* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Looking for Magnetic Monopoles AT The Large Hadron Collider
Survey
Document related concepts
Renormalization wikipedia , lookup
Standard Model wikipedia , lookup
Nuclear physics wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Neutron magnetic moment wikipedia , lookup
Minimal Supersymmetric Standard Model wikipedia , lookup
Elementary particle wikipedia , lookup
Photon polarization wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Grand Unified Theory wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Cross section (physics) wikipedia , lookup
Transcript
Looking for Magnetic Monopoles AT The Large Hadron Collider Vicente Vento Universidad de Valencia-IFIC martes 26 de junio de 12 · Luis Epele · Huner Fanchiotti · Carlos García Canal · Vasiliki Mitsou martes 26 de junio de 12 · Introduction · Monopoles · Monopole Production and Detection · Monopolium · Monopolium Production and Detection · Moedal · Concluding Remarks martes 26 de junio de 12 · Introduction In 1984 Pierre Curie suggested that magnetic monopoles could exist martes 26 de junio de 12 Restores Electric-Magnetic Symmetry in Maxwell’s Equations martes 26 de junio de 12 Monopoles Dirac 1931 : Monopole and Quantum Mechanics: Magnetic Coulomb Field: B=gr/ 2 r Conflict when defining the vector potential The solution of a Genius martes 26 de junio de 12 A particle with charge, say an electron, traveling around some path P in a region with zero magnetic field (B = 0 = ∇ x A) must acquire a phase φ; given by: . The only way we would NOT see the Dirac string is if the wave function of the electron only acquired a “trivial phase” i.e. ∆Φ = 2π N (n =1,2,3..). That is, if: Charge Quantization martes 26 de junio de 12 Monopole Properties · The Dirac monopole is a point like particle · magnetic charge g = 68.5 e and no electric charge · Monopoles accelerate along field lines according to the Equivalent Lorentz Eqn. F = gB + ep × B / γm0 · The monopole mass is not predicted within the Dirac’s€ theory. martes 26 de junio de 12 Monopoles and Grand Unification · Grand Unified gauge theories predict Monopoles: ‘t Hooft and Polyakov (1974) discovered that monopoles are fundamental solutions to nonAbelian gauge “GUT” theories · These Monopoles have structure and no string singularity. · The field of the GUT monopole is B ~ g/r2 outside · The Mass m(GUT)M ≥ mX/g > 1017 GeV. not producible by particle accelerators · primordial monopoles present in the Universe · GUT monopoles can catalyze proton decay! martes 26 de junio de 12 There are models For “the desert” where monopoles appear in a mass range accessible to the LHC: · The electroweak Cho-Maison monopole · The Troost-Vinciarelli monopole · The model of Weinberg et al. · Superstring models We shall take a phenomenological approach and assume that the mass is a parameter martes 26 de junio de 12 Monopole Production and Detection e -> β g martes 26 de junio de 12 term to be sufficient, for our purposes. Guided by simplicity and phenomenological inspiration we introduce an effective theory which is finite and well defined and we call this proposal the β scheme. Note that the Ginzburg-Schiller scheme and the β scheme are in some sense complementary. The former is valid below the monopole threshold, while the latter above since β vanishes below threshold. The aim here is to study possible signals of magnetic monopoles at LHC. According to previous studies [?], the most promising mechanism is photon fusion. The elementary diagrams contributing to pair production are those in Fig. ??, where the explicit couplings have been shown. The photon-fusion elementary cross section is obtained from the well-known QED electron-positron pair creation cross section [?], simply changing the coupling constant (e → gβ ) and the electron mass by the monopole mass me → m, leading to ! ! " " 4 4 2 4 3−β 1+β π g (1 − β ) β 2 σ(γ γ → mm) = log − (2 − β ) , (4) 2 2m 2β 1−β Monopole Production Σ!