diff --git a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_1JET_13TEV_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_1JET_13TEV_DIF/metadata.yaml
index 39154e9809..0c7d07cc06 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_1JET_13TEV_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_1JET_13TEV_DIF/metadata.yaml
@@ -18,7 +18,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. pT and y", label: '$\frac{d^2\sigma}{dp_T d|y|}$', units: "$pb/GeV$"}
+  - observable: {description: "double differential cross section w.r.t. pT and y", label: '$\frac{d^2\sigma}{dp_T d|y|}$ (pb/GeV)', units: "$pb/GeV$"}
     observable_name: PT-Y
     process_type: JET
     ndata: 177 # 33+32+31+31+28+22
@@ -36,9 +36,9 @@ implemented_observables:
     plotting:
       kinematics_override: identity
       x_scale: log
-      dataset_label: 'ATLAS Jet 13 TeV: $\frac{d^2\sigma}{dp_T d|y|}$'
+      dataset_label: 'ATLAS 13 TeV single-inclusive jets $\frac{d^2\sigma}{dp_T d|y|}$'
       plot_x: pT
-      y_label: '$\frac{d^2\sigma}{dp_T d|y|}$ ($\frac{pb}{GeV}$)'
+      y_label: '$d^2\sigma/dp_T d|y|$ (pb/GeV)'
       figure_by: 
         - y
     theory:
@@ -69,9 +69,9 @@ implemented_observables:
     plotting:
       kinematics_override: identity
       x_scale: log
-      dataset_label: 'ATLAS Jet 13 TeV: $\frac{d^2\sigma}{dp_T d|y|}$'
+      dataset_label: 'ATLAS single-inclusive 13 TeV: $\frac{d^2\sigma}{dp_T d|y|}$'
       plot_x: pT
-      y_label: '$\frac{d^2\sigma}{dp_T d|y|}$ ($\frac{pb}{GeV}$)'
+      y_label: '$d^2\sigma/dp_T d|y|$ (pb/GeV)'
       figure_by: 
         - y
     theory:
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_2JET_13TEV_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_2JET_13TEV_DIF/metadata.yaml
index 916e47fadf..d2a26465c0 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_2JET_13TEV_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_2JET_13TEV_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. m_jj and y*", label: '$\frac{d^2\sigma}{dm_{jj} d|y^*|}$', units: "$pb/GeV$"}
+  - observable: {description: "double differential cross section w.r.t. m_jj and y*", label: '$\frac{d^2\sigma}{dm_{jj}d|y^*|}$ (pb/GeV)', units: "$pb/GeV$"}
     observable_name: MJJ-Y
     process_type: DIJET
     ndata: 136 # 28+28+27+24+21+8
@@ -35,9 +35,9 @@ implemented_observables:
     plotting:
       kinematics_override: identity
       x_scale: log
-      dataset_label: 'ATLAS DiJet 13 TeV: $\frac{d^2\sigma}{dm_{jj} d|y^*|}$'
+      dataset_label: 'ATLAS 13 TeV di-jets $\frac{d^2\sigma}{dm_{jj} d|y^*|}$ (pb/GeV)'
       plot_x: m_jj
-      y_label: '$\frac{d^2\sigma}{dm_{jj} d|y^*|}$ ($\frac{pb}{GeV}$)'
+      y_label: '$d^2\sigma/dm_{jj} d|y^*|$ (pb/GeV)'
       figure_by: 
         - ystar
     theory:
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_HADR_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_HADR_DIF/metadata.yaml
index 512c6e0dd2..822c84037e 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_HADR_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_HADR_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "differential cross section w.r.t. mass of top pair", label: '$\frac{d\sigma}{dm_{t\bar{t}}}$', units: '$\frac{pb}{GeV}$'}
+  - observable: {description: "differential cross section w.r.t. mass of top pair", label: '$\frac{d\sigma}{dm_{t\bar{t}}}$ (pb/GeV)', units: '$\frac{pb}{GeV}$'}
     observable_name: MTTBAR
     process_type: HQP_MQQ
     ndata: 9
@@ -33,7 +33,7 @@ implemented_observables:
       - uncertainties_dSig_dmttBar.yaml
     kinematic_coverage: [m_ttBar, m_t2, sqrts]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair in hadronic channel: $\frac{d\sigma}{dm_{t\bar{t}}}$'
+      dataset_label: 'ATLAS 13 TeV $t\bar{t}$ all hadr. $\frac{d\sigma}{dm_{t\bar{t}}}$'
       kinematics_override: identity
       x_scale: log
       plot_x: m_ttBar
@@ -88,7 +88,7 @@ implemented_observables:
     plotting:
       dataset_label: 'ATLAS 13 TeV top quark pair in hadronic channel: $\frac{d\sigma}{d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{d\sigma}{d|y_{t\bar{t}}|}$ ($pb$)'
     theory:
@@ -112,9 +112,9 @@ implemented_observables:
       - uncertainties_dSig_dyttBar_norm.yaml
     kinematic_coverage: [y_ttBar, m_t2, sqrts]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair in hadronic channel: $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
+      dataset_label: 'ATLAS 13 TeV $t\bar{t}$ all hadr. $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
     theory:
@@ -123,7 +123,7 @@ implemented_observables:
         - - ATLAS_TTBAR_13TEV_HADR_DIF_YTTBAR-INTEGRATED
       operation: 'ratio'
 
