for < 126GeV In the "naive Standard Model", i.e. the Standard Model + MPP, the predicted Higgs mass is GeV. With the above diagram the predicted Higgs mass is pushed down to the observed 125 GeV a prediction from the assumption of MPP. C th The radius of the bound state

11 The radius of the bound state The correction of the "naive Standard Model" Higgs mass strongly depends on the radius b of the bound state, b being a radius defined in terms of the inverse Compton wavelength for the top quark. The biggest uncertainty in the correction of the Higgs mass comes from b. With a good estimate of b, we may claim to predict M s, the best estimates pointing at a mass close to the new resonance decaying into two photons at mass equal to 750 GeV. Form factors exponentially suppress the diagrams where are propagators. Consider a nonrelativistic situation of at rest emitting a Higgs G(H ) = 12g t 2 2M s For each such vertex, there is an exponential form factor F( ) = q 2 1 e 6 < r 2 > q 2 which diminishes the loop integral, giving T s = λ s 1 G(H ) 4π 2 ( ) r0m 2 s 4 1 ( 6g t M t ) π 2 b M s 4 If there is a resonance (with 300GeV or 750GeV ) which gives then a metastable vacuum is transformed into a stable vacuum. exact vacuum stability and exact MPP. Now where M s λ s 1 λ s 0.01, ( 6g t ξ) π 2 b ξ = M t M s 4

12 Vacuum stability corresponds to the condition or For the resonance with mass 750 GeV, we get ξ 1, and for the reonance with mass 300GeV we correspondingly get ξ 2 173/ This gives and b2. If both resonances contribute to ( ξ ) 4 b (6g t ) 4 ξ b, we have π b ξ / b1 (0.231/0.095) 2.43 (0.577/0.095) 6.07 ( ξ 1 ) b1 4 λ s ( ξ 2 ) 4 π b2 (6g t ) 4 which means that the vacuum stability condition is satisfied.

13 By MPP fine tuning, a condensate of the 750 GeV boson is organized to have energy density. The same fine tuning for the vacuum with a Higgs field of GeV also has energy density. For a mass around 750 GeV, a correction makes the two vacua degenerate for precisely = 125GeV vacuum. 0 M H = 6t GeV M s, a correction to the Higgs mass stability of our the instability of our vacuum that seems to result from the experimental Higgs mass is not really there. The two degenerate vacua stability. The bound state which would give this stability could be the newly found 2 γ boson of mass 750 GeV. 0