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CellLabel->"In[6]:=",ExpressionUUID->"12aa1448-b2ae-45f4-b52d-67d9e235142c"], Cell[BoxData["SMEFTOperatorsGrid"], "Input", CellChangeTimes->{{3.866047683426553*^9, 3.866047696656088*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"859dc339-3316-49e7-a858-af1360209ee7"], Cell[BoxData["LEFTOperatorsMenu"], "Input", CellChangeTimes->{{3.866047713151403*^9, 3.866047715526853*^9}, { 3.866048021690219*^9, 3.866048022127625*^9}}, CellLabel->"In[8]:=",ExpressionUUID->"0a4ede11-19d8-4fdb-833f-a7f9f48d97a4"] }, Open ]], Cell[CellGroupData[{ Cell["Introducing input values", "Section", CellChangeTimes->{{3.7669863297181997`*^9, 3.76698633331739*^9}, { 3.766986395921605*^9, 3.76698639990829*^9}, {3.7689136229400797`*^9, 3.7689136246250887`*^9}},ExpressionUUID->"1f86db78-40b9-45ac-a891-\ 6564b15bd187"], Cell[TextData[{ StyleBox["In ", FontSize->18, FontColor->GrayLevel[0], Background->None], StyleBox["DsixTools", FontSize->18, FontColor->RGBColor[0, 0, 1], Background->None], StyleBox[", the input values for the parameters of the effective theory at \ work (SMEFT or LEFT) are stored as replacement rules in a dispatch variable \ called ", FontSize->18, FontColor->GrayLevel[0], Background->None], StyleBox["Input Values", FontSize->18, FontWeight->"Bold", FontColor->GrayLevel[0], Background->None], StyleBox[".", FontSize->18, FontColor->GrayLevel[0], Background->None] }], "Text", CellChangeTimes->{{3.766986458621125*^9, 3.766986480811357*^9}, { 3.766986572646778*^9, 3.766986759367234*^9}, {3.7669871627960043`*^9, 3.766987165578465*^9}, {3.766998870952428*^9, 3.766998871156941*^9}, { 3.768913786891047*^9, 3.768913787048026*^9}, {3.865588795882143*^9, 3.86558880266354*^9}}, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"671992f2-d71f-4fe0-b4a5-f569e3a87b62"], Cell[TextData[{ "There are two methods to introduce input values in ", StyleBox["DsixTools", FontColor->RGBColor[0, 0, 1]], ": With the ", StyleBox["NewInput", FontWeight->"Bold"], " routine or from a file. Let us focus on the first case. In this case the \ user loads the input values directly in the notebook. Only the non-zero \ Wilson coefficients must be given. The rest will be assumed to vanish." }], "Text", CellChangeTimes->{{3.766986911631728*^9, 3.7669869779437227`*^9}, { 3.766987191827376*^9, 3.7669872353188477`*^9}, {3.7669872690801983`*^9, 3.76698745687743*^9}, 3.7669876724099407`*^9, 3.766987727142459*^9, { 3.768914040106789*^9, 3.768914069754035*^9}, {3.8655896236698017`*^9, 3.86558962390898*^9}}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"a1950661-126e-42bc-95f9-c5831d758ca1"], Cell[TextData[{ "Let us show an example with ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["C", "lq"], RowBox[{"(", "1", ")"}]], TraditionalForm]],ExpressionUUID-> "52f53fc0-65fc-4596-93b0-e77eea47b50c"], "[1,1,1,2] = ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["C", "lq"], RowBox[{"(", "1", ")"}]], TraditionalForm]],ExpressionUUID-> "034e082d-d9fe-4984-8bfc-2e788f9c51d8"], "[1,1,2,1] = 1 and ", Cell[BoxData[ FormBox[ SubscriptBox["C", "HBtilde"], TraditionalForm]],ExpressionUUID-> "6679906e-3dba-475d-b9d9-ce05f89895f3"], " = -0.5" }], "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, 3.7669877208888607`*^9, {3.766992104939149*^9, 3.7669921295660686`*^9}, { 3.766992183796858*^9, 