-  - observable: {description: "double differential cross section w.r.t. mass and absolute rapidity of top pair", label: '$\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$', units: '$\frac{pb}{GeV}$'}
+  - observable: {description: "double differential cross section w.r.t. mass and absolute rapidity of top pair", label: '$\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$ (pb/GeV)', units: '$\frac{pb}{GeV}$'}
     observable_name: MTTBAR-YTTBAR
     process_type: HQP_YQQ
     ndata: 11 # 4+4+3
@@ -140,9 +140,9 @@ implemented_observables:
       - uncertainties_d2Sig_dmttBar_dyttBar.yaml
     kinematic_coverage: [y_ttBar, m_ttBar, m_t2]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair in hadronic channel: $\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$'
+      dataset_label: 'ATLAS 13 TeV $t\bar{t}$ all hadr. $\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$ ($\frac{pb}{GeV}$)'
       figure_by:
@@ -171,7 +171,7 @@ implemented_observables:
     plotting:
       dataset_label: 'ATLAS 13 TeV top quark pair in hadronic channel: $\frac{1}{\sigma}\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$ ($\frac{1}{GeV}$)'
       figure_by:
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_LJ_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_LJ_DIF/metadata.yaml
index 20e1dd72e9..f896177c33 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_LJ_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_TTBAR_13TEV_LJ_DIF/metadata.yaml
@@ -43,7 +43,7 @@ implemented_observables:
         - - ATLAS_TTBAR_13TEV_LJ_DIF_MTTBAR
       operation: 'null'
 
-  - observable: {description: "normalized differential cross section w.r.t. ttBar invariant mass", label: '$\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$', units: "$\frac{1}{GeV}$"}
+  - observable: {description: "normalized differential cross section w.r.t. ttBar invariant mass", label: '$\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$ (1/GeV)', units: "$\frac{1}{GeV}$"}
     observable_name: MTTBAR-NORM
     process_type: HQP_MQQ
     ndata: 9
@@ -59,7 +59,7 @@ implemented_observables:
       - uncertainties_dSig_dmttBar_norm.yaml
     kinematic_coverage: [m_ttBar, m_t2, sqrts]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$'
+      dataset_label: 'ATLAS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$'
       kinematics_override: identity
       x_scale: log
       plot_x: m_ttBar
@@ -70,14 +70,14 @@ implemented_observables:
         - - ATLAS_TTBAR_13TEV_LJ_DIF_MTTBAR-INTEGRATED
       operation: 'ratio'
 
-  - observable: {description: "differential cross section w.r.t. transverse momentum of t", label: '$\frac{d\sigma}{dpT_t}$', units: '$\frac{pb}{GeV}$'}
+  - observable: {description: "differential cross section w.r.t. transverse momentum of t", label: '$\frac{d\sigma}{dp_T^t}$', units: '$\frac{pb}{GeV}$'}
     observable_name: PTT
     process_type: HQP_PTQ
     ndata: 8
     tables: [610] 
     kinematics:
       variables:
-        pT_t: {description: "transverse momentum of t", label: "$pT_t$", units: "$GeV$"}
+        pT_t: {description: "transverse momentum of t", label: "$p_T^t$", units: "$GeV$"}
         m_t2: {description: "mass of top quark squared", label: '$m_{t}^2$', units: '$GeV^2$'}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_dSig_dpTt.yaml
@@ -86,9 +86,9 @@ implemented_observables:
       - uncertainties_dSig_dpTt.yaml
     kinematic_coverage: [pT_t, m_t2, sqrts]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{d\sigma}{dpT_t}$'
+      dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{d\sigma}{dp_T^t}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: pT_t
       y_label: '$\frac{d\sigma}{dpT_t}$ ($\frac{pb}{GeV}$)'
     theory:
@@ -96,14 +96,14 @@ implemented_observables:
         - - ATLAS_TTBAR_13TEV_LJ_DIF_PTT
       operation: 'null'
 
-  - observable: {description: "normalized differential cross section w.r.t. transverse momentum of t", label: '$\frac{1}{\sigma}\frac{d\sigma}{dpT_t}$', units: '$\frac{1}{GeV}$'}
+  - observable: {description: "normalized differential cross section w.r.t. transverse momentum of t", label: '$\frac{1}{\sigma}\frac{d\sigma}{dp_T^t}$ (1/GeV)', units: '$\frac{1}{GeV}$'}
     observable_name: PTT-NORM
     process_type: HQP_PTQ
     ndata: 8
     tables: [608]
     kinematics:
       variables:
-        pT_t: {description: "transverse momentum of t", label: "$pT_t$", units: "$GeV$"}
+        pT_t: {description: "transverse momentum of t", label: "$p_T^t$", units: "$GeV$"}
         m_t2: {description: "mass of top quark squared", label: '$m_{t}^2$', units: '$GeV^2$'}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_dSig_dpTt_norm.yaml
@@ -112,9 +112,9 @@ implemented_observables:
       - uncertainties_dSig_dpTt_norm.yaml
     kinematic_coverage: [pT_t, m_t2, sqrts]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{dpT_t}$'
+      dataset_label: 'ATLAS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{dpT_t}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: pT_t
       y_label: '$\frac{1}{\sigma}\frac{d\sigma}{dpT_t}$ ($\frac{1}{GeV}$)'
     theory:
@@ -141,7 +141,7 @@ implemented_observables:
     plotting:
       dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{d\sigma}{d|y_{t}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_t
       y_label: '$\frac{d\sigma}{d|y_{t}|}$ ($pb$)'
     theory:
@@ -165,9 +165,9 @@ implemented_observables:
       - uncertainties_dSig_dyt_norm.yaml
     kinematic_coverage: [y_t, m_t2, sqrts]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t}|}$'
+      dataset_label: 'ATLAS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_t
       y_label: '$\frac{1}{\sigma}\frac{d\sigma}{d|y_{t}|}$'
     theory:
@@ -194,7 +194,7 @@ implemented_observables:
     plotting:
       dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{d\sigma}{d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{d\sigma}{d|y_{t\bar{t}}|}$ ($pb$)'
     theory:
@@ -218,9 +218,9 @@ implemented_observables:
       - uncertainties_dSig_dyttBar_norm.yaml
     kinematic_coverage: [y_ttBar, m_t2, sqrts]
     plotting:
-      dataset_label: 'ATLAS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
+      dataset_label: 'ATLAS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}}$'
     theory:
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0J_13TEV_PT/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0J_13TEV_PT/metadata.yaml
index 62867cefa8..b289ebd732 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0J_13TEV_PT/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0J_13TEV_PT/metadata.yaml
@@ -21,7 +21,7 @@ implemented_observables:
   - observable_name: "LL"
     observable: 
       description: "ATLAS 13 TeV, transverse momentum distribution of Drell-Yan lepton pairs."
-      label: r"$1/\sigma_{fid}d\\sigma/dp_{T}^{\\l\\l}$"
+      label: '$\frac{1}{\sigma}\,\frac{d\sigma}{dp_{T}^{\ell\ell}}$ (1/GeV)'
       units: "[1/GeV]"
 