Ω" where β is the monopole velocity, a function of the center-of-mass energy, E. In Fig. ?? we show the ω = E/2 m dependence of the adimensional functional form of Eq.(??) to 10. show the effect of the β g coupling. The solid curve corresponds to the electron-positron case, the dashed one to the monopole case which contains the β 4 factor. One should ! " e !e 1. notice the large effect associated with this factor in the vicinity of the threshold. LHC detectors, apart from the MoEDAL experiment [?], have not been designed m!m 0.1 4 0.01 0.001 1.0 1.5 2.0 3.0 5.0 7.0 10.0 Ω Figure 3: Adimensional functional form of the elementary photon-fusion cross section martes 26 de junio de 12 Production from photon fusion at Large Hadron Collider martes 26 de junio de 12 i) inelastic p + p -> X + X + M (photons radiated from partons) ii) iii) martes 26 de junio de 12 semielastic p + p -> p + X + M (one photon from partons the other from the other proton leaving the proton intact) elastic p + p -> p + p + M (both photons from protons) andapq'(s)= the choice ofdx) Ge& made is such Q2=1 dx2total dz) maximum the value of to be the mo mentioned above cross gedQtoscalars there pp 4m /sx& x& 4m /sx l 4m /s %'ith s be /4. er del applicable. cer structure function. There proton is a epforinelastic ferfermions. duction reads. charged These off'shel the hf thethat are photons sufficiently ~H+H cross for L semielastic section The (L in m We choose the logarithm to be pp (4). Eq. = = Q /Q2 ln( (z (z) ) is the inelastic where structure proton 2 F(2 deep Q &q &q r r 50 2~ z he choice of Ge& made the (4). is such that photo Q2=1 1 1 1 of the logarithm in the argument in Eq. W dz, dz, dx, — form as in more a compact write (3)given able. of Ge& Xis1 is Q2=1 by s/4 )pX 4mby/s m and4mthe/sxchoice 4m /sx z l l l ale Q has been chosen throughout cross sectionmodel for1 ppto ~H+H L )pX is1 given by be applicable. 1 (L = dx2 cross dz)for pp ~H+H )fq. dx)&~(x2, semielastic section The Q x2z, z2 ~(x&, (zz)8&r(x, g )fr&q(z, )fry. 4m 4m /sx x&z& 4m /sx 4m /s /sx& x& is now =Qsx, subprocess given by z2 energy z, l F~2(x, (4) (z2)o (z, z, , F~2(x, , Q')f, ( dz, dz, dx, o" — = — "'(s)=2f, beeno obtained 4m 4m /sx z elastic spectrum '„'&~(z) /s L*, photon dz, is the pi ',X and f4meither K or /sx e„='„ed4ml l/s dx,has —, 1 l 4m /sx l ~~ 4m /sx use an ap in we However, form of an integral [ll]. is=Qx&x2z&zzs. the inelastic structure function. T proton F(2 deep The structure functions have th which in expression given analytic ximate [12] 2, of the in We choose )fy(z) (z2)oyer(x)x2z)z2s), logarithm argument )f), (4). Q Eq. with is the is The inside now =Qsx, photon a WQ given quark. by spectrum z2. ergy z, +s is now =Q subprocess given by f„&q energy with 2. — Th results about 10%. to exact wn to reproduce (5) 2 and the choice of Ge& made m is Q2=1 obtained hasphoton been o has such been spectrum '„'&~(z) =— The elastic spectrum in'„'&~(z) is m use 2 2 we given by in 4)/$06. 00 2335 in [ll]. we However, form of an the integral .use 50 toabout be applicable. an apinthe[ll]. egral choiceHowever, of the2m scaleswe Q, in expression given analytic proximate ~H+H + ue of the momentum transfer cross for L [12] given semielastic section is which in (L cp- expression given )p [12]pp — results about to exact = known to reproduce off'shell ently for the quark-parton z) [1+(1 f'y'ip(z) ] The results about 10%. to exact ce zs+m )(s ) is 27TZ is form we use given by s/4 e f m & f (z):f f o" "'(s)=2f, f, f, f +s(x, z, s) )f"~ Q')f, f, f,f f, f, f 2f, +2 & & l l f =— Q;„= martes 26 de junio de 12 & +s — + [(s+m f Q;„= — 5000 2 M σ(γγ) 4000 3000 2000 1000 0 0 5 10 15 20 E/M gure 4: We show the photon fusion production cross section for monopolium (solid curve r R = 1.5 and Γ̄M = 0.1, and for monopole-antimonopole (dotted curve) as a function of th ergy martes 26variable de junio de 12 E = E/M . monopole mass limit martes 26 de junio de 12 Monopole Detection ted) scattering given in fb/GeV