Axion-like particle production from lepton-nucleon scattering in chiral effective theory

In this work we study the axion/axion-like particle production from the lepton–nucleon scattering in the low-energy region, i.e., the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo>ℓ</a:mo> <a:mi>N</a:mi> <a:mo stretchy="false">→</a:mo> <a:mo>ℓ</a:mo> <a:mi>N</a:mi> <a:mi>a</a:mi> </a:math> processes, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mo>ℓ</d:mo> </d:math> being the electron or muon and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>N</f:mi> </f:math> the proton or neutron. We simultaneously include three different types of axion interaction couplings within the chiral effective field theory, namely the axion–nucleon–nucleon couplings <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>g</h:mi> <h:mrow> <h:mi>a</h:mi> <h:mi>N</h:mi> <h:mi>N</h:mi> </h:mrow> </h:msub> </h:math> , axion–photon–photon coupling <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi>g</j:mi> <j:mrow> <j:mi>a</j:mi> <j:mi>γ</j:mi> <j:mi>γ</j:mi> </j:mrow> </j:msub> </j:math> , and axion–photon–vector meson resonance couplings <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>g</l:mi> <l:mrow> <l:mi>ρ</l:mi> <l:mi>a</l:mi> <l:mi>γ</l:mi> </l:mrow> </l:msub> </l:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>g</n:mi> <n:mrow> <n:mi>ω</n:mi> <n:mi>a</n:mi> <n:mi>γ</n:mi> </n:mrow> </n:msub> </n:math> . Vast inputs from the lattice QCD and hadron phenomenological studies are used to fix the unknown couplings. The relative strengths of different axion interactions in the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mo>ℓ</p:mo> <p:mi>N</p:mi> <p:mo stretchy="false">→</p:mo> <p:mo>ℓ</p:mo> <p:mi>N</p:mi> <p:mi>a</p:mi> </p:math> processes are then revealed. We provide detailed predictions for the differential cross sections with respect to various angles and axion energy, as well as the total cross sections in the low-energy region around production thresholds, both for the Kim-Shifman-Vainstein-Zakharov (KSVZ) and Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion models.