Production of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:math> pairs through the decay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ϕ</mml:mi> </mml:math> mesons
Bibliographic record
Abstract
We develop a theoretical framework for the production of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>K</a:mi> <a:mo>+</a:mo> </a:msup> <a:msup> <a:mi>K</a:mi> <a:mo>−</a:mo> </a:msup> </a:math> pairs through the decay of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ϕ</c:mi> </c:math> mesons produced from a thermal background, based on the Nambu-Jona-Lasinio (NJL) model. The differential production rate of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>K</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>K</e:mi> <e:mo>−</e:mo> </e:msup> </e:math> is related to the self-energy of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>ϕ</g:mi> </g:math> meson, incorporating the contributions of the quark loop at leading order and the kaon loop at next-to-leading order in the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mn>1</i:mn> <i:mo>/</i:mo> <i:msub> <i:mi>N</i:mi> <i:mi>c</i:mi> </i:msub> </i:math> expansion. We numerically evaluate the invariant mass spectrum of the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi>K</k:mi> <k:mo>+</k:mo> </k:msup> <k:msup> <k:mi>K</k:mi> <k:mo>−</k:mo> </k:msup> </k:math> pair both in vacuum and at finite temperature. The inclusion of the kaon loop results in a finite width of the spectrum, improving agreement with experimental data. We also investigate the spin alignment of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>ϕ</m:mi> </m:math> meson induced by its motion relative to the thermal background. In the NJL model with only chiral condensates, we find that deviations from the unpolarized limit of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mn>1</o:mn> <o:mo>/</o:mo> <o:mn>3</o:mn> </o:mrow> </o:math> are negligible.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.002 | 0.006 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.001 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".