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The origin of mass and the experiments on future high energy a elerators. B.L.Ioffe 6 0 Institute of Theoreti al and Experimental Physi s, 0 2 B.Cheremushkinskaya 25, 117218 Mos ow,Russia n a J Abstra t 0 3 1 v The visible universe (cid:21) it is the universe of nu leons and ele trons. The appearan e of 0 nu leon mass is aused by the violation of hiral symmetry in quantum hromodynami s 5 (QCD). For this reason, the experiments on high energy a elerators annot shed light on 2 1 the origin of the matter in the visible universe. The origin of the mass of matter will be 0 larified, when the me hanism of hiral symmetry violation in QCD will be elu idated. 6 0 / h PACS numbers: 12.15. Ff, 12.38 Aw, 14.80. Bn p - 7×7 p The Large Hadroni Collider (LHC) with TeV proton olliding beams is now under e onstru tion at CERN. It is planned, that the a elerator will be put into operation in 2007, h v: the experiments will start in 2008. The possibilities of onstru tione+oef−other high energy i a elerators are under dis ussion: the lineara elerator with olliding beams of energies X 0.5 - 1.0 TeV, muon and proton olliders. The goal of experiments on future high energy r a a elerators is to investigate physi s beyond the Standard Model, i.e, the study of pro esses at energies ina essible on existing a elerators, the sear h for parti les, whi h were not found till now, but expe ted: Higgs bosons, supersymmetri parti les et . The Standard SU(3) × SU(2) × (U(1) SU(3) Model is the gauge theory, where orresponds to quantum SU(2)×(U(1) hromodynmi s (cid:21) the theory of strong intera tions, (cid:21) to ele troweak theory, whi h unites the ele tromagneti and weak intera tions. The experiments, performed on high energy a elerators, whi h are (or were) in operation, agree with the Standard Model and give no indi ations for the presen e of any new physi s beyond it. The dis overy of neutrino os illations, the first data on the existen e of massive majorano neutrino, as well as the astrophysi al data (cid:21) the existen e of dark matter (cid:21) indi ate the eviden e for su h new physi s. For this reason, great expe tations are due to experiments on LHC and other future a elerators. One of the most important problems, unsolved in the ourse of the investigation of the Standard Model, the problem, whi h, as it is expe ted, will be solved by LHC experiments (and other future a elerators) is the problem of the origin of parti le masses. As it was mentioned in the report by De Roe k, J.Ellis and F.Gianotti [1℄, devoted to experiments on future a elerators, "The most prominent areas, where the Standard Model leaves unsolved 1 problems, in lude the origin of parti le masses ...". In the joint proposal of experiments on SU(3)×SU(2)×U(1) LHC, presented by ATLAS and CMS ollaborations [2℄ it said: "The gauge intera tions of the Standard Model ... give no explanea+tei−on of the origin of parti le masses".Themainproblemoftheinvestigationsonthelinear ollideris:"Theme anism of el troweak symmetry breaking, in other words, what is the origin of mass in parti le physi s"[3℄. This problem is formulated in a similar way in other papers and reports devoted to experiments on future a elerators (see, e.g. [4℄, [5℄). Thestatements, presented above, arebased on theinitialideaoftheStandardModel.The violation of the gauge SU(2) symmetry, whi h is needed in the Standard Model in order to W Z ϕ get masses to and intermediate bosons, is realized by introdu ing the s alar field , the ϕ W Z SU(2) doublet. The s alar field intera ts with the fields of , quarks, leptons and itself. ϕ = ϕ 0 It is supposed, that its self-a tion potential has a minimum at non-zero value , whi h ϕ is onstant in spa e and time. The field is represented as the expansion near the minimum ϕ = ϕ + χ χ 0 of the potential , where is the quantized field, the quants of whi h are Higgs bosons. Theϕmasses of intermediate bosons, quarksga2ϕnd2Wle2ptgo2nϕs2aZr2ise dhueϕto¯l lthe h onϕstqa¯nqt 0 1 0 2 0 li 0 i i qi 0 i i s alar field be ause of the presen e of the terms , , , l ,q h ,h i i li qi in the intera tion Lagrangian. (Here are the fields of leptons and quarks, are the oupling onstants). Therefore, the observation of Higgs boson and its intera tions with quarks and leptons will explain the origin of quark and lepton masses. Just su h a possibility was taken in mind in the ited above statements. The goal of this paper is to pay