3.766992188627717*^9}, {3.76699233574375*^9, 3.766992352282154*^9}, 3.766992799382238*^9, {3.767344077837455*^9, 3.76734407845041*^9}}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"a2108170-8b7e-4e9a-a80b-6bd06f5a2b2d"], Cell[BoxData[ RowBox[{ RowBox[{"NewInput", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Clq1", "[", RowBox[{"1", ",", "1", ",", "1", ",", "2"}], "]"}], "\[Rule]", "1"}], ",", RowBox[{ RowBox[{"Clq1", "[", RowBox[{"1", ",", "1", ",", "2", ",", "1"}], "]"}], "\[Rule]", "1"}], ",", RowBox[{"CHBtilde", "\[Rule]", RowBox[{"-", "0.5"}]}]}], "}"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.766992192309717*^9, 3.766992199297955*^9}, { 3.76699225526026*^9, 3.76699230841219*^9}, {3.766992748425928*^9, 3.766992766853602*^9}, 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3.766990927899529*^9, 3.76699093531253*^9}, {3.7669910145972013`*^9, 3.76699102371996*^9}, {3.766991210411605*^9, 3.7669912139326773`*^9}, { 3.7669912636361427`*^9, 3.766991264256855*^9}}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"2bef411e-3a7c-4c3d-b193-4badf9cb16fa"], Cell[BoxData[ RowBox[{"MClq1", "/.", "InputValues"}]], "Input", CellChangeTimes->{3.865588841313339*^9, 3.8655896969401007`*^9}, CellLabel->"In[11]:=",ExpressionUUID->"29a68159-926b-4b67-b1ae-9eb27db1f425"], Cell[TextData[{ "One can also check individual elements in Wilson coefficients with flavor \ indices: ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["C", "lq"], RowBox[{"(", "1", ")"}]], TraditionalForm]],ExpressionUUID-> "265ee0d9-6114-4e04-899c-899154238052"], "[1,1,1,2]" }], "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, { 3.766987741441463*^9, 3.766987744827812*^9}, {3.7669899608855886`*^9, 3.766989973974433*^9}, {3.766990811165653*^9, 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CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, 3.7669877208888607`*^9, {3.766992088811577*^9, 3.7669920976732397`*^9}, { 3.766992448189595*^9, 3.76699245382122*^9}, {3.76699248689631*^9, 3.766992503844933*^9}}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"38a0890b-9191-4b4c-aced-c44f0149a578"], Cell[BoxData[ RowBox[{"MCllHH", "/.", "InputValues"}]], "Input", CellChangeTimes->{{3.767344114402183*^9, 3.7673441158907137`*^9}, 3.865589335928197*^9, 3.8655898902660837`*^9}, CellLabel->"In[13]:=",ExpressionUUID->"ac43a0f7-b880-4632-84cf-fd5af18bac8a"], Cell[BoxData[ RowBox[{"MCdd", "/.", "InputValues"}]], "Input", CellChangeTimes->{{3.7669925061267443`*^9, 3.766992535436698*^9}, 3.768914132850678*^9, {3.768914221539098*^9, 3.7689142216744003`*^9}, 3.865589336789352*^9, 3.865589893134688*^9}, CellLabel->"In[14]:=",ExpressionUUID->"9ee7c61c-064c-4074-95f5-3160b5fa134c"], Cell[TextData[{ "The user may also give an invalid input using ", StyleBox["NewInput", FontWeight->"Bold"], ". In this case ", StyleBox["DsixTools", FontColor->RGBColor[0, 0, 1]], " will correct the input and save a valid set of input values." }], "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, 3.7669877208888607`*^9, {3.766992088811577*^9, 3.7669920976732397`*^9}, { 3.766992448189595*^9, 3.76699245382122*^9}, {3.766992606449501*^9, 3.7669926408808603`*^9}, {3.766992672913631*^9, 3.766992693700796*^9}, { 3.767029138729056*^9, 3.767029139061654*^9}, 3.768914030848466*^9}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"9f2397a8-5000-4900-bf47-adf3aa4697a4"], Cell[BoxData[ RowBox[{ RowBox[{"NewInput", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Clq1", "[", RowBox[{"1", ",", "1", ",", "1", ",", "2"}], "]"}], "\[Rule]", "1"}], ",", RowBox[{"CHBtilde", "\[Rule]", RowBox[{"-", "0.5"}]}]}], "}"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.766992726638359*^9, 3.7669927428275414`*^9}, { 3.766992793794608*^9, 3.7669927939255037`*^9}, {3.767344120276413*^9, 3.767344123055035*^9}, 3.865588863816255*^9, {3.8655897229202833`*^9, 3.865589723387813*^9}}, CellLabel->"In[15]:=",ExpressionUUID->"1e746bb2-d286-4428-b823-e217332026cf"], Cell[TextData[{ "We see that a warning message has been produced by ", StyleBox["DsixTools", FontColor->RGBColor[0, 0, 1]], ". This is because the Wilson coefficients provided by the user lead to an \ invalid set of input values. There are two possible reasons for this:\n\n1) \ ", StyleBox["Non-Hermiticity errors", FontVariations->{"Underline"->True}], ": Some Wilson coefficients are related due to the Hermiticity of the \ Lagrangian. For instance ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["C", "lq"], RowBox[{"(", "1", ")"}]], TraditionalForm]],ExpressionUUID-> "4fa6ab81-346b-4877-92dc-43d3fa465ff4"], "[1,1,1,2] = ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["C", "lq"], RowBox[{"(", "1", ")"}]], TraditionalForm]],ExpressionUUID-> "9990aad1-1da4-4e48-9a69-78a557b77511"], "[1,1,2,1] * must necessarily hold.\n2) ", StyleBox["Antisymmetry errors", FontVariations->{"Underline"->True}], ": Some Wilson coefficients are antisymmetric under the exchange of two \ flavor indices. For instance ", Cell[BoxData[ FormBox[ SubscriptBox["L", "\[Nu]\[Gamma]"], TraditionalForm]],ExpressionUUID-> "c14f5262-0baf-4810-9230-0c2ca024bf00"], "[1,1] = 0 must necessarily hold.\n\nWhen the user\[CloseCurlyQuote]s input \ is not consistent with any of these restrictions, a warning is issued and ", StyleBox["DsixTools", FontColor->RGBColor[0, 0, 1]], " corrects the input by replacing it by a new one that ensures a complete \ consistency of the Lagrangian. The list of invalid input values can be seen \ by clicking on the button ", StyleBox["Input errors", FontWeight->"Bold"], ". We note however that in some cases other Wilson coefficients, related to \ these by the two reasons given above, are also modified." }], "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, { 3.766993001880392*^9, 3.766993002074834*^9}, {3.766993139780293*^9, 3.766993221981073*^9}, {3.766993316123217*^9, 3.766993422538176*^9}, { 3.7669934888241796`*^9, 3.766993523482161*^9}, {3.766993565074419*^9, 3.766993657205092*^9}, {3.766993692784401*^9, 3.7669939410515127`*^9}, { 3.766998944467461*^9, 3.766998983266027*^9}, {3.7670290480927343`*^9, 3.767029048555543*^9}, {3.7689335900179996`*^9, 3.768933590084455*^9}, 3.8655888797240868`*^9}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"a5453a64-5a91-4f64-98a3-4dd9baa50013"], Cell[BoxData[{ RowBox[{ RowBox[{"Clq1", "[", RowBox[{"1", ",", "1", ",", "1", ",", "2"}], "]"}], "/.", "InputValues"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clq1", "[", RowBox[{"1", ",", "1", ",", "2", ",", "1"}], "]"}], "/.", "InputValues"}], "\[IndentingNewLine]", RowBox[{"CHBtilde", "/.", "InputValues"}]}], "Input", CellChangeTimes->{{3.7669923683328047`*^9, 3.7669923778733664`*^9}, { 3.7669924164000607`*^9, 3.76699241723977*^9}, {3.7673441249357147`*^9, 