as a function of the invariant mass a LogLog plot. The Higgs signal abov m. We have assumed a monopole of mass 750 in GeV, chosen because ns turned out to be close to the expected magnitude Higgs toThe figures correspond t makeofitthe visible. on above background. The cross sections are wide, gaussian, fromalmost the curves that monopole-antimonop g softly just above threshold (1500 GeV). LHC detectors are blind for of the cross section above the background ng and have black spots due to construction features in the non-forward expected from Standard Mo o not allow for a full detection of photons. Therefore in orderbackground to obtain Eγ 1 TeV. timation of the observable cross section we take region the right-angle crossHence the required selec ltiply it by 4π. This differential cross section is thus the smallest possible. of the photon pairs pro the majority from threshold, it corresponds quite well to a realistic since, Thus estimate, the search for monopole-antimonop n, the elementary differential cross section drops fast with angle and at the LHC. hould consider an efficiency factor for the various detectors. 400 4 300 H # ΓΓ %x 50& dΣ # 2 200 100 1 0 1500 GeV 3 fb GeV dΣ # fb $ $ 5 m $ m # ΓΓ 2000 2500 3000 EΓ !GeV" 3500 4000 0 200 400 600 800 1000 1200 1400 EΓ !GeV" ward (solid) and the right-angle cross sections forFigure a monopole of mass 12: Comparison of the γγ monopol martes 26 de junio de 12 Dirac (1934) “…The attractive force between two magnetic poles is 4692 1/4 time that between the electron and the proton. This very large force may perhaps account for why the monopoles have never been separated...” - Monopolium - martes 26 de junio de 12 Monopolium production Monopolium is a monopole - antimonopole boundstate rm −g martes 26 de junio de 12 rm -g2/r +g Monopolium production from photon fusion at Large Hadron Collider M martes 26 de junio de 12 i) inelastic p + p -> X + X + M (photons radiated from partons) ii) iii) martes 26 de junio de 12 semielastic p + p -> p + X + M (one photon from partons the other from the other proton leaving the proton intact) elastic p + p -> p + p + M (both photons from protons) andapq'(s)= the choice ofdx) Ge& made is such Q2=1 dx2total dz) maximum the value of to be the mom mentioned above cross gedQtoscalars there 4m pp 4m /sx l 4m /s /sx& x& %'ith s be /4. er del applicable. cer structure function. There proton is a epforinelastic ferfermions. duction reads. charged These off'shel the hf the that are photons sufficiently ~H+H cross for L semielastic section The (L in m We choose the logarithm to be pp (4). Eq. = = Q /Q2 ln( (z (z) ) is the inelastic where structure proton 2 F(2 deep Q &q &q r r 50 2~ z he choice of Ge& made the (4). is such that photo Q2=1 1 1 1 of the logarithm in the argument in Eq. W dz, dz, dx, — form as in more a compact write (3)given able. Ge& Xis1 m and4mthe/sxchoice of is Q2=1 by s/4 )pX by 4m 4m /sx z /s l l l ale Q has been chosen throughout cross sectionmodel for1 ppto ~H+H L )pX is1 given by be applicable. 1 (L = dx2 cross dz)for pp ~H+H )fq. dx)&~(x2, semielastic section The Q x2z, z2 ~(x&, (zz)8&r(x, g )fr&q(z, )fry. 4m 4m /sx x&z& 4m /sx 4m /s /sx& x& is now =Qsx, subprocess given by z2 energy z, . l F~2(x, (4) (z2)o (z, z, , F~2(x, , Q')f, ( dz, dz, dx, o" — = — "'(s)=2f, beeno obtained 4m 4m /sx z elastic spectrum '„'&~(z) /s L*, photon dz, is the pi ',X and f4meither K or /sx e„='„ed4ml l/s dx,has —, 1 l 4m /sx l ~~ 4m /sx use an ap in we However, form of an integral [ll]. is=Qx&x2z&zzs. the inelastic structure function. T proton F(2 deep The structure functions have th which in expression given analytic ximate [12] 2, of the in We choose )fy(z) (z2)oyer(x)x2z)z2s), logarithm argument )f), (4). Q Eq. with is the is The inside now =Qsx, photon a WQ given quark. by spectrum z2. ergy z, +s is now =Q subprocess given by f„&q energy with 2. — Th results about 10%. to exact wn to reproduce (5) 2 and the choice of Ge& made m is Q2=1 obtained hasphoton been o has such been spectrum '„'&~(z) =— The elastic spectrum in'„'&~(z) is m use 2 2 we given by in 4)/$06. 