Looking for Magnetic Monopoles AT The Large Hadron Collider. Vicente Vento Universidad de Valencia-IFIC

Transcription

1 Looking for Magnetic Monopoles AT The Large Hadron Collider Vicente Vento Universidad de Valencia-IFIC

2 Luis Epele Huner Fanchiotti Carlos García Canal Vasiliki Mitsou

3 Introduction Monopoles Monopole Production and Detection Monopolium Monopolium Production and Detection Moedal Concluding Remarks

4 Introduction In 1884 Pierre Curie suggested that magnetic monopoles could exist About the possibility of existence of magnetic conductivity and free magnetism. by M. P. Curie The paralelism between electric and magnetic phenomena leads to question us if this analogy is more complete. Is it absurd to assume that there exist bodies which are conductors of magnetism, of magnetic currents, of free magnetism?

5 Appealing because: It Restores Electric-Magnetic Symmetry in Maxwell s Equations

6 Monopoles Dirac 1931 : Monopole and Quantum Mechanics: Magnetic Coulomb Field: B = g r / r 2 Conflict when defining the vector potential The solution of a Genius

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8 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

9 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 /#m 0 The monopole mass is not predicted within the Dirac s theory.!

10 Monopoles and Grand Unification Grand Unified gauge theories predict Monopoles: t Hooft and Polyakov (1974) discovered that monopoles are fundamental solutions to non- Abelian gauge GUT theories These Monopoles have structure and no string singularity. The field of the GUT monopole is B ~ g/r 2 outside The Mass m(gut)m mx/g > GeV. not producible by particle accelerators primordial monopoles present in the Universe GUT monopoles can catalyze proton decay!

11 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, E. and collaborators Superstring models We shall take a phenomenological approach and assume that the mass is a parameter

12 The Monopole is a wishful object Dirac felt that he "would be surprised if Nature had made no use of it". 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. Polchinski 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,...

13 Monopole Production and Detection e -> β g generalization as an s dependent form factor

14 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.??, wheretheexplicit couplings have been shown. The photon-fusion elementary cross section is obtained fromthewell-knownqed electron-positron pair creation cross section [?], simply changing the coupling constant (e gβ )andtheelectronmassbythemonopolemassm e m, leadingto σ(γγ mm) = π ( ( ) ) g4 (1 β 2 ) β 4 3 β 4 1+β log (2 β 2 ), (4) 2 m 2 2β 1 β Monopole Production where β is the monopole velocity, a function of the center-of-mass energy, E. InFig.?? 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 notice the large effect associated 1. e e with this factor in the vicinity of the threshold. LHC detectors, apart from the MoEDAL experiment [?], have not beendesigned m m Σ Ω Figure 3: Ω Adimensional functional form of the elementary photon-fusion cross section

15 Production from photon fusion at Large Hadron Collider

16 i) inelastic p + p -> X + X + m + m (photons radiated from partons) ii) semielastic p + p -> p + X + m + m (one photon from partons the other from the other proton leaving the proton intact) iii) elastic p + p -> p + p + m + m (both photons from protons)

