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Search for magnetic monopoles using the fusion production mechanism at MoEDAL experiment

Arka Santra

3rd RED LHC Workshop Madrid, Spain based on 1. Baines, Mavromatos, Mitsou, Pinfold, AS, Eur. Phys. J. C (2018) 78: 966 2. MoEDAL Collaboration, arXiv:1903.08491 3. Sakurai, Felea, Mamuzic, Mavromatos, Mitsou, Pinfold, Ruiz de Austri, AS, Vives, arXiv:1903.11022

May 7, 2019

Arka Santra Magnetic Monopoles via Photon Fusion 1 / 48 Magnetic Monopoles:symmetrising Maxwell’s equation

No magnetic has been seen to date. The isolated magnetic charges were not present in Maxwell’s equation. The equations are asymmetric in electric and magnetic . A restores the symmetry to Maxwell’s equation

Symmetrised Maxwell’s equations are invariant under rotation in (E,B) plane. Distinction between electric and magnetic charge becomes just definition.

Arka Santra Magnetic Monopoles via Photon Fusion 2 / 48 Magnetic monopole properties and production at the colliders

Paul Dirac in 1931 thought of monopoles as the end of an infinitely long and thin . Dirac’s quantization condition: h c i h n i ge = n ~ or g = e, n = 1, 2, 3... 2 2α where g is the magnetic charge and α = 1/137. Single magnetic charge: gD= 68.5e. Large coupling constant: g ∼ 34, perturbative calculation impossible for general case. ~c Monopoles would accelerate along field lines- Lorentz equation: F~ = g(B~ − ~v × E~ ).

Dirac monopole properties Dirac monopole is a point-like . and mass are not determined by the theory.

Arka Santra Magnetic Monopoles via Photon Fusion 3 / 48 Cross-section calculation

Arka Santra Magnetic Monopoles via Photon Fusion 4 / 48 Monopole field theory

Electric-magnetic duality: The monopole enters the field as a field in a U(1) . In short: Spin 0: Scalar QED Spin 1/2: Dirac QED Spin 1: Lee-Yang Theory

β-dependent coupling Milton (arXiv:hep-ex/0602040) derived the -monopole scattering dσ 1 h eg 2i 1 cross-section for small scattering angle : = 2 4 dΩ (2µv0) c (θ/2) where g is the magnetic charge of the monopole.  2 dσ 1 e1e2 1 Rutherford scattering formula: = 2 4 can be dΩ (2µv0) v0 (θ/2) obtained from Milton’s calculation if e2 → g or e → gv0 = gβ. v0 c 2 c

Arka Santra Magnetic Monopoles via Photon Fusion 5 / 48 Introduction of a new magnetic-moment parameter κ

Spin 1/2 Such a term appears through spin interactions in minimally e± − γ QED coupling SM case:κ ˜ = κM = 0 (unitary and renormalisable)

Spin 1 Such a term appears through the coupling of W ± in rotated SU(2) × UY (1)/Uem(1). SM case: κ = 1 (unitary, renormalisable and no ghosts or gauge fixing)

Total cross-sections increase with κ. Kinematic distributions change with κ.

Perturbative limit: There can be a perturbative limit if: very slow monopoles with β → 0. κ becomes very large, κ → ∞. perturbative limit: gκ0β2 < 1, where κ0 =κ ˜ for spin 1/2 and κ0 = κ for spin 1 monopole. Cross-section remains finite for both spin 1/2 and 1 at this limit for γγ , but vanishes for DY.

Arka Santra Magnetic Monopoles via Photon Fusion 6 / 48 MadGraph Implementation of Photon Fusion Creating UFO models Validating the models From Baines, Mavromatos, Mitsou, Pinfold, AS, Eur. Phys. J. C (2018) 78: 966.

Arka Santra Magnetic Monopoles via Photon Fusion 7 / 48 Photon fusion in MadGraph :

Drell-Yan was implemented in MadGraph using Fortran code setup.

This process only had three-particle vertex for all three spins. Used in ATLAS and MoEDAL to interpret the data (upto leading order). Implementing photon fusion process in MadGraph Spin 0 and 1 monopoles have additional four-particle vertices. Fortran code setup is inadequate to describe them. Moved to the new python based UFO models. The new models include both the Drell-Yan and photon fusion method.

Arka Santra Magnetic Monopoles via Photon Fusion 8 / 48 UFO models

UFO: Universal FeynRules Output FeynRules : Mathematica package for describing Feynman rules. Based on Python objects. Requires the model Lagrangian as an input in Mathematica format. Model parameters (mass, spin, coupling etc) are kept in a text file.