attention on the fa t, that elu idation of the problem of Higgs boson existen e and larifi ation of the stru ture of its intera tions with quarks (and even more generally, the study of intera tions at high energies) has no relation (more pre isely, has very little relation) to the origin of mass of parti les of visible universe. The visible world - stars, planets, gala ti s, all bodies surrounding us, are built from protons, nu lei and ele trons. The ele trons ontributions to the mass of the matter is negligiblysmall (cid:21) less than 0.1 %. Therefore, in order to understand the origin of the mass of the observable world, it is ne essary to larify the origin of nu leon mass. (I leave temporarily aside the u d problem of the mass of dark matter). The nu leon onsists of - and -quarks. But the u d m +m ≈ 10 MeV u d masses of - and -quarks are small, and their mass ontributes a small m ,m → 0 u d part, about 1-2 % to the nu leon mass. It an be shown, that in the formallimit , the nu leon mass pra ti ally does not hange. The nu leon mass arises due to spontaneous violation of hiral symmetry in QCD and an be expressed through the hiral symmetry violating va uum ondensates [6℄. There is an approximate formula, whi h expresses the nu leon mass through quark ondensate [6℄, [7℄, [8℄: 1/3 m = −2(2π)2h0|q¯q|0i " # (1) m h0|q¯q|0i q u Here - is the nu leon mass, is the quark ondensate, is the field of - or d -quarks. (The re ent reviews of the modern status of hiral symmetry in QCD, its violation and the problem of proton mass were given in [9℄, [10℄.) The expression for quark ondensate (the Gell-Mann-Oakes-Renner formula) 1 m2f2 h0|q¯q|0i = − π π 2 m +m (2) u d 2 follows from hiral symmetry in QCD ( onservation of the axial urrent violated by quark m f π π masses). Here m ,amnd→ 0aremt2he pion mass and de ay onstant. In the lhi0m|q¯itq|o0fiquark masses going to zero, u d π is also going to zero in su h a way that is a onstant h0|q¯q|oi = i−n(t2h5i4sMlimeVit).3T±he10re% ent determination of the value of quark ondensate gamve=[101℄.09GeV . The substitution of this value into (1) results in in m = 0.94GeV omparison with the experimental value . Therefore, in order to lear up the origin of nu leon mass, it is ne essary to larify the me hanism of hir∼al 1syfmermmeitr=y v1i0o−la13ticomn in QCD. The hiral symmetry violation pro eeds at large distan es a∼nd10i−s17ncomt related to experiments at high energies, where the domain of small distan es is investigated. Clarifi ation of the me hanism of hiral symmetry violation in QCD (cid:21) is the theoreti al problem. Perhaps, latti e al ulation would be helpful here, as well as the experiments on heavy ions ollisions at high energies, from whi h some information on phase transitions in QCDD ould be extra ted. However, the baryon density is high in µ µ = 0 su h experiments, i.e., the hemi alpotential is large, whereas in va uum . The phase µ µ = 0 transition at finite and ould be quite different [12℄, [13℄. The mass of the ele tron arises in the Standard Model due to intera tion with the Higgs field. Therefore, the origin of the ele tron and the proton mass is quite different and their strong distin tion is not surprising. A short remark about dark matter. Its nature is unknown. Perhaps, dark matter parti les are very heavy and weakly intera t with usual matter. In this ase it is unprobably, that their mass arises be ause of intera tion with the Higgs field. I am thankful too A.V.Samsonov for olle tion of the material on planned experiments on future a elerators. This work was supported in part by CRDF Cooperative Grant Pro- gram, Proje t RUP2-2621-MO-04 and the funds from EC to the proje t "Study of Strongly Intera ting Matter"under ontra t 2004 No R113-CT-22004-506078. Ñïèñîê ëèòåðàòóðû [1℄ De Roe k A, Ellis J, Gianotti F Physi ss Motivations for Future CERN A elerators, report presented to CERN Coun il in De ember 20011, hep-ex/0112004 [2℄ Branson j G, Denegri D, hin hliffe I et al. (ATLAS Collab., CMS Collab) Eur.Phys.J. C4 No.1 (2004) hep-phh/0110021 [3℄ Ri hard F Int.J.Mod.Phys C4 1240 (2004) hep-ph/0312020 [4℄ Simmons E H Le tures presented at TASI 2004, Univ. of Colorado, Boulder, CO, June 4-30, 2000, hep-ph/0011244 [5℄ Froggatt F The origin of mass Le tures at 6-th International Mos ow S hool of physi s, ITEP, February 18-26, 2003, Survey High Energy Phys 18 77 (2003), hep-ph/03071138 [6℄ Ioffe B L Nu l.Phys. 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