Hadron structure from basis light-front quantization

I. A little context of why LFWF are a good/interesting strategy, and what alternative approaches exist would be useful for general readers.

Our response: We thank the referee for the suggestions. To implement the referee’s suggestion, we have added the following sentences at the end of the paragraph just after Eq. (2): →

“The LFWFs are boost invariant in the longitudinal and the transverse directions. The BLFQ approach employs a suite of analytical and numerical techniques for setting up and solving the eigenvalue problem in a convenient basis space [3-5]. Complementary insights into nonperturbative QCD can be achieved from the discretized space-time euclidean lattice [6] and the Dyson-Schwinger equations of QCD [7].”

II. Page 4: The EMFF description is derscribed as ”impressive”; there are, however, notable deviations from the data, with the LH plot systematically overshooting higher-Q^2 points. Quantitatively, how good is the fit; is the high-Q^2 mismatch understood; and how does this description look from other approaches ?

Our response: We adjusted the model parameters by fitting the light mesons mass-spectroscopy. Note that we did not fit the EMFF of the pion. This is our prediction. The notable deviation of our EMFF from the data at high-Q 2 can be understood from the basis truncation in the transverse direction (Nmax ) in our BLFQ approach. Our current truncation (Nmax = 14) implies the UV regulator ≈ 1 GeV, where b is the harmonic oscillator scale parameter. Thus, our predictions are most reliable in the low Q^2 region, where our result is also consistent with other theoretical approaches and phenomenological models (lattice QCD, Dyson-Schwinger equations, light-front holography, constituent quark model etc.).

Modification: We have modified the following sentence “We find an impressive agreement between our results and the precise low Q^2 EMFF data.” to

“We find consistency between our results and the precise low Q^2 EMFF data. Meanwhile, notable deviations have been observed at large Q 2 . Note that our choice of N max , implies the UV regulator ≈ 1 GeV [4]. Thus, our predictions are most reliable in the low Q ^2 region.”

III. The nucleon description shows plots of GPDs and TMDs, but not the collinear PDFs, where comparison to global-fit models would be interesting. Could such a plot be included?

Our response: As suggested by the referee, we have now included the plot for the nucleon PDFs in Fig. 5. The corresponding discussions have been added before conclusion.

IV. A short conclusion mentioning the next intended steps from here would be nice to have, and conclude the contribution well.

Our response: As suggested by the referee, a short conclusion and outlook have been included.

Attachment:

response_ISMD_de41iyQ.pdf