For β-dependent coupling, it is introduced as a Fortran form factor. q 2 Used the definition of β = 1 − 4M /ˆs with ˆs = 2P1 · P2 for LHC collision of , where P1 and P2 are the four momenta of the incoming colliding . Point to note: β → 0 when ˆs → (2M)2. The UFO models were validated by comparing the cross-section values coming from them and the theoretical cross-section values for several monopole masses, and all three spins: 0, 1/2 and 1.

Arka Santra Magnetic Monopoles via Photon Fusion 9 / 48 Latest Results from the MoEDAL Experiment.

Arka Santra Magnetic Monopoles via Photon Fusion 10 / 48 The MoEDAL Detector:

Arka Santra Magnetic Monopoles via Photon Fusion 11 / 48 Prospect of SUSY searches at the MoEDAL experiment (Sakurai, Felea, Mamuzic, Mavromatos, Mitsou, Pinfold, Ruiz de Austri, AS, Vives, arXiv:1903.11022):

0 0 ± MoEDAL can be useful for SUSY search, for exampleg ˜g˜,g ˜ → jjχ˜1,χ ˜1 → τ τ˜1. 0 0 χ˜1 long-lived despite large mass splitting betweenχ ˜1 andτ ˜1 : decays in tracker. ± 0 (massive) τ produces a kink betweenχ ˜1 andτ ˜1 tracks: large impact parameter dxy , dz . CMS sensitivity suffers because of no pixel hit (long lived ) and too large impact parameter forτ ˜. MoEDAL is useful here: can cover long-lifetime region with nominal NTD performance z/β > 5.

Figure:˜g decay diagram (left) and CMS exclusion with MoEDAL discovery potential requiring 2 signal events for MoEDAL (right).

Arka Santra Magnetic Monopoles via Photon Fusion 12 / 48 2015-2017 MoEDAL magnetic monopole trapper (MMT) deployment: Monopole search

MMT-1 and MMT-2 (sides) are newly added with respect to previous MoEDAL analyses. Latest analysis is based on data extracted from all MMTs. After the exposure, Al bars are passed through SQUID to check the presence of magnetic monopole.

NTDs – High Charge Catcher Geant 4 Panoramix

NTDs – Top NTDs – C-side

NTDs – A-side

VeLo – LHCb

MMT-1

MMT-2 NTDs – Forward MMT-3

Arka Santra Magnetic Monopoles via Photon Fusion 13 / 48 The SQUID Response of MMTs: Monopole search

Magnetic charges > 0.5 gD can be excluded at high confidence level.

A threshold of 0.4 gD was used to identify potential candidate samples. The candidate samples were passed through SQUID a number of times to check if they really contain any monopole.

Arka Santra Magnetic Monopoles via Photon Fusion 14 / 48 √ Latest MoEDAL Monopole Search Result at s = 13 TeV (arXiv: 1903.08491):

Arka Santra Magnetic Monopoles via Photon Fusion 15 / 48 √ Latest MoEDAL Monopole Search Result at s = 13 TeV (arXiv: 1903.08491):

Drell-Yan production with β-independent coupling April 2019 2.2 MoEDAL @ 13 TeV Cross-section 2 spin-1 upper limits as low as 11 fb were 1.8 set. 1.6 ATLAS MoEDAL @ 13 TeV 1 Mass limits in the @ 8 TeV spin- /2 1.4 1 range of 1500 GeV spin- /2 to 3750 GeV. 1.2 Mass limits are the strongest at a 1 collider 0.8 ATLAS MoEDAL @ 8 TeV @ 8 TeV experiment, spin-1/ spin-0 2 0.6 MoEDAL @ 13 TeV previous DY mass spin-0 limit were in the MoEDAL @ 8 TeV 0.4 spin-0 range of 450 to CDF @ 1.96 TeV Excluded magnetic monopole mass [TeV] 1 1790 GeV. 0.2 spin- /2 0 1 2 3 4 5 Magnetic charge [g ] D

Arka Santra Magnetic Monopoles via Photon Fusion 16 / 48 Summary and Conclusion:

Looked at the photon fusion method of monopole production. Generated and validated MadGraph UFO models for photon fusion process. Compared the kinematic distributions of photon fusion method with Drell-Yan method. Introduced a magnetic-moment parameter κ for spin 1/2 and 1 monopoles. Explored a possibility of perturbative calculation for spin 1/2 and 1 monopoles. Shown the results from MoEDAL experiment with both γγ and DY mechanism First instance of exclusion limit set using the γγ mechanism at the LHC. Mass limits in the range 1500-3750 GeV were set for magnetic charges up to 5 gD for monopoles of spin 0, 1/2 and 1 - strongest to date at a collider experiment for charges from 2 gD to 5 gD range.