     ndata: 38
@@ -30,7 +30,7 @@ implemented_observables:
     process_type: DY_NC_PT
 
     plotting:
-      dataset_label: 'ATLAS 13 TeV normalized differential cross section in $pT_{ll}$'
+      dataset_label: 'ATLAS 13 TeV $Z$ $\frac{1}{\sigma}\frac{d\sigma}{dp_{T}^{\ell\ell}}$'
       kinematics_override: identity
       x_scale: log
       plot_x: pT
@@ -39,7 +39,7 @@ implemented_observables:
 
     kinematics:
       variables:
-        pT: {description: "lepton pair transverse momentum", label: '$p_T$', units: ""}
+        pT: {description: "lepton pair transverse momentum", label: '$p_T^{\ell\ell}$', units: "GeV"}
         m_Z2: {description: "Z boson mass squared", label: '$M_Z^2$', units: "GeV"}
         sqrts: {description: "center of mass energy", label: '$\sqrt(s)$', units: "GeV"}
 
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0_8TEV_ZMASS/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0_8TEV_ZMASS/metadata.yaml
index 334c859db3..ba11be63c7 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0_8TEV_ZMASS/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ATLAS_Z0_8TEV_ZMASS/metadata.yaml
@@ -24,7 +24,7 @@ implemented_observables:
   - observable_name: "LL"
     observable: 
       description: "ATLAS 8 TeV, Z boson rapidity distribution in full phase space of decay leptons"
-      label: r"$d\\sigma/d|\|y_{ll}||$"
+      label: '$\frac{d\sigma}{d|y|}$ (pb)'
       units: "[pb]"
 
     ndata: 7
@@ -33,7 +33,7 @@ implemented_observables:
     process_type: DY_Z_Y
 
     plotting:
-      dataset_label: 'ATLAS 8 TeV $Z \to l^+ l^-$, absolute rapidity'
+      dataset_label: 'ATLAS 8 TeV $Z$ $\frac{d\sigma}{d|y|}$'
       kinematics_override: identity
       x_scale: linear
       plot_x: y
@@ -42,7 +42,7 @@ implemented_observables:
 
     kinematics:
       variables:
-        y: {description: "Z > l+ l- absolute rapidity", label: '$|y_{ll}|$', units: ""}
+        y: {description: "Z > l+ l- absolute rapidity", label: '$|y_{\ell\ell}|$', units: ""}
         m_Z2: {description: "Z boson mass squared", label: '$M_Z^2$', units: "GeV"}
         sqrts: {description: "center of mass energy", label: '$\sqrt(s)$', units: "GeV"}
       file: kinematics.yaml
diff --git a/nnpdf_data/nnpdf_data/new_commondata/CMS_1JET_13TEV_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/CMS_1JET_13TEV_DIF/metadata.yaml
index 90ddfd65b9..af8a755e60 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/CMS_1JET_13TEV_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/CMS_1JET_13TEV_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. pT and y", label: '$\frac{d^2\sigma}{dp_T d|y|}$', units: "$pb/GeV$"}
+  - observable: {description: "double differential cross section w.r.t. pT and y", label: '$\frac{d^2\sigma}{dp_T d|y|}$ (pb/GeV)', units: "$pb/GeV$"}
     observable_name: PT-Y-R04
     process_type: JET
     ndata: 78 # 22+21+19+16
@@ -34,7 +34,7 @@ implemented_observables:
     kinematic_coverage: [y, pT, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: 'CMS Jet 13 TeV R = 0.4: $\frac{d^2\sigma}{dp_T d|y|}$'
+      dataset_label: 'CMS 13 TeV single-inclusive jets (R=0.4) $\frac{d^2\sigma}{dp_T d|y|}$'
       plot_x: pT
       x_scale: log
       y_label: '$\frac{d^2\sigma}{dp_T d|y|}$ ($\frac{pb}{GeV}$)'
@@ -48,7 +48,7 @@ implemented_observables:
           - CMS_1JET_13TEV_DIF_PT-Y-R04_BIN4
       operation: 'null'
 
-  - observable: {description: "double differential cross section w.r.t. pT and y", label: '$\frac{d^2\sigma}{dp_T d|y|}$', units: "$pb/GeV$"}
+  - observable: {description: "double differential cross section w.r.t. pT and y", label: '$\frac{d^2\sigma}{dp_T d|y|}$ (pb/GeV)', units: "$pb/GeV$"}
     observable_name: PT-Y-R07
     process_type: JET
     ndata: 78 # 22+21+19+16
@@ -65,7 +65,7 @@ implemented_observables:
     kinematic_coverage: [y, pT, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: 'CMS Jet 13 TeV R = 0.7: $\frac{d^2\sigma}{dp_T d|y|}$'
+      dataset_label: 'CMS 13 TeV single-inclusive jets (R=0.7) $\frac{d^2\sigma}{dp_T d|y|}$'
       plot_x: pT
       x_scale: log
       y_label: '$\frac{d^2\sigma}{dp_T d|y|}$ ($\frac{pb}{GeV}$)'
diff --git a/nnpdf_data/nnpdf_data/new_commondata/CMS_TTBAR_13TEV_LJ_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/CMS_TTBAR_13TEV_LJ_DIF/metadata.yaml
index 473890ebd9..3afa498bf2 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/CMS_TTBAR_13TEV_LJ_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/CMS_TTBAR_13TEV_LJ_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "differential cross section w.r.t. invariant mass of ttBar", label: '$\frac{d\sigma}{dm_{t\bar{t}}}$', units: "$\frac{pb}{GeV}$"}
+  - observable: {description: "differential cross section w.r.t. invariant mass of ttBar", label: '$\frac{d\sigma}{dm_{t\bar{t}}}$ (pb/GeV)', units: "$\frac{pb}{GeV}$"}
     observable_name: MTTBAR
     process_type: HQP_MQQ
     ndata: 15
@@ -44,7 +44,7 @@ implemented_observables:
       conversion_factor: 0.2877 # as prescribed by arXiv:2108.02803, Sec. 3, ln. 7
       operation: 'null'
 