17 /4 m and the choice of Q2=1 Ge& is made such Q & to ed scalars el r to be s applicable. /4. mentioned above there %'ith 4m /s 4m /sx for that charged the fermions. photons These are fer- he semielastic cross section for ~H+H l 4m p inelastic proton structure function. There /sx& x& sufficiently duction is a cer reads. pp (L off'shel L be the m beapq'(s)= the maximum f dx) f value dx2total of the pp cross dz) mo z):f )=f the logarithm r (z in Eq. dx,f, f, &q r (z) (4). = We choose ln( Q /Q22 where F(2 Q to is the &q deep inelastic proton structure & o" 2~ 50 "'(s)=2f, z & 1 1 dz, 1 dz, e choice of Q2=1 Ge& is made such that the photo ble. write (3) in a more compact form as by s/4 m and the choice of Q2=1 Ge& is )px is given by le Q 4m /s 4m /sx l 4m /sx l z l X 1 has been chosen throughout f model dx) f to be applicable. The semielastic dx2 dz) (x&, g )fq.&~(x2, Q )fr&q(z, )fry. (zz)8&r(x, x2z, z2 dx,f, f, f, 4m /s 4m /sx l 4m /sx& x& 4m /sx (4) x&z& & either K or L*,e = ' ed dz, = dz, F~2(x,, Q')f, ( m /s 4m /sx l 4m /sx l z X l, 1 subprocess energy now is given by +s =Qsx, z, z2 elastic photon spectrum f' '&~(z) has been obtained i form 2 of an integral [ll]. (2 is =Qx&x2z&zzs. the deep inelastic Theproton structure However, structure functions wefunction. usehave an ap th T l l rgument of the logarithm +s rgy now is =Qsx, given by in Eq. z, (4). z2. We choose Q, imate Q )fy(z) analytic )f),(z2)oyer(x)x2z)z2s), expression given in [12] with which. withthe subprocess energy now is given by +s =Q n to reproduce exact results to about 10%. Th and the choice of Q2=1 Ge& is made such spectrum m f' '&~(z) The = elastic hasphoton been obtained spectrum in )/$06. nwe use 00is2 given by o be applicable. in the argument of the logarithm in Eq. (4). W ross section for pp ~H+H (L L )px is given by dx,f, (x,z, z,s) f, o" "'(s)=2f, ', and o dz, is the p 4m /s 4m /sx ~~ l 4m /sx F~2(x,, Q')f, (z, )f"~ (z2)o f &q is the photon spectrum inside a quark. W Q; = 2m cross section for pp ~H+H gral aboutin [ll]. the choicehowever, of the scales we Q,. use an apexpression given in [12] pp which is (L L emielastic cross section for ~H+H )p e- of the momentum proximate = transfer analytic [1+(1 given expression given in [12] ntly f'y'ip(z) off'shell known for the to quark-parton reproduce z) is ] exact results to about e exact results about 10%. The 27TZ form we use is given by (5) Q; = + 2 = f' '&~(z) has been o the form of an integral in [ll]. However, we + [(s+m )(s zs+m )

18 M 2!("") E/M ure 4: We show the photon fusion production cross section for monopolium (solid curve R =1.5 and Γ M =0.1, and for monopole-antimonopole (dotted curve) as a function of th rgy variable E = E/M.

19 monopole mass limit

20 Monopole Detection ed) scattering given in fb/gev as a function of the invariant mass. We have assumed a monopole of mass 750 GeV, chosen because s turned out to be close to the expected magnitude of the Higgs to n above background. The cross sections are wide, almostgaussian, softly just above threshold (1500 GeV). LHC detectors are blind for g and have black spots due to construction features in the non-forward not allow for a full detection of photons. Therefore in order to obtain imation of the observable cross section we take the right-angle cross tiply it by 4π. Thisdifferential cross section is the smallest possible. rom threshold, it corresponds quite well to a realistic estimate, since,, the elementary differential cross section drops fast with angle and at the LHC. ould consider an efficiency factor for the various detectors. in a LogLog plot. The Higgs signal abov make it visible. The figures correspond t from the curves that monopole-antimonop of the cross section above the background expected background from Standard Mo region E γ 1TeV. Hencetherequiredselec thus the majority of the photon pairs pro Thus the search for monopole-antimonop H ΓΓ x 50 dσ fb GeV dσ fb GeV m m ΓΓ EΓ GeV EΓ GeV ard (solid) and the right-angle cross sections for a monopole of mass Figure 12: Comparison of the γγ monopol

21 Dirac (1934) The attractive force between two magnetic poles is /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 -

22 Monopolium production Monopolium is a monopole - antimonopole boundstate r m r m g -g 2 /r +g

23 Monopolium production from photon fusion at Large Hadron Collider M

24 i) inelastic p + p -> X + X + M (photons radiated from partons) ii) semielastic p + p -> p + X + M (one photon from partons the other from the other proton leaving the proton intact) iii) elastic p + p -> p + p + M (both photons from protons)