00 2335 in [ll]. we However, form of an the integral .use 50 toabout be applicable. an apinthe[ll]. egral choiceHowever, of the2m scaleswe Q, in expression given analytic proximate ~H+H + ue of the momentum transfer cross for L [12] given semielastic section is which in (L c expression given )p [12]pp p— results about to exact = known to reproduce off'shell ently for the quark-parton z) [1+(1 f'y'ip(z) ] The results about 10%. to exact ce zs+m )(s ) is 27TZ is form we use given by s/4 f m & f (z):f f o" "'(s)=2f, f, f, f +s(x, z, s) )f"~ Q')f, f, f,f f, f, f 2f, +2 & & & l l f =— Q;„= martes 26 de junio de 12 +s — + [(s+m f Q;„= — Monopolium photon coupling martes 26 de junio de 12 Monopolium wave function · The monopole has been regarded as possessing some spatial extension that avoids the singularity at the origin. rm −g martes 26 de junio de 12 rm -g2/r +g We have represented this complex scenario by a potential which behaves like a magnetic Coulomb for r >> 2 rclassical and is finite at the origin. martes 26 de junio de 12 Excited Coulomb states Texto n > 13 well defined ρ= martes 26 de junio de 12 Two parameters : M , m M m-m martes 26 de junio de 12 Small Binding Large Binding =2m/M Lower mass threshold M < 2m martes 26 de junio de 12 Binding Effect Threshold effect Example: for m = 1 TeV and M= 1 TeV at LHC for 100 fb-1 106 monopoles and 108 monopolia. martes 26 de junio de 12 Total cross section for monopolium production at LHC with 3.5 TeV beams and monopole masses ranging from 500 to 1000 GeV, with binding energies 2 m/15 and widths 10 GeV. martes 26 de junio de 12 Monopolium detection at LHC with diphoton events ΨM martes 26 de junio de 12 ΨM Mass effect m= 750 GeV martes 26 de junio de 12 M= 1400 GeV ΓM = 10 GeV Moedal martes 26 de junio de 12 martes 26 de junio de 12 toughts... i) near threshold (grounstate -> l= 0) γ M γ · β small -> elastic multiparticle collisions · In presence of magnetic fields huge polarizability d ̴ rM3 B ̴ (α Ebinding)-3 B martes 26 de junio de 12 ii) boundstate -> excited states -> l > 0 multipoles -> bending (photon emission) -> excitation and ionization martes 26 de junio de 12 iii) Monopolium (weak binding and/or excited states) -> (capturing electrons or protons) -> Dions D −e +g M −g +e martes 26 de junio de 12 D̄ M D D̄ martes 26 de junio de 12 Concluding remarks Dirac felt that he "would be surprised if Nature had made no use of it". It, being the Magnetic Monopole. · Ed Witten once asserted in his Loeb Lecture at Harvard, “almost all theoretical physicists believe in the existence of magnetic monopoles, or at least hope that there is one.” · · · Joseph Polchinski, a string-theorist, described the existence of monopoles as "one of the safest bets that one can make about physics not yet seen" and that “their existence seems inevitable in any framework that explains the quantization of electric charge. Of course their mass scale and abundance are highly uncertain,... ” martes 26 de junio de 12 · We have shown that if non relic monopoles exist and their masses are in the TeV region they are soon to be found either as m - m pairs or monopolium much effort is going to go both in the more traditional schemes, Atlas and CMS, and in Moedal. Magnetic monopoles can be detected by their high ionization, their binding to conventional particles and nuclei, diphoton events, ... martes 26 de junio de 12 · Monopolium groud state a very heavy neutral object -> good diphoton signal (Z0, W±, ...) -> large magnetic polarizability (in the presence of large B-fields) -> naively : difficult object for Moedal (?? elastic collisions) · Monopolium excitations -> multiphoton processes (pseudo-polynomial trajectories) -> excitation and ionization (multipole interactions) · Dion formation -> good Moedal candidates martes 26 de junio de 12 Thank you for your attention! martes 26 de junio de 12