Arka Santra Magnetic Monopoles via Photon Fusion 17 / 48 Arka Santra Magnetic Monopoles via Photon Fusion 18 / 48 Bonus slides

Arka Santra Magnetic Monopoles via Photon Fusion 19 / 48 Why consider photon fusion?:

The reason: Dougall and Wick (arXiv:0706.1042) showed that the γγ → mm+mm− /DY cross section ratio of monopole production is ∼ 4700 times that of production. Drees et.al. (Phys. Rev. D 50, 2335 (1994)) showed that the γγ → mm+mm− production of 2 is nearly 10√below DY for pp collisions at s = 14 TeV. Hence a factor of ∼ 47 dominance of γγ → mm+mm− over DY for monopole Figure: Cross-section vs mass plot for photon fusion and production (when β ≈ 1) DY process. (arXiv:0706.1042)

Arka Santra Magnetic Monopoles via Photon Fusion 20 / 48 MoEDAL result with persistent current:

Arka Santra Magnetic Monopoles via Photon Fusion 21 / 48 √ Latest MoEDAL Monopole Search Result at s = 13 TeV (arXiv: 1903.08491):

Arka Santra Magnetic Monopoles via Photon Fusion 22 / 48 Acceptance plots for γγ :

Arka Santra Magnetic Monopoles via Photon Fusion 23 / 48 Acceptance plots for DY:

Arka Santra Magnetic Monopoles via Photon Fusion 24 / 48 The mass limits:

Arka Santra Magnetic Monopoles via Photon Fusion 25 / 48 Arka Santra Magnetic Monopoles via Photon Fusion 26 / 48 Arka Santra Magnetic Monopoles via Photon Fusion 27 / 48 Spin 0 monopoles

Scalar QED. monopole obeying U(1)-gauged Klein-Gordon equation. 1 µν µ † 2 † L = − 4 F Fµν + (D φ) (Dµφ) − M φ φ

Arka Santra Magnetic Monopoles via Photon Fusion 28 / 48 Spin 1/2 monopole

Dirac QED. monopole as a spinor field obeying a U(1)-gauged . S=1/2 1 µν ¯ / 1 ¯ µ ν L = − 4 Fµν F + ψ(iD − M)ψ − i 4 g(β)κFµν ψ[γ , γ ]ψ

Arka Santra Magnetic Monopoles via Photon Fusion 29 / 48 Spin 1/2 cross-sections

Arka Santra Magnetic Monopoles via Photon Fusion 30 / 48 Spin 1 monopoles

Lee-Yang field theory. monopole as a vector field obeying a U(1)-gauged Klein Gordon equation with a gauge fixing parameter and ghosts.

    S=1 1 ∂Aµ ∂Aν 1 † 2 † µ † L = − − G Gµν − M W W − ig(β)κFµν W Wν 2 ∂xν ∂xµ 2 µν µ µ

Arka Santra Magnetic Monopoles via Photon Fusion 31 / 48 Total cross-section of spin 0,1/2 and 1:

Arka Santra Magnetic Monopoles via Photon Fusion 32 / 48 Theoretical expressions of cross-section:

4πα2  1 − β4  1 + β  σs=0(ˆs) = g β 2 − β2 − ln (1) γγ ˆs 2β 1 − β

4πα2  3 − β4  1 + β  σs=1/2(ˆs) = g β −2 + β2 + ln (2) γγ ˆs 2β 1 − β

πα2  22 − 9β2 + 3β4 1 − β4  1 + β  σs=1(ˆs) = g β 2 − 3 ln (3) γγ ˆs 1 − β2 β 1 − β where 2 2 p 2 αg = g β , β = 1 − 4M /ˆs, ˆs = z1z2s (4) . p 1 g = 137/4 = 5.85 2 αg = 34.25 3 form factor = 1.0 4 √z1 = z2 = 1 5 s = 13 TeV −9 −2 6 1 pb = 2.5819 × 10 GeV 2 7 ˆs = 13 × 13 TeV

Arka Santra Magnetic Monopoles via Photon Fusion 33 / 48 LHC Phenomenology

Arka Santra Magnetic Monopoles via Photon Fusion 34 / 48 MadGraph settings for kinematic distribution plots:

Kinematic distribution plots: Comparison between photon fusion and DY production mechanism, β-dependent coupling. Simulation setup -proton collision at 13 TeV center of mass energy. Monopole mass 1500 GeV. magnetic charge of monopole: 1 gD. For photon fusion, LUXqed is used as the PDF. For DY, NNLOPDF23 is used as the PDF.