-  - observable: {description: "normalized differential cross section w.r.t. invariant mass of ttBar", label: '$\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$', units: "$\frac{1}{GeV}$"}
+  - observable: {description: "normalized differential cross section w.r.t. invariant mass of ttBar", label: '$\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$ (1/GeV)', units: "$\frac{1}{GeV}$"}
     observable_name: MTTBAR-NORM
     process_type: HQP_MQQ
     ndata: 15
@@ -60,7 +60,7 @@ implemented_observables:
       - uncertainties_dSig_dmttBar_norm.yaml
     kinematic_coverage: [m_ttBar, m_t2, sqrts]
     plotting:
-      dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$'
+      dataset_label: 'CMS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{dm_{t\bar{t}}}$'
       kinematics_override: identity
       x_scale: log
       plot_x: m_ttBar
@@ -89,7 +89,7 @@ implemented_observables:
     plotting:
       dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{d\sigma}{d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{d\sigma}{d|y_{t\bar{t}}|}$ ($pb$)'
     theory:
@@ -114,9 +114,9 @@ implemented_observables:
       - uncertainties_dSig_dyttBar_norm.yaml
     kinematic_coverage: [y_ttBar, m_t2, sqrts]
     plotting:
-      dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
+      dataset_label: 'CMS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{1}{\sigma}\frac{d\sigma}{d|y_{t\bar{t}}|}$'
     theory:
@@ -125,7 +125,7 @@ implemented_observables:
         - - CMS_TTBAR_13TEV_LJ_DIF_YTTBAR-INTEGRATED
       operation: 'ratio'
 
-  - observable: {description: "double differential cross section w.r.t. invariant mass and absolute rapidity of ttBar", label: '$\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$', units: "$\frac{pb}{GeV}$"}
+  - observable: {description: "double differential cross section w.r.t. invariant mass and absolute rapidity of ttBar", label: '$\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$ (pb/GeV)', units: "$\frac{pb}{GeV}$"}
     observable_name: MTTBAR-YTTBAR
     process_type: HQP_YQQ
     ndata: 35
@@ -144,7 +144,7 @@ implemented_observables:
     plotting:
       dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$ ($\frac{pb}{GeV}$)'
       figure_by: 
@@ -155,7 +155,7 @@ implemented_observables:
       conversion_factor: 0.2877 # as prescribed by arXiv:2108.02803, Sec. 3, ln. 7
       operation: 'null'
 
-  - observable: {description: "normalized double differential cross section w.r.t. invariant mass and absolute rapidity of ttBar", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$', units: "$\frac{1}{GeV}$"}
+  - observable: {description: "normalized double differential cross section w.r.t. invariant mass and absolute rapidity of ttBar", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$ (1/GeV)', units: "$\frac{1}{GeV}$"}
     observable_name: MTTBAR-YTTBAR-NORM
     process_type: HQP_YQQ
     ndata: 35
@@ -172,9 +172,9 @@ implemented_observables:
       - uncertainties_d2Sig_dyttBar_dmttBar_norm.yaml
     kinematic_coverage: [y_ttBar, m_ttBar, m_t2]
     plotting:
-      dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$'
+      dataset_label: 'CMS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_ttBar
       y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dm_{t\bar{t}}d|y_{t\bar{t}}|}$ ($\frac{1}{GeV}$)'
       figure_by: 
@@ -185,7 +185,7 @@ implemented_observables:
         - - CMS_TTBAR_13TEV_LJ_DIF_MTTBAR-YTTBAR-INTEGRATED
       operation: 'ratio'
       
-  - observable: {description: "differential cross section w.r.t. transverse momentum of t", label: '$\frac{d\sigma}{dpT_t}$', units: "$\frac{pb}{GeV}$"}
+  - observable: {description: "differential cross section w.r.t. transverse momentum of t", label: '$\frac{d\sigma}{dp_T^t}$ (pb/GeV)', units: "$\frac{pb}{GeV}$"}
     observable_name: PTT
     process_type: HQP_PTQ
     ndata: 16
@@ -203,7 +203,7 @@ implemented_observables:
     plotting:
       dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{d\sigma}{dpT_t}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: pT_t
       y_label: '$\frac{d\sigma}{dpT_t}$ ($\frac{pb}{GeV}$)'
     theory:
@@ -212,14 +212,14 @@ implemented_observables:
       conversion_factor: 0.2877 # as prescribed by arXiv:2108.02803, Sec. 3, ln. 7
       operation: 'null'
 
