We confront the malaphoric $$B_3-L_2$$ model with bounds coming from a search for resonances in the di-lepton channels at the 13 TeV LHC. In contrast to the original $$B_3-L_2$$ model, the $$Z^\prime $$ of the $$B_3-L_2$$ model has sizeable couplings to the lighter two families; these originate from order unity kinetic mixing with the hypercharge gauge boson and ameliorate the fit to lepton flavour universality measurements in -meson decays. The $$Z^\prime $$ coupling to the first two families of quark means that the resulting constraints from resonant di-lepton searches are stronger. Nevertheless, we find that for $$M_{Z^\prime }>2.8$$ TeV there remains a non-negligible region of allowed parameter space where the model significantly improves upon several Standard Model predictions for observables involving the $$b \rightarrow s l^+ l^-$$ transition. We estimate that the 3000 fb $$^{-1}$$ HL-LHC will extend this sensitivity to $$M_{Z^\prime }= 4.2$$ TeV.

United Kingdom

Ben Allanach

Constraints on the malaphoric $$B_3-L_2$$ model from di-lepton resonance searches at the LHC

We study some phenomenological effects of kinetic mixing between the hypercharge field and a new (1) gauge field in specific $$Z^\prime $$ models that ameliorate the tensions between measurements and Standard Model predictions in $$b \rightarrow s\ell ^+ \ell ^-$$ decays. To this end, we rederive the dimension-6 SMEFT coefficients resulting from integrating out the kinetically-mixed (‘malaphoric’) $$Z^\prime $$ field. The kinetic mixing provides a family-universal component to the couplings of the $$Z^\prime $$ field, which can improve fits to lepton flavour universality observables. We show how kinetic mixing improves the best fit of the $$B_3-L_2$$ model to $$b\rightarrow s$$ data by 7.0 units of $$\chi ^2$$ while remaining compatible with other relevant data sets such as electroweak precision observables and measurements of $$e^+ e^- \rightarrow \ell ^+ \ell ^-$$ at LEP2.

Nico Gubernari

Malaphoric $$Z^\prime $$ models for $$b \rightarrow s \ell ^+ \ell ^-$$ anomalies

Several current measurements of <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>l</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>l</mi></mrow><mrow><mo>−</mo></mrow></msup></math> processes are in tension with Standard Model predictions, whereas others (e.g. <math><msub><mrow><mi>R</mi></mrow><mrow><mi>K</mi></mrow></msub></math> and <math><msub><mrow><mi>R</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow></msub></math>) are in reasonable agreement with them. We examine some recent <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> models that fit the data as a whole appreciably better than does the Standard Model, confronting the models with ATLAS resonance searches in the <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> and <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> channels. The models are constrained by both channels; we find that the searches rule out less than one fifth of the allowed range of <math><msub><mrow><mi>M</mi></mrow><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math>. We estimate that the HL-LHC can roughly double the current sensitivity in <math><msub><mrow><mi>M</mi></mrow><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math>, but to cover the whole of the parameter space would take a more powerful machine, such as a 100 TeV pp collider.

LHC di-lepton searches for ′ Bosons Which Explain Measurements of → Transitions

Measurements of b → sμ + μ  −  transitions indicate that there may be a new physics field coupling to di-muon pairs associated with the b to s flavour transition. Including the 2022 LHCb reanalysis of R  K  and   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mo>∗</mo> </msup> </msub> </math>  $$ {R}_{K^{\ast }} $$ , one infers that there may also be associated new physics in b → se + e  −  transitions. Here, we examine the extent of the statistical preference for Z′ models coupling to di-electron pairs taking into account the relevant constraints, in particular from experiments at LEP-2. We identify an anomaly-free set of models which interpolates between the Z′ not coupling to electrons at all, to one in which there is an equal Z′ coupling to muons and electrons (but where in all models in the set, the Z′ boson can mediate b → sμ + μ  −  transitions). A 3B 3 − L  e  − 2L  μ  model provides a close-to-optimal fit to the pertinent measurements along the line of interpolation. We have (re-)calculated predictions for the relevant LEP-2 observables in terms of dimension-6 SMEFT operators and put them into the flavio computer program, so that they are available for global fits.

Anna Mullin

Plan B: new Z′ models for b → sℓ + ℓ  −  anomalies

We juxtapose global fits of two bottom-up models (an S 3 scalar leptoquark model and a B 3 – L 2 Z′ model) of b → sμ + μ  −  anomalies to flavour data in order to quantify statistical preference or lack thereof. The leptoquark model couples directly to left-handed di-muon pairs, whereas the Z′ model couples to di-muon pairs with a vector-like coupling.   <math> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>−</mo> <mover> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>¯</mo> </mover> </math>  $$ {B}_s-\overline{B_s} $$  mixing is a focus because it is typically expected to disfavour Z′ explanations. In two-parameter fits to 247 flavour observables, including B  s/d  → μ + μ  −  branching ratios for which we provide an updated combination and LHCb   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{K^{\left(\ast \right)}} $$  measurements from December 2022, we show that each model provides a similar improvement in quality-of-fit of   <math> <msqrt> <mrow> <mtext>∆</mtext> <msup> <mi>χ</mi> <mn>2</mn> </msup> </mrow> </msqrt> </math>  $$ \sqrt{\Delta {\chi}^2} $$  = 3.6 with respect to the Standard Model. The main effect of the   <math> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>−</mo> <mover> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>¯</mo> </mover> </math>  $$ {B}_s-\overline{B_s} $$  mixing constraint in the Z′ model is to disfavour values of the s  L  – b  L  mixing angle greater than about 5|V  cb |. This limit is rather loose, meaning that a good fit to data does not require ‘alignment’ in either quark Yukawa matrix. No curtailment of the s  L  − b  L  mixing angle is evident in the S 3 model.

