skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Ising field theory in a magnetic field: φ3 coupling at T > Tc
A<sc>bstract</sc> We study the “three particle coupling”$$ {\Gamma}_{11}^1\left(\xi \right) $$ Γ 11 1 ξ , in 2dIsing Field Theory in a magnetic field, as the function of the scaling parameterξ:=h/(−m)15/8, wherem∼Tc−Tandh∼Hare scaled deviation from the critical temperature and scaled external field, respectively. The “φ3coupling”$$ {\Gamma}_{11}^1 $$ Γ 11 1 is defined in terms of the residue of the 2 → 2 elastic scattering amplitude at its pole associated with the lightest particle itself. We limit attention to the High-Temperature domain, so thatmis negative. We suggest “standard analyticity”:$$ {\left({\Gamma}_{11}^1\right)}^2 $$ Γ 11 1 2 , as the function ofu:=ξ2, is analytic in the whole complexu-plane except for the branch cut from – ∞ to –u0≈ – 0.03585, the latter branching point –u0being associated with the Yang-Lee edge singularity. Under this assumption, the values of$$ {\Gamma}_{11}^1 $$ Γ 11 1 at any complexuare expressed through the discontinuity across the branch cut. We suggest approximation for this discontinuity which accounts for singular expansion of$$ {\Gamma}_{11}^1 $$ Γ 11 1 near the Yang-Lee branching point, as well as its known asymptotic atu →+∞. The resulting dispersion relation agrees well with known exact data, and with numerics obtained via Truncated Free Fermion Space Approach. This work is part of extended project of studying the S-matrix of the Ising Field Theory in a magnetic field.  more » « less
Award ID(s):
2210533
PAR ID:
10509760
Author(s) / Creator(s):
;
Publisher / Repository:
JHEP
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2023
Issue:
8
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. A<sc>bstract</sc> A measurement of theCP-violating parameters in$$ {B}_s^0\boldsymbol{\to}{D}_s^{\mp }{K}^{\pm} $$ B s 0 D s K ± decays is reported, based on the analysis of proton-proton collision data collected by the LHCb experiment corresponding to an integrated luminosity of 6 fb−1at a centre-of-mass energy of 13 TeV. The measured parameters are obtained with a decay-time dependent analysis yieldingCf= 0.791 ± 0.061 ± 0.022,$$ {A}_f^{\Delta \Gamma} $$ A f Γ = −0.051 ± 0.134 ± 0.058,$$ {A}_{\overline{f}}^{\Delta \Gamma} $$ A f ¯ Γ = −0.303 ± 0.125 ± 0.055,Sf= −0.571 ± 0.084 ± 0.023 and$$ {S}_{\overline{f}} $$ S f ¯ = −0.503 ± 0.084 ± 0.025, where the first uncertainty is statistical and the second systematic. This corresponds to CP violation in the interference between mixing and decay of about 8.6σ. Together with the value of the$$ {B}_s^0 $$ B s 0 mixing phase −2βs, these parameters are used to obtain a measurement of the CKM angleγequal to (74 ± 12)° modulo 180°, where the uncertainty contains both statistical and systematic contributions. This result is combined with the previous LHCb measurement in this channel using 3 fb−1resulting in a determination of$$ \gamma ={\left({81}_{-11}^{+12}\right)}^{\circ } $$ γ = 81 11 + 12
    more » « less
  2. A<sc>bstract</sc> In this paper we explorepp→W±(ℓ±ν)γto$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ O 1 / Λ 4 in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at$$ \mathcal{O}\left(1/{\Lambda}^2\right) $$ O 1 / Λ 2 and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~$$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ O E 4 / Λ 4 , as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ O 1 / Λ 4 SMEFT effects consistent with U(3)5flavor symmetry. Additionally, we include the decay of theW±→ ℓ±ν, making the calculation actually$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ q ¯ q ± νγ . As such, we are able to study the impact of non-resonant SMEFT operators, such as$$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$ L σ ¯ μ τ I L Q σ ¯ ν τ I Q Bμν, which contribute to$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ q ¯ q ± νγ directly and not to$$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ q ¯ q W ± γ . We show several distributions to illustrate the shape differences of the different contributions. 
    more » « less
  3. A<sc>bstract</sc> A search for the fully reconstructed$$ {B}_s^0 $$ B s 0 → μ+μγdecay is performed at the LHCb experiment using proton-proton collisions at$$ \sqrt{s} $$ s = 13 TeV corresponding to an integrated luminosity of 5.4 fb−1. No significant signal is found and upper limits on the branching fraction in intervals of the dimuon mass are set$$ {\displaystyle \begin{array}{cc}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[2{m}_{\mu },1.70\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<7.7\times {10}^{-8},&\ m\left({\mu}^{+}{\mu}^{-}\right)\in \left[\textrm{1.70,2.88}\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[3.92,{m}_{B_s^0}\right]\textrm{GeV}/{c}^2,\end{array}} $$ B B s 0 μ + μ γ < 4.2 × 10 8 , m μ + μ 2 m μ 1.70 GeV / c 2 , B B s 0 μ + μ γ < 7.7 × 10 8 , m μ + μ 1.70, 2.88 GeV / c 2 , B B s 0 μ + μ γ < 4.2 × 10 8 , m μ + μ 3.92 m B s 0 GeV / c 2 , at 95% confidence level. Additionally, upper limits are set on the branching fraction in the [2mμ,1.70] GeV/c2dimuon mass region excluding the contribution from the intermediateϕ(1020) meson, and in the region combining all dimuon-mass intervals. 
