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The leptonic decay of charged pions is investigated in the presence of background magnetic fields. In this situation, Lorentz symmetry is broken, and new fundamental decay constants need to be introduced, associated with the decay via the vector part of the electroweak current. We calculate the magnetic field dependence of both the usual and a new decay constant nonperturbatively on the lattice. We employ both Wilson and staggered quarks and extrapolate the results to the continuum limit. With this nonperturbative input, we calculate the tree level electroweak amplitude for the full decay rate in strong magnetic fields. We find that the muonic decay of the charged pion is enhanced drastically by the magnetic field. We comment on possible astrophysical implications.

Strong (electro)magnetic fields bear a significant impact on the physics of various systems, ranging from off-central heavy-ion collisions through the evolution of the early universe to magnetized neutron stars (magnetars). In particular, many novel phenomena emerge from the competition between electromagnetism and color interactions if the magnetic field

Such a background magnetic field is known, for instance, to affect the phase diagram of quantum chromodynamics (QCD)

The

In this Letter, we investigate the magnetic field dependence of the decay rate of charged pions at zero temperature. We demonstrate that the previous studies in this direction are incomplete: in the presence of the magnetic field, both neutral and charged pions have two independent decay constants, of which only one has been investigated up to now. We determine both decay constants for charged pions nonperturbatively on the lattice, employing two different fermionic discretizations. Using this QCD input, we proceed to calculate the weak decay rate using leading-order electroweak perturbation theory. For this calculation, we employ the lowest Landau level (LLL) approximation for the outgoing charged lepton state, which is a viable simplification for strong background magnetic fields. Our preliminary results using Wilson fermions on a reduced set of lattice spacings were presented in Ref.

The pion decay constant is related to the hadronic matrix elements

In the presence of a background electromagnetic field

We consider a background magnetic field

The matrix element of the vector current can also be interpreted from a different perspective: the magnetic field mixes the pion with the

We mention that for nonzero temperature, an additional vector

The weak interaction matrix element

We work at the tree level of electroweak perturbation theory and employ the effective, four-fermion interaction with Fermi’s constant

The decay rate

For strong fields, the dominant contribution stems from the lowest Landau level. The sum over the multiplicity of the LLL states gives

Having determined

Equation

In the second set of simulations, we work with

The general measurement strategy involves the analysis of the matrix elements

For Wilson quarks, we employ smeared pseudoscalar sources (for more details, see Ref.

Inspecting the

The normalized combinations

Continuum extrapolation (gray bands) of the decay constants for staggered (upper panel) and Wilson quarks (lower panel). Both panels include results for

Motivated by the dependence of

For low magnetic fields, the ratio

To determine the decay rate

The muonic decay rate in units of its

We remark that Eq.

In this Letter, we computed the rate for the leptonic decay of charged pions in the presence of strong background magnetic fields. The result is given by Eq.

We demonstrated that—besides the ordinary pion decay constant

Our final result for the full decay rate is visualized in Fig.

Similarly to the pion decay rate, the magnetic field will have an impact on (inverse)

This research was funded by the DFG (Emmy Noether Programme EN 1064/2-1 and SFB/TRR 55). G. B. thanks Basudeb Dasgupta for discussion. The computations were carried out on the GPU, iDataCool and Athene 2 clusters of Universität Regensburg.