I am very surprised by your References, it looks like you have decided to rewrite history by neglecting relevant contributions. As far as the Higgs basis is concerned ..... everything was clarified years ago ... no need to repeat.
I did not read everything. also not ordered in terms of importance.
page 1: cite higgs discovery ? also, not all concrete bsm models are necessarily renormalizable and unitary... i would say. maybe debatable. what are "low degrees of freedom" ? then i think you are missing "e+e-" in "linear collider". then a reference for limits of lhc measurements for direct determination of the width ?
page 2/ others as well: why do you refer to the sections in footnotes ? would put it in the text
page 3: i dont quite understand the sentence about operators beyond doublets; this might have to be explained better; which oblique parameter is meant here ? reference ?
page 4: if i understand it correctly the current bound on higgs to invisible is now 11% from atlas combination. then, i think you do not really need the << in the relation between additional scalar mass and Higgs mass for this channel to open, if couplings are large enough it opens up instantaneously. maybe the expression for the partial width is in this limit ?
page 5: i think the figure needs better explanation. why is there only a band around the flat direction ? maybe clear to others, not so much to me.
figures 2.2 and 2.3: by dashed contour you mean dashed line ? which region is "enclosed by" the contour ? and why were these specific values chosec for the s_Vh,bb for each case/ is there a motivation ? i would also put the tilde in the caption, just to be consistent
page 43: initially means in the beginning/ first chapter ? you could also read it differently. maybe reformulate
Thank you for your comments. We have added the Higgs discovery and direct Higgs width limit references in the introduction. Since explicit BSM models may also have a limited range of validity, we have dropped the attributes renormalisable and unitary. We have clarified the meaning of low degrees of freedom. "linear collider" has been replaced with "e+e- collider". In the introduction, some cross references are included in footnotes as following them would be disruptive on first reading. The paragraphs on Higgs sectors beyond EW doublets and the oblique parameter (see arXiv:1903.07725) have been dropped. The invisible Higgs width reference and text have been updated and the h -> 2 phi statement has been clarified. The caption of Fig. 2.1 was improved. Changes were made to address the line/contour misunderstanding for Figs. 2.2 and 2.3. In the summary and conclusions chapter, "Initially" was replaced with "First" to guarantee nobody misinterprets it to mean "At the beginning of time".
Thanks a lot for the excellent and comprehensive work on the off-shell Higgs. I have some comments or maybe some silly questions, especially from the experimental and data analysis sides which I am working on currently in ATLAS. Not quite familiar with the theoretical parts for me.
page 2. the Footnote 3, Beyond LO... Could you specify the difficulties in more detail, (except for tools availability)? Because in the off-shell region, one of the most important diagrams gg->H*->ZZ is loop induced (or maybe we could say NLO for this diagram.). The detailed difficulty for which bases (except for tools availability) is very interesting.
page 13. The cross-sections of every process can be changed dramatically due to the different mass windows we choose (and negative + positive cancellation). Could you specify which mass window you choose? Maybe from 200GeV - 1000GeV shown in figure 3.2 ? From my results, the cross-sections of ctp for Squared term and Interference term are 0.00104 fb and -0.00079 fb in the process gg->H*->Z*Z* (two off-shell Z's) in mass windows 130GeV to 2TeV. Huge differences between us. And your Squared term is much large than mine.
page 13. Table 3.2 title: renormalization scale has been set to M_Z. The renormalization scale could be very important for the off-shell region, I suppose? It would be very great if you could include some discussions or references on this? Especially how much impact the renormalization scale could have. Currently, I need to estimate the theoretical uncertainties of the off-shell Higgs coupling constraints on EFT coefficients, say ctp, cpG. I would like to estimate the impact of the renormalization scale on the EFT coefficient fit.
page 13. Table 3.2 again but for dim-8 constraints and page 3 second paragraph. The squared term of ctp is significantly larger than its interference term. As the dim-8 interference term is the same \Lambda order as the dim-6 squared term (both of them are \Lambda^{-4}), is it possible to estimate the dim-8 and higher-dim using dim-6 squared term corrections for ctp? How to estimate if it's possible? Or some other ways to estimate dim-8 and higher-dim?
