Correlating $h\to\mu^+\mu^-$ to the Anomalous Magnetic Moment of the Muon via Leptoquarks

Recently, both ATLAS and CMS measured the decay <math display="inline"><mrow><mi>h</mi><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math>, finding a signal strength with respect to the standard model expectation of <math display="inline"><mrow><mn>1.2</mn><mo>±</mo><mn>0.6</mn></mrow></math> and <math display="inline"><mrow><msubsup><mrow><mn>1.19</mn></mrow><mrow><mo>-</mo><mn>0.39</mn><mo>-</mo><mn>0.16</mn></mrow><mrow><mo>+</mo><mn>0.41</mn><mo>+</mo><mn>0.17</mn></mrow></msubsup></mrow></math>, respectively. This provides, for the first time, evidence that the standard model Higgs couples to second generation fermions. This measurement is particularly interesting in the context of the intriguing hints for lepton flavor universality violation, accumulated within recent years, as new physics explanations could also be tested in the <math display="inline"><mrow><mi>h</mi><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> decay mode. Leptoquarks are prime candidates to account for the flavor anomalies. In particular, they can provide the necessary chiral enhancement (by a factor <math display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>t</mi></mrow></msub><mo stretchy="false">/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math>) to address <math display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math> with tera-electron-volt scale new physics. In this Letter we point out that such explanations of <math display="inline"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math> also lead to enhanced effects in <math display="inline"><mrow><mi>h</mi><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> and we examine the correlations between <math display="inline"><mrow><mi>h</mi><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> and <math display="inline"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math> within leptoquark models. We find that the effect in the branching ratio of <math display="inline"><mrow><mi>h</mi><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> ranges from several percent up to a factor of 3, if one aims at accounting for <math display="inline"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math> at the <math display="inline"><mrow><mn>2</mn><mi>σ</mi></mrow></math> level. Hence, the new ATLAS and CMS Collaboration measurements already provide important constraints on the parameter space, rule out specific <math display="inline"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math> explanations, and will be very important to test the flavor anomalies in the future.