-  - observable: {description: "normalized differential cross section w.r.t. transverse momentum of t", label: '$\frac{1}{\sigma}\frac{d\sigma}{dpT_t}$', units: "$\frac{1}{GeV}$"}
+  - observable: {description: "normalized differential cross section w.r.t. transverse momentum of t", label: '$\frac{1}{\sigma}\frac{d\sigma}{dp_T^t}$ (1/GeV)', units: "$\frac{1}{GeV}$"}
     observable_name: PTT-NORM
     process_type: HQP_PTQ
     ndata: 16
     tables: ['parton_norm_tleppt']
     kinematics:
       variables:
-        pT_t: {description: "transverse momentum of t", label: '$pT_t$', units: "$GeV$"}
+        pT_t: {description: "transverse momentum of t", label: '$p_T^t$', units: "$GeV$"}
         m_t2: {description: "mass of top quark squared", label: '$m_{t}^2$', units: '$GeV^2$'}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_dSig_dpTt_norm.yaml
@@ -228,9 +228,9 @@ implemented_observables:
       - uncertainties_dSig_dpTt_norm.yaml
     kinematic_coverage: [pT_t, m_t2, sqrts]
     plotting:
-      dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{dpT_t}$'
+      dataset_label: 'CMS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{dp_T^t}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: pT_t
       y_label: '$\frac{1}{\sigma}\frac{d\sigma}{dpT_t}$ ($\frac{1}{GeV}$)'
     theory:
@@ -257,7 +257,7 @@ implemented_observables:
     plotting:
       dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{d\sigma}{d|y_t|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_t
       y_label: '$\frac{d\sigma}{d|y_t|}$ ($pb$)'
     theory:
@@ -282,9 +282,9 @@ implemented_observables:
       - uncertainties_dSig_dyt_norm.yaml
     kinematic_coverage: [y_t, m_t2, sqrts]
     plotting:
-      dataset_label: 'CMS 13 TeV top quark pair l+j channel: $\frac{1}{\sigma}\frac{d\sigma}{d|y_t|}$'
+      dataset_label: 'CMS 13 TeV $t\bar{t}$ $\ell+j$ $\frac{1}{\sigma}\frac{d\sigma}{d|y_t|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: y_t
       y_label: '$\frac{1}{\sigma}\frac{d\sigma}{d|y_t|}$'
     theory:
diff --git a/nnpdf_data/nnpdf_data/new_commondata/CMS_WPWM_13TEV_ETA/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/CMS_WPWM_13TEV_ETA/metadata.yaml
index 1e209b5451..61e3b444ea 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/CMS_WPWM_13TEV_ETA/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/CMS_WPWM_13TEV_ETA/metadata.yaml
@@ -24,7 +24,7 @@ implemented_observables:
   - observable_name: "WP"
     observable: 
       description: "CMS 13 TeV, differential cross section in W+ > l+ v boson pseudo rapidity. Combination of muon and electron channel"
-      label: r"$d\\sigma/d|\eta|$"
+      label: '$\frac{d\sigma}{d|\eta|}$ (pb)'
       units: "[pb]"
 
     ndata: 18
@@ -33,16 +33,16 @@ implemented_observables:
     process_type: DY_W_ETA
 
     plotting:
-      dataset_label: 'CMS 13 TeV $W^+ \to l^+ \nu$, $l^+$ pseudo rapidity'
+      dataset_label: 'CMS 13 TeV $W^+$ $\frac{d\sigma}{d|\eta|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: eta
     
     kinematic_coverage: [eta, m_W2, sqrts]
 
     kinematics:
       variables:
-        eta: {description: "W+ > l+ v pseudorapidity", label: '$\eta$', units: ""}
+        eta: {description: "W+ > l+ v pseudorapidity", label: '$|\eta|$', units: ""}
         m_W2: {description: "W+ boson mass squared", label: '$M_W^2$', units: "GeV"}
         sqrts: {description: "center of mass energy", label: '$\sqrt(s)$', units: "GeV"}
       file: kinematics_WP.yaml
@@ -62,7 +62,7 @@ implemented_observables:
   - observable_name: "WM"
     observable: 
       description: "CMS 13 TeV, differential cross section in W- > l- vb boson pseudo rapidity. Combination of muon and electron channel"
-      label: r"$d\\sigma/d|\eta|$"
+      label: '$\frac{d\sigma}{d|\eta|}$ (pb)'
       units: "[pb]"
 
     ndata: 18
@@ -71,16 +71,16 @@ implemented_observables:
     process_type: DY_W_ETA
 
     plotting:
-      dataset_label: 'CMS 13 TeV $W^- \to l^- \bar{\nu}$, $l^-$ pseudo rapidity'
+      dataset_label: 'CMS 13 TeV $W^-$ $\frac{d\sigma}{d|\eta|}$'
       kinematics_override: identity
-      x_scale: log
+      x_scale: linear
       plot_x: eta
     
     kinematic_coverage: [eta, m_W2, sqrts]
 
     kinematics:
       variables:
-        eta: {description: "W- > l- vb pseudorapidity", label: '$\eta$', units: ""}
+        eta: {description: "W- > l- vb pseudorapidity", label: '$|\eta|$', units: ""}
         m_W2: {description: "W- boson mass squared", label: '$M_W^2$', units: "GeV"}
         sqrts: {description: "center of mass energy", label: '$\sqrt(s)$', units: "GeV"}
       file: kinematics_WM.yaml
diff --git a/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_290PB-1_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_290PB-1_DIF/metadata.yaml
index d3e518ce3d..7fb1c28127 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_290PB-1_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_290PB-1_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dq^{2}dpT}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dQ^{2}dp_T}$ (pb/GeV$^3$)', units: "$pb/GeV^3$"}
     observable_name: PTQ2
     process_type: HERAJET
     ndata: 48
@@ -25,7 +25,7 @@ implemented_observables:
     kinematics:
       variables:
         pT: {description: "mean transverse momentum", label: '$pT$', units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: '$q^2$', units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: '$Q^2$', units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics.yaml
     data_central: data.yaml
@@ -34,7 +34,7 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ Jet\ 290\ pb^{-1}:\ \frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 single-inclusive jets (low $Q^2$) $\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
       y_label: '$\frac{d^2\sigma}{dq^{2}dpT}$ ($pb/GeV^3$)'
       x_scale: log
@@ -52,7 +52,7 @@ implemented_observables:
           - H1_1JET_319GEV_290PB-1_DIF_PTQ2_BIN8
       operation: 'null'
 
-  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$', units: "$1/GeV^3$"}
+  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$', units: "$1/GeV^3$"}
     observable_name: PTQ2-NORM
     process_type: HERAJET
     ndata: 48
@@ -69,14 +69,14 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ Jet\ 290\ pb^{-1}:\ \frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 single-inclusive jets (low $Q^2$) $\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
       y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$ ($1/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
 