3.767344128851818*^9}, {3.865588894040049*^9, 3.865588899701076*^9}}, CellLabel->"In[16]:=",ExpressionUUID->"873a682e-1d2d-43b3-b0fb-96f4f2d91d9c"] }, Open ]], Cell[CellGroupData[{ Cell["How to change input values", "Section", CellChangeTimes->{{3.7669863297181997`*^9, 3.76698633331739*^9}, { 3.766986395921605*^9, 3.76698639990829*^9}, {3.766994129581229*^9, 3.766994129998157*^9}},ExpressionUUID->"35776110-bc1d-4005-8640-\ 3deec2ea4b3d"], Cell[TextData[{ "Once the input values have been set, the user can change them individually \ at any moment in the notebook. This is done with the ", StyleBox["ChangeInput", FontWeight->"Bold"], " routine." }], "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, 3.7669877208888607`*^9, {3.766992088811577*^9, 3.7669920976732397`*^9}, { 3.766992448189595*^9, 3.76699245382122*^9}, {3.76699248689631*^9, 3.766992503844933*^9}, {3.766994269645252*^9, 3.7669943213566103`*^9}, { 3.7670294439771023`*^9, 3.7670294462100973`*^9}}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"ea5ac39d-ff54-4c6c-8f3c-b2a3067e7703"], Cell["We can see some examples:", "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, 3.7669877208888607`*^9, {3.766992088811577*^9, 3.7669920976732397`*^9}, { 3.766992448189595*^9, 3.76699245382122*^9}, {3.76699248689631*^9, 3.766992503844933*^9}, {3.766994269645252*^9, 3.7669943213566103`*^9}, { 3.766994453501418*^9, 3.766994456442659*^9}}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"e81de9aa-6b43-46da-bf5f-77436c4db0aa"], Cell[BoxData[ RowBox[{"ChangeInput", "[", RowBox[{"{", RowBox[{"CHBtilde", "\[Rule]", "0.6"}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.766994475461074*^9, 3.7669944908024178`*^9}, { 3.767344135025202*^9, 3.76734413549509*^9}}, CellLabel->"In[19]:=",ExpressionUUID->"241cf197-7511-45c4-8cab-dd27e84075f2"], Cell[BoxData[ RowBox[{"CHBtilde", "/.", "InputValues"}]], "Input", CellChangeTimes->{{3.7669944978107758`*^9, 3.7669944988143263`*^9}, { 3.767344137554194*^9, 3.767344138087924*^9}, 3.865588945675803*^9}, CellLabel->"In[20]:=",ExpressionUUID->"6196ff50-1034-4b5d-97f3-016df9686963"], Cell[BoxData[ RowBox[{"ChangeInput", "[", RowBox[{"{", RowBox[{"CHBtilde", "\[Rule]", RowBox[{"-", "0.1"}]}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.7669945097391243`*^9, 3.7669945111100082`*^9}, { 3.767344140041355*^9, 3.7673441405545397`*^9}}, CellLabel->"In[21]:=",ExpressionUUID->"d12b0088-3d57-40b8-832c-cd0554a688e9"], Cell[BoxData[ RowBox[{"CHBtilde", "/.", "InputValues"}]], "Input", CellChangeTimes->{3.767344143360857*^9, 3.865588946567721*^9}, CellLabel->"In[22]:=",ExpressionUUID->"7d8080ba-bb50-46bc-bc26-5a8e4312bac5"] }, Open ]], Cell[CellGroupData[{ Cell["RunDsixTools routine", "Section", CellChangeTimes->{{3.7669863297181997`*^9, 3.76698633331739*^9}, { 3.766986395921605*^9, 3.76698639990829*^9}, {3.766994129581229*^9, 3.766994129998157*^9}, 3.768914434044003*^9},ExpressionUUID->"cbdcf641-28b2-462e-8599-\ 7a28051fa0ea"], Cell[TextData[{ "We consider an example input with ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["C", "lq"], RowBox[{"(", "1", ")"}]], TraditionalForm]],ExpressionUUID-> "290a0170-e4a1-4223-9381-c6a7c9cdea9f"], "[2,2,3,3] = 1 / ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["\[CapitalLambda]", "2"], ",", " ", RowBox[{"given", " ", "at", " ", "\[CapitalLambda]"}], ",", " ", RowBox[{ RowBox[{"with", " ", "\[CapitalLambda]"}], " ", "=", " ", RowBox[{"HIGHSCALE", " ", "=", " ", "10"}]}]}], TraditionalForm]], ExpressionUUID->"7655f755-3676-4fa6-bb66-4323f2d5ecf8"], " TeV. 