Talk:Electroweak interaction/Archive 1

Archive 1

Unification with Strong Interaction

Should someone point out that this force has been shown to be identical to the strong force at high enough energy states? —Preceding unsigned comment added by 167.206.78.2 (talk) 6 March 2002

Duh?!!! Thaz something new to me.. can you state some external websites for reference plz? —Preceding unsigned comment added by 62.211.62.220 (talk) 6 March 2002

Identical isn't perhaps the best description. It is believed to unify with strong force to form the hyperweak force at high enough energies in the same way as the elctromagnetic and weak forces unify to make the electroweak force itself. Anyway, this is all somewhat speculative as I don't think there is any fully developed theory of how this works (at least that is successful in producing other aspects of the SM). Additionally, I belive supersymmetry is required to make this unification take place, and that in itself is still a hotly debated area with little or no experimental backup. —Preceding unsigned comment added by Jcobb (talk • contribs) 22:58, 20 February 2004

The unification with the strong force is the subject of grand unified theories. Maybe just a "see also"? —Preceding unsigned comment added by 24.147.149.53 (talk) 19:01, 12 September 2004

Here's one: see electronuclear force. — Herbee 13:06, 29 December 2005 (UTC)

Name of article

Shouldn't this article be entitled 'Electroweak theory' (or something along those lines) instead of 'Electroweak force '? The other fundamental forces have separate pages for the forces and the theories describing those forces. MP (talk) 10:27, 28 December 2005 (UTC)

Experimental evidence

If I am not mistaken, there should be discussion of experimental evidence. The article posits the union of the electromagnetic interaction with the weak interaction at energies of 100 GeV. Energies of 200 GeV are not uncommon in accelerators these days. The Tevatron at Fermilab reaches 2 TeV, and the Large Hadron Collider will reach 14 TeV (combined energy). Hu 05:39, 24 March 2006 (UTC)

I second that motion. On the QGP page, it says "The theory of weak interactions has been tested and found correct to a few parts in a thousand". Examples, anyone? Wikipedia brown 06:35, 19 July 2006 (UTC)

To-do List?

Would someone be willing to make up at least a tenative to-do list for this article? Its kind of a shame that Katie Holmes had a featured article on the main page, but this article, based on Nobel prize winning research is still a stub. I'd do it, but I'm afraid I'm woefully unqualified, being only an undergraduate, with limited experience in this specific segement of high-energy physics. -Davepetr 06:56, 9 April 2006 (UTC)

At least, someone could write something about Quantum flavordynamics (QFD). I think that Electroweak Theory = QED + QFD. I do not know what is the current status of QFD... Urvabara 10:03, 2 November 2007 (UTC)

As a layman I'd like to know how the forces can be unified when different carriers are employed for EM and WNF. --Belg4mit (talk) 04:12, 2 July 2011 (UTC)

Lagrangian diagram

As the first thing to do, may I suggest someone correct the Lagrangian diagram?

• The lambda in the Higgs field self-interaction has the wrong sign (and possibly the mu squared as well, although that might depend on convention; these two terms having opposite sign is clearer IMO).
• The gauge field term coefficient in B in the left-handed field should be 1/2 the coefficient in the right handed field. They are currently shown as identical.
• Would be nice if the two gauge fields associated the Higgs differential operator were made explicit, as they have been made for the electron and neutrino.

See Quantum Field Theory: A Modern Introduction (1993), ISBN 0-19-507652-4 page 336 by Michio Kaku . I'd make the changes myself, but I'm not sure how.--Michael C. Price ^talk 12:21, 8 June 2007 (UTC)

Is there a reason we have this as an image? It's not as clear as it would be as LaTeX. --Taejo|대조 12:16, 16 June 2007 (UTC)

I see some much needed updates are being done. Suggestion: that we have a before and after symmetry-breaking version. --Michael C. Price ^talk 20:09, 10 July 2007 (UTC)

Agreed on the need for a lot of work and on the usefulness of a post EWSB Lagrangian, including the CKM matrix. This was a first pass at getting something that was correct and aligned with standard notation. jay 22:57, 10 July 2007 (UTC)

I made several corrections to the lagrangean before realizing I wasn't logged in. Sorry about that. There are still corrections to be made. Dauto (talk) 17:59, 19 January 2008 (UTC)