page 32. Eqn 4.45. Although it's very common that the fermion terms are only u,d,e, I was wondering why there is no "t", the top quark? Especially in the off-shell region, the mass term of the top quark is also very important in gg->top loop->H*-> whatever.
page 40-42, NLO corrections. In the SM or nominal analysis, we apply (multiply) a k-factor to account for the NLO or NNLO or even higher-order corrections. Such a k-factor is not small, like 1.7. (1) Due to the lack of precise NNLO or higher-order corrections now, is it correct to apply the same k-factor in the EFT analysis, say on ctp or cpG cross-section? (2) Are the systematics on the k-factor in EFT analysis the same as the SM or nominal analysis?
Thank you for your comments. Regarding footnote 3: In principle, all bases are equivalent. Any preference has to arise from practical or application-specific considerations. At NLO and beyond, multiple, interlinked subprocesses contribute, which inhibits the latter. Replies for Section 3.1: gg -> ZZ is computed inclusively, with no cuts on mZZ and with no Z decays. This is already clarified in the text. Therefore one cannot possibly compare with the numbers quoted in your comment. The renormalisation scale choice will substantially change the results. This is expected for a LO computation. In SMEFTatNLO, dynamical scales are not available (as this requires running the coefficients). Therefore, the fixed scale MZ was chosen. To compute scale uncertainties one has to vary the scale which is beyond the scope of this contribution. There is no easy way to compute all O(Lambda^-4) terms. What is shown in Table 3.2 is what one obtains from dim-6 operators. The contribution is focussing on the dim-6 operators of the SMEFT and doesn’t claim these are the dominant contributions at O(Lambda^-4). Regarding Chapter 4, Eq. (4.45): The symbols u, d and e represent sets of particles that also include the corresponding second and third generation particles. Regarding NLO corrections: There is no method to reliably estimate k-factors without the proper higher order calculations.
I am very surprised by your References, it looks like you have decided to rewrite history by neglecting relevant contributions. As far as the Higgs basis is concerned ..... everything was clarified years ago ... no need to repeat.
We have added theory references in the introduction. The dismissive, unspecific statement regarding the Higgs basis chapter is not helpful.
I did not read everything. also not ordered in terms of importance.
page 1: cite higgs discovery ? also, not all concrete bsm models are necessarily renormalizable and unitary... i would say. maybe debatable. what are "low degrees of freedom" ? then i think you are missing "e+e-" in "linear collider". then a reference for limits of lhc measurements for direct determination of the width ?
page 2/ others as well: why do you refer to the sections in footnotes ? would put it in the text
page 3: i dont quite understand the sentence about operators beyond doublets; this might have to be explained better; which oblique parameter is meant here ? reference ?
page 4: if i understand it correctly the current bound on higgs to invisible is now 11% from atlas combination. then, i think you do not really need the << in the relation between additional scalar mass and Higgs mass for this channel to open, if couplings are large enough it opens up instantaneously. maybe the expression for the partial width is in this limit ?
page 5: i think the figure needs better explanation. why is there only a band around the flat direction ? maybe clear to others, not so much to me.
figures 2.2 and 2.3: by dashed contour you mean dashed line ? which region is "enclosed by" the contour ? and why were these specific values chosec for the s_Vh,bb for each case/ is there a motivation ? i would also put the tilde in the caption, just to be consistent
page 43: initially means in the beginning/ first chapter ? you could also read it differently. maybe reformulate
Thank you for your comments. We have added the Higgs discovery and direct Higgs width limit references in the introduction. Since explicit BSM models may also have a limited range of validity, we have dropped the attributes renormalisable and unitary. We have clarified the meaning of low degrees of freedom. "linear collider" has been replaced with "e+e- collider". In the introduction, some cross references are included in footnotes as following them would be disruptive on first reading. The paragraphs on Higgs sectors beyond EW doublets and the oblique parameter (see arXiv:1903.07725) have been dropped. The invisible Higgs width reference and text have been updated and the h -> 2 phi statement has been clarified. The caption of Fig. 2.1 was improved. Changes were made to address the line/contour misunderstanding for Figs. 2.2 and 2.3. In the summary and conclusions chapter, "Initially" was replaced with "First" to guarantee nobody misinterprets it to mean "At the beginning of time".