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", StyleBox["NewInput", FontWeight->"Bold"], " can also be used to introduce energy scales." }], "Text", CellChangeTimes->{{3.7669868520574217`*^9, 3.766986856873249*^9}, { 3.768561762279228*^9, 3.768561846279765*^9}, {3.76884471274957*^9, 3.768844716283449*^9}, {3.8655891525087233`*^9, 3.865589244205975*^9}, { 3.865589354506515*^9, 3.865589377567006*^9}}, FontSize->18, Background->RGBColor[ 1, 1, 0.85],ExpressionUUID->"c0847da6-56d5-4f8e-91f0-f68f6d29c380"], Cell[BoxData[ RowBox[{ RowBox[{"NewInput", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Clq1", "[", RowBox[{"2", ",", "2", ",", "3", ",", "3"}], "]"}], "\[Rule]", RowBox[{"1.0", "/", RowBox[{"HIGHSCALE", "^", "2"}]}]}], "}"}], ",", RowBox[{"HIGHSCALE", "\[Rule]", RowBox[{"10", "^", "4"}]}]}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.766898889835154*^9, 3.766898889966345*^9}, 3.767343996069416*^9, 3.768043674174203*^9, {3.768539217528573*^9, 3.768539252925907*^9}, {3.768540692579809*^9, 3.768540705397846*^9}, 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CellChangeTimes->{{3.7669863297181997`*^9, 3.76698633331739*^9}, { 3.766986395921605*^9, 3.76698639990829*^9}, {3.766994129581229*^9, 3.766994129998157*^9}, {3.7685621132681913`*^9, 3.768562113839582*^9}},ExpressionUUID->"91fb3985-753c-4d44-b7d2-\ bef46b5eac5b"], Cell[TextData[{ "The results of the running can be obtained by means of the ", StyleBox["D6run", FontWeight->"Bold"], " function, which returns interpolating functions that can be evaluated for \ any value of t = Log[10,\[Mu]]." }], "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, 3.7669877208888607`*^9, {3.766992088811577*^9, 3.7669920976732397`*^9}, { 3.766992448189595*^9, 3.76699245382122*^9}, {3.76699248689631*^9, 3.766992503844933*^9}, {3.766994269645252*^9, 3.7669943213566103`*^9}, { 3.766994453501418*^9, 3.766994456442659*^9}, {3.7685621232321177`*^9, 3.76856213214377*^9}, {3.768562251106583*^9, 3.7685623494471903`*^9}, { 3.8655889867987413`*^9, 3.8655889980803623`*^9}}, FontSize->18, 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"[", RowBox[{"2", ",", "2", ",", "1", ",", "1"}], "]"}], "/.", "Match"}]], "Input", CellChangeTimes->{{3.768562432805089*^9, 3.768562434195997*^9}, { 3.86558974419138*^9, 3.865589744243868*^9}}, CellLabel->"In[29]:=",ExpressionUUID->"4b94d367-9392-428c-a517-9005780c095e"], Cell[TextData[{ "One can also use the dispatch ", StyleBox["MatchAnalytical", FontWeight->"Bold"], " to print the analytical expressions used for the SMEFT-LEFT matching" }], "Text", CellChangeTimes->{{3.766987637898347*^9, 3.766987646815774*^9}, 3.7669877208888607`*^9, {3.766992088811577*^9, 3.7669920976732397`*^9}, { 3.766992448189595*^9, 3.76699245382122*^9}, {3.76699248689631*^9, 3.766992503844933*^9}, {3.766994269645252*^9, 3.7669943213566103`*^9}, { 3.766994453501418*^9, 3.766994456442659*^9}, {3.7685621232321177`*^9, 3.76856213214377*^9}, {3.768562396094005*^9, 3.7685624402724247`*^9}, { 3.7685624876096287`*^9, 3.7685625139159603`*^9}, 3.7688157341649523`*^9}, FontSize->18, Background->RGBColor[ 1, 1, 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