-  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dq^{2}dpT}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dQ^{2}dp_T}$ (pb/GeV$^3$)', units: "$pb/GeV^3$"}
     observable_name: HIGH-PTQ2
     process_type: HERAJET
     ndata: 6
@@ -84,7 +84,7 @@ implemented_observables:
     kinematics:
       variables:
         pT: {description: "mean transverse momentum", label: '$pT$', units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: '$q^2$', units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: '$Q^2$', units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_highQ2.yaml
     data_central: data_highQ2.yaml
@@ -93,7 +93,7 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ Jet\ 290\ pb^{-1}\ high\ Q2:\ \frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 single-inclusive jets (high $Q^2$) $\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
       y_label: '$\frac{d^2\sigma}{dq^{2}dpT}$ ($pb/GeV^3$)'
       x_scale: log
@@ -117,7 +117,7 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ Jet\ 290\ pb^{-1}\ high\ Q2:\ \frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 single-inclusive jets (high $Q^2$) $\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
       y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$ ($1/GeV^3$)'
       x_scale: log
diff --git a/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_351PB-1_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_351PB-1_DIF/metadata.yaml
index d104756007..69b10d45aa 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_351PB-1_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/H1_1JET_319GEV_351PB-1_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: 'NA'
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dq^{2}dpT}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dQ^{2}dp_T}$ (pb/GeV$^3$)', units: "$pb/GeV^3$"}
     observable_name: PTQ2
     process_type: HERAJET
     ndata: 24
@@ -25,7 +25,7 @@ implemented_observables:
     kinematics:
       variables:
         pT: {description: "transverse momentum", label: '$pT$', units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: '$q^2$', units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: '$Q^2$', units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics.yaml
     data_central: data.yaml
@@ -34,9 +34,9 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ Jet\ 351\ pb^{-1}:\ \frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 single-inclusive jets (high $Q^2$) $\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
-      y_label: '$\frac{d^2\sigma}{dq^{2}dpT}$ ($pb/GeV^3$)'
+      y_label: '$\frac{d^2\sigma}{dQ^{2}dpT}$ ($pb/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
@@ -50,7 +50,7 @@ implemented_observables:
           - H1_1JET_319GEV_351PB-1_DIF_PTQ2_BIN6
       operation: 'null'
 
-  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$', units: "$1/GeV^3$"}
+  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$', units: "$1/GeV^3$"}
     observable_name: PTQ2-NORM
     process_type: HERAJET
     ndata: 24
@@ -67,9 +67,9 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ Jet\ 351\ pb^{-1}:\ \frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 single-inclusive jets (high $Q^2$) $\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
-      y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$ ($1/GeV^3$)'
+      y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$ ($1/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
diff --git a/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_290PB-1_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_290PB-1_DIF/metadata.yaml
index d4524615b6..780a3695c0 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_290PB-1_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_290PB-1_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dq^{2}d\langle pT \rangle}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dQ^{2}d\langle p_T \rangle}$ (pb/GeV$^3$)', units: "$pb/GeV^3$"}
     observable_name: PTQ2
     process_type: HERADIJET
     ndata: 48
@@ -25,7 +25,7 @@ implemented_observables:
     kinematics:
       variables:
         pT: {description: "mean transverse momentum", label: '$\langle pT \rangle$', units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: '$q^2$', units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: '$Q^2$', units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics.yaml
     data_central: data.yaml
@@ -34,7 +34,7 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ DiJet\ 290\ pb^{-1}:\ \frac{d^2\sigma}{dq^{2}d\langle pT \rangle}$'
+      dataset_label: 'H1 di-jets (low $Q^2$) $\frac{d^2\sigma}{dQ^{2}d\langle pT \rangle}$'
       plot_x: pT
       x_scale: log
       y_label: '$\frac{d^2\sigma}{dq^{2}d\langle pT \rangle}$ ($pb/GeV^3$)'
@@ -52,7 +52,7 @@ implemented_observables:
           - H1_2JET_319GEV_290PB-1_DIF_PTQ2_BIN8
       operation: 'null'
 
-  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}d\langle pT \rangle}$', units: "$1/GeV^3$"}
+  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}d\langle pT \rangle}$', units: "$1/GeV^3$"}
     observable_name: PTQ2-NORM
     process_type: HERADIJET
     ndata: 48
@@ -60,7 +60,7 @@ implemented_observables:
     kinematics:
       variables:
         pT: {description: "mean transverse momentum", label: '$\langle pT \rangle$', units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: 'q^2$', units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: 'Q^2$', units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_norm.yaml
     data_central: data_norm.yaml
@@ -69,7 +69,7 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ DiJet\ 290\ pb^{-1}:\ \frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}d\langle pT \rangle}$'
+      dataset_label: 'H1 di-jets (low $Q^2$) $\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}d\langle pT \rangle}$'
       plot_x: pT
       y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}d\langle pT \rangle}$ ($1/GeV^3$)'
       x_scale: log
diff --git a/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_351PB-1_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_351PB-1_DIF/metadata.yaml
index aa3f2ec2c4..a4cb8566d9 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_351PB-1_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/H1_2JET_319GEV_351PB-1_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: 'NA'
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dq^{2}dpT}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. q^2 and pT", label: '$\frac{d^2\sigma}{dQ^{2}dp_T}$ (pb/GeV$^3$)', units: "$pb/GeV^3$"}
     observable_name: PTQ2
     process_type: HERADIJET
     ndata: 24
@@ -25,7 +25,7 @@ implemented_observables:
     kinematics:
       variables:
         pT: {description: "mean transverse momentum", label: '$\langle pT \rangle$', units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: "$q^2$", units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: "$Q^2$", units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics.yaml
     data_central: data.yaml
@@ -34,9 +34,9 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ DiJet\ 351\ pb^{-1}:\ \frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 di-jets (high $Q^2$) $\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
-      y_label: '$\frac{d^2\sigma}{dq^{2}dpT}$ ($pb/GeV^3$)'
+      y_label: '$\frac{d^2\sigma}{dQ^{2}dpT}$ ($pb/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
@@ -50,7 +50,7 @@ implemented_observables:
           - H1_2JET_319GEV_351PB-1_DIF_PTQ2_BIN6
       operation: 'null'
 