25 /4 m and the choice of Q2=1 Ge& is made such Q & to ed scalars el r to be s applicable. /4. mentioned above there %'ith 4m /s 4m /sx for that charged the photons fermions. These are fer- he semielastic cross section for ~H+H l 4m p inelastic proton structure function. There /sx& x& sufficiently duction is a cer off'shel reads. pp (L L be the m beapq'(s)= the maximum f dx) f value dx2total of the pp cross mom dz) z):f )=f the logarithm r (z in Eq. dx,f, f, &q r (z) (4). = We choose ln( Q /Q22 where F(2 Q to is the &q deep inelastic proton structure & o" 2~ 50 "'(s)=2f, z & 1 1 dz, 1 dz, e choice of Q2=1 Ge& is made such that the photo ble. write (3) in a more compact form as by s/4 m and the choice of Q2=1 Ge& is )px is given by le Q 4m /s 4m /sx l 4m /sx l z l X 1 has been chosen throughout f model dx) f to be applicable. The semielastic dx2 dz) (x&, g )fq.&~(x2, Q )fr&q(z, )fry. (zz)8&r(x, x2z, z2 dx,f, f, f, dx,f, either elastic Kphoton or L*,e = ' ed o" = spectrum dz, "'(s)=2f, dz, f' '&~(z) has ', F~2(x,, Q')f, ( been obtained i, and o dz, is the p 4m /s 4m /sx ~~ l 4m /sx ~2(x, Q')f, 4m /s 4m /sx l 4m /sx& x& 4m /sx, (z, )f"~(4)(z2)o (x,z, z,s) x&z&. & subprocess energy now is given by +s =Qsx, z, z2 form 2 of an integral [ll]. (2 is =Qx&x2z&zzs. the deep inelastic Theproton structure However, structure functions wefunction. usehave an ap th T l l rgument of the logarithm +s rgy now is =Qsx, given by in Eq. z, (4). z2. We choose Q, imate Q )fy(z) analytic )f),(z2)oyer(x)x2z)z2s), expression given in [12] with which f &q is the photon spectrum inside a quark. W withthe subprocess energy now is given by +s =Q n to reproduce exact results to about 10%. Th. and the choice of Q2=1 Ge& is made such spectrum m f' '&~(z) The = elastic hasphoton been obtained spectrum in )/$06. we use 00is2 given by n Q; = 2m o be applicable. in the argument of the logarithm in Eq. (4). W ross section for pp ~H+H (L L )px is given by m /s 4m /sx l 4m /sx l z l X 1 cross section for pp ~H+H gral aboutin [ll]. the choicehowever, of the scales we Q,. use an apexpression given in [12] pp which is (L L emielastic cross section for ~H+H )p e- of the momentum proximate = transfer analytic [1+(1 given expression given in [12] ntly f'y'ip(z) off'shell known for the to quark-parton reproduce z) s ] exact results to about e exact results about 10%. The 27TZ form we use is given by (5) Q; = + 2 = f' '&~(z) has been o the form of an integral in [ll]. However, we + [(s+m )(s zs+m )

26 Monopolium photon coupling

27 Monopolium wave function The monopole can be regarded as possessing some spatial extension that avoids the singularity at the origin. r m r m g -g 2 /r +g

28 We have represented this complex scenario by a potential which behaves like a magnetic Coulomb for r >> 2 r classical and is finite at the origin.

29 Excited Coulomb states Texto n > 13 well defined ρ = Two parameters : M, m

30 M m-m

31 Small Binding Large Binding =2m/M Lower mass threshold M < 2m

32 Binding Effect Threshold effect Example: for m = 1 TeV and M= 1 TeV at LHC for 100 fb monopoles and 10 8 monopolia.

33 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.

34 Monopolium detection at LHC with diphoton events Ψ M Ψ M

35 Mass effect m= 750 GeV M= 1400 GeV Γ M = 10 GeV

36 Moedal

37

38 Some toughts for monopolium detection i) near threshold (grounstate -> l= 0) M γ β small -> elastic multiparticle collisions In presence of magnetic fields huge polarizability d r 3 M B (α E binding ) -3 B γ

39 ii) boundstate -> excited states -> l > 0 multipoles -> bending (photon emission) -> excitation and ionization

40 iii) Monopolium (weak binding and/or excited states) -> (capturing electrons or protons) -> Dions e D +g M g +e D

41 M D D

42 Concluding remarks 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, but also in a dedicated experiment Moedal. Magnetic monopoles can be detected by their high ionization, their binding to conventional particles and nuclei, diphoton events,...

43 Monopolium groud state is a very heavy neutral object -> good diphoton signal (Z 0, 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

44 Thank you for your attention!