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• W4386257013 abstract "Abstract The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in $$alpha $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>α</mml:mi> </mml:math> , which is $$O(alpha ^5)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>5</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (B $$chi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>χ</mml:mi> </mml:math> PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen ( $$mu $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>μ</mml:mi> </mml:math> H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the B $$chi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>χ</mml:mi> </mml:math> PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius $$R_textrm{Z}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>R</mml:mi> <mml:mtext>Z</mml:mtext> </mml:msub> </mml:math> , if one uses the well-known experimental 1 S hfs in H or the 2 S hfs in $$mu $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>μ</mml:mi> </mml:math> H. We, respectively, obtain $$R_textrm{Z}(textrm{H}) = 1.010(9)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mtext>Z</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mtext>H</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1.010</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>9</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> fm, $$R_textrm{Z}(mu textrm{H}) = 1.040(33)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mtext>Z</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>μ</mml:mi> <mml:mtext>H</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1.040</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>33</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> fm. The total proton-structure effect to the hfs at $$O(alpha ^5)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>5</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the 1 S hfs in $$mu text {H}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mtext>H</mml:mtext> </mml:mrow> </mml:math> is $$182.640(18),textrm{meV}.$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mn>182.640</mml:mn> <mml:mo>(</mml:mo> <mml:mn>18</mml:mn> <mml:mo>)</mml:mo> <mml:mspace /> <mml:mtext>meV</mml:mtext> <mml:mo>.</mml:mo> </mml:mrow> </mml:math>" @default.
• W4386257013 created "2023-08-30" @default.
• W4386257013 creator A5010665511 @default.
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• W4386257013 creator A5073455286 @default.
• W4386257013 date "2023-08-29" @default.
• W4386257013 modified "2023-10-18" @default.
• W4386257013 title "Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen" @default.
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• W4386257013 doi "https://doi.org/10.1140/epjc/s10052-023-11866-4" @default.
• W4386257013 hasPublicationYear "2023" @default.
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