-  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$', units: "$1/GeV^3$"}
+  - observable: {description: "normalized double differential cross section w.r.t. q^2 and pT", label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$', units: "$1/GeV^3$"}
     observable_name: PTQ2-NORM
     process_type: HERADIJET
     ndata: 24
@@ -67,9 +67,9 @@ implemented_observables:
     kinematic_coverage: [pT, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$H1\ Jet\ 351\ pb^{-1}:\ \frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$'
+      dataset_label: 'H1 di-jets (high $Q^2$) $\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$'
       plot_x: pT
-      y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dq^{2}dpT}$ ($1/GeV^3$)'
+      y_label: '$\frac{1}{\sigma}\frac{d^2\sigma}{dQ^{2}dpT}$ ($1/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
diff --git a/nnpdf_data/nnpdf_data/new_commondata/LHCB_Z0_13TEV_2022/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/LHCB_Z0_13TEV_2022/metadata.yaml
index 67d526d66d..2022e06271 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/LHCB_Z0_13TEV_2022/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/LHCB_Z0_13TEV_2022/metadata.yaml
@@ -18,7 +18,7 @@ version_comment: "First implementation of the Z boson rapidity set"
 implemented_observables:
   # y^Z data
   - observable: { description: "Differential cross-section of Z-->µµ as a function of Z-rapidity",
-                  label: '$\frac{d\sigma}{dy^Z}$',
+                  label: '$\frac{d\sigma}{dy^Z}$ (pb)',
                   units: "[pb]"}
     observable_name: DIMUON-Y
     process_type: DY_Z_Y
@@ -38,10 +38,10 @@ implemented_observables:
     kinematic_coverage: [y, m_Z2, sqrts]
     plotting:
       kinematics_override: identity
-      x_scale: log
-      dataset_label: "LHCb $Z\\to µµ$"
+      x_scale: linear
+      dataset_label: 'LHCb 13 TeV $Z$ $\frac{d\sigma}{dy^Z}$'
       plot_x: y
-      y_label: '$d\sigma_{Z}/dy^Z$ (pb)'
+      y_label: '$\frac{d\sigma_{Z}}{dy^Z}$ (pb)'
     theory:
       FK_tables: 
         - - LHCB_Z0_13TEV_DIMUON_2022
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_300GEV_38P6PB-1_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_300GEV_38P6PB-1_DIF/metadata.yaml
index ebe5804927..6c3072dee8 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_300GEV_38P6PB-1_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_300GEV_38P6PB-1_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. E_T and q^2", label: '$\frac{d^2\sigma}{dE_{T}dq^2}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. E_T and q^2", label: '$\frac{d^2\sigma}{dQ^2dE_{T}}$ (pb/GeV$^3$)', units: "$pb/GeV^3$"}
     observable_name: ETQ2
     process_type: HERAJET
     ndata: 30
@@ -25,7 +25,7 @@ implemented_observables:
     kinematics:
       variables:
         ET: {description: "transverse energy", label: "$E_{T}$", units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: "$q^2$", units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: "$Q^2$", units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_q2_et.yaml
     data_central: data_q2_et.yaml
@@ -34,9 +34,9 @@ implemented_observables:
     kinematic_coverage: [ET, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$ZEUS\ Jet\ 38.6\ pb^{-1}:\ \frac{d^2\sigma}{dE_{T}dq^2}$'
+      dataset_label: 'ZEUS single-inclusive jets (high luminosity) $\frac{d^2\sigma}{dQ^2dE_{T}}$'
       plot_x: ET
-      y_label: '$\frac{d^2\sigma}{dE_{T}dq^2}$ ($pb/GeV^3$)'
+      y_label: '$\frac{d^2\sigma}{dQ^2dE_{T}}$ ($pb/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_319GEV_82PB-1_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_319GEV_82PB-1_DIF/metadata.yaml
index 89bae76b2c..d2c64ab9c3 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_319GEV_82PB-1_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ZEUS_1JET_319GEV_82PB-1_DIF/metadata.yaml
@@ -17,7 +17,7 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. E_T and q^2", label: '$\frac{d^2\sigma}{dE_Tdq^2}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. E_T and q^2", label: '$\frac{d^2\sigma}{dQ^2dE_T}$ (pb/GeV$^3$)', units: "$pb/GeV^3$"}
     observable_name: ETQ2
     process_type: HERAJET
     ndata: 30
@@ -25,7 +25,7 @@ implemented_observables:
     kinematics:
       variables:
         ET: {description: "transverse energy", label: "$E_T$", units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: "$q^2$", units: "$GeV^2$"}
+        Q2: {description: "momentum transferred squared", label: "$Q^2$", units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_q2_et.yaml
     data_central: data_q2_et.yaml
@@ -34,9 +34,9 @@ implemented_observables:
     kinematic_coverage: [ET, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$ZEUS\ Jet\ 82\ pb^{-1}:\ \frac{d^2\sigma}{dE_Tdq^2}$'
+      dataset_label: 'ZEUS single-inclusive jets (low luminosity) $\frac{d^2\sigma}{dQ^2dE_T}$'
       plot_x: ET
-      y_label: '$\frac{d^2\sigma}{dE_Tdq^2}$ ($pb/GeV^3$)'
+      y_label: '$\frac{d^2\sigma}{dQ^2dE_T}$ ($pb/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
diff --git a/nnpdf_data/nnpdf_data/new_commondata/ZEUS_2JET_319GEV_374PB-1_DIF/metadata.yaml b/nnpdf_data/nnpdf_data/new_commondata/ZEUS_2JET_319GEV_374PB-1_DIF/metadata.yaml
index 05bde3f06a..0fd14cc490 100644
--- a/nnpdf_data/nnpdf_data/new_commondata/ZEUS_2JET_319GEV_374PB-1_DIF/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/new_commondata/ZEUS_2JET_319GEV_374PB-1_DIF/metadata.yaml
@@ -17,15 +17,15 @@ version_comment: "NA"
 
 implemented_observables:
 