Thanks a lot for the excellent and comprehensive work on the off-shell Higgs. I have some comments or maybe some silly questions, especially from the experimental and data analysis sides which I am working on currently in ATLAS. Not quite familiar with the theoretical parts for me.
page 2. the Footnote 3, Beyond LO... Could you specify the difficulties in more detail, (except for tools availability)? Because in the off-shell region, one of the most important diagrams gg->H*->ZZ is loop induced (or maybe we could say NLO for this diagram.). The detailed difficulty for which bases (except for tools availability) is very interesting.
page 13. The cross-sections of every process can be changed dramatically due to the different mass windows we choose (and negative + positive cancellation). Could you specify which mass window you choose? Maybe from 200GeV - 1000GeV shown in figure 3.2 ? From my results, the cross-sections of ctp for Squared term and Interference term are 0.00104 fb and -0.00079 fb in the process gg->H*->Z*Z* (two off-shell Z's) in mass windows 130GeV to 2TeV. Huge differences between us. And your Squared term is much large than mine.
page 13. Table 3.2 title: renormalization scale has been set to M_Z. The renormalization scale could be very important for the off-shell region, I suppose? It would be very great if you could include some discussions or references on this? Especially how much impact the renormalization scale could have. Currently, I need to estimate the theoretical uncertainties of the off-shell Higgs coupling constraints on EFT coefficients, say ctp, cpG. I would like to estimate the impact of the renormalization scale on the EFT coefficient fit.
page 13. Table 3.2 again but for dim-8 constraints and page 3 second paragraph. The squared term of ctp is significantly larger than its interference term. As the dim-8 interference term is the same \Lambda order as the dim-6 squared term (both of them are \Lambda^{-4}), is it possible to estimate the dim-8 and higher-dim using dim-6 squared term corrections for ctp? How to estimate if it's possible? Or some other ways to estimate dim-8 and higher-dim?
page 32. Eqn 4.45. Although it's very common that the fermion terms are only u,d,e, I was wondering why there is no "t", the top quark? Especially in the off-shell region, the mass term of the top quark is also very important in gg->top loop->H*-> whatever.
page 40-42, NLO corrections. In the SM or nominal analysis, we apply (multiply) a k-factor to account for the NLO or NNLO or even higher-order corrections. Such a k-factor is not small, like 1.7. (1) Due to the lack of precise NNLO or higher-order corrections now, is it correct to apply the same k-factor in the EFT analysis, say on ctp or cpG cross-section? (2) Are the systematics on the k-factor in EFT analysis the same as the SM or nominal analysis?
Thanks a lot!
Cheers,
Yingjie Wei
yingjie.wei@cern.ch
Thank you for your comments. Regarding footnote 3: In principle, all bases are equivalent. Any preference has to arise from practical or application-specific considerations. At NLO and beyond, multiple, interlinked subprocesses contribute, which inhibits the latter. Replies for Section 3.1: gg -> ZZ is computed inclusively, with no cuts on mZZ and with no Z decays. This is already clarified in the text. Therefore one cannot possibly compare with the numbers quoted in your comment. The renormalisation scale choice will substantially change the results. This is expected for a LO computation. In SMEFTatNLO, dynamical scales are not available (as this requires running the coefficients). Therefore, the fixed scale MZ was chosen. To compute scale uncertainties one has to vary the scale which is beyond the scope of this contribution. There is no easy way to compute all O(Lambda^-4) terms. What is shown in Table 3.2 is what one obtains from dim-6 operators. The contribution is focussing on the dim-6 operators of the SMEFT and doesn’t claim these are the dominant contributions at O(Lambda^-4). Regarding Chapter 4, Eq. (4.45): The symbols u, d and e represent sets of particles that also include the corresponding second and third generation particles. Regarding NLO corrections: There is no method to reliably estimate k-factors without the proper higher order calculations.