Arka Santra Magnetic Monopoles via Photon Fusion 35 / 48 Spin 0 monopoles, charge 1 gD, monopole mass 1500 GeV

s=13 TeV s=13 TeV 105 105 Photon fusion (γγ) Photon fusion (γγ) Drell-Yan (DY) Drell-Yan (DY) 104 104 Events/0.25

Events/80 GeV 103 103

102 102

10 monopole mass: 1500 GeV 10 monopole mass: 1500 GeV

Spin 0, β-dependent coupling Spin 0, β-dependent coupling 1 1

3 3

2 2 γ γ γ γ DY 1 DY 1

0 0 0 500 1000 1500 2000 2500 3000 3500 4000 −5 −4 −3 −2 −1 0 1 2 3 4 5 kinetic energy (GeV) η

For spin 0 monopoles, DY kinetic energy η distributions are different-DY events are distribution is similar to the γγ . more centrally produced.

Arka Santra Magnetic Monopoles via Photon Fusion 36 / 48 Validation of the UFO models

Arka Santra Magnetic Monopoles via Photon Fusion 37 / 48 Cross-section for γγ → mm+mm− , β-independent coupling, spin 0 monopole, charge 1 gD

No PDF used in MadGraph to compare with the theoretical value.

Mass (GeV) σ (pb) σ (pb) Ratio γγ → mm+mm− γγ → mm+mm− UFO model/Theory (UFO model) (Theory values) 1000.0 1.518 × 104 1.5039 × 104 1.009 2000.0 1.202 × 104 1.1945 × 104 1.006 3000.0 9218 9108.09 1.012 4000.0 7366 7218.79 1.020 5000.0 6558 6519.68 1.006 6000.0 5378 5325.76 1.010

Arka Santra Magnetic Monopoles via Photon Fusion 38 / 48 Cross-section for γγ → mm+mm− , β-dependent coupling, spin 0 monopole, charge 1 gD

No PDF used in MadGraph to compare with the theoretical value.

Mass (GeV) σ (pb) σ (pb) Ratio β Ratio γγ → mm+mm− γγ → mm+mm− UFO model/Theory β-dep/β-ind (UFO model) (Theory values) (UFO model) 1000 1.4493 × 104 1.4336 × 104 0.99 0.9881 0.9547 (∼ 0.98814) 2000 9.851 × 103 9.791 × 103 1.006 0.9515 0.8196 (∼ 0.95154) 3000 5.685 × 103 5.640 × 103 1.007 0.8871 0.6167 (∼ 0.88714) 4000 2847 2810.5 1.013 0.7882 0.3866 (∼ 0.78824) 5000 1094 1087 1.006 0.639 0.1658 (∼ 0.6394) 6000 117.8 116.53 1.011 0.3846 0.022 (∼ 0.38464)

Arka Santra Magnetic Monopoles via Photon Fusion 39 / 48 Cross-section for γγ → mm+mm− , β-independent coupling, spin 1/2 monopole, charge 1 gD

No PDF used in MadGraph to compare with the theoretical value.

Mass (GeV) σ (pb) σ (pb) Ratio γγ → mm+mm− γγ → mm+mm− UFO model/Theory (UFO model) (Theory values) 1000 1.431 × 105 1.425 × 105 1.004 2000 1.018 × 105 1.007 × 105 1.010 3000 7.755 × 104 7.679 × 104 1.010 4000 5.830 × 104 5.7404 × 104 1.016 5000 3.817 × 104 3.797 × 104 1.005 6000 1.691 × 104 1.6705 × 104 1.012

Arka Santra Magnetic Monopoles via Photon Fusion 40 / 48 Cross-section for γγ → mm+mm− , β-dependent coupling, spin 1/2 monopole, charge 1 gD

No PDF used in MadGraph to compare with the theoretical value.