What a bunch of formulae (: each of those would deserve an article of its own --82.130.14.173 (talk) 21:55, 4 March 2008 (UTC)

I would suggest someone add the definitions of all the variables involved in the lagrangian, even to the point of saying that the "a" sub/superscripts on the W run over 1,2,3. This would make it more parseable to nonphysicists. —Preceding unsigned comment added by 134.107.13.185 (talk) 14:17, 11 March 2010 (UTC)

Agreed. I'd particularly like to see the substitutions that were necessary to get from the unbroken- to the broken-symmetry Lagrangian. — Preceding unsigned comment added by 130.246.132.177 (talk • contribs) 19:25, 9 July 2012‎ (UTC)

I think that "h.c." means the Hermitian conjugate of the preceding terms (the anti-matter analogue). But I still have not figured out what "g" and "f^abc " mean. JRSpriggs (talk) 10:16, 23 July 2012 (UTC)

"g" is the electroweak coupling constant.

"f^abc " are the structure constants of the Lie algebra. (i.e. if g^a is a basis of the lie algebra (su(2)x u(1) in this case), then [g^a,g^b]=i f^abcg^c).

(Also, wow this article is an unreadable mess)TR 10:43, 23 July 2012 (UTC)

In the before Lagrangian, in this term:

${\mathcal {L}}_{f}={\overline {Q}}_{i}iD\!\!\!\!/\;Q_{i}+{\overline {u}}_{i}^{c}iD\!\!\!\!/\;u_{i}^{c}+{\overline {d}}_{i}^{c}iD\!\!\!\!/\;d_{i}^{c}+{\overline {L}}_{i}iD\!\!\!\!/\;L_{i}+{\overline {e}}_{i}^{c}iD\!\!\!\!/\;e_{i}^{c}$

I take it that $e_{i}\,$ varies over the spinors for the electron, muon, and tauon as i=1,2,3. Right?
Similarly, $d_{i}\,$ varies over the spinors for the down quark, strange quark, and bottom quark as i=1,2,3. Right?
And, $u_{i}\,$ varies over the spinors for the up quark, charm quark, and top quark as i=1,2,3. Right?
So what do $L_{i}\,$ and $Q_{i}\,$ mean? And what does the superscript ^c mean? JRSpriggs (talk) 21:01, 23 July 2012 (UTC)

Yes, the "i" index appears to enumerate the generation.

The lower case letters (u,d,e) indicate the right-handed fermions (each forms a singlet under the weak SU(2) symmetry). The uppercase letters (Q,L) indicated the left handed SU(2) doublets. I.e. Q=(u_L,d_L) L=(ν_L,e_L).

As for the ^c superscript. This is normally used to indicate the charge conjugated field. However, I am puzzled why somebody would use it in the Lagrangian like that. (the sources I checked simply have the plain fields in that location.) It might have to do with specific conventions used by the author.

The c does indeed denote charge conjugation. It's a convention to write it like this so that it's clear that the fields appearing in the lagrangian are all left handed. That is, rather than using the right-handed singlet states, the charge conjugate fields of them are used. It's not hard to argue that it's mathematically (more) valid, but I think it's an unnecessary complication in the equation, and I will remove it in some other edits that I'm making. --Certain (talk) 00:37, 16 August 2012 (UTC)

BTW, if you are trying to figure out what the hell is going on in this Lagrangian, I recommend NOT using this article. Instead pick up a proper book on QFT. For example this Lagrangian is treated in depth in chapter 20.2 of Peskin&Schroeder, Introduction to Quantum Field Theory. It may be though for a lay reader, but at least they explain what their notation means, making it a lot easier to parse than this article.TR 22:04, 23 July 2012 (UTC)

OK---I did a little cleaning up to the lagrangian in the section before EWSB, but when I got to the last two terms I realized this is just a complete mess. It seems odd to include the Higgs VEV explicitly in the higgs term in the section before EWSB. (Maybe even silly to include the higgs term at all, no?). The Yukawa term should also probably be reformatted to just have the coupling of the left- and right-handed fields by the masses, without mention of the Higgs field. This term can then be redescrbed in the post EWSB section as a Yukawa interaction with the higgs field. Overall: this article is a mess. --Certain (talk) 00:47, 16 August 2012 (UTC)