CERN

Switzerland

Joe Davighi

The Rumble in the Meson: a leptoquark versus a Z′ to fit b → sμ + μ − anomalies including 2022 LHCb   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{K^{\left(\ast \right)}} $$  measurements

The B 3 − L 2 Z′ model may explain some gross features of the fermion mass spectrum as well as b → sℓℓ anomalies. A TeV-scale physical scalar field associated with gauged   <math> <mi>U</mi> <msub> <mfenced> <mn>1</mn> </mfenced> <mrow> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>−</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </msub> </math>  $$ U{(1)}_{B_3-{L}_2} $$  spontaneous symmetry breaking, the flavon field ϑ, affects Higgs phenomenology via mixing. In this paper, we investigate the collider phenomenology of the flavon field. Higgs and W boson mass data are used to place bounds upon parameter space. We then examine flavonstrahlung (Z′ → Z′ϑ production) at colliders as a means to directly produce and discover flavon particles, which would provide direct empirical evidence tying the flavon to   <math> <mi>U</mi> <msub> <mfenced> <mn>1</mn> </mfenced> <mrow> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>−</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </msub> </math>  $$ U{(1)}_{B_3-{L}_2} $$  symmetry breaking. A 100 TeV FCC-hh or a 10 TeV muon collider would have high sensitivity to flavonstrahlung, whereas the HL-LHC can observe it only in extreme corners of parameter space.

Eetu Loisa

Flavonstrahlung in the B 3 − L 2 Z′ model at current and future colliders

As shown in Allanach et al. (Global fits of third family hypercharge models to neutral current B-anomalies and electroweak precision observables.  arXiv:2103.12056  ), the Third Family Hypercharge ( $$Y_3$$  <math> <msub> <mi>Y</mi> <mn>3</mn> </msub> </math>  ) Model changes the Standard Model prediction for  $$M_W$$  <math> <msub> <mi>M</mi> <mi>W</mi> </msub> </math>   whilst simultaneously explaining anomalies in  $$b\rightarrow s\ell \ell $$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <mi>ℓ</mi> <mi>ℓ</mi> </mrow> </math>   transitions via a heavy  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   gauge boson which is spawned by a spontaneously broken gauged  $$U(1)_{Y_3}$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>Y</mi> <mn>3</mn> </msub> </msub> </mrow> </math>   symmetry. The 2022 CDF II measurement of  $$M_W$$  <math> <msub> <mi>M</mi> <mi>W</mi> </msub> </math>  , which is far from the Standard Model prediction in the statistical sense, somewhat disfavours the  $$Y_3$$  <math> <msub> <mi>Y</mi> <mn>3</mn> </msub> </math>   model. Here, we generalise the gauge charge assignments to the anomaly-free combination  $$s Y_3 + t (B_3-L_3)$$  <math> <mrow> <mi>s</mi> <msub> <mi>Y</mi> <mn>3</mn> </msub> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>L</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> </mrow> </math>   and show that incorporating the 2022 CDF II measurement of  $$M_W$$  <math> <msub> <mi>M</mi> <mi>W</mi> </msub> </math>   selects a viable domain of integers s and t. For example,  $$s=1, t=-3$$  <math> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>t</mi> <mo>=</mo> <mo>-</mo> <mn>3</mn> </mrow> </math>   yields a p value of .08 in a two-parameter global fit to 277 electroweak and flavour changing b data, much improving a SM p value of  $$1\times 10^{-6}$$  <math> <mrow> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> </math>  .

$$M_W$$  <math> <msub> <mi>M</mi> <mi>W</mi> </msub> </math>   helps select  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   models for  $$b\rightarrow s \ell \ell $$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <mi>ℓ</mi> <mi>ℓ</mi> </mrow> </math>   anomalies

We extend and complete our analysis arXiv:1608.02380 and study the induced world volume metrics and Hawking temperatures of all type IIB rotating probe Dp-branes, dual to the temperature of different flavors at finite R-charge, in the Ben Ami–Kuperstein–Sonnenschein holographic models including the effects of spontaneous conformal and chiral flavor symmetry breakdown. The model embeds type IIB probe flavor Dp-branes into the Klebanov-Witten gravity dual of conformal gauge theory, with the embedding parameter, given by the minimal radial extension of the probes, dual to the IR scale of conformal and chiral flavor symmetry breakdown. We show that when the minimal extension is positive definite, the induced world volume metrics of type IIB rotating probe branes admit thermal horizons and Hawking temperatures despite the absence of black holes in the bulk subject to the world volume and topology of the nontrivial internal cycle wrapped by the probe. We also derive the energy–stress tensor of the thermal probes and study their backreaction and energy dissipation. We show that at the IR scale the backreaction is nonnegligible and find the energy can flow from the probes to the bulk, dual to the energy dissipation from the flavor sectors into the gauge theory.