Mass (GeV) σ (pb) σ (pb) Ratio β Ratio γγ → mm+mm− γγ → mm+mm− UFO model/Theory β-dep/β-ind (UFO model) (Theory values) (UFO model) 1000 1.364 × 105 1.358 × 105 1.004 0.9881 0.9531 (∼ 0.98814) 2000 8.341 × 104 8.2551 × 104 1.010 0.9515 0.8193 (∼ 0.95154) 3000 4.803 × 104 4.7554 × 104 1.010 0.8871 0.6193 (∼ 0.88714) 4000 2.251 × 104 2.2156 × 104 1.012 0.7882 0.3861 (∼ 0.78824) 5000 6362 6331 1.005 0.639 0.1667(∼ 0.6394) 6000 370 365.5 1.012 0.3846 0.0219(∼ 0.38464)

Arka Santra Magnetic Monopoles via Photon Fusion 41 / 48 Cross-section for γγ → mm+mm− , β-independent coupling, spin 1 monopole, charge 1 gD

No PDF used in MadGraph to compare with the theoretical value.

Mass (GeV) σ (pb) σ (pb) Ratio γγ → mm+mm− γγ → mm+mm− UFO model/Theory (UFO model) (Theory values) 1000 1.131 × 107 1.131 × 107 1.000 2000 2.765 × 106 2.747 × 106 1.007 3000 1.164 × 106 1.151 × 106 1.011 4000 5.879 × 105 5.835 × 105 1.008 5000 3.161 × 105 3.109 × 105 1.017 6000 1.39 × 105 1.378 × 105 1.009

Arka Santra Magnetic Monopoles via Photon Fusion 42 / 48 Cross-section for γγ → mm+mm− , β-dependent coupling, spin 1 monopole, charge 1 gD

No PDF used in MadGraph to compare with the theoretical value.

Mass (GeV) σ (pb) σ (pb) Ratio β Ratio γγ → mm+mm− γγ → mm+mm− UFO model/Theory β-dep/β-ind (UFO model) (Theory values) (UFO model) 1000 1.078 × 107 1.0781 × 107 0.999 0.9881 0.9531 (∼ 0.98814) 2000 2.277 × 106 2.2520 × 106 1.011 0.9515 0.8235 (∼ 0.95154) 3000 7.214 × 105 7.1290 × 105 1.012 0.8871 0.6198 (∼ 0.88714) 4000 2.275 × 105 2.2523 × 105 1.010 0.7882 0.3870 (∼ 0.78824) 5000 5.256 × 104 5.1833 × 104 1.014 0.639 0.1663(∼ 0.6394) 6000 3.034 × 103 3.014 × 103 1.007 0.3846 0.0218(∼ 0.38464)

Arka Santra Magnetic Monopoles via Photon Fusion 43 / 48 Argument against β-dependent monopole coupling

Milton (arXiv:hep-ex/0602040) derived the electron-monopole scattering cross-section dσ 1 h eg 2i 1 for small scattering angle : = 2 4 where g is the magnetic charge dΩ (2µv0) c (θ/2) of the monopole. h 2i dσ 1 e1e2  1 Rutherford scattering formula: = 2 4 can be obtained from dΩ (2µv0) v0 (θ/2) e2 g gv0 Milton’s calculation if → or e2 → = gβ. v0 c c e2 (gβ)2 This leads to α = → αm = . ~c ~c The law: F~ = eE~ + eβ~c × B~ ; even though the interaction with the 2 magnetic field depends on β, the QED coupling depends only on e: α = e . ~c Force on the monopole: F~ = gB~ − gβ~c × E~ . This does not necessarily imply that the photon-monopole coupling should be β-dependent.

Arka Santra Magnetic Monopoles via Photon Fusion 44 / 48 SQUID Calibration

A more direct approach to inferring the magnetometer response to a monopole is to use a long solenoid since the magnetic field from one end of a “semi-infinite” solenoid acts just like a monopole.

Arka Santra Magnetic Monopoles via Photon Fusion 45 / 48 The SQUID Magnetometer:

Arka Santra Magnetic Monopoles via Photon Fusion 46 / 48 MoEDAL’s sensitivity:

Cross-section limits for magnetic (left) and (right) [arXiv:1112.2999v2 [hep-ph]]. MoEDAL compliments the physics reach of the existing LHC experiments.

Arka Santra Magnetic Monopoles via Photon Fusion 47 / 48 The MoEDAL Sub-detector Resolution:

NTDs Tracking resolution: 10 mm/pit (∼10 pits). Pointing resolution to the interaction point: ∼ 1 cm. Charge resolution: 0.1e.

Trapping Detector:

Magnetic charge resolution: < 0.1 gD.

TimePix chips Pixel size 55× 55 mm2. Silicon thickness: 300 µm.

Arka Santra Magnetic Monopoles via Photon Fusion 48 / 48