I think that "before EWSB" here is supposed to mean "before expanding the Higgs field around its ground state", i.e. the Lagrangian in its explicit symmetric form. Not, the Lagrangian of the SM before anybody included terms that lead to EWSB.TR 06:35, 16 August 2012 (UTC)

Then it's definitely incorrect to include the vev in that section, because then the field is already being expanded around the vev. It might just be best to scrap almost all of this page and put a link to the higgs mechanism page. (Though I haven't thoroughly read that page, it does appear more correct.) This won't show the specific application of the mechanism to the SM a la Weinberg & Salam, but it will be more valuable as a properly formatted reference.--88.64.10.112 (talk) 22:59, 19 August 2012 (UTC)

The only place where the vev appears in that section is in the potential of the Higgs field, where it is a parameter. That is certainly correct. In fact, despite being badly written as an encyclopedic entry, the treatment given here is mostly consistent with the treatment of this very subject in Peskin & Schroeder.TR 07:33, 20 August 2012 (UTC)

Unified theory of Eletroweak Interactions

I guess I should also point out that, as it stands, the article implies that the Electroweak theory (EWT) is a theory of the unified electromagnetic and weak interactions. That's an extremely common misconception. Correct would be to call it the unified theory of the electromagnetic and weak interactions. What's the difference? It is an unified theory in the sense that describes both interactions in one single self-consistent framework, but the theory still requires two different coupling constants and as such does not constitute a unification of interactions in the same sense that the term is used when talking about grand unified theory (GUT). Unlike EWT, GUT models do indeed unify three interaction (electromagnetic, weak, and strong) as three different aspects of a single interaction. only one coupling constant is needed. —Preceding unsigned comment added by Dauto (talk • contribs) 18:30, 19 January 2008 (UTC)

Hot Universe?

How is a hot Universe different than hot matter in a universe? Does the entire universe need to be hot in order to unify the forces or is it enough for only the part of the universe inside a box to be hot in order to unify the forces inside a box? —Preceding unsigned comment added by 76.126.215.43 (talk) 18:57, 9 July 2009 (UTC)

The term "hot universe" refers to a situation where the entire universe contains particles that are "hot" (in this case, posessing energies above the electroweak unification scale). You are correct in noting that any finite region satisfying this condition would also have unification-type behavior occur within that region. That's more or less how particle accelerators attempt to study it (you can consider the colliding particles as producing a very small region in which this condition is satisfied, though there are many other ways of looking at it that are also valid). The whole-universe case is interesting because we're reasonably sure our universe went through a period where it was this hot, which may have left some detectable signature or imprint that tells us about the exact nature of the unification. --Christopher Thomas (talk) 05:14, 10 July 2009 (UTC)

And where are Maxwell's Equations?

if they can't pull Maxwell's equations out of their particle theory then they have not unified anything at all. It is a gross exaggeration to claim they have unified electro with weak. And without the hypothetical big bang the conditions for their theory don't even exist in nature. Also, what they are really playing with is QED which is just a shell game as Feynman admitted. 173.169.90.98 (talk) 13:37, 20 April 2010 (UTC)

But you can pull ME out of EW theory. --Michael C. Price ^talk 16:36, 20 April 2010 (UTC)

Do you have a question about the article or are you simply ranting? FYI Maxwell equations come out of the Lagrangian as part of the equations of motion. Dauto (talk) 16:52, 28 April 2011 (UTC)

Maxwell's equations are that 1/4 A^uv A_uv term in the broken Lagrangian. "A" is made up of various combinations of derivatives of the E and B fields. — Preceding unsigned comment added by 130.246.132.177 (talk • contribs) 19:25, 9 July 2012‎ (UTC)

Redirect

Would anyone like to create a redirect from electroweak unification? 70.247.169.197 (talk) 01:14, 11 August 2010 (UTC)

More on history

The article needs more on the history of this theory, e.g., what was the first paper written on it and when did it appear? What precursor work was done? What persons/groups were "also-rans"? The theory is part of the Standard Model now, but were/are there any objections to it? Etc. --96.233.94.233 (talk) 02:04, 27 April 2011 (UTC)

Remove reference to W0

There is a reference to a W0 boson in this article, which is should be a Z0 boson, surely. Just checking in here before I fix it. — Preceding unsigned comment added by 202.36.29.1 (talk) 02:27, 13 November 2012 (UTC)

