The measurements of the total cross section of the <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M2"><ns0:msup><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow><ns0:mrow><ns0:mo>+</ns0:mo></ns0:mrow></ns0:msup><ns0:msup><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow><ns0:mrow><ns0:mo>&#8722;</ns0:mo></ns0:mrow></ns0:msup><ns0:mo>&#10230;</ns0:mo><ns0:mi>&#947;</ns0:mi><ns0:mi>&#947;</ns0:mi><ns0:mfenced open="(" close=")"><ns0:mrow><ns0:mi>&#947;</ns0:mi></ns0:mrow></ns0:mfenced></ns0:math> reaction from the VENUS, TOPAS, OPAL, DELPHI, ALEPH, and L3 collaborations, collected between 1989 and 2003, are used to perform a <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M3"><ns0:msup><ns0:mrow><ns0:mi>&#967;</ns0:mi></ns0:mrow><ns0:mrow><ns0:mn>2</ns0:mn></ns0:mrow></ns0:msup></ns0:math> test to validate the current quantum electrodynamics (QED) theory and search for possible deviations with the direct contact term annihilation. By observing a deviation from the QED predictions on the total cross section of the <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M4"><ns0:msup><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow><ns0:mrow><ns0:mo>+</ns0:mo></ns0:mrow></ns0:msup><ns0:msup><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow><ns0:mrow><ns0:mo>&#8722;</ns0:mo></ns0:mrow></ns0:msup><ns0:mo>&#10230;</ns0:mo><ns0:mi>&#947;</ns0:mi><ns0:mi>&#947;</ns0:mi><ns0:mfenced open="(" close=")"><ns0:mrow><ns0:mi>&#947;</ns0:mi></ns0:mrow></ns0:mfenced></ns0:math> reaction above <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M5"><ns0:msqrt><ns0:mrow><ns0:mi>s</ns0:mi></ns0:mrow></ns0:msqrt><ns0:mo>=</ns0:mo><ns0:mn>180.0</ns0:mn></ns0:math>&#8201;GeV, a non-QED direct contact term is introduced following the dimension 6 effective theory to explain the deviation. In the non-QED direct contact term, a threshold energy scale <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M6"><ns0:mi>&#923;</ns0:mi></ns0:math> is included and explained to the finite interaction length in direct contact term and in consequence the size of the electron involved in the annihilation area. The experimental data of the total cross section is compared to the QED cross section by a <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M7"><ns0:msup><ns0:mrow><ns0:mi>&#967;</ns0:mi></ns0:mrow><ns0:mrow><ns0:mn>2</ns0:mn></ns0:mrow></ns0:msup></ns0:math> test, which gives a best fit of the <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M8"><ns0:mi>&#923;</ns0:mi></ns0:math> to be <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M9"><ns0:mn>1576</ns0:mn><ns0:mo>&#177;</ns0:mo><ns0:mn>202</ns0:mn></ns0:math>&#8201;GeV, corresponding to a finite interaction length of <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M10"><ns0:msub><ns0:mrow><ns0:mi>r</ns0:mi></ns0:mrow><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow></ns0:msub><ns0:mo>=</ns0:mo><ns0:mfenced open="(" close=")"><ns0:mrow><ns0:mn>1.25</ns0:mn><ns0:mo>&#177;</ns0:mo><ns0:mn>0.16</ns0:mn></ns0:mrow></ns0:mfenced><ns0:mo>&#215;</ns0:mo><ns0:mn>1</ns0:mn><ns0:msup><ns0:mrow><ns0:mn>0</ns0:mn></ns0:mrow><ns0:mrow><ns0:mo>&#8722;</ns0:mo><ns0:mn>17</ns0:mn></ns0:mrow></ns0:msup></ns0:math> (cm). In the direct contact term annihilation, this interaction length is a measure of the size of an electron <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M11"><ns0:msub><ns0:mrow><ns0:mi>r</ns0:mi></ns0:mrow><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow></ns0:msub></ns0:math>. By combining all the data results from the mentioned collaborations, we have at least 2 to 3 times more statistics than every single experiment at high <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M12"><ns0:msqrt><ns0:mrow><ns0:mi>s</ns0:mi></ns0:mrow></ns0:msqrt></ns0:math> region. This induces the best precision on <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M13"><ns0:msub><ns0:mrow><ns0:mi>r</ns0:mi></ns0:mrow><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow></ns0:msub></ns0:math> compared to the previous measurements.

China

Minghui Liu

Yutao Chen

Switzerland

Jürgen Ulbricht

Hint for a Minimal Interaction Length in <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M1"><ns0:msup><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow><ns0:mrow><ns0:mo>+</ns0:mo></ns0:mrow></ns0:msup><ns0:msup><ns0:mrow><ns0:mi>e</ns0:mi></ns0:mrow><ns0:mrow><ns0:mo>&#8722;</ns0:mo></ns0:mrow></ns0:msup><ns0:mo>&#10230;</ns0:mo><ns0:mi>&#947;</ns0:mi><ns0:mi>&#947;</ns0:mi></ns0:math> Annihilation in Total Cross Section of Center-of-Mass Energies 55-207&#8201;GeV

Experimental data reveal with a 5<math id="M2"><mrow><mi>σ</mi></mrow></math> significance the existence of a characteristic minimal length <math id="M3"><msub><mrow><mi>l</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>=</mo><mn>1.57</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>-</mo><mn>17</mn></mrow></msup></math> cm at the scale <math id="M4"><mi>E</mi><mo>=</mo><mn>1.253</mn></math> TeV in the annihilation reaction <math id="M5"><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>→</mo><mi>γ</mi><mi>γ</mi><mo>(</mo><mi>γ</mi><mo>)</mo></math>. Nonlinear electrodynamics coupled to gravity and satisfying the weak energy condition predicts, for an arbitrary gauge invariant Lagrangian, the existence of spinning charged electromagnetic soliton asymptotically Kerr-Newman for a distant observer with the gyromagnetic ratio <math id="M6"><mi>g</mi><mo>=</mo><mn>2</mn></math>. Its internal structure includes a rotating equatorial disk of de Sitter vacuum which has properties of a perfect conductor and ideal diamagnetic, displays superconducting behavior, supplies a particle with the finite positive electromagnetic mass related to breaking of space-time symmetry, and gives some idea about the physical origin of a minimal length in annihilation.