-  - observable: {description: "double differential cross section w.r.t. E_T and q^2", label: '$\frac{d^2\sigma}{dE_Tdq^2}$', units: "$pb/GeV^3$"}
+  - observable: {description: "double differential cross section w.r.t. E_T and q^2", label: '$\frac{d^2\sigma}{dQ^2d\langle E_T\rangle}$ (pb/GeV$^3$))', units: "$pb/GeV^3$"}
     observable_name: ETQ2
     process_type: HERADIJET
     ndata: 22
     tables: [13, 14, 15, 16, 17, 18]
     kinematics:
       variables:
-        ET: {description: "mean jet transverse energy of the dijet system in the Breit frame", label: '$\langle E_{T, B} \rangle$', units: "$GeV$"}
-        Q2: {description: "momentum transferred squared", label: "$q^2$", units: "$GeV^2$"}
+        ET: {description: "mean jet transverse energy of the dijet system in the Breit frame", label: '$\langle E_{T} \rangle$', units: "$GeV$"}
+        Q2: {description: "momentum transferred squared", label: "$Q^2$", units: "$GeV^2$"}
         sqrts: {description: "center of mass energy", label: '$\sqrt{s}$', units: "$GeV$"}
       file: kinematics_q2_et.yaml
     data_central: data_q2_et.yaml
@@ -34,9 +34,9 @@ implemented_observables:
     kinematic_coverage: [ET, Q2, sqrts]
     plotting:
       kinematics_override: identity
-      dataset_label: '$ZEUS\ DiJet\ 374\ pb^{-1}:\ \frac{d^2\sigma}{dE_Tdq^2}$'
+      dataset_label: 'ZEUS di-jets $\frac{d^2\sigma}{dQ^2d\langle E_T\rangle }$'
       plot_x: ET
-      y_label: '$\frac{d^2\sigma}{dE_Tdq^2}$ ($pb/GeV^3$)'
+      y_label: '$\frac{d^2\sigma}{dQ^2d\langle E_T\rangle }$ ($pb/GeV^3$)'
       x_scale: log
       figure_by: 
         - Q2
diff --git a/validphys2/src/validphys/covmats.py b/validphys2/src/validphys/covmats.py
index dec41cd2ba..6d1abc64fc 100644
--- a/validphys2/src/validphys/covmats.py
+++ b/validphys2/src/validphys/covmats.py
@@ -121,6 +121,91 @@ def covmat_from_systematics(
         covmat = regularize_covmat(covmat, norm_threshold=norm_threshold)
     return covmat
 
+def shifts_from_systematics(
+    loaded_commondata_with_cuts,
+    results_without_covmat,
+    dataset_input,
+    pdf,
+): 
+
+    """Take the statistical uncertainty and systematics table from
+    a :py:class:`validphys.coredata.CommonData` object and
+    the corresponding theoretical predictions from :py:funct:`results`
+    to compute the shifts on experimental data due to correlated uncertainties 
+    according to Eqs.(7)-(9) of arXiv:hep-ph/0201195.
+
+    The treatment of uncertainties is as in covmat_from_systematics.
+
+    The shifts must be added to the central value of the unshifted data.
+
+    Parameters
+    ----------
+
+    loaded_commondata_with_cuts : validphys.coredata.CommonData
+        CommonData which stores information about systematic errors,
+        their treatment and description.
+    results_without_covmat : py:funct:
+        A results object with a diagonal covmat
+    dataset_input: validphys.core.DataSetInput
+        Dataset settings (includes specification on cuts and theoryID)
+    pdf: string
+        The input pdf set used to compute theoretical predictions
+
+    Returns
+    -------
+    shifts: np.array
+        Numpy array of dimension N_dat (where N_dat is the number of data points)
+        containing the numerical value of the systematic shifts due to correlated uncertainties
+
+    Example
+    -------
+    In order to use this function, simply call it from the API
+
+    >>> from validphys.api import API
+    >>> inp = dict(
+    ...     dataset_input={'dataset': 'CMSZDIFF12', 'cfac':('QCD', 'NRM'), 'sys':10},
+    ...     theoryid=162,
+    ...     use_cuts="internal",
+    ...     pdf="NNPDF40_nnlo_as_01180",
+    ... )
+    >>> shift = API.shift_from_systematics(**inp)
+    """
+    
+    stat_errors = loaded_commondata_with_cuts.stat_errors.to_numpy()
+    syst_errors = loaded_commondata_with_cuts.systematic_errors(None)
+
+    # Determine the uncorrelated part of the error
+    alpha2 = stat_errors**2
+    is_uncorr = syst_errors.columns.isin(("UNCORR", "THEORYUNCORR"))
+    alpha2 += (syst_errors.loc[:, is_uncorr].to_numpy() ** 2).sum(axis=1)
+    alpha = np.sqrt(alpha2)
+
+    # Determine the correlated part of the error
+    beta = syst_errors.loc[:, ~is_uncorr].to_numpy()
+    beta = beta/alpha[:, np.newaxis]
+    
+    # The number of data points and the number of correlated systematics
+    (n_data, n_corr_syst) = np.shape(beta)
+        
+    # Get experimental central values and the corresponding theoretical predictions
+    D = loaded_commondata_with_cuts.central_values.to_numpy()
+    D = np.divide(D,alpha)    
+    _, th = results_without_covmat
+    T = th.central_value
+    T = np.divide(T,alpha)
+
+    # Construct the matrices A and B (Eq. 9)
+    A = np.identity(n_corr_syst) + np.matmul(beta.T,beta)
+    A_inverse = np.linalg.inv(A)
+    B = np.matmul(D-T,beta)
+
+    # Compute the nuisance parameters r (Eq. 8)
+    r = np.matmul(np.linalg.inv(A),B)
+    
+    # Compute the shifts
+    shifts = - np.matmul(beta*alpha[:, np.newaxis], r)
+    
+    return shifts
 
 def dataset_inputs_covmat_from_systematics(
     dataset_inputs_loaded_cd_with_cuts,