Do not "fix" it; it is OK as is. If you read the article, you will see that the W⁰ mixes with the B⁰ to produce the Z⁰ and the photon. JRSpriggs (talk) 07:55, 13 November 2012 (UTC)

Does it add same teams twice?

in the section After electroweak symmetry breaking, the quadratic terms L(K) was including mass terms, which are repeated in the terms L(HV) and L(Y). But they are added up in the first formula. Am I right?--Haojian (talk) 03:34, 18 February 2014 (UTC)

L_K contains only terms with two fields, while L_HV and L_Y contain only terms with more than two, so there can't be repeated terms.-Dilaton (talk) 18:55, 19 February 2014 (UTC)

Could I say that, the mass terms in L_K are interactions between particle fields and Higgs field, in which the Higgs field was regarded as constant and then was packed into the mass values, so contain only two particle fields; on the other hand, L_HV and L_Y contain SAME terms in which the Higgs field was regarded as one of fields, so these teams contain more than two fields?--Haojian (talk) 02:39, 10 March 2014 (UTC)

This is after symmetry breaking, so the masses were established via the Higgs mechanism, and there is now the "seperate" Higgs field.-Dilaton (talk) 06:12, 10 March 2014 (UTC)

The fields can be separate, but the teams are still identity?--Haojian (talk) 07:55, 10 March 2014 (UTC)

codata 2014

CODATA 2014 gives sw²=0.2223(21) thus sw=0.471487

$M_{Z}={\frac {M_{W}}{\cos \theta _{W}}}$ gives $c_{w}=\cos \theta _{W}=M_{W}/M_{Z}={\sqrt {1-s_{w}^{2}}}=0.88187$

the 2nd diagram gives

$e=\sin \theta _{W}\cdot g$ giving $g=e/\sin \theta _{W}=3.398\cdot 10^{-19}$C

$e=\cos \theta _{W}\cdot g'$ giving $g'=e/\cos \theta _{W}=1.81679\cdot 10^{-19}$C

all correct? Ra-raisch (talk) 21:44, 3 August 2017 (UTC)

By and large, yes. Cuzkatzimhut (talk) 13:25, 4 August 2017 (UTC)

good, I think it would be an enrichment, I'm not sure which page would be the appropriate place. Besides these quantities and formulas could be posted alongside:

$\alpha _{s}=\alpha /c_{w}^{2}=(g'/q_{P})^{2}=0.009383$

$\alpha _{w}=\alpha /s_{w}^{2}=(g/q_{P})^{2}=0.03283$

and may-be these too:

$g_{s}={\sqrt {4\pi \alpha _{s}}}=0.34338$

$g_{w}={\sqrt {4\pi \alpha _{w}}}=0.6423$

only I am not sure how to name all of these quantities. (gauge parameters: gs and gw, coupling strength = charge: g and g', coupling constants αw and αs). Anybody feel free to fulfill the job. Ra-raisch (talk) 15:47, 4 August 2017 (UTC)

I am not inclined to do this myself. I feel that anyone looking at it would go back and forth to Planck charge half a dozen times, and tweak the obvious formulas wondering why, oh why, wasn't the standard q_P' used. Nobody I've ever met looks at the hypercharge coupling g' as anything but a tanθ multiple of g, and, really, g as anything but e/sinθ . So once one is at peace, truly at peace, with the $e\approx 0.30282212088~q_{\text{P}}'$, suitably updated, of course, of that article, I don't see the point of idle lists of symbols. Perhaps one could insert a footnote with just that value, or else a link to the definitions. In any and all applications, final answers are related to the electric charge, (and, frankly, the dimensionless fine structure constant α), multiplied by suitable powers of ħ and c. I would doubt that this is a proper venue for electric charge metrology... Perhaps other editor has bright ideas on this.... Cuzkatzimhut (talk) 16:39, 4 August 2017 (UTC)

citation of the main text: Above the unification energy, on the order of 246 GeV, ...

We most times think that the grand unified theory it's only about extremely high energy, but it can work as well if the higgs field at a phase transition causes the threshold of quantum noise of the void to lower even more. Theoretically that will lead to big bang. We shouldn't add that here, but electromagnetism is well attested, so filtering our thoughts through what works well, might help.

