Symmetry-preserving calculation of pion light-front wave functions
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| Format: | Preprint |
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2025
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| _version_ | 1866911462224560128 |
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| author | Yao, Zhao-Qian Xu, Zhen-Ni Xiao, Yu-Yang Roberts, Craig D. Rodriguez-Quintero, Jose |
| author_facet | Yao, Zhao-Qian Xu, Zhen-Ni Xiao, Yu-Yang Roberts, Craig D. Rodriguez-Quintero, Jose |
| contents | Poincaré-covariant Bethe-Salpeter wave functions are used to calculate light-front wave functions (LFWFs) of the pion, $π$, and an analogue state, $π_{s\bar s}$. The current masses of the degenerate valence constituents in the $π_{s\bar s}$ are around $25$-times larger than those of the pion's valence constituents. Both valence spin-antialigned ($\mathcal L=0$) and valence spin-aligned ($\mathcal L=1$) components are obtained and combined to produce the complete LFWF for each system. Comparing predictions delivered by two distinct Bethe-Salpeter kernels, the impact of nonperturbative dynamical effects contained in the more sophisticated (bRL) kernel are seen to be significant; and contrasts between $π$, $π_{s \bar s}$ results reveal the interplay between emergent hadron mass and mass effects owing to Higgs-boson couplings. Amongst the results, one finds that for $π$, $π_{s\bar s}$, the LFWFs can be approximated by a separable form, with that representation being pointwise reliable in the bRL cases. Moreover, the $\mathcal L=1$ component is important; so a LFWF obtained after omission of this piece is typically a poor representation of the system. These features are naturally expressed in $π$, $π_{s\bar s}$ transverse momentum dependent parton distribution functions (TMDs). In this connection, it is found that a Gaussian \textit{Ansatz} can only provide a rough guide to TMD pointwise behaviour: magnitude deviations between \textit{Ansatz} and prediction exceed a factor of two on $k_\perp^2 \gtrsim 0.55\,$GeV$^2$. One should therefore be cautious in interpreting conclusions drawn from phenomenological analyses based upon Gaussian \textit{Ansätze}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry-preserving calculation of pion light-front wave functions Yao, Zhao-Qian Xu, Zhen-Ni Xiao, Yu-Yang Roberts, Craig D. Rodriguez-Quintero, Jose High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory Poincaré-covariant Bethe-Salpeter wave functions are used to calculate light-front wave functions (LFWFs) of the pion, $π$, and an analogue state, $π_{s\bar s}$. The current masses of the degenerate valence constituents in the $π_{s\bar s}$ are around $25$-times larger than those of the pion's valence constituents. Both valence spin-antialigned ($\mathcal L=0$) and valence spin-aligned ($\mathcal L=1$) components are obtained and combined to produce the complete LFWF for each system. Comparing predictions delivered by two distinct Bethe-Salpeter kernels, the impact of nonperturbative dynamical effects contained in the more sophisticated (bRL) kernel are seen to be significant; and contrasts between $π$, $π_{s \bar s}$ results reveal the interplay between emergent hadron mass and mass effects owing to Higgs-boson couplings. Amongst the results, one finds that for $π$, $π_{s\bar s}$, the LFWFs can be approximated by a separable form, with that representation being pointwise reliable in the bRL cases. Moreover, the $\mathcal L=1$ component is important; so a LFWF obtained after omission of this piece is typically a poor representation of the system. These features are naturally expressed in $π$, $π_{s\bar s}$ transverse momentum dependent parton distribution functions (TMDs). In this connection, it is found that a Gaussian \textit{Ansatz} can only provide a rough guide to TMD pointwise behaviour: magnitude deviations between \textit{Ansatz} and prediction exceed a factor of two on $k_\perp^2 \gtrsim 0.55\,$GeV$^2$. One should therefore be cautious in interpreting conclusions drawn from phenomenological analyses based upon Gaussian \textit{Ansätze}. |
| title | Symmetry-preserving calculation of pion light-front wave functions |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2512.13938 |