Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions
Magnetic monopole production in heavy ion collisions
Oliver Gould Imperial College London
Based on: arXiv:1704.04801 arXiv:1705.07052 (with Arttu Rajantie)
August 18, 2017
1 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Why magnetic monopoles?
Magnetic monopoles are theoretically important They imply electric charge quantisation,
∃ Monopoles ⇒ q/e ∈ Z.
Can be added to Standard Model with source term. Predicted by GUTs
G → SU(3) × SU(2) × U(1),
and by string theory.
2 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Key questions of this talk
1 If composite magnetic monopoles exist, how can we make them? pp collisions? e+e− collisions? . . . P bP b collisions? AuAu collisions? . . .
2 If elementary magnetic monopoles exist, how can we make them? pp collisions? e+e− collisions? . . . P bP b collisions? AuAu collisions? . . .
3 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Composite magnetic monopoles
Figure: from Patrizii and Spurio ’15.
’t Hooft-Polyakov ’74 No monopole source term in Lagrangian. Composite monopoles made up of particles lighter by a factor of O(α). Generally too heavy for LHC searches (except Cho-Maison?).
4 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Elementary magnetic monopoles
Elementary magnetic monopoles are a much overlooked possibility!
The Dirac string is just a coordinate singularity. Wu & Yang ’75
Consistent QFT of elementary monopoles exists, with monopole source term in Lagrangian.
Cabibbo & Ferrari ’62, Schwinger ’66, Zwanzinger ’71 Any mass possible, so could in principle be found in LHC searches.
5 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Can we make composite monopoles in “small” particle collisions?
Composite monopoles are not visible in perturbation theory, hence one expects that Witten ’79
−c/α −137c σMM¯ ∼ e ≈ e .
It has been argued that c ≈ 4. Drukier & Nussinov ’82 Such monopoles will never be produced in pp collisions.
Similar suppression explicitly demonstrated for:
– Kink production, Levkov et al. ’05, ’11
– Vacuum decays. Kuznetsov & Tinyakov ’97, Bezrukov et al. ’03
6 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Composite monopoles aren’t so easy to make
1 If composite magnetic monopoles exist, how can we make them? ((h hh((((h +h−hh((( (pp(collisions,(hhh (e (e(collisions,.hhhh . . P bP b collisions? AuAu collisions? . . .
2 If elementary magnetic monopoles exist, how can we make them? pp collisions? e+e− collisions? . . . P bP b collisions? AuAu collisions? . . .
7 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Can we make elementary monopoles in “small” particle collisions? Strong coupling
Large charge of magnetic monopoles, g = ngD, where gD := 2π/e and n ∈ Z, invalidates perturbation theory.
3 gqg gqg
Cross section for elementary monopole production in collisions of “small” particles is completely unknown,
σMM¯ ? 8 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Nothing learnt about elementary monopoles
1 If composite magnetic monopoles exist, how can we make them? ((h hh((((h +h−hh((( (pp(collisions,(hhh (e (e(collisions,.hhhh . . P bP b collisions? AuAu collisions? . . .
2 If elementary magnetic monopoles exist, how can we make them? pp collisions? e+e− collisions?. . . P bP b collisions? AuAu collisions? . . .
9 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions How else can we make magnetic monopoles?
Thermal Schwinger pair production Spontaneous production of magnetic monopoles in strong magnetic fields. Affleck & Manton ’82 Rate of production enhanced by energy from thermal bath.
10 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions The rate of pair production
Probability of producing one magnetic monopole pair,
PMM¯ = VΓT ,
where V is spacetime volume of the region with magnetic field and ΓT is the rate per unit volume at temperature T .
11 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions The calculation
Calculation of rate at strong coupling amounts to an all-orders summation of Feynman diagrams,
......
2 For sufficiently heavy monopoles, m gB, the calculation of ΓT is semiclassical, even at strong coupling, giving
m2 g3B mT Γ ∼ exp − S˜ , . T gB m2 gB
The results are valid for both elementary and composite magnetic monopoles. 12 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Understanding the rate
Viewed as a function of mass, m, for fixed g, B and T , ( slow , m & mthr(g, B, T ), ΓT (m) = fast , m . mthr(g, B, T ).
The threshold mass, mthr, can be deduced from S˜.
OG & Rajantie ’17
13 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Conditions in heavy ion collisions
Strong magnetic fields due to fast moving charges. Thermalisation appears to happen surprisingly quickly.
14 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions The cross section for heavy ion collisions Thermal Schwinger effect → cross section Magnetic monopole pair production cross section,
σMM¯ ≈ σN V ΓT
where σN is the inelastic nuclear cross section, V is the spacetime volume of the fireball and ΓT is the thermal Schwinger rate for magnetic monopoles.
Kinematic expectations: Azimuthally symmetric on average. Peaked transversally to beam. (γ − 1) = O(1). 15 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Heavy ion collisions can produce monopoles
1 If composite magnetic monopoles exist, how can we make them? ((h hh (((h +h−hh((( (pp(collisions,(h(hh (e (e(collisions,hhhh . . . P bP b collisions X, AuAu collisions X,. . .
2 If elementary magnetic monopoles exist, how can we make them? pp collisions? e+e− collisions? . . . P bP b collisions X, AuAu collisions X,. . .
16 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Heavy ion collisions at SPS
Magnetic monopole search in heavy ion collisions at SPS (He 1997) √ Pb-Pb collisions at sNN ≈ 17GeV. Experimental bound derived,
σMM¯ . σUB = 1.9nb.
Only sensitive to g ≥ 2gD.
From this, and by comparison with the calculated cross section, we find the following mass bound. ! g 3/2 m & 2.0 + 2.6 GeV gD
17 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Higher energy heavy ion collisions
What to expect from higher energies? √ For centre of mass energies per nucleon, sNN , well above ΛQCD, it is expected that √ B ∝ sNN , √ T ∝ log ( sNN ) .
However, at higher energies, a new issue arises: the short lifetime, τB, of the magnetic field, 1 τB ∝ √ . sNN
At LHC energies, this effect is significant and calls for new work.
18 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Experimental prospects MoEDAL had trapping detectors in place during the 2015 Pb-Pb collisions. Scanning these will give exciting new results, as much higher masses could have been reached. Higher energy Pb-Pb collisions at LHC scheduled for 2018.
Figure: from MoEDAL (2017).
19 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Magnetic monopole mass bounds
m/GeV 1000 ○ Pb-Pb(LHC 2018) ● Pb-Pb(SPS) ○ ★ Neutron stars ○ 100 ◆ Reheating/BBN ○
○ ● ● 10 ●
★ ★ 1 ★ ◆ ◆ ◆ ◆ ★
0.1 g/gD 1 2 3 4
Figure: from OG & Arttu Rajantie ’17.
20 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Theoretical prospects
Theory to-do list: Calculation of the cross section to next order. OG & Rajantie forthcoming Non-constant magnetic fields and temperatures. Kinematic distribution. Better understanding of instanton phase diagram.
21 / 22 Introduction Collisions of “small” particles Thermal Schwinger pair production Heavy ion collisions Conclusions Current best answers to our questions
1 If composite magnetic monopoles exist, how can we make them? ((h hh (((h +h−hh((( (pp(collisions,(h(hh (e (e(collisionshhhh . . . P bP b collisions X, AuAu collisions X,. . .
2 If elementary magnetic monopoles exist, how can we make them? pp collisions? e+e− collisions? . . . P bP b collisions X, AuAu collisions X,. . .
22 / 22