Meaning of "before" and "after"

In the sections titled Before (and after) Spontaneous Symmetry Breaking, I think it would be good to clarify whether (a) Before and After refer to the sequence in which the equations are derived, or (b) Before and After refer to some event in cosmology when the forces diverged, or (c) both (a) and (b) Spope3 (talk) 04:07, 6 April 2018 (UTC)

Well, I suspect it is left open-ended to accommodate all points of view: Strictly speaking, "before" would be for a vanishing order parameter v, and "after" for a non-vanishing one. However, traditionally, SSB is introduced pedagogically as some sort of an option to expand fields around the proper vanishing v.e.v. for non-vanishing v, as though SSB were a matter of variable choice!?! Still, hopefully, nobody is confused when "before" refers to the field operators and "after" to excitations around the physical vacuum. Cosmological transitions might be best described by situations above or below SSB energy scales. In any case, if there were a sound, pithy, concise, qualification or footnote you'd propose, it could be helpful; provided no torrent of ambiguous verbiage were introduced that would raise more questions than it could answer. Cuzkatzimhut (talk) 18:36, 6 April 2018 (UTC)

I think it's clear that "before" and "after" refer to the derivation. Whether they also refer, or should refer, to the cosmological sequence is not clear to me. The article on "Electroweak Epoch" refers the the (merged) electroweak force, so that might mean before SSB, but also refers to W and Z bosons being created during this epoch (not the pre-SSB massless bosons). I don't have the technical understanding to know what's up with that, but it seems to suggest the weak mixing angle was already a law of nature and did not only come into existence when the weak force froze out.

So, I'm not adding any verbiage to the main text here.

Spope3 (talk) 01:29, 7 April 2018 (UTC)

Accessibility

I'm writing this here to discuss some of my thoughts regarding a recent edit I made. While it is not my intention to duplicate content across pages, or to "dumb down" this page, I do believe strongly that each article should stand by itself and be accessible to as wide of an audience as possible - many people who are not physicists will be curious to understand the fundamental ways in which our universe works. This page, particularly as it was before my recent edit, relies heavily on jargon and opaque-seeming equations that can scare away many readers - including readers who may have a strong amount of curiousity and ambient knowledge about particle physics, but have never actually taken a physics class. Per WP:MTAU, such a reader should be able to read the article and come away having learned something meaningful, and in the form the article has been, it very much fails in that regard. I would also like to note that while some of the information in my edit was informed by the Mathematical formulation of the Standard Model page, most of it either was simply a better presentation of the information already present here, or explained in a relatively straightforward, accessible way that many pages here on Wikipedia don't present the information in, including that page.

Considering that this page describes a fundamental aspect of how our universe works, a reader should be able to read this article having never heard "symmetry" used in a physics context, having no idea what spontaneous symmetry breaking actually means, and with little prior knowledge of Lie algebra, or group theory in general, among many other concepts physicists take for granted, because many readers will come here and otherwise be very confused, meaning that we will have failed to accomplish the very task Wikipedia exists to fulfill. - Ramzuiv (talk) 18:07, 25 September 2019 (UTC)

Your basic intent appears salutary, but a cornerstone of WP is that it is not a tutorial: Wikiuniversity does that. So, for instance, referring explanations to articles on symmetry or symmetry breaking should be enough to steer the interested novice to more elaborate features of QFT. Aspiring to an illusory completeness in one place overburdens articles and makes them unreadable to the experts seeking a crib-sheet summary as this article. There is a standard model article doing the nontechnical stuff, and there is nothing wrong improving this one with useful additions and footnotes, even, beyond wikilinks. However, I feel sticking in "unfunded mandate" comments instead for boldly profering improvements may be self defeating. It might get experts to shrug off, and nonexperts to rush to stick in crank material, which happens all too often. For instance, the gauge fileds' adjoint to adjoint current complaint, relying on how fermion doublet bilinears yield an adjoint current is thoroughly unwarranted: any group theory book or SM text explains it, and WP simply cannot (and should not!) explain it. That's what WU tutorials are for. Short articles like this may well be the wrong venue. In any case, good luck with your efforts... Cuzkatzimhut (talk) 18:51, 25 September 2019 (UTC)

I'll update this later when I have more developed thoughts. In the mean time, would you mind linking me to the page that lays down the cornerstone that WP is not a tutorial? I don't think I have been familiarized with that perspective yet, and a (very) quick search didn't pull anything up. -Ramzuiv (talk) 20:04, 25 September 2019 (UTC)