    more » « less
  4. A<sc>bstract</sc> Using data samples of 983.0 fb−1and 427.9 fb−1accumulated with the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energye+ecolliders, singly Cabibbo-suppressed decays$$ {\Xi}_c^{+}\to p{K}_S^0 $$ Ξ c + p K S 0 ,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ Ξ c + Λ π + , and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ Ξ c + Σ 0 π + are observed for the first time. The ratios of branching fractions of$$ {\Xi}_c^{+}\to p{K}_S^0 $$ Ξ c + p K S 0 ,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ Ξ c + Λ π + , and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ Ξ c + Σ 0 π + relative to that of$$ {\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+} $$ Ξ c + Ξ π + π + are measured to be$$ {\displaystyle \begin{array}{c}\frac{\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(2.47\pm 0.16\pm 0.07\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(1.56\pm 0.14\pm 0.09\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(4.13\pm 0.26\pm 0.22\right)\%.\end{array}} $$ B Ξ c + p K S 0 B Ξ c + Ξ π + π + = 2.47 ± 0.16 ± 0.07 % , B Ξ c + Λ π + B Ξ c + Ξ π + π + = 1.56 ± 0.14 ± 0.09 % , B Ξ c + Σ 0 π + B Ξ c + Ξ π + π + = 4.13 ± 0.26 ± 0.22 % . Multiplying these values by the branching fraction of the normalization channel,$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)=\left(2.9\pm 1.3\right)\% $$ B Ξ c + Ξ π + π + = 2.9 ± 1.3 % , the absolute branching fractions are determined to be$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)=\left(7.16\pm 0.46\pm 0.20\pm 3.21\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)=\left(4.52\pm 0.41\pm 0.26\pm 2.03\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)=\left(1.20\pm 0.08\pm 0.07\pm 0.54\right)\times {10}^{-3}.\end{array}} $$ B Ξ c + p K S 0 = 7.16 ± 0.46 ± 0.20 ± 3.21 × 10 4 , B Ξ c + Λ π + = 4.52 ± 0.41 ± 0.26 ± 2.03 × 10 4 , B Ξ c + Σ 0 π + = 1.20 ± 0.08 ± 0.07 ± 0.54 × 10 3 . The first and second uncertainties above are statistical and systematic, respectively, while the third ones arise from the uncertainty in$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right) $$ B Ξ c + Ξ π + π +
    more » « less
  5. A<sc>bstract</sc> We develop Standard Model Effective Field Theory (SMEFT) predictions ofσ($$ \mathcal{GG} $$ GG →h), Γ(h→$$ \mathcal{GG} $$ GG ), Γ(h→$$ \mathcal{AA} $$ AA ) to incorporate full two loop Standard Model results at the amplitude level, in conjunction with dimension eight SMEFT corrections. We simultaneously report consistent Γ(h→$$ \overline{\Psi}\Psi $$ Ψ ¯ Ψ ) results including leading QCD corrections and dimension eight SMEFT corrections. This extends the predictions of the former processes Γ, σto a full set of corrections at$$ \mathcal{O}\left({\overline{v}}_T^2/{\varLambda}^2{\left(16{\pi}^2\right)}^2\right) $$ O v ¯ T 2 / Λ 2 16 π 2 2 and$$ \mathcal{O}\left({\overline{v}}_T^4/{\Lambda}^4\right) $$ O v ¯ T 4 / Λ 4 , where$$ {\overline{v}}_T $$ v ¯ T is the electroweak scale vacuum expectation value and Λ is the cut off scale of the SMEFT. Throughout, cross consistency between the operator and loop expansions is maintained by the use of the geometric SMEFT formalism. For Γ(h→$$ \overline{\Psi}\Psi $$ Ψ ¯ Ψ ), we include results at$$ \mathcal{O}\left({\overline{v}}_T^2/{\Lambda}^2\left(16{\pi}^2\right)\right) $$ O v ¯ T 2 / Λ 2 16 π 2 in the limit where subleadingmΨ→ 0 corrections are neglected. We clarify how gauge invariant SMEFT renormalization counterterms combine with the Standard Model counter terms in higher order SMEFT calculations when the Background Field Method is used. We also update the prediction of the total Higgs width in the SMEFT to consistently include some of these higher order perturbative effects. 
    more » « less