Closest might be this but you really should get to the physics project pages and especially the wikiversity ones. They are the venues you are envisioning. Cuzkatzimhut (talk) 22:34, 25 September 2019 (UTC)

Ah, I see, I think you misunderstand my intention in my edits. Indeed, it is not my intention to make a textbook out of Wikipedia, nor to make this page an introduction to quantum physics, particle physics, nor the standard model. I will readily admit that there are criticisms about the specifics details of my edits that I would happily concede as perhaps being overly detailed, or placing information in the wrong spot. It is a fact that in general, this domain of physics is explained here almost purely in terms that are too opaque for an average reader to understand - not just this page, but many of the pages linked to in this page, and the pages those pages link to. Even a reader willing to "dive in" to the rabbit hole of links is at high risk of coming out scratching their head.

It is almost certainly true that for parts of my recent edits on this page, I placed an explanation here that really should be explained on a different page, and that other page is itself poorly written, and lacks a good explanation. It would be a valid criticism to say that the explanation should be moved to the relevant page, and this thought even did cross my mind as I was labouring to clarify what is presented here. However, that does not change the fact that Wikipedia policy (including the page you linked to) mandates that all pages (or almost all), including this one, should be presented in terms as accessible to an uninformed reader as possible, and should explain or avoid jargon and technical language whenever possible. This is not simply my personal endeavor, but the very cornerstone of what makes Wikipedia such a valuable resource for so many.

I am happy to consider and discuss specific details about my improvements to this page, and how to further guide it towards being an A-class encyclopedia-worthy article (which my edits are two steps towards and one step away from), but to criticize the general spirit of my work here either reflects a misunderstanding of my motivations here, or a disregard for the actual principles of Wikipedia's mission - Ramzuiv (talk) 21:09, 26 September 2019 (UTC)

I am going to be frank with you, at the expense of tact: the September 8 version of the article is substantially superior to the present one, in the eyes of anyone who has taken a basic particle physics or QFT course. It has the basic information, correctly, and concisely summarized. The present version is roiling with subtle misconceptions and diversions that would confuse all students and teachers of such courses; I cannot tell what the nonexpert will gain from "complex-valued" etc... The organization of the Weinberg rotation is distincly pathological: look at the figure! I fully approve of your salutary intent to make it accessible, but at present it reads like the kind of discursive, distracting blather that popular science magazines are notoriously unhelpful with cartooning. I personally am not ready to fuss chapter and verse of every parenthesis, but I suspect all your explanatory remarks would easily fit in a long footnote, or, better, as a proposal on this Talk page, to have somebody else discuss and help with. I repeat, popularizations of the standard model in the inexpert press have done untold damage to the public appreciation, despite their good intentions, and are worse than attempts of accessibility to math articles, which most people avoid, wisely. "First, do no damage", as Hippocrates opined... But this is an open beach to write on its sands, I guess... Cuzkatzimhut (talk) 13:56, 27 September 2019 (UTC)

I can acknowledge that there are imperfections. I am not an expert in this field, and I'm trying my best to explain it based off of... what was on this page previously and other pages here on this Wiki (that is, any misconceptions are thanks to the vagueness of the previous version of the page). I agree that it makes little sense to include that the fields are complex valued. My question, why not edit the page, to maintain the clearer explanations where they are, and change what really fell flat?

I'm sure you can imagine, all my effort in this page stems from my curiousity about this subject. This is not a subject that belongs only to physicists. This website does not exist to serve physicists at everyone else's expense. Yes, I would prefer an accessible explanation from someone who actually knows about this subject, but in lack of that previous effort, I have done my part to move things forward, and if someone who actually is knowledgeable sees mistakes I have made, they should do their part to fix those inaccuracies where they exist while remembering what Wikipedia strives to be. -Ramzuiv (talk) 15:34, 27 September 2019 (UTC)

OK, I rearranged the furniture, hopefully consistent with your focus. I am afraid spontaneous symmetry breaking and its co9mbination with the Higgs mechanism is something not easily outlined with a few poetic sentences--it confuses even students, routinely. But at least it is segregated here to suggest it should not quite be obvious.... Cuzkatzimhut (talk) 16:42, 27 September 2019 (UTC)

Thanks, it looks good. - Ramzuiv (talk) 03:34, 28 September 2019 (UTC)